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namus:
prophanas nouitates uerborum deuita
however, the shrewdly oblique statement, as
if
",
Praef.
uttered tongue-in-cheek.
6).
One
of illud
auctoritas
Apostoli should note,
Ronca
338
nowhere about
is
claimed that the one
it
trivial
questions
make
about important questions
The
based
are
superior to the other.
is
on
either
use of both.
of the
two;
15
Arguments arguments
16
quantitative upgrading of auctoritas diuinae paginae, while re
establishing the correct balance in the eyes of the religious, has another function: to harmonise Reason with Scripture. At the same
important
God on
time, what William grants to
the
other,
so
reducing
the one hand, he gives to Caesar on the
considerably
sphere
of
of
competence
scriptural authority.
The harmonisation between
and rationes
auctoritates diuinae paginae
generally achieved by a shrewd re-interpretation of the philosophonim 17 and is certainly a part of former according to Abelard s fourth rule is
the grand apologetic plan. Predictably, therefore,
who
it
is
always the
Duke
points out a discrepancy and asks for an explanation of a particular
auctoritas.
But quotes,
only one side of the coin. Sometimes the Philosopher unsolicited, a new scriptural authority to support a bold rethis
is
interpretation, as in the heated debate about the alleged
above
the
legitimated
mentioned reason
at
111,75
"that
at
11,59
birds
all
at III,65ff.
and
et
procedure
may become
opinion uel
is
argumentis
certainty of
The
necessariis".
auctores.
fishes
induxeris".
"Auctoritate
does not move); or
s
sapientum
are obviously
frozen waters
supported and fully epistemological definition of opinio and ratio
Indeed the
the uncertainty of
assensu
rationem uel auctoritatem
As
18 .
by William earlier:
"uel
"sapicntes"
As
firmament
originated
The Duke
ratione,
is
non
from waters I shall not believe, Ambrosius auctoritas.
nisi
satisfied with
conuiciis,
ilium
conuince"
(that
the
Earth
(on the frozen waters above the firmament).
Abelard s five rules to reconcile found in the Prologue to the Sic et
conflicting
Non (PL
biblical
or
178,1339-1349)
patristic
authorities
and summarised
in
are
M.
der scholastischen Methode, vol.2, Graz 1957, p.200-202 (but see matters cit, p.362, n.l). The fourth rule applies to controversial in which the disagreement is more apparent than real, due to the semantic ambivalence of certain terms. In such cases the solution will be easier if one can prove that the different authors with different meanings" (si eadem controversial term is used
Grabmann s Geschichte also M. D. Chenu, op.
"by
verba 178,
18
in
diversis
significationibus
a
diversis
auctoribus posita defendere poterimus:
PL
1344D). Cf.
Dragm.
auibus caeli biblical
111,65
"Aliquando
"
illudunt
term caelum).
(to
explain
aer dicitur caelum, ut that the sense of acr
ibi is
[= Baruch 3,17] Qui in sometimes implicit in the
Reason and Faith
9.
As
the restriction
for
of the
in the
Dragmaticon
field
of competence of the auctoritas
diuinae paginae, the crucial evidence
is
339
provided by the discussion of the
frozen waters above the firmament. In the Philosophia the frozen waters
reported as anonymous, the opinion
is
theory
end of
the Dragmaticon
in
it;
Duke
the
Bede. This prompts the Philosopher to
pertain
contradict
catholic
or
faith
is
disproved, and that
attributes
s
bold reply:
moral
instruction
is
the
to the Venerable
it
those matters which
"In
is
it
not
allowed
to
Bede or any other of the holy
Fathers. If, however, they err matters pertaining to physics, it is permitted to state an opposite view. 19 For, although greater than we, they were only human beings". This statement has been quoted out of context to make of William of Conches in
an idealised pre-Galilean martyr for freedom of thought. 20 not the authority of the Bible that
is
at stake here,
It is,
however,
but only that of the
Church Fathers (represented by Bede, certainly not the greatest authority among them). William would hardly have dared to raise such a fundamental objection against the Bible (as did Galilei, but only in the 17th century) or the Gospel, the authority of which he rates higher than that of the Fathers. 21
Here he merely emphasises the human condition of and plays them off against each other (using Abelard s
two
authorities, 22 rule ). That
fifth
William had
auctoritates
heterogenous
can
mind
in
be
a certain hierarchy within the
reasonably
assumed. 23
That
he
did
19
eis quae ad fidem catholicam, uel ad institutionem morum Dragm. 111,65-66 non est fas Bedae uel alicui alii sanctorum patrum contradicere. In eis tamen quae ad philosophiam [read: physicam] pertinent, si in aliquo errant, licet diuersum affirmare. Etsi enim maiores nobis, homines tamen fuere". Note that in the Gratarolus "In
pertinent,
a
edition
line
is
scripturae sacrae
added,
in
brackets but
nevertheless arbitrarily,
after
"patrum":
"(citra
authoritatem)".
Tina Stiefel, "Science, Reason and Faith in the Twelfth Century: The CosAttacks on Tradition", Journal of European Studies, vi (1976), 1-16. The article does not take into consideration the development of William s thought and gives a one-sided picture of it, based almost the Philosophia. Incidentally, entirely on Stiefel s translation of the above statement, on p.6, is incorrect. Cf.
mologists
He words
retracts,
"quia
nee
for in
instance,
on
Euangelio nee
his
view on the divine sanctorum patrum illud
early
in scriptis
Persons inuenimus"
with
the
(Dragm.
Praef., 6).
This applies to controversies where the disagreement is real. In such cases no semantic trick will do, but the different authorities should be weighed against each other and preference given to that which appears be supported by the most solid evidence and best confirmed" (Quod si forte adeo manifesta sit controversia, ut nulla "to
aboliri ratione, conferendae sunt auctoritates, et quae potioris est testimonii et maioris confirmationis, potissimum retinenda: PL 178, 1345A). 23 In addition to the above evidence, cf. Dragm. 1,23 (the Duke should feel free to compare what is going to be said about the elements with any other available authority
possit
Ronca
340
distinguish the hierarchical status of the Gospel is
from that of the Fathers,
beyond doubt.
To sum
With the proviso
up:
Bede
that
authority should be taken
s
drawing of a line between the domains of Reason and Sacred Authority still remains a clear sign of to
William
and
bold
s
of
separation
Fathers
the
represent
modernistic
amazingly
two
the
the
alone,
of
spheres
The
attitude.
competence
is
clear-cut
tantamount
to
a
declaration of independence of Science (natural philosophy) from Religion,
or
the
to
dogma.
autonomy of
of
right
research
scientific
from
theological
24
To
The new
form of the Dragmaticon is shrewdly exploited for apologetic purposes: the Philosopher wants to convince his religious readers that they can safely use his new work as a companion 10.
conclude:
dialogical
philosophorum; he also formally appeases his theological opponents by ostensibly redressing the imbalance between secular reason and sacred authority; and, last but not least, William of St Thierry is
to
their lectio
granted his retractatio errorum and confessio the
in
"retreat"
sense
of
Flatten
s
fidei. All this is
"Rikkzug".
In
fact,
connected with the Riickzug are ambivalent and subtly
not a
mere
most passages Even for
allusive.
the apparently most fideistic of those passages, as are the conclusion of
the confessio fidei and the miraculous creation of Eve, William explanations, and
to provide the necessary rational that:
he ends his Profession of Faith by saying that he believes
a)
these
manages
ironically allusive
things,
contrary to believes:
approving
human
"because
some
reason";
the
men
with
human
reason,
others,
at "all
although
he then promptly gives the reason why he who wrote them were inspired by the Holy
nor to affirm anything but epistemological certainty guaranteed assensu certainty". sapientum; and against those inspired holy writers are played off all contemporary (by implication religious) liarsl b) As for the miraculous Spirit
(...)
and they profess neither to
In
creation of Eve, he "plausible
lie
other words:
reasons"
is
willing to accept
it,
but only because
God had
to intervene personally in such an act contra naturam:
to the most convincing of them - another application of Abelard s enim quaerendum est qui dixerint, sed quid dixerint. Non tamen nego conferre qualitatem personae bono open maiorem gratiam conferre". Of course gratiam is not quite the same as auctoritatem conferre
and give fifth
his assent
rule):
"Non
.
24
von Conches, Koln Cf. H. Flatten, Die Philosophic erster Linie betont unser Scholastiker die Selbstandigkeit der Wissenschaft". des
Wilhelm
1929,
p.34:
"In
Reason and Faith
"He
in the
did this not from a shortage of material, but 1) to
should be joined to sacrality of marriage,
His side
man and be and
subject to
him
3) to prefigure the
in the sacraments".
25
That
341
Dragmaticon
(...);
show
that
woman
2) to confirm the
Church which issued from
in defiance of the laws of physical
is,
causation, he exceptionally admits the possibility of miracle, evidence can be produced to prove that such a miracle
if
substantial
is
reasonably
6
justified?-
University of South Africa
25
Dragm. et
111,77:
suhditam
esse
"quod
non penuria materiae
debere
significaret,
et
fecit,
sed ut mulierem uiro coniunctam
sacr[ament]um
ecclesiam, quae ex latere eius in sacramentis profluxit,
coniugii
confirmaret
et
praefiguraret".
Elsewhere, in reply to the objection that God can intervene any time to change natural course of events, he had rejoined: "Quid est stultius quam affirmare aliquid quia Creator potest illud facere? Fecitne quicquid potest? Qui igitur Deum aliquid contra naturam facere dicit, uel sic esse oculis uideat, uel rationem quare the
<esse>
hoc
sit
ostendat, uel utilitatem
ad quam hoc
sit praetendat"
(Dragm.
111,68-9).
CECILIA TRIFOGLI
The Place
of the Last Sphere in Late-Ancient and
Medieval Commentaries
Aristotle
treatment
s
frequently discussed
of
the
place
of
the
last
of his doctrine of place
topic
the
is
sphere
most
Late-ancient
among
and Medieval commentators. 1 They raise many questions about it and attempt different solutions which often reflect either conceptions of place different
from Aristotle
The
exposition
primary concern of consider
the
to the
it
of
Rome
To
this paper.
s
position
on
this
context
of
the
and
problem
doctrine of place seems to be inconsistent
s
same
topic
we
introduce his position
is
the
shall briefly
the
major
when
applied
proposed by the commentators.
heavens since
but, at the
or innovations introduced in the doctrine.
Aristotelian
interpretations of
Aristotle
s
of Giles
it
turns out that the heavens cannot be in a place,
time, must be in a place. In particular, the definition of
place as an external
container"
and the derived
criterion for being in a
3
deny a place to the heavens. For this criterion claims that only bodies which are contained by another external body are in a place. As a consequence, the heavens or the outermost body of the universe cannot place
be
in a place, since they are not
however,
heavens
other
must
contained by another body. There are,
primary assumptions about place which show that the be in a place. They concern the essential connection
between place and
local
motion;
this requires that
every body that moves
wish to thank prof. F. Del Punta for advice and comments on this paper; I am Rega Wood for her patience in helping me to elucidate some of the linguistic oddities and for her precious remarks and encouragement. I
also indebted to dr.
On
the
history
of Aristotle
Systeme du
Monde
(10 vols.),
s
of place, see, for instance: P. Duhem, Le A. Hermann, 1913-1959; vol.1, pp.197-205, 297-300,
doctrine
Paris,
313-320, 333-350; vol.7, pp.158-302; vol. 10, pp.50, 79-81, 100, 157-160, 204-210, 396-412; E. Grant, "The Medieval Doctrine of Place: some Fundamental Problems and Solutions",
XIV
secolo
Paravicini Bagliani)
Roma,
in:
Studi sul
in
memoria
di Anneliese
Maier
(a
cura
di
A.
Maieru e A.
Edizioni di Storia e Letteratura, 1981, pp.57-59.
See Aristotle s Physics (a Revised Text with Introduction and 1 Ross), Oxford, Clarendon Press, 1936 IV.4, 212a20-21. 3 See Aristotle, Physics, IV.5, 212a31-32. ,
Commentary by W.D.
TJie
with
motion must be
local
circular
motion,
Aristotle
s
in
Place of the Last Sphere
i.e.
4
a
in
343
But the heavens move with
place.
with a kind of local motion. So the problem with
doctrine can be
summed up
as follows: the heavens cannot
be
a place, since they are not contained, but must be in a place, since
they
move with In
local motion. this
facing
the
problem,
Aristotelian
reached
two
unavoidable
and
tradition
different positions:
the
1)
first
declares
that
contradiction
the
is
the Aristotelian doctrine of place completely. This position was
rejects
who
supported by Simplicius and Philoponus, Following
place.
Damascius
doctrine,
formulate other doctrines of defines
Simplicius
as
place
measure of the position of the bodies, whereas Philoponus defines three-dimensional incorporeal extension.
Proponents
2)
of
second
the
the
it
as a
remove
the
5
to
attempt
position
contradiction without giving up the whole Aristotelian doctrine, but by
some
modifying
principles
from
which
it
This
derives.
was
position
supported by some Greek commentators and commonly by the Medieval commentators. These commentators, however, followed different routes to save
Aristotle
difficult
s
doctrine;
all
them
of
reflect
of
interpretations
the
passage of Physics IV.5 where Aristotle attempts to deal with the 6
place of the heavens.
Aristotle claims that only the parts of the heavens are in a place
move from
since only they
a place to another; the heavens as a whole
are not in a place since they do not change place, as they rotate. This solution assumes that circular motion for
right, its
it
is
not the rotating body
is
not a local motion in
parts.
There are two main terminological ambiguities which
commentators.
The
first
for the
concerns
ambiguity
the
See, in particular, Aristotle, Physics,
See Simplicii In
Aristotelis
term
and the universe,
continuous parts which compose the
(
Aristotle
text
s
this
last
parts
.
Since
term can stand
sphere or
(ii)
for
IV A, 211al2-14.
Physicorum
Physicorum Commentaria, ed. H. Regia Borussica, Berlin 1887, pp.557,8-585,4.
Aristotelis
See Aristotle, Physics, IV.5, 212a31-b22.
ed. H. Diels (CA.G. vol.IX), 1882, pp.601, 1-645, 19; loannis Philoponi In
Commentaria,
Academia Litterarum Regia Borussica, Berlin
6
in
justify the different reconstructions of his solution offered by the
Aristotle mentions both the heavens (i)
own
its
changes place, but only
itself that
Vitelli
(C.A.G.
vol. XVI),
Academia Litterarum
344
Trifogli
the single celestial spheres
as
parts of the celestial region or
(iii)
for
spheres and the sublunar elements as parts of the universe. The second ambiguity concerns the expression per accidens
both the
celestial
.
For Aristotle
s
heavens
the
account of the place of the heavens clearly indicates that are in a place in virtue of their parts, but Aristotle
concludes that they are If
only
the
second
of
Aristotle
reconstructions
The
traditions.
per paries
in a place per accidens.
ambiguity solution
s
1)
the
different
broad
exegetic
considered,
two
into
assumes that per accidens simply means the second tradition makes a distinction between the meaning
;
tradition
first
of per accidens and that of per paries
The
.
seems chronologically
tradition also
first
and
Themistius
in
is
fall
for
first
it
appears
and
in
Philoponus paraphrasis Simplicius commentaries. 7 These commentaries also show that this tradition divides into two, according to the interpretation given to the first ambiguity, to
the term
refers
are
parts
According
.
continuous
the
second they are the single the Middle
the
Ages
commentary, who Themistius, in faithful
of
parts celestial
the
it
i.e.
the parts to which Aristotle
first,
last
sphere,
according
to
the
spheres and the sublunar elements. In
interpretation reappears in
first
accepts
to the
but falsely ascribes
it
Thomas Aquinas
to Themistius.
8
For
follows the second. Both these interpretations remain
fact,
on two important aspects: 1) they accept motion of a body can be reduced to the local
to Aristotle s doctrine
the view that the circular
motion of
its
parts;
definition of place
is
2)
they assume
that
an essential element of the
containing the located body. Both these aspects are
rejected by the second exegetic tradition. 2)
This
second tradition
Albert the Great, criticized by
Rome
and such important
See Themistii In
starts
from Averroes;
it
followed
is
Thomas Aquinas, and defended by
later
authors as Walter Burley.
Aristotelis Physica Paraphrasis,
Academia Litterarum Regia Borussica,
Berlin,
ed.
9
Its
by
Giles of peculiar
H. Schenk (C.A.G. vol.V,
p.
II),
1900, pp.119,12-121,20. Simplicius, Physics,
pp.588,1-595,26. loannes Philoponus, Physics, pp.593,1 1-597,4; 600,25-604,19. o See S. Thomae Aquinatis In octo Libras Physicorum Expositio, ed. Torino-Roma, Marietti 1965, Bk.IV, lectio 7, pars. 478-480, pp.232-233.
P.M. Maggiolo,
See Averrois Cordubensis Aristotelis de Physico audito (Aristotelis Opera cum Averrois Commentariis, vol. IV), Venetiis 1562 (repr. Minerva G.M.B.H., Frankfurt 1963), Bk.IV, Comment 43, fol.!41L-M; Comment 45, fols. 143M-144E. Alberti Magni Physicorum Libri
VIII (Opera
Omnia,
Thomas Aquinas, Romani Commentaria in
p.269.
ed. A. Borgnet, Parisiis 1890, Bk.IV, tract.I, cap.XIII, Bk.IV, lectio 7, par.477, p.232; par.486, p.234. Aegidii octo Libros Physicorum Aristotelis, Venetiis 1502 (repr. Minerva vol.III),
Physics,
The Place of the Last Sphere
the distinction between being in a place per paries and being in a
trait is
which refer
place per accidens,
heavens
When
.
turn
in
to
different
meanings of
the
the heavens are conceived as the whole celestial region,
because the single celestial spheres a place; but when the heavens are conceived as the last sphere,
they are in a place per paries, are in
345
i.e.
they are in a place per accidens,
i.e.
per centrum, namely the earth. This is clearly an innovation
account of the accidental location of the heavens introduced by Averroes and, furthermore, Aristotle
it presupposes the rejection of which reduces circular motion to the motion of the principle
s
parts of the rotating body. I
will
discuss
treatment of the accidental location of
Giles
next
the heavens.
To
Giles
clarify
position
claim that the last sphere
is
in
it is necessary to analyze further the a place in virtue of the earth. It includes
two assumptions which are conceptually and factually distinct. The first comes out from the spatial relationship between the sphere and the not contain
earth.
So
The
earth
is
contained by the
last
last
sphere but does
in
attempting to solve the problem of the place of the heavens, the second tradition gives up the primary axiom on place, that of containment, and admits an internal place, at least for the bodies it.
which move with circular motion.
But
this
does not yet explain why,
contained inside the is
chosen to define
last its
among
all
the bodies which are
sphere, the one most distant from
place.
The explanation
is
it,
the earth,
provided by the second
assumption concerning the immobility of place: place must be immobile and the earth is the only body in Aristotle s universe which is properly immobile. All the followers of the second exegetic tradition share both these
assumptions and occasionally repeat the arguments which Averroes used to support them.
Regarding internal place, Averroes declares that it is not necessary to have an external place, since they move circa and not in continente. aliquid Furthermore, he seems to accept for
spherical bodies
Avempace
G.M.B.H., Aristotelis
s
arguments on
Frankfurt Expositio
et
1968),
this
Bk.IV,
Quaestiones,
York, 1972), Bk.IV, fol.l02vb.
topic:
lectio
Venetiis
8,
unlike the rectilinear bodies,
fol.82ra-b.
1501
(repr.
Walter
Hurley,
In
the
Physicam
Georg Olms, Hildesheim-New
346
Trifogli
sphere
is
by something
does not need to be completed
in itself and, therefore,
complete else, a
10
containing place.
Regarding the immobility of place, he declares that the heavens are in
a place because of the earth since the immobility of the earth
cause of the /lv/0 of the heavens.
is
the
11
Besides repeating these arguments, Giles formulates other arguments in
favour of the opinion that the heavens are in a place per centrum.
These arguments describe a new interpretation of the connection between place and local motion. For they stress the function of place in the description of local motion, but they deny any real dependence of local
A
motion on place. from this function. In
new
quantitative concept of place
what follows
aspects
I
shall
try to
Giles
in
appear
sphere and of the immobility of the treatment of the
In
framework
within
emphasi/ed. Giles against
Thomas
of
virtue
its
parts,
before and after
it.
claim, showing that these last
first
problem, the function of place as a
and
are
rest
described
is
chiefly
main argument formulated by
position.
Thomas
Following Aristotle, in
derive
place.
appears, for instance, in the
It
to
treatment both of the place of the
motion
which
this
prove
seems also
held that the
since each
Giles
part
criticism
is
is
last
sphere
in a place
is
contained by those which are
the following:
with the relative order of the parts of the
last
if
place
is
identified
sphere, the last sphere
undergoes motion, but it cannot be recogni/.ed and described, since this order does not change, as it moves. The correct frame of reference is an internal
i.e.
the
because the position of the
last
sphere changes with respect to the earth, as it rotates. For, as Giles explains: Moto enim celo, partes celi habent alium ordinem ad paries centri. Pars
enim
place,
earth,
que prius respiciebat hanc partem aliam partem terre. Totum ergo celum semper ilia
terre,
moto
respicit
celo,
respicit
totam terram, sed
non semper respicit earn eodem modo, partes vero celi non semper respiciunt easdcm partes terre, propter quod, si comparamus celum ad centrum
10
See
Comment 11
et
partes celi ad partes centri, inveniemus
Averroes,
Physics, 45, fol.l44B.
Bk.IV,
See Averroes, Physics, Bk.IV,
Comment
Comment
43,
quod totum celum
fols.!41M-142B,
43, fo!.142G.
142E,
142M-143A;
347
The Place of the Last Sphere
mutat locum secundum dispositionem, partes vero eius mutant locum
secundum substantiam
The same
12 .
criticism
raised against the opinion that identifies the
is
place of the last sphere with
cum ad
convex surface:
its
huiusmodi superficies
Si
celum semper uniformiter se habeat, sequeretur quod celum ex motu suo nullo modo mutaret locum, esset locus celi,
quod
est
illam superficiem
omnino inconveniens
The
function
description of local
of place in the
underlined
definitively
13 .
the
in
third
argument
motion
favour
in
is
also
of Averroes
Tertia via sumitur ex parte eorum que debemus salvare circa locum. Sic enim tribuendus est alicui locus ut per motum eius localem opinion:
modo
mutet locum. Si enim ponemus celum nullo Alexander, vel
ponemus ipsum
si
posuit Themistius, vel ultime, ut
Sed
si
quidam
alii
si
esse in loco solum
diceremus ipsum esse
posuerunt,
ponimus ipsum esse
esse in loco, ut posuit
secundum
nunquam per motum
in loco per
partes, ut
in loco ratione superficiei
eius mutaret locum.
comparationem ad centrum
vel per
comparationem ad terram, cum totum celum semper respicit eandem terram, partes vero celi non semper respiciant easdem partes terre, salvabimus in celo quod per eius
motum mutet locum
et
salvabimus quod
quantum ad eius partes mutet locum secundum substantiam, quantum ad se totum mutet locum secundum dispositionem 14 .
These passages show first that the causal connection between the motion or rest of the heavens and the earth, maintained by Averroes, has completely
disappeared.
Furthermore,
they
show a
sharp
distinction
between the existence of motion and the elements necessary to describe it it, and place appears to be relevant only for the description. From this follows that Giles gives
of
place.
Place,
Aristotelian
surface
provided that this function
it
it it
no
clear indications about the physical properties
be
seems,
could
of
container,
the
either
a
of
space
several
or
things
an internal
-
the
place-
allows a suitable description of motion. But to perform
must meet an
essential requirement:
it
must not only be
physically separated from the mobile body but immobile since, as Giles Omnis enim motus fit respectu alicuius immobilis; nunquam explains: 12
Aegidius Romanus, Physics, Bk.IV, lectio
8,
fol.82vb.
fol.83ra. This opinion is not mentioned Aegidius Romanus, Physics, Bk.IV, by Averroes, but by Albert the Great, who ascribes it to Gilbertus Porretanus (see Albertus Magnus, Physics, Bk.IV, tract.I, cap.XIII, p.270). lectio 8,
14
Aegidius Romanus, Physics, Bk.IV, lectio
8, fol.83rb.
348
Trifogli
cnim possumus imaginari motum 15 cuius aliquid dicatur moveri
nisi
imagincmur
aliquid
immobile respectu
.
The
espoused by all the followers of the second exegetic tradition, whereas the second is introduced by Giles. It contains an explanation of the immobility of place that is clearly conclusion in this passage
first
congenial to the
new
is
function of place. Averroes himself, for instance,
explained this point in a different way: the place towards which a body moves must be immobile because: Si aliquid movetur ad motam rem, tune
motus eius This Aristotle
esset ociosus
explanation,
16 .
that
real connection
absent
completely
in
it
to
assumes a
between place and motion based on the nature of bodies. of the immobility of place also shows which
physical properties place
These
rest.
refers
Giles,
treatment
Giles
and
is
doctrine of natural place and motion. Therefore,
s
must have
out
turn
properties
provide a description of motion
to
be
to
different
from
those
of
Aristotle s place.
To
explain
this
point
we must
turn
Giles
to
distinction
between
introduced to counter an
formal and material place. This distinction
is
objection against the immobility of place:
place, according to Aristotle,
if
the surface of a natural body, since each natural
is
can
be
place
answered
if
and
body
immobile?
Giles
admits
that
this
body can move, how objection cannot be
completely reduced to the surface of the containing place Locus est immobilis formulates the following distinction: is
formalitcr, mobilis vero materialiter.
The of the place fixed
material place coincides with the Aristotelian place as surface
containing body in
is
the ordo
points
contact
ad universum of
of the
universe
with
the
contained,
this surface,
(the
earth
i.e.
and the
its
whereas formal
relationship to the poles). The Thomas Aquinas
celestial
of this distinction already appear commentators offer an explicit definition of the ordo Neither commentary. ad universum; there are, however, some differences in the terms and essential
in
traits
examples they use which
illustrate
Giles
place.
15
16
Acgidius Romanus, Physics, Bk.IV, lectio Averroes, Physics, Bk.IV,
Comment
8, fol.83rb.
41, fol.!40A.
1
Aegidius Romanus, Physics, Bk.IV, lectio
7, fol.Slra.
quantitative
notion of formal
The Place of the Last Sphere
To
how
349
ad universum remains unchanged when the founded vary Thomas introduces the following analogy: Sicut etiam dicitur idem ignis manere quantum ad formam, licet secundum materiam varietur, consumptis et additis quibusdam lignis 18 explain
on which
surfaces
the ordo is
it
.
Thomas
ordo, therefore,
common
to
the
all
similar to Aristotle s form, being a quality
is
containing surfaces and conferring the function of
place upon them. But there
no analogy between place and form
is
in
commentary. For Giles explains the permanence of place by the permanence of the distance between the located body and the fixed points Giles
consequenter ponitur, ideo locus est immobilis quia, licet, te quiescente, possit moveri aer qui est iuxta te vel aliquod aliud corpus circumdans te, semper tamen diceris esse in eodem loco quia of universe:
semper
es in
From
Nam,
ut
eadem
distantia
this
it
passage
ad centrum evident
is
et
ad polos
that
19 .
Giles
replaces
the
generic
notion of ordo with the quantitative notion of distantia. This distance
can be measured and, therefore, the formal place conceived as distance is
a suitable
framework
The comparison
for the description of local
motion and
rest.
of the quoted example with other similar examples
offered by Giles reveals a doctrinal aspect that, though not systematically
developed
by
position. For,
located
body
the
consequences of his example, Giles refers to the distance between the and the fixed points of the universe, whereas in the elucidates
Giles,
theoretical
in this itself
examples he refers to the distance between the surface of the containing body and these points. How can this be explained? Perhaps, other
the explanation could be
when considering formal
found place,
remark by Edward Grant 20 that, the Medieval authors speak indifferently a
in
measured from the place itself or from the body in that since place and the external surface of the located body are
of the distances place,
coincident, according to Aristotle. Consequently, the distance
both cases formal
is
place,
identified
with
simply completes Aristotle but
seems
to
replace
essentially to evaluate
it.
s
a
no longer something
is
distance,
in
Thomas Aquinas,
motion and
in
rest
fact,
and
it
according
performs
Physics, Bk.IV, lectio 6, par.468, p.227.
10
Aegidius Romanus, Physics, Bk.IV, lectio
7,
See E. Grant,
Place"...,
"The
that
notion of place as surface of the container, Place,
10
?n
measured
the same. This explanation has a further implication: the
Medieval Doctrine of
fol.Slrb.
p.65, note 25.
to
Giles,
this function
serves
when
350
it
is
Trifogli
defined as a distance that remains the same,
at rest,
and
indifferently itself
varies,
if
satisfied
the located body
when
the
is
distance
if
the located
to
introduce
the
is
motion. Both conditions are
is
measured from the located
and from the surface of the body containing
body it seems superfluous
body
in
containing
located body, at least as far as the description of motion
it.
Consequently, besides the
surface is
concerned.
emphasis on the role of place in the description of motion seems to lead to a quantitative and relational notion of place. In conclusion, Giles
Giles, however,
does not completely substitute the Aristotelian notion of is only one of the
place for that of place as a distance. Place as distance
two notions of place which appear in his commentary. The other, which is related to material place, assumes an intrinsic connection between place and the located body
that cannot
Universita degli Studi di Pisa
be founded on distance alone.
WHITE
G.
Ockham and Hume s Question
There has been, bring of
Ockham
scepticism",
secondary
some
no shortage of attempts to
literature,
sort of meaningful relationship with
however
Such
conceived.
Ockham
link
to
attempts
in the
into
with
later
attempts
figures;
thus
about induction and the
possibility of a scepticism
Goddu 1
problem with
go
generally
the
raises
reliability of causal
Ockham
connections, which gains a hold because of
"the
s
principle that the
existence of one thing cannot necessitate the existence of another thing.
Even though have, as
this
later did
it
Goddu seems fact
principle did not lead
Hume; and
to think, needs to
Ockham
the fact that
to scepticism,
didn
t
is
it
could
something
that,
be explained.
We
find a similar chain of thought in
that
Ockham subscribed to that God could cause
principle
it
a
certain
us
to
Adams. 2 Again, we have principle
believe
-
in
this
falsehoods
assertion that this principle leads to a form of scepticism
-
-
case,
the the
and the
in this case,
3 scepticism about mind-independent material objects. Here, too, the path from the principle to fully-fledged scepticism is one that Ockham didn t
take, but
1.
somebody
else
-
in this case
Prepositional Structure, Assent,
Descartes
-
did.
and Cause
Ockham s key texts: the Prologue to concerned here with the structure4 of acts of
Let us start by examining one of his
Ordinatio.
Ockham
is
Andre Goddu, The Physics of William of Gcistesgeschichte des Mittelalters 16 (Leiden 1984), p. 217. "
Marilyn Ockham",
In
McCord Adams,
Cognition,
Certainty,
Studien
und
and Scepticism
Texte
in
zur
William
Traditio 26 (1970), pp. 389-398. See p. 394.
her
Scepticism",
A. C. Pegis,
definition in
of
scepticism,
she
follows
Etienne
Gilson,
The
Road
to
The Unity of Philosophical Experience (New York 1937), pp. 61-91, and
"Concerning
John Boler, 85-98. See p. 86: Cf.
"Intuitive
Ockham.
William of
"Ockham "the
Ockham",
doctrine
Traditio 2 (1944), pp. 465-480.
Cognition", Franciscan Studies NS 36 (1976), pp. of intuitive cognition depends upon an analysis of the
on Evident
White
352
assent
more
with
(specifically
evident
assent
to
theological
here interested
He
the evident assent which belongs to science
in
but
propositions,
generally with evident assent to propositions in general.)
not
is
(i.e.
that
comes from knowledge of first principles and the like; 5 such in principles are known when the terms occurring in them are known
which
Ockham
fact,
statement
of
knowledge
first
(complcxa) which
knowledge of called
I
terms. it
-
their
knowledge
(notitia
someone
broad definition of
s
it
know
-
applies
is
white.
Ockham
as
sees
Socrates and being
at
9
and whiteness existing
Socrates
sees
intuitively
knowledge of
intuitive
extends to the sort of knowledge of
it
someone has when looking
Socrates, then (s)he can
evidently that Socrates
is
in
white.
thought."
Sent.
Ockham, Bonavcnture "Si
with
contrast
by
intuitiva),
a rather general definition, and
able to judge on that basis that Socrates
structure of
However,
with will be like
(notitia abstracted).
Ockham
empirical facts which
if
the
to
to a variety of cases. Firstly,
...
6
in that it is knowledge of propositions be caused simply by (a certain sort of) terms (incomplexa}? The sort of knowledge of terms
able
knowledge
is
contains
terms".
principles
is
shall call this It
which
Aristotle
we know their Ockham is concerned
in that
principles
intuitive
abstractive
in
passage
of evident assent that
the sort
is
a
to
refers
know
"We
NY
dicatur
Prol.
qu.
quod
Opera
1,
Theologica
ed.
I,
G.
Brown
S.
Gal,
(St.
6:
1967), p.
cvidens veritatis
notitia
contingentis
nunquam
causatur sufficicnter
incomplcxa terminorum, quia tune scirctur cognitis terminis. Sed omnc tale 18est principium per se notum, secundum Philosophum I Posteriorum [c. 3 t. 21, 72 26]. Sed nulla veritas contingens est per se nota; igitur etc.: Dicendum quod propositio per se nota est ilia quae scitur evidentcr ex quacumque notitia terminorum ipsius propositionis, sive abstractive sive intuitiva. Sed de propositione contingente non est hoc possibile ex
notitia
..."
"Principia
cognoscimus
in
quantum terminos
cognoscimus."
Post. Anal.
3
c.
t.
21, 72
18-26. "Notitia
evidens
est
cognitio
vcri
alicuius
incomplexa immediate vel mediate nata sufficientcr O.Th. I, p. 5.
complexi, causari."
ex
terminorum
notitia
Ockham,
Sent.
Prol.
qu.l,
Q
The this is
existence
proved
"...si
in
aliquis
of such a
Ockham, videat
ibid.
distinction
intuitive
evidenter scire quod Sortes est
is
Conclusio
1
of qu.
1
(Ockham,
ibid.
p.
15);
pp. 22-30.
Sortem
albus."
et
Ockham,
albedinem
Sent. Prol. qu.
exsistentem 1,
O.Th.
I,
in
p. 6.
Sorte,
potest
Ockham and Hume s much
applies to
it
Secondly,
evident
is
Ockham mental
states.
above;
such
(This
mental
associated with terms
-
-
incomplexa
and thus
we have
in the technical -
things
huiusmodi
et
tristitiae
delectationes,
are
the
-
our
argues
own
of our
described
way
intellectiones,
and
-
10
have:
love, are happy or are
fact,
that
intuitiva
be interpreted
states
we
that
contingent
to notitia
to
is
of a
is
knowledge,
must be due
-
we
introspective knowledge that
knowledge that we understand something, sad
353
Question
affectiones,
notitia
intuitiva
is
referring to these things.)
polemics against Scotus, Ockham seems to insist on this precisely property of intuitive cognition - that it guarantees of the propositions that it occurs in. But we can also see now knowledge in
And,
the
his
of
point
certain
Ockham
that
objections
made
Scotus
to
characterisation of the distinction:
When
(1)
Scotus
said
some diminished whatever
11
When
(2)
the
in
est
quod
notitia
aliqua
refers
not
-
"according
to
objects to this that, according to
anything,
and,
one
can
must be
it
consequently,
doubt
12 abstractively under that description.
in
that,
whereas
intelligibile
cuius
or
exist
know something
Scotus said
omne
"...
sensibile,
one
description
motive,
Ockham
similitude".
whether that thing possible to
intuitive
knowledge only has to do with the object
abstractive
to
knowledge has to do with the description" (sub perfecta ratione), whereas
that
a complete
"under
object
a
intuitive
knowledge, the thing
abstractive
solo
intellectu sufficit
incomplexa
knowledge
ad
itself
is
it
is
some
apprehensibile et nullo modo notitiam evidentiam alicuius
de eo et aliqua notitia incomplexa eiusdem non sufficit, potest duabus cognitionibus specie distinctis. Sed intellectiones, affec tiones, delectationes, tristitiae et huiusmodi sunt intelligibiles et nullo modo sensibiles, et aliqua notitia incomplexa earum sufficit ad notitia evidentem utrum sint vel non sint,
veritatis
contingentis
ab
cognosci
et etc.
intellectu
utrum sint in tali subiecto vel non, Minor quantum ad primum partem
et
aliqua
patet,
notitia
earundem non
sufficit;
delectatur, tristatur; et ista notitia, cum sit respectu contingentis, ligit, diligit, potest accipi ex propositionibus necessariis." Ockham, Sent. Prol. qu. 1, O.Th. I, p. 28.
qu. 6 n.
Scotus, Quodl.
Ockham,
Sent. Prol.
O.Th.
1
Ockham,
Sent.
(Oxford
1982), misidentification
Prol.
p.
I,
8;
Wadding, XII,
145; ed.
and
tr.
non
Wolter, pp. 135f. Cf.
p. 34.
O.Th.
219:
ed.
igitur
quia quilibet experitur in se quod intel-
"...
pp. 36f. Cf. the property
I,
Gareth Evans, The of
being
Varieties
of Reference through of a term] is not one
immune
to
error
[which corresponds to Ockham s notitia intuitiva which applies to propositions simpliciter, but one which applies only to judgments made on this or that basis. Once we appreciate this relativity to a basis, which arguably must be taken into account in the case of mental self-ascription as well, the fact that there
are
cases
the involving the self-ascription of physical predicates in which error has been provided for [these correspond to Ockham s notitia abstractiva] will be seen not to impugn the fact that there are cases in which it just as clearly has not." possibility
of
White
354
representative of the thing.
comes about by natural acting
God
directly;
13
Ockham thus
located at
God
Rome
about
bring
knowledge of things without the things point talks of
God
can be brought about by
causality
can
objects to this that whatever
14
acting.
an
such
intuitive
And Ockham
at
one
bringing about intuitive knowledge of something
(presumably when he
is
15 away from Rome.)
A
modern philosopher may have a few reservations good. describing mental states as things, and describing psychological
So about
far so
language as referential tout court, but otherwise John Boler seems to be more or less on track when he remarks, citing Jerry Fodor, that 16 I think Ockham s enterprise [could] be ... fruitfully compared to ... those recent studies which claim some relation between logical form and linguistic structure, and between those and cognitive psychology.
And
Ockham
all
Socrates
we
that
way
white
is
attitudes (let
has surely done I
,
am happy
-
to
is
and
certain
analyse
to
claim that,
propositions
we
if
-
analyse the
deal with such propositions there must be different mental us say) corresponding to the terms; these mental attitudes
give us, for each term, a grasp of the corresponding object.
Very
similar
made by Gareth Evans when he
talks
about
been
have
distinctions
personal pronouns; he 17 "Ideas".
Now
in
the mental attitudes corresponding to terms
calls
Ockham
s
analysis,
there
two ways of having a
are
we know
grasp of objects, corresponding to whether or not proposition evidently;
too,
so,
in
knowledge that we can have of propositions such 13
Scotus, Quodl. qu. 13,
Ockham, 14
15
Sent. Prol.
Ockham,
O.Th.
Sent. Prol.
Ockham,
II
Sent.
I,
n.
cd Wadding, XII,
p.
My
as
311; ed.
and
tr.
legs are crossed
Woltcr,
p.
292. Cf.
p. 34.
O.Th. qq.
10;
the relevant
theory, there are two sorts of
Evans
I,
p. 37.
12/13,
O.Th. V, ed. G. Gal, R.
Wood
(St.
Bonaventure
NY
per cognitio intuitivam iudicamus rem esse quando hoc est, et cognitio naturaliter causetur sive supernaturaliter a solo Deo. Nam si naturaliter causaretur, tune non potest esse nisi obiectum exsistat praesens in debito approximatione, quia tanta potest esse distantia inter obiectum et potcntiam quod naturaliter non potest potentia tale obiectum intueri. Et quando p.
258:
obiectum
est
1981),
igitur patet quod gcneraliter sive intuitiva "Sic
sic
praesens
modo approximatum, modo praedicto. Si autem
tali
potest
intellectus
per
actum
supernaturalis, puta si Deus causaret in me cognitionem intuitivam de aliqua obiecto exsistente Romae, statim habita ita bene cognitione eius intuitiva possum iudicare quod illud quod intueor et video est, ilia sicut si cognitio haberetur naturaliter." Ockham does say elsewhere that
assentiendi iudicare
rem
esse,
sit
"in
cognitione intuitiva [obiectum] est praesens in 16 J. Boler, "Ockham on Evident Cognition",
se";
Thought (New York, 1975). Evans, The Varieties of Reference, p. 104.
II
p.
Sent. 12/13, 86;
he
O.Th. V,
cites J.
p. 310.
Fodor, The Language of
Ockham and Hume s or
(evident
corresponding precisely to two different
this
non-evident);
355
Question
18 And these two uses will differ person pronoun. in whether the utterances precisely they are used in are grounded by
uses
of
other
the
first
or
propositions
concerns and
Adams
not;
this
analysis of
establishes
Ockham
s
a
these
19
position.
However, things are not as simple as illuminating to say that
continuity between
that.
It
is
possible,
and
20
... the doctrine of intuitive cognition depends on an analysis of the structure of thought, an analysis which is controlled directly not by any observation of the parade of cognitive activity but rather by the demands of the analysis of propositions.
It is maybe even when he says: 21
true.
a concept
And Ockham
himself says something very similar
given so that
it corresponds to utterances, so understood by an external utterance, so understood] by the concept signified [by the utterance]. ...
However,
Ockham
is
as something
just
the
is
continuities
that
this
establishes,
is
between
thought and modern philosophy of mind, are entirely of one are to do, that is, with the functional role of language, mental they
sort;
s
attitudes,
and the
like.
Now
there are two sides to the philosophy of
mind; on the one hand, you have to
talk
various theoretical entities that you use. tell
analysis
that, [it
certain causal stories which describe
about the functional role of the
On
the other hand, you have to
how our
brains (or our souls)
And the work that I have just described ignores another in Ockham s theory, besides the analysis of ingredient propositions; it ignores, that is, Ockham s ontology and his physics. My claim is that it is these which give Ockham s theory some of its most actually do the
distinctive
and
stuff.
features,
and which are responsible
for
its
major
difficulties
peculiarities.
10
Evans, The Varieties of Reference pp. 215-220. Cf. Sidney Shoemaker, "SelfReference and Self-Awareness", in S. Shoemaker, Identity, Cause and Mind (Cambridge ,
1984), pp. 6-18; 1958), pp. 66-7.
19
Adams,
and Ludwig Wittgenstein, The Blue and Brown Books (Blackwell, Oxford
"Intuitive
Cognition in
Ockham", p.
393.
on J.
Boler,
21
"Ockham
on Evident
Cognition",
p. 86.
conceptus ponitur ut correspondeat vocibus, ut sicut aliquid intelligeretur prolata voce et concepto suo significato." Ockham, Questione in Libras Physicorum Aristotelis qu. 5, ed. Stephen Brown, Opera Philosophica VI (St. Bonaventure NY 1984), p. 405. (Cf. Ockham, Exp. Periherm. I, Proem, 4, O.Ph. II, pp. 349f.) ...
White
356
1.1
Logical Atomism
Now Ockham evident
a
to
proposition.
I
proposition was;
and immediately by
Now
as
this quaestio,
began
assent
it
(a certain sort of)
this definition is not,
have described, by defining what is assent that is caused solely
knowledge of the terms of
any particular analysis of the proposition
in
that
biased in favour of
at this stage,
question.
One
for
could,
example, very well introduce the distinction in the way that Gareth Evans does: in Evans terms, such knowledge is not identification-dependent; is not the result of knowledge that b is thus, knowledge that a is
F
F
and
a
that
firstly,
is
that
propositions
work
b\ But Evans
done
is
it
terms
in
he
from Ockham
subject-predicate 22
interested
is
differs
a
of
in;
two ways;
in
s
of
analysis
secondly, he does not
the as
talk,
23 does Ockham, of knowledge being caused by other pieces of knowledge - Evans talks, rather, of propositions being deduced from, or grounded
on, others.
However, elsewhere Ockham imports a bias intuitive
knowledge of terms (this
is,
remember,
just that
knowledge of
terms that causes evident assent to the propositions that they occur
He
defines
it
as follows:
of
definition
his
in
in).
24
knowledge of a thing is such knowledge by virtue of can be known whether the thing exists or not, in such a way that if the thing exists, the intellect always judges that it unless perhaps it is it exists and evidently Knows that exists, impeded because of an imperfection of that knowledge. And, in the same way, if a perfect such knowledge were conserved, by divine power, when the thing did not exist, by virtue of that knowledge of a term [notitia incomplexa] it would evidently be known that the thing did not exist." ...
Now
intuitive
which
it
this
is,
on
the
of
face
it,
term can occur
propositions that the
of a term a, then, according to
a
on
restriction
in;
Ockham
if
we have
s
broad
the
of
analysis
intuitive
knowledge this
definition,
should
guarantee knowledge of a whole variety of propositions with a occurring 22 23
Evans, The Varieties of Reference, pp. 180ff.
Note
that
praemissorum
Ockham est
causa
explicitly talks of efficient causality notitiae conclusionis" (Ockham, Sent.
in
this
Prol.
qu.
context; 8;
"notitia
O.Th.
I,
p.
Furthermore, he defines per se notae propositions in this way, "propositio per se nota cognoscitur ex notitia terminorum" (Sent. Prol. qu. 2, O.Th. I, p. 81), as well as ratione propositions scibilis est quod eius the idea of a knowable proposition;
222).
"de
notitia possit causari ex notitia principiorum" (ibid., p. 82).
24
Ockham,
Sent. Prol. qu.
1;
O.Th.
I,
p. 31.
Ockham and Hume s them.
in
In
actual
a
Ockham
though,
fact,
and a does not
357
Question
two
about
talks
only
25
(And, in fact, only the propositions; former applies in the normal course of events.) Let us call this Ockham s narrow definition of intuitive knowledge of a term. He adds to it (as an exists
extension? a corollary?
it is
exist
not quite clear) that
.
26
knowledge is such that, when several things are of which one inheres in the other, or one is spatially distant from the other, or is related to the other in some other way, then always, by virtue of that knowledge of terms [corresponding to] those things, it is known if the things inhere in each other or not, if they are distant from each other or not, and so on for other contingent truths ... Thus, if Socrates is, in fact, white, that knowledge of Socrates and of whiteness, by virtue of which it can evidently be known that Socrates is white, is called intuitive knowledge. And generally every knowledge of terms ... by virtue of which some contingent truth can evidently be known ... is intuitive Similarly, intuitive
known
knowledge.
Ockham
thus seems to be sliding between the narrow definition and
There are probably several reasons
the broad definition.
One
for this.
Scotus originally defined intuitive cognition by saying that
that
se
"per
existence."
This
of
existence,
27
This
is
and
one
the
attains
it
the
factor;
fact
in
object that
intuitive
was
it
own
its
is
actual
was
cognition
not simply an isolated oversight;
in Ockham, II Sent. qq. 12/13, O.Th. V, mediante qua cognoscitur res esse quando est, et non esse quando non (p. 256); and ibid.: quolibet sensu, qui habet aliquam cognitionem virtute cuius potest cognoscere rem esse quando est et non esse quando non est, est cognitio intuitiva et experimentalis. Quia ilia est cognitio intuitiva per quam sic cognosce rem esse vel non esse". (pp. 268f.) See also ibid., pp. 286f.
we
is
have:
est
intuitiva
"[cognitia]
ilia
est"
notitia
"Similiter,
una inhaeret statim
virtute si
inhaeret,
Sortes
in
omnis I,
aliqua
intuitiva
una
vel
non
veritate
sit
quod
est
distat
talis
res
quod quando aliquae
loco
ab altera vel
alio
modo
cognoscuntur quarum habet ad alteram,
se
incomplexae illarum rerum scitur si res inhaeret vel non et sic de aliis veritatibus contingentibus ... Sicut si
notitiae
vel
cognosci
notitia
cognosci
illius
distat rei
evidenter
O.Th.
alteri
"in
distat,
albus,
Sortes
incomplexa termini veritas contingens
albus,
vel ...
Sortis
notitia
ilia
est
dicitur
terminorum
est
notitia
et
albedinis
notitia ...
virtute
intuitiva."
virtute
Et
intuitiva.
cuius
Ockham,
cuius
potest Sent.
potest
universaliter
evidenter
Prol.
qu.
1,
pp. 31f.
Similarly, immediately after the passage similar analysis of the proposition
from
II
Sent,
above
cited
(n.
25),
there
is
a
this is introduced with corpus est album so it seems as if it is supposed to follow from the definition in terms of quia existence and non-existence. (Nothing of the sort is added after the second passage referred to there.) And in IV Sent. qu. 2 there is the claim that per cognitionem alicuius accidentis absoluti devenitur in O.Th. VII subiecti"; cognitionem (St. Bonaventure NY 1984), p. 23. There is no indication of whether this happens necessarily, or only in the normal course of events.
very
;
,
"...
27 Scotus,
Ockham Logic in
s
Quodl.
and
Italy in the
XXV:521. Cf. Katherine M. Tachau, "The Response to Epistemology (1320-1340)", in Alfonso Maieru (ed.), English and 15th Centuries (Naples 1982), pp. 185-217. See p. 192. Vives
13;
Aureol If"
s
White
358
designed,
Another
the
factor
is
to
which
according
the
solve
to
initially,
shape
many
of
problem
Ockham
of
semantics
s
are
propositions
of
existence.
and
ontology,
knowledge
equivalent
logically
propositions which assert that a certain relation holds between a
set
to
of
Now
this corresponds to a very important strain in Ockham s Goddu rather vigorously summarises his views, 28 reduced natural phenomena to Ockham s philosophy of nature
terms.
thought; as
...
and their functions, [and] existences expression of relations, acts, and events functionally. absolute
Now
this
is
rather problematic. For example,
the
prescribed
leads to an analysis of
it
I am happy into a proposition asserting that there is a 29 in Ockham was which inheres me; and, as we have seen, happiness in and to describe our such terms, correspondingly, quite willing to talk 5
the proposition
knowledge of our mental
states in
terms of
However, those of us
things as happinesses.
intuitive
probably find such reification disturbing. This semantic assumption, however, explains
will
so
between
easily
broad
the
and
the
interested
the
in
intuitive
was mainly interested
in
it
read Wittgenstein
how Ockham
could
slip
definitions.
Since
his
narrow
semantics treated individuals so prominently,
knowledge of such
who have
why he was so and why he
explains
knowledge of referential terms,
one particular
sort of proposition: a proposition
asserting the existence, or non-existence, of an individual. to
this
has
it
later;
to
do
with
We
narrow definition
the
return
will
of
intuitive
knowledge.
1.2
The Razor at Work
However, there
one of Ockham
is
s
objections to Scotus which seems
much more
problematic, and which has attained
Scotus
that
says 30
objects,
capacity,
28
29
Ockham and
essential
its
intuitive
its
objects to this that
30 Scotus, 552f.
(Vivs
intuitive
When
notoriety. existent,
knowledge
is
present
a mental
object (the thing the term refers to) cannot be one of
causes.
It
can therefore continue to
Goddu, The Physics of William of Ockham, Above,
some
knowledge can only be of
exist
with
the
thing
p. 236.
p. 2.
Opus Oxoniense II dist. 3 pars 2 qu. 2 nn. 318-322 Ockham, Sent. Prol., O.Th. I, p. 33.
qu. 9 n. 6.) Cf.
(ed. Vaticana
1973), pp.
Ockham and Hume s we can
destroyed;
have
therefore
359
Question
intuitive
knowledge
nonexistent
of
31
objects.
Now
there are two separate things here that
may seem
problematic,
only one of which is, I think, genuinely so. The first is the very idea that we can have intuitive knowledge of nonexistent objects at all. Now if we think of this in terms of Ockham s broad definition of intuitive
knowledge,
this
knowledge
in
will
terms
lead us to give an abstract definition of intuitive
of
a
functional
but
role;
a
functional
role
is
something which is manifested when the term occurs in a range of propositions; and here this range of propositions seems to include the a does not exist Now in the normal course of events, we have intuitive knowledge of a when we stand in certain causal relations to it (when we can see it, and so on). Thus, the empirical realities of the proposition
way
that
that
we
.
we have
intuitive
knowledge rule out the semantic
could have intuitive knowledge form. However, there
this particular
about by direct divine causality that -
nonexistents
just
knowledge of what chains
apparently
we
general
could,
going on in sort
problematic
nonexistents; and
very
is
usual
of the
as
Ockham
definition
lets
of
nothing to prevent
we could have divine
by
Rome
about
and the
himself in for intuitive
it
causality,
us.
causing
component
bringing
it
knowledge of have
intuitive
there are no causal
This
is
one of the
knowledge of because he gives a simply intuitive
knowledge
of the truth
God
intuitive
(that
knowledge of some component of a proposition which evident
possibility
figured in a proposition of
Rome, even though
between things
is
when a
is,
is
that
is
it
suitable
for
of propositions containing the
knowledge and because he does not specify any particular
in question),
how this knowledge should arise. I also suspect that much about intuitive knowledge of nonexistents because
causal story about
Ockham
talks so
existence assertions are so prominent in his semantics anyway, so that
if
he wanted to establish a clear difference from Scotus, since Scotus would not have found the intuitive knowledge of existence problematic,
Ockham
had to commit himself firmly to the intuitive knowledge of nonexistence. In fact, one of the major differences between Ockham and
his
contemporaries seems to be that his contemporaries would define intuitive
and abstractive cognition case by case, in terms of such things as the presence or absence of the object; e.g. Richard Campsall says that the Sent. Prol., O.Th. I, pp. 35f. There is an extensive A. Goddu, The Physics of William of Ockham, pp. 32-51.
Ockham, argument
in
treatment
of
this
White
360
same mental
when
intuitive cognition 32
is
entity
abstractive cognition
when
it is
the object
is
present,
and
absent.
However, there is something genuinely problematic about Ockham 33 position, and that is the way that he argues for it. He says:
s
... every absolute thing, different in place and subject from some other absolute thing, can, by absolute divine power, exist without the latter thing (since it does not seem likely that, if God wanted to destroy one absolute thing existing in the sky, that (s)he would necessarily have to destroy another thing existing on the earth.) But intuitive vision - sensitive or intellectual - is an absolute thing, distinct in place and subject from its object. Just as, if I see whether intuitively a star existing in the sky, that intuitive vision sensitive or intellectual - is distinct in place and subject from the object seen; therefore, that vision can remain, with the star destroyed; therefore, etc.
What
is
here
problematic
is
Ockham
that
simply
of the
thinks
vision, or, generally, the intuitive knowledge corresponding to a term, as 34
which
Ockham
talks
an absolute thing, generally,
mental
of
naturally supposit for their objects.
when
that,
of
knowledge
guarantee
A
constant.
absoluta
res
this
36
propositions
modern philosopher
-
entities
mind.
s
And Ockham seems
held
is
constant, that
it
for example,
its
Evans
of the grasp of propositional components in the
that
Ockham
32
is,
Katherine M. Tachau,
Oxford
Thought",
in
is
"The
in)
who
-
same
is is
of Richard
(to
held
willing to
of
way
same
sort
Campsall on Fourteenth-Century
(eds.), From 1987), p. 112.
Anne Hudson, Michael Wilks
Studies in Church History, Subsidia 5 (Blackwcll, Oxford
role also
sort
willing to talk of certainty in the
Influence
assume
to just
functional
occurs
talk
and who
35
And, more which ("intellectiones")
located in the knower
is
Ockham
to
Wyclif;
1
res absoluta, distincta loco et subiecto ab alia re absoluta, potest per "...omnis divinam potentiam absolutam existere sine ilia, quia non videtur verisimile quod si Deus vult destruere unam rem absolutam exsistentem in caelo quod necessitetur destruere unam aliam rem exsistentem in terra. Sed visio intuitiva, tarn sensitiva quam intellective, est res absoluta, distincta loco et subiecto ab obiecto. Sicut si videam
exsistentem in caelo, ilia visio intuitiva, sive sit sensitiva sive manere distinguitur loco et subiecto ab obiecto viso; igitur ista visio potest
stellam
intuitive
intellectiva,
Stella destructa; igitur
34 35
Cf.
etc."
Ockham,
Sent. Pro/, qu.
1,
O.Th.
A. Goddu, The Physics of William of Ockham, pp.
I,
pp. 38f.
30f.
One
be careful, however, to notice that, for Ockham, something should intellectual does not per se have a physical location; it is "subiective in intellectu, non extensive in aliquo composite sive organo corporali" (II Sent. qq. 12/13, O.Th. V, p. est in loco, quia corpus est in loco" 285). Correspondingly, "Anima enim per accidensh O.Ph. V, p. 100). (Expositio in Libros Physicorum IV cap. 8 3, t. 45 212 7-13, 36 sicut vox ita 411: O.Ph. VI, p. Ockham, Quaestiones physicorum qu. 7, naturaliter pro supponit ex institutione pro suo significato, ita ista intellectio supponit "Et
re cuius
est."
Ockham and Hume s would probably be much more
of way,
knowledge
components would
prepositional
-
reticent about talking of intuitive
In fact, such an intuitive grasp of
a thing in this sense.
as
361
Question
normal case
the
in
-
involve
the
functioning of suitable causal chains from the object to the knower, and if
the object, or the causal chains
Such an
also go.
This
head.
Fontaines.
1.2.1
"intuitive
grasp",
is
someone
not really located in
made by Godfrey
already
s
of
37
Action at a Distance
However, we should notice
Ockham
explanation in believed
action
in
propagation of
medium 39
-
lynxes
e.g.
then,
objection which was
an
is
were destroyed, then the grasp would
means of
s
-
light
41
in
this
is
he
that
connection
the
in the
Now when Ockham fulfills
of
Rega Wood,
In this connection, one can even talk of
of a distant object, brought about by divine power, and
me and
without anything caused between
Century
cited
which does not happen by means of species
action at a distance.
cognitions
he
distance;
a strong element of causal
still
of the crucial factors
and the action of magnets. 40 Furthermore, certain animalcan see through walls, and this too is to be explained by
intuitive vision
which
is
One 38
a
at
that there
theory.
a
certain
the
of
in
42
of a notitia intuitiva,
functional
existence
"Intuitive
Perspective",
talks
the object.
the
role:
namely,
when
object
it
Cognition and Divine Omnipotence:
Anne Hudson, Michael Wilks
(eds.),
this it
is
something
causes
and of
exists,
Ockham
evident
in
its
Fourteenth-
From Ockham
to
Wyclif,
pp. 51-61.
38
Ockham,
III Sent.
qu.
2,
O.Th. VI
(St.
Bonaventure
NY
1982), pp. 48-58.
-JO
Although sometimes the light source causes illumination of the medium: aliquando causatur aliquid a colore in medio, sicut prius dictum est ... Sed quando est et quando non, difficile est dare experientiam in visu..." Ockham, III Sent. qu. 2, O.Th. "...
VI, p. 81.
Tertia experientia est de magnete, qui secundum Commentatorem, commento ferrum distans ab eo localiter: trahit, dico, immediate et non virtute aliqua medio vel in ferro." Ockham, III Sent. qu. 2, O.Th. VI, p. 53. trahit
aliquod
"...
murum, 2,
et
O.Th. VI,
illud
animal videt per
medium non
medium opacem,
recipit
sicut
speciem aliquam,
patet
igitur
9,
in
de lynce qui videt per
etc."
Ockham,
III
Sent.
qu.
p. 81.
objectum distans ab angelo et a me potest intuitive videri ab angelo et a me, per potentiam divinam objectum nihil causet in medio, nee speciem nee cognitionem." Ockham, III Sent. qu. 2, O.Th. VI, pp. 55f. "...
etiam
si
White
362
when
noncxistencc
be told
to
it
does not
each case:
in
exist.
"the
And
there are relevant causal stories
judgment of existence
is
caused by the
cognition together with the object, while the judgment of nonexistence
is
43
caused by the cognition in the absence of its object." Thus, we have an which fulfills a certain functional and a causal role, entity story about how it does it; the difference from the modern theory is this, that
nowadays one talks about information propagating through the physical environment by means of physical processes, whereas Ockham talked of things acting directly at a distance.
Now
one asked him why this intuitive cognition was a cognition 44 And object, he would have a story about similitude to tell.
of this
Ockham
if
about representation quite generally
talks
in
terms of similitude;
Ockham
example, representation is transitive because similitude is. had clearly not read Nelson Goodman. And since, quite for
causation
of
is
46
like
by
like,
as
is
this
representation,
generally,
brings
the
semantic and causal categories very close to one another, in Ockham s view. Tfms he can talk of knowledge of the premises of an argument being the efficient cause of the knowledge of the conclusion, he can talk first principles as being those propositions knowledge of whose terms causes assent to the proposition, and of a demonstration being the cause of assent to its conclusion (so that one cannot demonstrate
of the
principles;
2.
one already assents
to
them when one knows
their terms.)
Hume now
Let us
think about
Hume. Why was Hume
a sceptic? Well, he
project of basing a philosophical methodology upon a
and such a science of of
associative
Rcga Wood, 44 "...
anima
sensitivam
utraque
est
relations
"Intuitive
est
by which the
45
46
man",
Cognition and Divine
mind constructed thoughts and
Omnipotence", pp. 51-61.
per cognitionem omnium. Nam per cogmtionem per cognitionem intellectivam omnia intelligibilia. Et
est
sensibilia ita
et
perfecta
similitudo
obiecti
Ockham, II Sent. qq. 12/13, O.Th. V, p. of Later Medical Philosophy (Cambridge
Campsall", p.
had a
have, as a major component, a theory
ligibilis]."
History
of
quoddammodo omnia
omnia
cognitio
man would
"science
121.
Ockham,
II
Sent. qq. 12/13,
O.Th. V,
p. 304.
Ockham,
II
Sent. qq. 12/13,
O.Th. V,
p.
287 f.
et perfectio quam species [intel309. Cf. M. Adams, in the Cambridge
1982),
p.
439;
K.M. Tachau,
"Richard
Ockham and Hume s theories out of the ideas presented to
was constructed
man"
in the
way
363
Question 47
it.
And, because
his
"science
of
was, he thought he had a grasp of
it
mechanisms underlying the functioning of the mind which (although not complete) was enough to undermine the usual views of common sense. Thus, one s causal theory of the mind has to have a the
causal
certain sort of their
pursue
autonomy
for
one
be a Humean; causal explanations the world, and do not satisfy the to
own way through
requirements of grounding propositions.
Not so they do not
seem
be
to
for
Ockham. Although he does
seem
postulated
in
order
semantic facts he has discovered. very interested in
And
because of
talk of causal
to figure in his theory in their
"the
physics,
He
to
implement
own
mechanisms,
right;
whatever
they mostly interesting
does not, as Tachau remarks, seem
psychology, or mathematics of
this disinterest,
48 vision".
even though he assumed a rather naive
psychological parallelism, the causal mechanisms that he proposed were so flexible
that
he
ended
Wittgenstinian malgre is
lui\
up
as
what
one
can
only
describe
the significant factor in his philosophy of
as
a
mind
given by the prepositional and semantic component, not by the causal
mechanisms.
Clare Hall, Cambridge
Cf.
J.
Passmore,
Tachau,
Hume s Intentions (London
"Response",
p. 198.
1980), p. 106.
JOHN
Thomas
WIPPEL
F.
of Sutton on Divine Knowledge of Future Contingents
(Quodlibet
While the date of Thomas Sutton
comes some time
clearly
comes
after
after the criticism of
Moreover, Sutton with
Henry
would suggest
s
s
theory
.
death
Aquinas
treatment of
Ghent
of
qu 5)
Quodlibet
s
the
of future contingents by William of
II,
s
of
intention
Sutton
s
is
still
uncertain,
Thomas Aquinas.
it
also
It
views concerning divine knowledge
Mare
la
this issue
in the latter s
Correctoriwn
presupposes that he
of essential
is
.
familiar
being (esse essentiae). This
that Sutton s Quodlibet should date
1280s, or as other indications suggest,
the
II
in
some time from
the
1290s.
1
It
is
within
not
my
here to attempt to settle the question of the exact dating of Quodlibet, but rather to turn to him as one representative of the
English Dominican school who was strongly influenced by the views of Thomas Aquinas. This should be useful in enabling us to determine of future divine knowledge s of and Aquinas position. understanding application As regards Aquinas s position, medieval, renaissance, and twentiethcentury interpreters have differed with respect to one issue in particular.
Sutton
s
contingents, and
Qn
Aquinas
I -"or
views
personal
s
detailed
concerning
his
by reason of their eternal presence to
account,
is
it
discussion
of
conflicting
opinions
concerning
the
dating
of
God
Sutton
s
two quodlibets see the Introduction to M. Schmaus s edition of Sutton s Quodlibeta (Munich, 1969), pp. xvi-xxii (as early as 1284-1285 or as late as the mid-1290s). Schmaus s remark that Sutton s Quodlibet I, qu. 14 is refuted by Godfrey of Fontaines first
Quodlibet VII, qu. 9 (of 1290, or possibly 1291/1292, as I have suggested elsewhere) is need not be to highly questionable, it seems to me. The alleged reference by Godfrey Sutton. But Schmaus is correct in noting how difficult it is to arrive at any exact of these dating for these first two Quodlibets, and in his acknowledgment that any proposed datings seems to be too early if Sutton only became a Master in Theology in 1299/1300 (see p. xix, commenting on Gloricux). For a strong defense of an early see F. dating for Sutton s becoming a Master and for Quodlibet I, i.e., 1284 or before, Kellcy,
Introduction
Aristotelis
1976),
De
1-31.
pp.
For
SchneyJer^ Introduction pp. 44 .57 .
Thomae Aquinatis in Libros edition of Expositionis D. de Sutona (Munich, corruptions. Continuatio per Thomam reaction to this and defense of a later dating see J. critical
to
his
generatione
et
to
his
ed.
of Sutton
s
Quaestiones
Ordinariae
(Munich,
1977),
Thomas of Sutton on Divine Knowledge of Future he knows future contingents? Or
that
awareness of the eternal decrees of that
is
365
Contingents
God
rather by reason of
it
s
concerning such contingents
his will
he knows them? 2 In Quodlibet
II,
qu. 5, the following question
Did God have from
was posed
aetemo) certain knowledge of future
eternity (ab
contingents insofar as they are contingents?
3
Sutton comments that the
question has been properly phrased since the reduplication they are
-
contingents"
would pose only by fact that
little
God
is
-
"insofar
as
Without the reduplication, the question is contingent can be known not
crucial.
difficulty;
even what
but by us once
you are now
for Sutton:
has been realized in actuality. Thus the
it
Even
anyone here can be once such a contingent Hence, not undetermined but necessary in the
sitting is contingent.
so,
certain of this simply by using his eyes.
event
is
realized in actuality,
one
sense that while
When
is
it
is
sitting,
it
is
necessary for him to be
sitting.
viewed as future and as contingent, however, it is not something yet determined to one side or the other. Therefore, when it is so viewed, it cannot be known with certainty. Hence it seems to remain in doubt is
whether even
God
can know such a contingent as contingent.
It
is
clear,
continues Sutton, that no created intellect can do so; for then
it
could
only
know such
a contingent as
it
exists in its causes.
And
these causes
4
may be impeded from producing their effect. Sutton now begins to develop his reply by
God knows But God knows God s knowledge is
arguing that
all future contingents insofar as they are in their causes.
them with
certainty
measured by
and from
eternity. This
is
because
But eternity is iota simul and nonetheless contains the whole of time. Therefore all things which are in eternity just as
is
his being.
time or in any part of time are always present to God, and were so present from eternity.
2
For
Hence Sutton reasons
that the divine vision bears
recent interpreters of Aquinas concerning this see J. Dei futurorum contingentium secundum S. Thomam eiusque primos sequaces (Krakow, 1938), pp. 7-10. For this in classical commentators on Thomas see F. Schmitt, Die Lehre des hi. Thomas von Aquin vom gottlichen Wissen des Zukunftig Kontingenten bet seinen grossen Kommentatoren (Nijmegen, 1950), especially pp. 196-202. differences
Groblicki,
De
among
scientia
Schmaus ed., p. 202. "...utrum deus ab aeterno futurorum contingentium, secundum quod contingentia sunt." 4
Ed.
cit.,
pp. 202-03.
habuit
certam
cognitionem
366
Wippcl
such things from eternity (ab aeterno) even though they take 5 place only in the course of time. Moreover, Sutton continues, it is not only the essences of such all
upon
known by God from eternity when such a contingent exists even Therefore,
things but their actual existences which are as
present in
only
God its
s
himself.
to
its
its
cause,
coming in
knowledge and,
when
cause as
future
it
time.
This
is
when
contingent himself.
6
because
In
it
is
support
cause
its
as present before
is
actually does
the is
future for us as
upon
Sutton
comes
it
present forth
same degree of
bears
of this
still
to
from
turns
certainty
actually realized in itself in
God s knowledge
still
is
Hence, argues Sutton, any such
so.
future in itself as
still
is
fact,
from
known by God with when it
is
contingent
when
it
forth
to
upon any such future that
the
which
well
is
present to
known view
of
Boethius as set forth in his Consolation of Philosophy, V. This follows, Sutton continues, because for
Then Sutton present to
God from
God
there
is
no past or
warning. Even though
a
issues
eternity in
future. all
things
have been
terms of their actual existence,
it
does
not follow from this that they have actually existed in themselves from 8
of la
reminded of an objection raised by William Mare against the position of Thomas Aquinas, and of Henry of
Ghent
s
Here the reader
eternity.
effort to avoid
the objection
is
this:
is
being driven to if
this
same
conclusion.
The
point of
things are eternally present to God, they must
9 have actually existed from eternity. Sutton counters that for something to be said to be present to God s knowledge from eternity, it is enough
5 Ibid.,
p.
quacumque 6
203.
See
parte eius,
especially:
"...et
ideo
semper sunt deo praesentia
omnia, quae sunt in toto et ab aeterno fuerunt...."
tempore
vel
Ed.cit., pp. 203-04.
^
For Boethius see The Theological Tractates. The Consolation of Philosophy, by H.F. Stewart, E.K. Rand, S.J. Tester (Cambridge, Mass., 1978), Bk V, 6, p. 426:77-80, 61-66. Sutton also cites Augustine. See De ch itate Dei XI, c. 21 (CSEL 40.1, p. 541). 8
Ed.
cit.,
p. 205.
See William s criticism of Aquinas s ST I, q. 14, a. 13 in his Correctorium. See ed. by P. Glorieux Les premieres polemiques thomistes: I. - Le Correctorium Quare (Le Saulchoir, Kain, Belgium, 1927), p. 18. While the date of this work has been disputed for some time, the general consensus now is that it falls ca. 1278-1279. See R. Wielockx, ,
IILI. Apologia (Florence, 1985), p. 39, n. 68, for the and especially V. Heynck, "Zur Datierung des Correctorium Wilhelms de la Mare," Franziskanische Studien 49 (1967), pp. 1-21. For fratris Thomae Henry see Quodlibet VIII, qu. 2 (Paris, 1518), fol. 303v. For discussion see my Meta 267-70. physical Themes in Thomas Aquinas (Washington, D.C., 1984), pp.
Aegidii
Romani opera omnia
important
references,
Tfiomas of Sutton on Divine Knowledge of Future Contingents for
it
God
to enjoy actual existence at any point in time. This
s
to
present
future.
support from
embraces
It
other texts in
existence in
existing
in
This
itself.
when viewed
future
in
that
something
God from
is
it
one
that
it
Henry
defend in meeting William s challenge. As Sutton continues, something its
when
existence
present exceeds
the
as
owing
divine
to the
To
warning.
now
does not
time. This
actually
distinguish
essence
immensity of
possibles
that to say its
existence
enjoys actual existence from
of
la
Mare
in his critique
Ghent had attempted
to
may be
present to
God
in
terms of
actually exist in itself; for the divine that the divine present contains both
exists
and that
in
which
it
does not,
a
proper likeness for all creatures 12 But now Sutton introduces a perfection.
itself its
of pure
11
means
which the contingent
that time in just
all
it
to
eternity in terms of
eternity. This point was not granted by William of
of Aquinas, though
Sutton
Thus Sutton can hold
not the same as to say that
is
(esse)
enable
God s knowledge
and
in actuality.
present to
is
should
as
of any contingent, whether past or present or
itself,
which are never realized
God
be viewed by
not
precision
God s knowledge
between
finds
1
helpful point. If something never enjoys
will
it
itself,
Once more Sutton
Consolation.
s
so because
is
from past through
transition
of time.
all
Boethius
Here Sutton has made a actual
no
eternal and admits of
is
present
367
hold that things are
is
known by God from
eternity because
they are eternally present to him should not be taken as implying that
from eternity they are what they are through their own essences as distinct from the divine essence and as realized in some way outside God. This would be contrary to the faith which maintains that thing (res)
from
Sutton essential
Sutton to
nature, 10
12 13
refers to
what
I
existential
i.e.,
Ed.
cit.,
See
n.
an
p. 205.
is
true
Pp. 205-06.
we
is
a
intrinsic
theory of hold that Henry, might
i.e.,
limit the
name
"thing"
s
(res)
to that
which enjoys or is a of It would be contrary to principle operation.
being belongs,
or
See Boethius, Consolation V, 6
9 above. For Sutton see p. 205.
Ibid.
if
Henry of Ghent
take to be
being (esse essentiae). Someone,
which
alone
eternity.
now
previous denial
s
God
13
to
that
(p. 432).
368
Wippcl hold that any such
to
faith
from God. 14 But
if
divine
or
intellect,
by
"thing"
we
"thing"
mean
be such things from
God
it
is
not opposed to faith for essences to
One
might even argue that it is necessary to be things in this sense from eternity. And
eternity.
for essences other than
that
thereby
impossible, one might hold that
such things might also be said to be outside the expression
from eternity in distinction mind an object of the which is not intrinsically
existed
rather have in
God from
eternity
if
we
take
in the negative sense,
meaning thereby that such things are not God. Defenders of this view, i.e. Henry, would not claim that such things exist outside God in the subjective sense from "outside
God"
15
eternity.
other words, Sutton
In
is
presenting in his
own way Henry s view
because the essences of things arc objects of God s knowledge from eternity and thereby constituted as intrinsically possible in themselves, that
may
they often
put
also it,
be called
one
may
"things"
(res)
accordingly
from
ascribe
eternity.
an
As Henry would
eternal
esse
essentiae
Yet, Henry would always insist, this is not to (essential being) say that they actually exist in themselves from eternity. Existence comes to them only in the course of time owing to the added intervention of to them.
the divine will, to them.
when
it
communicates
existential being (esse existenliae)
16
Sutton will have no part of this theory. But, like Henry, he has defended the eternal presence of contingents to God s knowledge against the
by William of la Mare that this entails admitting But now he quickly distances himself from theory of an eternal essential being (esse essentiae) which the
charge
raised
eternally existing creatures.
Henry s P. 206.
Ibid. For discussions of Henry s complicated theory see J. Paulus, Henri de Gand. Essai sur les tendances de sa metaphysique (Paris, 1938), pp. 69-74, 123-25; J. Gomez Caffarena, Ser participado y ser subsistente en la mctafisica de Enrique de Gante (Rome, 1958), pp. 65-92; J. Wippel, The Metaphysical Thought of Godfrey of Fontaines (Washington, D.C., 1981), pp. 66-79; "Thomas Aquinas, Henry of Ghent, and Godfrey of Fontaines on the Reality of Nonexisting Possibles," in Metaphysical Themes in Thomas Aquinas, pp. 173-80; S. Marrone, Truth and Scientific Knowledge in the Thought of Henry of Ghent (Cambridge, Mass., 1985), pp. 104-29.
On my (as distinguished from Godfrey s) reading of Henry, he assigns an eternal real (but not actual) being to possibles or essences insofar as they are objects of God s eternal knowledge. Marrone (pp. 122, 123, and n. 83, and 124-29) seems to overlook this distinction in my reading; hence the need for me to state it explicitly here.
Thomas of Sutton on Divine Knowledge of Future
And
Master from Ghent assigns to such possible creatures.
Henry
appreciates
that
such a theory
is
Sutton clearly
taken from
as
res
reor,
one
if
required
to
is
not merely
fact that nonexisting possibles are truly res,
account for the
chimerae (or
claim
s
369
Contingents
but genuine essences and
reris),
1
objects of knowledge (res as taken from ratitudine.}.^ Sutton begins his criticism of this part of
observing that in this case poison
from
the
eternity
intellect.
But
intellect
it
it
were
objects
does not follow that whenever something
also
is
hidden under honey.
creatures
of
essences
is
Henry
a thing
especially
(res),
when
s
by
position
He
grants that
of
the
is
the latter
divine
an object of is taken in
Henry s strict sense. For something can be understood by human intellects even when it does not exist. For instance, today I can understand yesterday even though yesterday
is
not
now
a thing
(res). If
the fact that
something is known suffices for it to be called a res, it would follow from the fact that I understand yesterday here and now that yesterday is 18 here and now a res, and, adds Sutton, an actually existing thing. In
like
fashion,
continues
Sutton,
God knew
all
creatures
from
eternity, not merely in terms of their essences but also in terms of their
actual existences.
enough
for us to regard
existed,
for the sake of discussion
them
as things (res).
they were understood by
that
fact
Suppose
such creatures were understood by
the fact that
which now
exist,
God
It will
that
or which ever will
all
we
Henry
grant
God from
that
eternity
also follow
is
from the
creatures which have
exist
must have enjoyed
actual existence from eternity. Sutton rejects this conclusion. Therefore
he also rejects the claim that whatever
is
an object of
intellect
must
also
19
be a
thing.
Sutton
from
counters
eternity
and
that that
the
they
essences
were
of
not
creatures
essences
were not things from
In
eternity.
themselves from eternity they were simply nothing. Otherwise they would not have been created by God in the course of time; for creation is
production ex nihilo. But if they were nothing from eternity, they were not for nothing means the same as thing" (nulla res). This "no
"things";
For a good presentation of 18
this distinction in
Henry see Marrone,
pp. 108-13.
Ed.cit., pp. 206-07.
19
P. 207. Henry, of course, would not admit that, simply because a creature thing (res) in the sense of enjoying essential being, it therefore enjoys actual existence.
is
a
370
Wippel
objection
creation
concerning
was frequently
others, for instance, by Godfrey of Fontaines.
Nor, continues Sutton, does the mere
something to
for it
be realized
raised
fact that
it
as a thing (res). In other words, intrinsic possibility
technical sense.
not repugnant
is
in actual existence suffice for
us to describe something as a
when
"thing"
Here Sutton appears
Henry by
against
20
is
us to refer to
not enough for
term
is taken in Henry s mind Henry s claim that
that
to have in
something is not contradictory in itself, i.e., if it is be a res. Against possible, it must enjoy essential being and
if
counters that such a possible
still
is
of the soul of the Antichrist.
true
nothing
21
in
his
(In
itself,
own
intrinsically this
much
as
Sutton is
now
discussion of divine
2, Henry had contingents 22 of the the issue to attention considerable devoted Antichrist.)
knowledge
Sutton is
in
of future
insists
not enough for
Quodlibet VIII, qu.
that the fact that it
to
be a
thing.
something
He
they have actually existed
recall that, as
to say that
God
(extra Deutri) amounts to from eternity. 23 Here we should
essences were things from eternity outside saying that
the object of an idea
is
repeats his criticism:
Sutton had earlier presented Henry
s
position,
Henry does
not admit that essences were things from eternity and outside God sense, i.e., as existing apart from God. They are "subjective"
in the
"outside"
God
in
the
in
not
are
that
God. Sutton
they negative sense, only apparently regards this distinction as a subterfuge: to say that essences other than God were things from eternity and outside God in the negative
20
For Godfrey see Quodlibet VIII, qu. 3 (1292/1293 by my dating). If he things he has created in the same way he knows things he is to create, must know their existence as well as their essential being from eternity. Hence Henry should grant the eternity of all things, past, present, and future, both as regards their essence and existence (Les Philosophes Beiges, Vol. 4, p. 37). Moreover, Godfrey argues P.
207.
God knows
Henry s view really implies God, they are not thereby created
that
that
when
(p. 45).
creatures
receive
existential
See Quodlibet IX, qu. 2
(p.
190),
being
and
from
my The
Metaphysical Thought of Godfrey, pp. 136, 140. 21 Ed. cit., p. 207. For other texts from Henry see, for instance, Quodlibet III, 9 (Macken ed., pp. 53-55); Quodlibet IX, qq. 1-2 q. 1 (f. 61r, bottom); Quodlibet I, q. (Macken ed., pp. 7-8, 22-23, 34-37); Quodlibet X, q. 7 (Macken ed., pp. 151-52); Summa
quaestionum Ordinariarum, 22 23
See Quodlibet VIII, qu. P. 207.
a. 28, q.
2, ff.
4 (Paris, 1520), Vol.
301v-302v.
1, fol
167v.
Thomas of Sutton on Divine Knowledge of Future sense
is
ho-d they existed outside
to
really
sense, that
"subjective"
is,
in
that they actually existed apart
sums up by
Sutton
God
the
and
stronger
from God. 24
from eternity
that
stating
371
Contingents
God had
certain
knowledge of future contingents insofar as they are contingents; but from eternity. 25
such contingents did not enjoy the status of In assessing Sutton s position, which
"things"
we
should
Sutton
that
recall
grounds
contingents on the eternal mode of God
s
taken largely from Aquinas,
is
God
knowledge of future knowledge and therefore on the s
eternal presence of such contingents to God. There is no indication that Sutton would account for this by appealing to God s knowledge of the
decrees of his
will,
Sutton
therefore,
as
Henry of Ghent ends by
appears
me
to
be
to
an
doing.
accurate
On
this
point,
interpreter
of
Aquinas.
to
On the other hand, Sutton states that God in terms of their actual existence,
eternal existence in themselves. First of
God
his
were eternally present
terminology could be misleading.
as did Aquinas, Sutton speaks of things as being present to
all,
"from
Here
things
without their having enjoyed
eternity"
(ab aeterno}. This could give the mistaken impression
27 In fact temporal succession. both Sutton and Aquinas would deny this. Secondly, for Sutton to say that things were eternally present to God is misleading. It would be
that he regards eternity itself as subject to
better for
him
to say that they are eternally present to
Sutton
Finally,
Cf.
p.
the
rejects
God
presence of creatures to
claim
as their
that
God. 28
admission
knower
entails
of
the
ascribing eternal
For Sutton s rejection of a third esse between being extra intellectum see Quaest. Ord. 26 (Schneider ed., p. 725).
206.
and ens naturae
eternal
in
the
mind
dicendum quod ab aeterno deus habuit certain cognitionem futurorum contingentium secundum quod contingentia, quae tamen non fuerunt res ab aeterno" (p. "Et
207).
See the references given reading of Aquinas see
in
n.
2
above.
my Metaphysical Themes,
For
justification
of this
as
the
correct
pp. 244-64.
For Thomas see ST I, q. 14, a. 13: "Unde omnia quae sunt in tempore, sunt Deo ab aeterno praesentia, non solum ea ratione qua habet rationes rerum apud se praesentes, ut quidam dicunt: sed quia eius intuitus fertur ab aeterno super omnia, prout sunt in sua praesentialitate" (Marietti ed., Turin-Rome, 1950, pp. 86-87). For discussion see my Metaphysical Themes, 28 Perhaps Sutton
p. 268, n. 82.
s usage was partly determined by the way the question was framed (see n. 3 above). But for other texts where he uses similar language see p. 205:73-74; and the concluding text cited above in n. 25.
372
Wippel
(actual) existence to them. In
making this point, he is in agreement with Henry of Ghent. But Sutton has distanced himself from Henry s theory of an eternal essential being which would be enjoyed by all possibles insofar as they are eternally objects of
God s
The Catholic University of America
knowledge.
REGA WOOD
Calculating Grace:
The Debate about
Latitude of Forms
According to Adam de
Most
today believe
Christians
the
that
and
Scholastics
Wodeham
nature
of
is
grace
veiled
in
achieved
sought greater precision. They determined that grace was an accident not a subject. They asked: to which of the nine categories of accidents, described by Aristotle in his mystery.
was
a
to which of the four species of quality does
it
does
Categories,
inquired:
it
belong?
Concluding
that
it
quality,
they
belong? They
belonged to the first species; it was a habit or disposition. And since any such quality is subject to increase and decrease, they felt obliged to ask how grace increased or decreased. The intensification and decided that
remission
it
of
was
grace
one
of
most
the
hotly
debated
theological
questions in fourteenth century Oxford.
At the same
time, increasing and decreasing forms, like grace,
a subject of intense controversy
among
were
natural philosophers. Although
masters of arts were forbidden to discuss theological questions, most fourteenth century philosophers and theologians assumed that degrees of charity were gained or lost in exactly the same way heat was intensified or
Whether spiritual or physical, any quality which was and subject to change by degree was considered a form with Arguments about latitude of forms dealt with continua and the
diminished.
divisible latitude.
1
nature of gradual change.
Many
of the
same
issues raised in discussion of
the intensification of charity were also topics in the discussion of time
and motion. 2 Hence fourteenth century theology on degrees of charity Chatton, Reportatio,
I,
d.
17,
q.
2,
a.
1,
cod.
Paris.
Bibl.
Nat.
lat.
15,887, fol. 48rb:
subiectum sub calore corrumpendo, et ille non est indivisibilis, cum sit eiusdem rationis cum praecedente, et per consequens habeat latitudinem, ergo adhuc restat pars corrumpenda post istud instans ... Si in illo instanti est sub frigore, idem argumentum est, quia illud non est indivisible sed habet latitudinem." "Si
2
in
instanti
Wodeham,
[alteratione,
illo
Tractatus
motu
indivisibilibus,
est
et
quaest.
1,
50 omnibus his cap. (Continuum): "[D]e par ratio sicut de continue." fol. 139va); Tractatus de quaest. 3, dub. 4: "(Djifficultas est aequalis de omnibus
alphabeticus,
tempore] art.
1;
est
Wood
374
was
scientific
not just
also in the sense that
it
sense that
the
in
was a
was
it
logically
but
rigorous,
topic in natural science: latitude of forms.
Edith Sylla discusses the debate about latitude of forms among the 3 Oxford Mertonians from about 1320 to 1337. Sylla describes three positions:
(1)
and
the
(3)
succession of forms theory (2) the admixture theory
the
addition
intensification of
theory.
The
succession
theory
describes
the
forms as a series of instantaneous changes. The addition
theory describes a gradual change over time as infinitesimal parts are gained or lost. Sylla considers Walter Burley as a proponent of the succession
admixture
the
represented by Roger Swineshead, and the addition theory by John Dumbleton and Richard theory;
is
theory
Swineshead.
The English Franciscan
theologian,
Adam Wodeham
discusses Oxford
opinions on the subject of latitude of form, in the period 1316-1329, in his Tractatus alphabeticus,
dated about 1333.
4
Thus Wodeham was writing
about a period that overlaps with the earlier period Sylla has described for the Mertonians. Wodeham was chiefly concerned with the views of
Wodeham
and
5
Ockham,
Fitzralph.
Fitzralph,
and
himself are addition theorists. Chatton adheres to an admixture
identified
theory,
Chatton
Ockham,
Campsall,
by
Wodeham
Thomas Aquinas. 6 Campsall
as
held a
a
"modern
associated
theory"
new theory according
to
with
Wodeham,
compositis divisibilibus, sivc intensive sive extensive ... [et] apud me ilia quae inducunt difficultatem [in] inquisito, omnia inducunt difficultatem circa continuum, licet non e converse."
et
...
"Et
nota quod omnia haec duhia aequaliter possunt fieri in augmentatione sicut de continue." (ed. R. Wood, Dordrecht, 1988, pp. 34, 180).
decremento formarum
of dating Burley s works, it is not clear exactly what the difficulty under discussion. But Weisheipl dates Burley s Tractatus primus, 1320 to 1327. Roger Swineshead wrote his Descriptiones motuum between 1328 and 1337. See James Weisheipl, "Ockham and Some Mertonians," Mediac\>al Studies 30 (1968), p. 185, 1%, 212 and Sylla, "Medieval Concepts of the Latitude of Forms," Archives d histoire doctrinale et litteraire du Moyen age 40 (1973), p. 240n.
Given
period
4
is
Codex
Re
Erfurt, Stadtsbibliothek,
CampsalPs
Wyclif, ed.
see
dates,
Amplon., Folio 133,
Tachau,
A. Hudson and M. Wilks,
p.
134ra-145va.
fol.
"Richard
K.,
Campsall,"
in
From
Ockham
to
HOn.
Tractatus alphabeticus, cap. 2 (Aciio maxime reperitur in qualitate): contra hoc et pro ista conclusione arguitur et contra argumentum Thomae, I Sent. d. 17, q. 2, art. 2, cuius est opinio quod calor remissus per <prima parte Summae
Wodeham,
"Sed
E>,
approximationem agentis modernos eadem res ut esse, est
A
calor."
great
(fol.
many
fit
est
postea intensus, nulla (!) sibi addito, ita quod secundum transmutatione est latitudo quaedam, ut autem in quieto
in
134ra).
theories
were
theories. Quaest. in III Sent., q. 8
current.
(OTh
Ockham
list
four
kinds
of
addition
VI, 220s.). Aureol describes six possible opinions
Calculating Grace: Adam de
one which we
will
succession of forms
is
In this paper
I
call
connotation
a
Wodeham
theory.
No
375
of
proponent
the
named. 8 will discuss three issues in the
theory of latitude of
Do
forms undergo intension and remission? (2) How are intensified? and (3) Are maximal degrees in the intensity of qualities forms possible? I will be chiefly concerned with the views presented by forms:
(1)
Adam Wodeham
by reference to the views discussed by another fourteenth Walter Chatton, and by Edith Sylla. The least
amplified
century
but the discussion will be
in his Tractatus alphabeticus,
Franciscan,
controversial of these issues for fourteenth century philosophers
1.
is first:
Do forms undergo intension and remission?
Addition and succession of forms theorists agree on this issue; in no sense is it true that the same form undergoes remission or intension.
For the simultaneous existence of contrary forms in exactly the same subject is impossible. Ockham and Wodeham held that strictly speaking it is the subject, not the form, which becomes more white, more hot or
more
charitable.
added
of intensification, parts are
case
same form which was remiss does not become new form appears in which the additional parts are and the new form is more intense than the previous form
As Anneliese Maier
succession
like
the
in
though
Rather, a
incorporated, 10
And
to the form, the
intense.
was.
9
succession of
theorists,
new
forms.
pointed out, this means that addition theorists,
hold
They
on augmentation. Scriptum super 1 Sent.,
that
intensification
differ only in
dist. 17,
pars 17,
is
the
result
of
a
claiming that the parts of
a. 1
(ed.
Romae 15%,
427-35).
Q
Scotus,
and
Ockham
Scotus, Ordinatio, I Sent., dist. 17, q. 5
loquendo de ipsa
fit
Non quod ideo
talis
plures
1
vi
si
intensior,
this
2,
q.
(ed.
non vel
(OTh
III,
de quantitate
extensiva."
(OTh
Ockham, Scriptum
in
V, 418s.).
481ss.).
<
lectio
dubia>
"Ultra dico (Augmentatio): quod etiam et remitti. Sed auctores hoc errant, quod additur formae alia forma, ex qua
subtrahitur aliqua
pars ut
forma remissior
numero primo sit intensa forma habet veram latitudinem intensivam realiter
Godfrey of Fontaines.
15 alphabeticus, cap. nulla forma potest intendi,
aliqua una forma
partes
view to
Vaticana, V, 234ss.).
pars
485); Quaest. in II Sent., q. 19
in I Sent., dist. 17, q. 4
vocis,
attribute
III,
Tractatus
dicentes intendunt, et
him,
17,
(OTh
Ockham, Scriptum
Wodeham,
d.
I,
following
distinctas (fol.
constituentes earn
135rb).
sit
quam
praefuit.
et post remissa vel e converse. vel gradualem, quia habet in
[ut]
qualitatem,
sicut
suo
modo
Et se est
Wood
376
11
the old form are not destroyed in the process. at
stake
lower
whether there
is
is
As
Sylla puts
it
"What
is
within the higher degree a part equal to the
12 degree."
Chatton subject
too
agrees
that
undergoes
statement forma suscepit magis
speaking
strictly
and
intension
et
remission.
minus
not
the
form
but
its
13
Strictly
the
speaking
is false.
Wodeham
is expressing a common view when he argues that properly dearness cannot be increased, because no underlying, constant speaking 14 subject remains. According to Wodeham, when we say that the dearness
increases, this
greater than
more and
it
less.
parts of the
means
same dearness
that the
that formerly existed
is
now
formerly was. But one and the same thing cannot be both 15
However, according
same form can be added
to
proponents of the addition theory, which were
to the parts of dearness
and the new parts together with the old parts make which the form inheres more dear. And wherever there
originally present,
the substance in
genuine latitude of form, it must be possible to add and subtract parts of that form to an underlying substance. When Peter become dearer, his is
former
dearness
is
not
really
intensified.
Rather
additional
parts
of
dearness reach him and combine with the preexisting form to produce a
Annclicsc Maier, Zwei Grundprobleme der scholastischen Naturphilosophie, zur Naturphilosophie dcr Spatseholastik II (Rome, 2nd cd., 1951), p. 54.
Studien
"
Sylla, "Medieval Concepts," p. 231s.
est hie una opinio quod non est Chatton, Reportatio, I, d. 17, q. 3, a. 4: dicendum quod forma suscipiat magis et minus Contra. Unde calorem suscipere magis et minus non est nisi subiectum suum esse calidius. Sed tamen ad hoc bene requiritur quod forma sit maior vel perfection Et si hoc intendebant quidam dicentes "Et
...
istam augmentationem
fieri
Norman Kretzmann
per inesse subiecto, discusses
a
similar
bene."
(fol.
problem
Aristotelian Anti-Atomism," History of Philosophy Quarterly
Wodeham, secundo quod vel
logice
Tractatus sicut
loquendo,
non per
alphabeticus, suscipit,
illo
cap.
...
51va). in 1
his
"Adam
Wodeham
s
Anti-
(1984), 381-97.
(Augmentatio): "Dico
E>
modo
praedicationem
crementum huiusmodi cum hoc adverbio
magis quia non potest dici quod forma talis, puta albedo sit magis albedo quam ante. Immo, quod plus est, nee intensa albedo est talis magis albedo quam sit remissa, licet sit maior, id est intension Sed
C>
minus album
et
postea magis vel e
converse." (fol.
135 ra).
Calculating Grace:
Adam
16
form of greater
377
form combine
distinct parts of a
Numerically
intensity.
Wodeham
de
to constitute a unified whole.
When
intensify,
qualities
according to this account, the preexisting
form becomes part of something greater. Only Richard Campsall presented obvious
the
to
objection
view:
this
this
"On
account
is
nothing
more
intense; and neither augmented." the resulting whole nor the new part existed before, so they cannot have been intensified.
For what was there before
not
is
But though most fourteenth century medievals agree on
common
their views are not the result of
views
are
contrary
sense observation. Indeed, these
our ordinary experience
to
increase and decrease in their intensity.
another;
was a
God
-
namely, that qualities wall can be whiter than
The ground
by Aristotle
supported
consideration,
logical
One
love for Peter can increase.
s
this subject,
s
for this denial
authority:
a form
cannot increase or decrease while retaining its identity any more than a number can. 18 Different accidents can inhere in the same subject at different times,
of the
19
but different degrees of whiteness cannot be predicated to examples: Peter can be dearer, but his
same form. Returning
grace cannot increase while retaining its identity. If one wall is whiter than another, a different form of whiteness inheres in it; a wall which increases in whiteness by being painted gains a
new form.
How are forms intensified?
2.
Considering qualities as Aristotelian forms,
change more
qualitative
1
Tractatus
Wodeham, intelligi
non
ad
etiam bene
vim
vocis,
difficult.
Emphasis on
alphabeticus,
cap.
15
commune dictum quod
illud
alicui
quia
made medieval
formae
advenit
(Augmentatio):
forma aliquid
discussions of
a related logical dictum
suscipit
modo
"Alio
magis
constituens
et
cum
potest
minus ilia
-
,
licet
formam
perfectiorem. Et ideo dicitur suscipere magis et minus. Aliquando veto subtrahitur pars aliqua, qua subtracta non remanet ilia forma sed alia minor priore, non quod eadem sit et post minor, nee e converse. Et potest improprie dici quod maior cuius pars subtrahitur minuitur, vel adhuc magis proprie quod minor quae remanet minuitur,
primo maior pro eo quod
ista est
minor
ilia totali
quae
praefuit."
(fol. 135ra).
est 3: I, 17, 2, opinio (marg.: Campsale), q. augmentatio per additionem], quia si aliquando sic, tune nihil esset auctum, quia nee pars nova, cum ilia non praefuit, nee praecedens, quia ilia non est intensior quam prius, nee totum, quia non praefuit." (fol. 49ra).
Chatton,
d.
Reportatio,
quod nunquam
[est
18 Aristot., Metaph., VIII,
19 Aristot., Topica,
II, c.
c.
3 (1044a 9-10).
7 (113a 34-35).
a.
"Et
Wood
378
contrary
cannot
qualities
raises similar
What
problems
inhere
simultaneously
same
the
in
subject
-
second issue discussed here.
in considering the
the process by which forms intensify? Fourteenth century medieval authors tried to answer this question in such a way as would is
allow them to affirm that (1) qualitative change
is
gradual (2) the quality
resulting
from change constitutes a unified whole and
do
exist
not
simultaneously
of
paradigm
of qualities
The
are added.
parts
nature of change.
added
same
also allows that as a quality increases,
It
a
is
would combine
parts are
new
qualitative
it
could not account for
whole. According to Richard
unified
Campsall, a Mertonian contemporary of believe that old and
new
form which remains.
new form
the
that
change.
theory readily accounts for the gradual
addition
to the preexisting
fact
quantitative
forms
theorists
a successive process in which infinitesimal
is
Opponents of the addition theory claimed the
(3) contrary
Addition
subject.
resembles
change
qualitative
Intensification
the
in
Ockham, there -
parts
is
no reason
or individuals of a form
to -
produce a unified whole. For the only things which one, are actual beings which can be combined with
to
when combined make or
beings,
potential
entities
receiving
which
can
combined
be
with
would be parts of the same the same subject, they would not constitute a
received entities. But parts of a single form kind, so
if
they inhered in
whole, but remain separate individuals. Consequently, any intensible form
acquired over time would be composed of an infinite number of separate 20 parts and constitute an actual infinity, which is absurd.
Campsall claims
the infinitely
that
many new and
preexisting parts
posited by addition theorists would remain separate and unintegrated and
an
constitute
20
actual
Chatton, Reportatio,
91
detur
secundum,
Addition
alphabeticus,
quod
in
cap.
quolibet
secundum inconveniens,
scquitur
21
scilicet
sit
sequitur:
quod alteratum
consequentiae, quia quacumque infinitae albedines tantae virtutis sunt
est infinitae virtutis
maioris virtutis ilia.
-
argumentum
Et in
si
sit
in
fine
virtutis
infinitae
in
demonstrata in actu, hoc subiecto, igitur hoc subiectum
albedine in
Consequentia patet, quia actualiter habet infinitas quia cito post hoc instans habebit tune
quam
and
data,
.
isto posito, erit
Aristotle
57 (Infmitum in augmentatione conlinua): nova albedo praecedcntibus remanentibus,
Probatio
vigore.
like
theorists,
d. 17, q. 2, a. 3, fol. 49rb.
Tractatus
Wodeham,
"Si
I,
infinite.
quam
virtutes.
Hoc dato antecedens patet quarum quaelibet
infinitas qualitates
quia quaelibet adquisita post datam erit intensior rcmissior ordinate, contra: illo modo tenet ipse fundasti TE, igitur argumentum tuum contra TE
virtus data,
quaelibet
sequens
hoc argumento
cum
fuerit
(Campsall).
Respondeo concedendo
illud
quod
infertur
in
ista
forma qua
infertur.
Et hoc etiam
Calculating Grace:
almost
all
actual
medieval thinkers,
in
agreed
de
Wodeham
Wodeham
that
states
simply
379
the
rejecting
But addition theorists had no
infinity.
objection.
Adam
possibility
replying to this
difficulty
infinitely
of an
many
parts
qualitative
infinite, provided each producing successive part is less than the part which preceded it. Although attacks of this kind were not taken seriously by addition
added
be
can
an
without
actual
were committed
theorists, they did take seriously the claim that they
holding that contraries simultaneously coexisted in the
same
subject.
to
By
same genus but are maximally different appears to be the case that when something
definition contraries belong the
from
each
other.
gradually changes
period
22 its
It
color from white to black, there
when we might
say that
is
it
is
an intermediate
both black and white, which
is
a
contradiction.
Ockham and Wodeham
agree with succession of forms theorists that contraries cannot inhere in the same subject. They disagree with Chatton
who
holds that addition theorists must embrace the claim that remiss 23
Ockham degrees of contrary forms can coexist in the same subject. explains that it is unnecessary to posit that remiss degrees of contrary qualities inhere in the
same
subject; the degrees of quality
added when
forms are intensified are not contraries, but individuals of the same kind, numerically not specifically different. It is the addition of numerically distinct individuals of a form which produces intension. And these distinct constitute together a single unified form. No change in when tepid water is added to tepid water, because recorded intensity 24 the forms involved remain in distinct subjects. Change takes place individuals
is
successively, part
CAMPSALE,
25
by
part.
cuius est argumentum, concedere habct de partibus albedinis extensae,
neget indivisibilia." (fol. 140vb). Chatton, Reportatio, I, d. 17, q. componeretur ex infinitis partibus,
2,
a.
3:
tempore mensurante ilium motum sunt novum quod nunquam praefuit." (fol. 49ra). 22 23 2,
Aquinas, In Metaph.
Ockham, Quaest. a.
sis,...
1:
Sed
gradibus, formae."
24 25
"Dicunt
isti
quidquid quia
(fol.
aliter
X,
nulla
infinita
lect. 5, n.
19
in II Sent.,
q.
quod aqua
est
tune quaelibet forma augmentabilis alia nee pars alterius, quia in
est
instantia,
in
quolibet
est
aliquid
V, 418s.). Chatton, Reportatio, I, d. 17, q. quia calor et frigus sunt in partibus diver-
(OTh
tepida
de hoc, teneo quod non salvaretur successio
sit
in I Sent., dist. 17, q.
Quaest. in II Sent., q. 19
et
2032^4.
[contraria] in
motu
et
48va).
Ockham, Scriptum Ockham,
Aristot.,
"Item,
quarum
cum
7
(OTh
(OTh V,
III,
418s.).
542-5).
compatiuntur in
se
adquisitione
in
remissis
partiali
talis
Wood
380
The forms.
addition theory
We
come now
was the most popular theory of the
to the minority views. Succession of
latitude of
forms
theories
change on substantial change, the kind of change described as generation and corruption. According to succession theorists,
model
qualitative
a quality appears to increase, a more remiss quality is replaced by an entirely different form of greater intensity. When something changes
when
from white to black, there is no intermediate period when the subject is partly white and partly black, rather there are a series of entirely forms; all the various shades of white, grey and black succeed each other. This means that what appears to be gradual change is really different
a series of sudden changes.
A
succession theorist can readily deny that contrary forms coexist
same
the
in
subject.
forms with
entirely
For intensification
new
intense
is
the result of replacing remiss
But
forms.
succession
difficulty accounting for the fact that qualitative
is
have
theorists
gradual, since
change change takes place suddenly, and forms cannot be intensified by adding parts.
Not only was the succession theory vulnerable was contrary
to the charge that
to our experience of gradual qualitative change,
it
was
it
also
attacked as a form of indivisibilism. According to Richard Campsall,
if
qualitative change involves the annihilation and replacement of forms,
it
is
is
instantaneous. But
composed
principles,
if
this is
motion,
of indivisibles, which as a
common
is
we have
to conclude that
motion
contrary to Aristotelian philosophical
opinion concedes. So according to
Wodeham,
Campsall claimed that adherents of the succession theory were committed to indivisibilism, just as addition theorists were committed to defending an actual
infinity.
Tractatus alphabeticus, cap. 57 (Infmitum in augmentatione continua): hoc ALIQUI arguunt quod si in tola transmutatione non maneat eadem lectio dubia> mensuretur instanti vel qualitas maior et minor, sequitur vel quod motio quod alteratum sit infinitae perfectionis in vigore. Consequentiam probant, quia si non maneat etc., aut igitur in quolibet instanti est alia et alia forma corrupta priori; aut priori manente si corrupta praecedente, tune ille motus solum mensuratur instanti, quia ille motus non est nisi ista qualitas secundum quam movetur mobile. Ire enim ad calorem est calor quoquo modo. Sed ista qualitas tune non mensuratur nisi instanti. Et praeterea lectio dubia> si motus ille tune non sit haec qualitas nunc exsistens,
Wodeham,
"Et
ideo ex
<
<
quaero a
Nee
TE
praeterita,
est iste motus: aut qualitas praesens aut praeterita aut futura. nee futura, quia non sunt, nee aggregatum ex his propter Deum. Igitur
quae res
motus ille sit qualitas praesens, et tune sequitur expositorie est motus, igitur ille non manet nisi per instans, ilia qualitas
oportet ista
tune dicere quod
qualitas
E>
,
est contra philosophiam." (fol. 140vb).
Calculating Grace:
Succession
theories
sacrifice
Adam
de Wodehatn
other
all
retain a strong interpretation of the dictum,
or
By
decreased."
eccentric
can
seldom
theory,
supporters, however, a view attributed to
is
s
same to
according
espoused,
Wodeham
order
to
an
is
It
subject. 27
Among
Sylla.
bete noire, Walter Chatton;
28
its
also
is
it
Thomas Aquinas. admixture
the
of
Roger Swineshead. Swineshead
is
in
cannot be increased
"forms
the
in
coexist
The Mertonian advocate Sylla,
consideration
contrast, the admixture theory embraces an apparent
contraries
contradiction:
381
s
described
theory,
model of
qualitative
by
change
both from quantitative change and from substantial change. In answer to the question "what causes an increase in the intensity of a differs
form?"
Swineshead argues that
qualities
intense without anything being added, that
weakened. So
is
subject
this
that intensification involves a
In fact
Wodeham
addition of any
new
the contrary quality inhering in
same
subject, but not in the sense
new admixture
of forms or parts of forms.
characterizes this view as the view that
same form can be
remiss and afterward intense,
first
become more
a subject can
in
an admixture theory in the sense
is
that contrary qualities inhere in the
if
"altogether ...
the
without the
29 [part]."
contrary Wodeham argues that there cannot be any the addition of a new part. Against the admixture without augmentation
To
theory,
the
Wodeham 30
The
Fitzralph. quality 27
can be
repeatedly adduces an argument presented by Richard
gist
of this argument
without
increased
is
that
extrinsic
it
is
absurd to claim that
change and addition.
It
is
Sylla, "Medieval Concepts," p. 232n.
98 1
Sylla, "Medieval Concepts," p. 232n.;
29
Wodeham,
Tractatus
d. 17, q. 1, a. 1.
forma potest 1 "Nulla (Augmentatio): cap. sua specie sine additione novae partis ad praeteritam ex
augmentari nee fieri maior in quibus fiat una forma. Et haec
omnino primo
Chatton, Rcportatio,
alphabeticus, est
contra opinionem tenentium quod eadem forma est eodem subiecto et e converse." (fol. 134ra).
intensa et post remissa in
30
alphabeticus, cap. 2 (Actio maxime reperitur in qualitate): quod aliqua parva albedo potest fieri perfectior quam aliqua creatura mundi de facto sit, nullo sibi addito, quod est absurdum. Probatur consequentia secundum Fitzralph (Fi-r), quia secundum istam opinionem aliqua res potest fieri duplo perfectior absque aliquo novo sibi addito, sicut caritas remissior potest fieri duplo intensior, nullo sibi adveniente. Et eadem ratione, adhuc duplo intensior, et adhuc, et
Wodeham,
"Contra:
Si
hoc,
Tractatus
sequitur
in infinitum. Sed quidquid praeter Deum potest imaginari intellectus simplici apprehensione sine conceptu composite ex repugnantibus, potest Deus facere cum sit omnipotens. Et tune patet ista consequentia, quia omnis creatura perfectior ista caritate excedit earn in proportione finita, et quacumque finita potest Deus facere perfectiorem."
sic
(fol.
134ra).
Wood
382
of a quality could incongruous to suggest that the perfection or intensity without be increased ad infinitum adding anything.
Swineshead
how more
s
admixture theory encounters no
difficulty in explaining
intense forms constitute a unified whole, since no
Gradual
added.
are
of
new
parts
also
readily qualitative change between contrary equilibrium changing theory explained by would be hard-put to show that he was not qualities. But Swineshead
are
degrees of
his
committed
to the view that
a
contrary qualities could inhere in the
His views are also vulnerable to Fit/ralph
subject.
view would be consistent with increase without
s
same
that
argument
his
addition.
The form of admixture theory espoused by Walter Chatton and attributed to Thomas Aquinas is not vulnerable to Fitzralph s attack, since
it
does not explain
between
equilibrium
Swineshead qualities
s
qualitative
contrary
change as a It
qualities.
result
has
of a
shifting
common
in
with
version of the admixture theory only the view that contrary
can inhere
in
the
same
subject at the
same
time.
31
Even
this
view does not appear to be a distinctive tenet of admixture theories; 32 also held that such as Scotus many medieval addition theorists -
remiss degrees of contrary qualities could coexist. Unlike other medieval theories of qualitative
change,
Chatton
s
version of the admixture theory treats spiritual qualities differently from
31
Chatton, Rcportatio, I, d. 17, q. 2, a. 3: "teneo ... oppositam, scilicet quod aliquac contrariae compatiuntur se in ecxJcm suhiccto in gradihus rcmissis. ... (fol. additioncm partis novae 49rh) ... Contra: quod aliquando fiat augmcntatio formarum per ad praecedcntem probo." (fol. 49ra-49rb) qualitates
est enim ... quod qualitates eiusdcm speciei cum contrariis compatiun hoc multipliciter .... (fol. 49vb) ... tenco quod parte subiecti, et probavi caritas augetur et aliae formae multae. Sed quomodo? Aliqua per additionem partis ad ubi est successio propter incompossibilitatem partem, aliqua non. Ilia videlicet non,
Art. 4:
tur sc in
"Dictum
eadcm
formae prioris ad sequentem. Unde si in intcllcctionibus procederctur continue a forma minus pcrfecta ad maius perfectam, ibi foret unus modus augmentationis non per additioncm partium sed per successionem continuam formae perfections, novae totaliter, post
impcrfecliorem
totaliter
corruptam.
...
Unde
in
talibus,
ubi
est
successio propter
etiam casu ubi formae sunt simplices, nunquam incompossibilitatem formarum, vel alio est augmentatio per additionem. Sed tamen aliquando est augmentatio formae per de imperfecto ad additionem, quando scilicet ita est quod successio motus et processus formarum sed ex hoc quod passum est perfectum non provenit ex incompossibilitate remissam cuius diminutio requitur ... et ita in isto indispositum per formam contrariam casu habetur in fine motus forma quaedam composite, cuius adquisitio erat partis post "
partem. (fol. 49va-49vb) Quaest. 3, art. 3: Tenui
ex ... quod aliquando est augmentatio ubi successio provenit ilia non est per additionem, praecedentis et sequentis, et ubi non ex hoc sed magis ex indispositione passi per contrariam aliquando formam vel propter limitationem agentis (fol. 50va). 32 242 (ed. Vaticana, V, 255). num. Scotus, Ordinatio, I, d. 17, pars 2, q. 2, incompossibilitate
formae
P>
..."
Calculating Grace: Adam de
Spiritual
are
Wodeham
indivisible
383
and
increase
or
physical
qualities.
decrease
manner described by the succession theory; physical are divisible and increase or decrease in the manner described
qualities
in
qualities
the
by the addition theory. Chatton s claim that some forms are, and other forms are not augmented by addition was anticipated by Thomas Aquinas, who also held, as Chatton does, that charity does not increase by addition.
33
was
Chatton
on
strong
ground
when he argued
indivisible
subject like
that
spiritual
He
could not increase by addition.
qualities
argued that a simple or the soul could not have a compound accident. 34
But
if the accident or quality being intensified is indivisible, it does not have parts. It would be nonsense to say that an indivisible quality could be intensified by adding parts. Since he adheres both to the addition and the succession theory, Chatton s views have most of the same strengths
And
and weaknesses as those theories.
like
Wodeham, Chatton
the view that there could be increase without addition.
attacked
35
Chatton
s versions of the addition and succession theories provide a account of the successive or gradual character of qualitative change. He claims that gradual change is always the result of some form
distinctive
In
of resistance.
cases
where increase by addition
is
impossible,
the
successive quality of change arises from introducing incompatible forms. In the case of forms susceptible of increase by addition, the successive quality of the intension of forms,
as
or,
subject; qualities
could
we might not
inhere
say,
in
is its
the
a result of the indisposition of the resistance
same
to
subject,
change. the
If
contrary
intensification
of
forms which results from the addition of parts would not be successive. 36
34
Thomas Aquinas, Summa
theol., 1-2, q. 52, a. 2, resp.
See Chatton, as quoted
note 36.
in
d. "luxta istam imaginationem diceretur I, 17, q. 3, a. 3: augmentatione et remissione formarum, quod eadem forma prius remissa, sine productione cuiuscumque novi, eadem penitus sit forma intensa ad praesentiam activi nati augmentare, non quod aliqua pars praefuerit, et aliqua non; et tune consequenter dicendum esset quod totum est novum et quod totum praefuerit." (fol. 51ra).
Chatton,
quod
ita
Reportatio,
est in
Chatton, Reportatio, I, d. 17, q. 2, a. 4: "Ex his ergo simul cum tertio articulo infero solutionem quaestionis, et teneo quod caritas augetur et aliae formae multae. Sed quomodo? Aliqua per additionem partis ad partem, aliqua non - ilia, videlicet, non, ubi
propter incompossibilitatem formae prioris ad sequentem. ... Et hoc, primo quia intellectio non habet partes, et secundo quia forma prior et forma posterior non compatiuntur se naturaliter. Unde in talibus ubi est successio propter incompossibilitatem formarum, vel in alio etiam casu ubi formae sunt simplices, nunquam est augmentatio est successio
per additionem.
Wood
384
Thus Chatton holds
that
takes
change
place
the
result
in
successively
cases of intensification and remission, but not for the
same reason.
all It
is
forms of resistance, incompatible forms or an
of different
indisposition in the underlying subject.
The
last
we encounter
theory
Adam
in
Tractatus alphabeticus
s
is
Richard Campsall, a Mertonian, most of whose works are lost. CampsalPs cogent attacks on the succession and addition theories were that of
mentioned earlier. They are clearly reported by Wodeham and Chatton. But CampsalPs own views are more difficult to discover, and Wodeham s account differs from that of Chatton. What follows is a reconstruction which
may be mistaken
some
in
respects.
Most probably Campsall began
his
career as an adherent of the
succession of forms theory. Chatton says that he had heard Campsall, 37
and that Campsall s attempt to defend the succession theory had been Chatton tells us that Campsall had had to come up with new
refuted.
views because the succession theory had been disproved. 38 At the time of Chatton s Reportatio, Campsall evidently entertained three views: (1) succession of forms (2) an addition theory according to
which an to
number
infinite
make
whole
a
augmentation and
same;
they
remain
altogether
are
discrete,
in
acquired
(3) a form of admixture theory. Chatton quotes long
arguments by Campsall, the
of individuals of a form, which do not combine
but
are
39
the proponent of the view that forms are never annihilated
being
constantly
and replaced. 40
But
Scd tamen aliquando est augmentatio formae per additioncm, quando scilicet ita est quod successio motus et processus de impcrfccto ad perfcctum non provenit ex incompossibilitate formarum sed ex hoc quod passum est indispositum per formam contrariam remissam cuius diminutio requiritur et ita in isto casu habetur in fine motus forma quaedam composita, cuius adquisitio erat partis post partem." (fol. 49vb). ...
Chatton,
Reportatio,
d.
I,
17,
de partibus continui, ex quo negant
4:
a.
2,
q.
"Ad
aliud,
indivisibilia, sicut audivi
eos
a.
via
38
Chatton, [erat]
Reportatio,
d.
I,
17,
improbata. Ideo excogitaret
q.
homo
3,
3;
"Ista
duplicem aliam viam
..."
est
illud
negare."
non (fol.
aeque contra eos
(fol.
placet
50ra).
mihi,
et
prius
50vb).
39
We discussed only two or three of the eight arguments against addition theory by Campsall quoted by Chatton. According to one argument not mentioned above, addition by parts could not result in a more perfect form. The more perfect a form is, the simpler it is, so adding parts detracts from the perfection of the resulting form. Chatton, Rcportatio,
I,
d. 17, q. 3, a. 3, fol. 49rb.
Chatton, Reportatio,
I,
d.
17,
q.
2,
a.
3-4:
Tertius articulus
est
utrum generaliter
nunquam sit augmentatio per additionem novae partis ad praecedentem facientem per se unam cum ilia. Et est opinio (marg.: Campsale) quod nunquam. Ideo (fol. 49rb) dicunt quod semper in materialibus forma perfectior est totaliter alia numero a ...
...
praecedenti
cui
succedit,
ita
quod
ibi
oportct
recipiens
denudari
a
natura
recepti
...
Calculating Grace:
on the
although
385
Wodeham
it
third
connotations.
of
Wodeham
de
s Tractatus alphabeticus, Campsall had can be called a connotation theory which theory, does not describe the process of qualitative change in terms
evidently by the time of settled
Adam
Chatton describes
view as one which could be
this
consistently maintained by adherents of connotation theories; Campsall
was a connotation
What held
when
that
to
According "possible
theorist
when
discussing relations.
the CampsalPs theory? According to
is
intensification
matter
Chatton,
object."
"In
Wodeham, Campsall
quality
be other than
it
way
that
hi
place
remiss
whole
is
the
is
a
becomes
the agent does not cause
form."
same
No
thing
addition
presence of the agent. The same form which was
new,
and
description of the process
when forms
called
being,
was. Rather altogether the
intense in the presence of a suitable agent. In
form
same.
the
the presence of a natural agent, this being
something which was previously potential becomes the actual takes
remains
diminished
a
contains
the form. This happens in such a to
the
occurs,
the
whole
makes
it
form
clear
existed
that
some sense 41
previously.
a potential
is
are intensified. So the denial that intensification
the
This
actualized is
motion
(fol. 49vb) ... Ad primum argumentum opinionis Campsal in tertio articulo, ilia consequentia maxime procedit contra eos. Si enim semper in processu illo est totaliter alia forma numero, nulla erit aucta, igitur directe est hoc contra ipsos." (fol. 49ra-vb) Quaest. 3, art. 3, dub. 2: "Item, quantitas potest augeri etiam in rarefactione, et non
per partes eiusdem rationis, sed potest esse absque hoc quod quantum recipiat aliquid eiusdem rationis. Ergo eodem modo in formis aliis est .... possibilis quod sit augmentatio sine additione et compositione partium eiusdem rationis. Qui teneret istam conclusionem quam inferunt haec argumenta ... posset earn ponere secundum triplicem viam, quarum una est quod quaelibet augmentatio est successio formarum simplicium, ita quod [vetus] semper totaliter corrumpitur et succedit totaliter nova forma. Ista via non placet mini, et prius [erat] improbata. Ideo excogitaret homo duplicem aliam viam: una est quod prior et posterior forma non semper sunt incompossibiles, nee tamen unquam faciunt unum, sed remanent distinctae simul in eodem subiecto, sicut dicunt quidam de duabus caritatibus simul manentibus in anima, scilicet CAMPSAL et sui sequaces, ut superius recitatum est. Ita posset dici quod agens naturale continue inducit aliud et aliud individuum formae, sed illae non faciunt unum, sed simul manent (fol. 50vb). ..."
Chatton,
Reportatio,
I,
d.
17,
q.
3,
a.
3:
"Alia
est
quod
in
materia
est
unum
diminutum, quod vocatur possibile obiectum, et quod istud ens diminutum ad praesentiam naturalis agentis fit forma, ita quod agens non facit aliud quam prius, sed illud idem penitus quod prius erat in potentia, illud idem absque omni addito ad praesen tiam agentis fit forma actu. luxta istam imaginationem diceretur quod ita est in augmentatione et remissione formarum, quod eadem forma prius remissa, sine productione cuiuscumque novi, eadem penitus fit forma intensa ad praesentiam activi nati augmentare, non quod aliqua pars praefuerit et aliqua non. Et tune consequenter dicendum esset quod totum est novum et quod totum praefuit. Et maxime TENENTES CONNOTAens
TIONES in in
dicere possent
praesentia agentis
quod formam et formam
talis,
praesentia alterius agentis
contrarii."
formam esse talem qualis nata est esse esse remissam est esse talem qualis nata est esse
intendi est
(fol. 51ra).
Wood
386
means only
change involved
that the
instantaneous and hence properly
is
described not as motion but as transmutation. This explains the claim
quoted by Wodeham: throughout the entire transmutation, the 4 both greater and lesser, remains the same.
quality,
Like a succession of forms theorist, Campsall describes qualitative change as a series of instantaneous changes which resemble substantive
Hence CampsalPs theory does
change. nature
of
On
change.
qualitative
not account well for the gradual
other
the
the
hand,
was
theory
designed to explain how the resulting quality constitutes a unified whole. It was for this reason that Campsall, like the admixture especially
Roger Swineshead, held that in the process of intensification added, there are no new parts. But unlike succession theorists, nothing would maintain that the form was the same, and had retained its Campsall theorist
is
same time
underlying nature at the
To sum up treated
like
change
by
by Chatton
theory.
like
theory,
treated
is
substantial
intensifying
spiritual
instances of substantial change and physical qualities like
change. Roger Swineshead and Richard Campsall discussed
quantitative qualitative
was new.
it
addition
change
quantitative
succession
like
qualities
that
the major points of disagreement: qualitative change
change as a unique case. Campsall agrees with Swineshead that same in intensification. Roger Swineshead holds that
the form remains the
what changes
of contrary
forms
are
objects
potential
balance
a
is
in
qualities.
Campsall holds that
presence of the appropriate natural
the
agent.
The
connotation
successively of the to
inhere
allows
theory
same
contraries
be
to
predicated
subject; the admixture theory allows contraries in
simultaneously
same
the
a
in
subject
remiss
degree
according to Chatton. But most fourteenth century addition and succession Fit/ralph and Burley deny that the
Wodeham, Ockham,
theorists like
form can have different
intensities
and
43
Addition
and
in
the
same
Wodeham,
subject.
Tractatus
ideo ex hoc
"Et
qualitas
maior
quod alteratum
ALIQUI
alphabeticus,
cap.
arguunt quod
si
succession
57
et
minor, sequitur vel quod motio
sit
infinitae perfectionis in
Ockham, Scriptum q.
13
(dist.
Oxford, Oriel fol.
17, 15,
135ra. Burley,
q.
I
Sent.,
Utrum
dist.
17,
intensio
agree
that
q.
4
lectio
dubia>
mensuretur
instanti vel
140vb).
(OTh
III,
formae accidentalis
481ss.). fiat
Fitzralph,
per additionem,
Sent.,
cod.
Tractatus alphabeticus, cap. 15 (Augmentatio), instanti, as cited by Sylla, "Medieval Concepts," p. 234n.
fol.
De
in 1),
<
(fol.
1
I,
theorists
(fnfinitum in augmentations continud): tola transmutatione non maneat eadem
in
vigore."
same
that contrary qualities can inhere
48vb-49rb.
Wodeham,
Calculating Grace:
intensification involves
new
Adam
de
Wodeham
387
forms, but differ on the question of whether
the old form in annihilated, whether forms have parts, and whether the
change takes place successively or instantaneously.
The appearance that intensifying whole was an argument against addition takes
change
place
constitute
theorists,
who maintained
by
part
successively,
a
qualities
part.
unified that
Opponents of addition
theory maintained that parts, or individuals, of quality would not combine to
form a unified whole.
The appearance theorists
of
and connotation
change
gradual
A
theorists.
mitigates
against
succession
connotation theorist would maintain
was the result of one or more instantaneous changes. succession theorist would agree that change takes place suddenly, and
that intensification
A
forms cannot be intensified by adding parts. Though intensification or rather changes - really take appears to be continuous, the change that
place suddenly. Proponents of the addition theory disagree, claiming that intensification
is
a successive process, in which parts are added. Chatton
holds that both successive and sudden changes in intensity occur. In cases of successive change, where parts are added, those parts do combine to constitute a single form. In the case of forms which have no parts,
change
is
sudden.
3. Is there
a
maximum
degree in the intensity of a form?
Most medievals were addition
theorist
who
followed Aristotle in denying
form can be greater or lesser, and Wodeham was an adherent of the common view on both these subjects. But Wodeham and the older that a
he most respected, Richard Fitzralph44 and William disagreed with common opinion on the subject of maximal
contemporaries
Ockham,
whom
45
degrees.
Most medievals maintained quality.
Both admixture
argue that there
is
a
theorists,
were maximal degrees of Roger Swineshead and Walter Chatton, there
that
maximal degree
in
the
intensification
of forms.
Chatton holds that we should not deny that God could create such a degree. The succession theorist, Walter Burley, holds that maximal degrees 44 Fitzralph,
Sent.,
I,
q.
15
(dist.
cantos possit augeri, cod. Oxford, Oriel 45 See note 48.
17,
15, fol.
q.
3),
Ad
53vb-54rb.
quaestionem
principalem:
Utrum
Wood
388
of a quality are possible. Godfrey of Fontaines defends this claim, on the
grounds that
this possibility is
not repugnant to the nature of charity or
A
beyond the power of God. John Duns Scotus, also held
number
this view.
4
of addition theorists, including
Wodeham and Ockham
denied
be a maximal degree of charity which could be produced. specify, God could add a part and create a
that there could
For whatever degree we 48
greater degree.
Thus both proponents and opponents of maximum degrees base their arguments on divine omnipotence. Those who deny maximal degrees argue that
God
because
is
omnipotent, he could add a part and create a greater
degree, however intense the existing form was. Proponents of a
degree
-
such
Scotus, Chatton and Godfrey
as,
-
claim that
maximum God is so
powerful that he could create a maximal degree.
Conclusion
This brings to an end our discussion of the debate about latitude of
forms as
it
raised in
is
Adam
de
Wodeham
s
Tractatus alphabeticus
.
This
was part of an intense debate, one which was conducted with vocabulary like individuals of form (individua formarum) and
Tractatus
novel
To
quantities of quality. 46 III,
Godcfridus
de
389s.). Burley,
47 Scotus,
48
Fontibus,
De
Ockham, Scriptum cap.
17
in
it
was a
by
VII, q. 12 (cd. M. de Wulf Sylla, "Medieval Concepts," p. 235n.
III, d. 13, q. 4, n.
I Sent.,
dist.
17,
(Augmentari potest
2 (cd.
8
Wadding,
(O q. quantum
lTi
VIM,
III,
debate, in
scientific
Quodlibet
instanti, as cited
Opus Oxoniense,
alphabeticus,
a limited extent
Hoffmans,
J.
261ss.
547-67).
infinitum):
-
Wodeham,
"Item,
tria
Tractatus
sunt
quae
quod Deus non potest facere maius in specie illius dati. Primum: si illud esset indivisible. Unum enim indivisibile eiusdem speciei non potest esse maius alio, ut supra patct. Secundum: quia variatio quantitatis variat speciem. Ideo Deus non potest facere unum ternarium maiorem alio, quia omnis unitas variat speciem. Et hoc etiam est ex causa quare Deus non potest facere unum bicubitum maius alio. Tertium
E>:
non potest esse aliquod individuum in specie temporis praeter illud et partes suas. Et hoc etiam est ratio quare est contradictio quod sit unum individuum maius et perfectius Deo. Ubicumque ergo nullum istorum trium impedit, ibi quocumque dato potest Deus facere maius. Sic est de gratia, ergo etc. ... Quinto apparet mihi, similiter cum Ockham et multis aliis doctoribus, quod omnis forma augmentabilis secundum intensionem in infinitum potest intensive crescere, modo superius posito et concesso. Hoc est quod non est dare ita intensam quin possit a Deo fieri
duplo intensior
(Lumen
et
quadruple, et
sic
infinitae intensionis), fol. 142ra-142rb.
in
infinitum."
(fol.
135va-135vb).
Cf.
cap.
61
Calculating Grace:
s
today
Adam
Wodeham
de
389
sense of an investigation of the results of experience.
Ockham
argued that his conclusions accord with reason and experience. Chatton replied that in discussing simple substances, our reason and experience
Ockham
mitigate against an acceptance of
were
participants in this debate their
experience
intensity.
Strictly
forma non
-
suscepit magis.
account.
Nonetheless
deny the most basic increase and decrease
most participants
And
4
willing to
namely, that qualities speaking,
s
many
result of in
their
the debate agreed that
in
proponents of the theory of succession of
forms even denied the evidence of their senses that such changes were gradual.
Clearly logical considerations about the nature of forms and contrary qualities
were
just
compelling as the result of experience. Perhaps
as
fourteenth century medievals were correct to place as high a value on as
logic
on what experience appears
counterintuitive scientific doctrines.
confront situations in which the
of naive
basis
situation
like
observation.
And
all
theory depends both on
In
is,
we
often
no one
the appearances.
it
We
today also accept
we sometimes
like the medievals,
fact is
how compatible
attractive
teach.
not decide between viable theories on
the medievals. There
which can account for
philosophically
we do
to
it
The is
find
ourselves
logically coherent
in
a
theory
decision to accept a given
with observation and on
from a mathematical or
logical
how
point of
view.
How did fourteenth century medievals decide between rival theories about latitude of forms? The greatest difference was between admixture theories
and
realization
all
other
theories.
Admixture
of a qualitative change without any
form. Since the form remains the same as
it
is
theories
allow
new form
for
the
or part of a
transmuted, such theories
49
Chatton, Reportatio, I, d. 17, q. 2, a. 2: "Dicunt respondendum, turn secundo quia duae partes albedinis sunt componibiles, saltern secundum extensionem faciunt unum per agens creatum, quare ergo non eadem parte praecise, cum sic solvantur multae difficultates,
nee ratio nee experientia
obviet."
(fol.
48va)
concede ilium modum augmentations in albedine et multis aliis, sed non generaliter in omnibus. Et cum dicunt, "bonum est ex quo et quando non est contra "Ad
aliud
solvuntur multae difficultates," ita dico quod bonum est habemus rationem et experientiam in oppositum, sicut in formis simplicibus, ut in speciebus in medio et in angelis et in anima Christi et ludae et in actibus intellectus vel voluntatis, quae omnia sunt formae simplices." (fol.
rationem nee experientiam negare ilium modum unde <sic
49ra) Art.
et
P>
4: "tamen dico quod experientia vadit ad hoc, quod unum contrariorum remittit reliquum, et non totaliter corrumpit, quia tune in motu remissionis contrarium suum causaret contrarium, quod repute magis absurdum." (fol. 50ra). Cf. Ockham, Scriptum in I Sent., dist. 17, q. 5 (OTh III, 487).
Wood
390
allow their adherents to explain the appearance that qualities intensify while remaining unified, straightforwardly; these theories would also have little
are
accounting for gradual change. But admixture theories
difficulty in
from a
unattractive
and Aristotelian point of view. Their
logical
proponents must maintain that there can be increase without addition, and they must affirm that forms can be intensified which is contrary to Aristotle.
other
All
followed
theories
cannot be intensified. Chatton
be called a mixed theory; addition
theories.
And
without
addition,
nor
identity.
The
physical
and
it
Aristotle
is
that
can
qualities
intensify
as
differently,
From an Aristotelian point position when they claimed
while
theory offers
s
and
can be increase
there
that
suggests
forms
greatest attraction Chatton spiritual
forms
that
maintaining
a combination of succession
really
neither
it
in
so-called admixture theory might better
s
retaining that
is
and
divisible
it
their treats
indivisible
qualities.
of view, addition theorists were in a
weak
that
divisible
inhered
accidents
in
50 Chatton even claims that his Chatton points out. 51 The position on indivisible qualities is an argument from experience. weakness in Chatton s view is that it requires that he account for
indivisible subjects as
continuous changes Chatton accepted.
in
terms of
indivisibles.
This was a consequence that
Chatton also accepted the old-fashioned view that contrary qualities could inhere
the
in
addition
century
same
subject
and succession
in
a
remiss degree. Most fourteenth unlike
theorists,
contraries could inhere simultaneously in the is
the
greatest
espoused
itself,
contribution its
of the
same
succession
Chatton, subject.
theory.
denied that
Here perhaps
Though seldom
influence led addition theorists to alter the account of
change presented by Scotus in this regard. Addition and succession theories present very similar accounts of qualitative change. A decision between these views could not be based on qualitative
empirical considerations.
The
addition theory preserves the appearance of
gradual motion better, but the succession theory accounts better for the unified character of the
new
intensified or
addition
and
succession
to
Campsall,
unattractive
weakened theories
quality.
were
from an Aristotelian point of view: Addition
See above, note
36.
See above, note 49.
According
also
equally
theorists
were
Calculating Grace:
committed
to defending an actual infinite,
committed to
hand,
But
indivisibilism.
disprove Campsall
other
Adam
it
s
Wodeham
391
and succession
in fact addition theorists
we saw
argument, as
would be
de
difficult
in
a
for
Wodeham
succession
theorists
found s
it
reply.
theorist
were
easy to
On
the
to
deny Campsall s charge. And once committed to indivisibilism, a theorist must abandon Aristotle s account of continua. For, according to Aristotelian physics,
makes
instants
good
serve
sense
not as the locus of change but as
to
the
reject
assimilation
of
its
limits.
intensification
It
and
remission to a series of mutations. Not only does addition theory allow its proponents to describe intensification as a gradual change, but as
continuous successive motion,
A
further
advantage
really divisible like time
it is
of
theory was
addition
and motion.
its
assimilation
of
qualitative to quantitative change.
For by describing
result of the addition of parts,
ensured that the units of change were Mertonians in their schemes for
commensurable. This was useful
it
intensification as the
to later
quantifying change.
But the basic advantage of addition theory was the adaptation of Aristotelian theories about continua. theorist
to
deny maximal degrees,
inhere in the their
same
subject,
is
And
their
like
fourteenth century
denial that contraries can
new view
of divine power, but a
of the potentially infinite parts of a divisible quantity
accounts for this novel theological doctrine.
St.
move by
a reflection of the greater sophistication of
understanding of Aristotle. Not a
new understanding
the
Bonaventure University
JACK ZUPKO
John Buridan
On Abstraction and Universal Cognition
For the nominalist, the claim that the mind can cognize universally, or that its thoughts can range over non-individual objects such as human being
whiteness
or
,
further
requires
,
when
happens, psychologically speaking,
What
explanation.
is
that
it
cognize universally? Given the
I
standard assumption of nominalist ontologies that the world contains no non-individual entities, what status do the objects of universal thought
how do
have, and
come
they
There are two
to
be entertained?
distinct questions here:
one semantic, asking how a and the other psychological,
mental act can mean something universal, asking about the genesis of universal thoughts. Aristotle second can be found even
thinking,
if
he
in
De memoria, where he not
is
thinking
says,
1
thus, the intellect thinks of
triangularity, -
particular
s
what
is
common
answer to the
someone who
of something with
something with a size before his eyes, and thinks of size;"
"...
a
or universal, such as
by an effort of abstraction from what is determinate or 2 triangles having physical dimensions. His answer to the first
can be reconstructed from his famous remark 3 identical."
perceiving,
without
The
defined
identity
the
as
does
whenever
Arist.,
U.
P.,
this I
in
question of
sort
De anima
in
mean
my
is
that
is
change
formal in
that
intellect
there
is
becoming
something
"in
is
the
thought is,
like
received
triangularity
a
triangularity formally.
universal
in
my mind
think universally?
De mem.
1.450a4-6;
Arist.,
De
an. I.1.403bl5;
Arist.,
De
an. III.4.430a3-5.
3
is
thinking
which form
tr.
Sorahji,
Aristotle
On Memory
1972), 48-49.
2
-
makes my thought of
and so what
matter
thought of that universal
But
places
size,
not as having a
it
case of objects which involve no matter, what thinks and what are
is
cf.
HI.4.429518, III.7.431bl2, III.8.432a5.
(Providence:
Brown
John Buridan on Abstraction and Universal Cognition
John
was
with
this
of his Questions on Aristotle s
"De
Buridan
Question
8,
quite
taken
393
Book
in
problem
III,
4 anima"
lectura).
(tertia
This Question, which asks Whether the intellect understands the universal before the singular, or vice versa
contains several lengthy digressions on
,
the nature and objects of universal cognition, including a psychological
how
of
explanation
the
mind can cognize
without
universals
As
a universal or containing any universal entities.
becoming
actually
a nominalist,
Buridan often asserts the particularity of the mind s conceptual contents. But he also wants to claim that this presents no obstacle to some paper some of he the consequences of the theory of universal cognition develops in concepts being about universals.
Question
Does
8.
want to explore
his explanation of
how
in this
concepts are generated
on what universal thoughts are about?
views
his
I
this
Is
compatible with his nominalistic assumption that the mind all
of
them
s
fit
with
explanation contents are
particular?
Buridan
never
To do
universally.
attempts
to
deny
that
can
intellect
so would be absurd, since this
is
cognize
usually taken to be
paradigmatic function. His task is rather to explain the evident fact of universal cognition in view of his nominalistic assumptions about the its
sorts of entities
which might figure
example, both
for
soul
and not
represented
that
"intelligible
as
universally,
the
to
singularity
assumption
claim that
"our
Plato
intellect is
in
such an explanation. exist
things thought",
singularly
He
assumes, the
outside
singularly
and that they are also
from
extended to the mind
the s
5 beginning."
"...
This
contents in the further
concepts exist in our intellect as singularly and distinctly
from one another and from other things as colours and flavours do
in
have edited this Question as part of a complete edition of Book III of Buridan s I Quaestiones in libros De anima Aristotelis secundum tertiam lecturam [hereafter QDA ], prepared from four manuscripts: Vat. lat. 2164 ff. 197vb-233rb; Vat. lat. 11575 ff. 65va87ra; Reg.lat. 1959 ff. 47va-69rb; and Codex Vindobonensis Pal. 5454 ff. 41ra-56vb. References to this work will be given using (1) the line numbers of the corresponding folio[s] of the last ms. listed above [hereafter ]. There are twenty questions in the tertia lectura of Book III.
V
Item sicut
cum
res
intelligibiles
posuit Plato, et
existunt
singulariter
cum etiam cognoscuntur
extra
animam
my
et
edition,
non
and
(2)
universaliter,
a sensu singulariter et per consequens a
principio repraesentantur intellectui singulariter ... [QDA III.8, 11. 130-134] [V f.46ra]. Buridan comes closest to defending the claim that there are no non-individual entities
in
his
Quaestiones
M: Minerva, 1964)
[hereafter
in
QM
Metaphysicen Aristotelis (Paris: 1518, rpr. Frankfurt-amVII.15 ff. 50rb-51ra, and VII.16, ff. 51ra-52ra. ],
394
Zupko and that
bodies",
such
"although
extension or corporeal location, they
Now location,
do not
concepts
themselves have
in
all exist singularly."
6
given that concepts are singular but lack extension or corporeal
might
it
embodying
look
as
if
are
they
kind
a
of metaphysical hybrid,
the numerical distinctness of particulars together with the lack
of physical dimension associated with universals. But the rather of the
word
to describe
singular
semantic side of Buridan the
first
question above.
the universal
is
s
concepts
theory of universal cognition
As he
odd use
actually a feature of the
is
-
answer to
his
on the Physics, the mind by which we
says in his Questions
properly a term or a concept in
conceive simultaneously and indifferently outside the soul, and that concept
is
many
strictly
"...
things existing singularly
posterior to those singular
His strategy is to recast objectively caused by them. metaphysical questions about universal cognition semantically, so that the
things, since
problem what is
it
is
no longer one of explaining away the apparent universality of my mind when I think universally, but rather of giving an
is
in
account of the universality of universal terms in mental language. This linguistic turn on a metaphysical question does have precedent elsewhere
Buridan
in
s
It
writings.
problem of universals the
strictest
sense,
approach to the and universality as being, in
characteristic of his general individuality
terms
of
properties
Whether
discussing the question, to the individual
is
to treat
rather
than
substances the species
in
by a substantial or accidental differentia
Item conccptus nostri
nostro
intcllcctu
in
singulariter et
ita
,
8
of
he
things. is
contracted
says:
distincte
ab invicem
Quamvis conceptus tales non hahcant extensioncm ncc situm corporcum. immo omnia cxistunt singulariter.
ah
aliis
III.8,
II.
cxistunt
sicut
In
colorcs ct sapores in corporihus.
in
et eis
[QDA
207-210] [V f.46rh].
Quaestiones
subtillisimae
Frankfurt-am-M, Minerva, terminus sive conceptus singulariter
extra
super 1964) in
animam
mente
existentes,
singularibus, quia est ab eis objective
Although I concentrate III.8, Buridan also treats
QM VII.15-16
(ff.
octo
in
this
Physicorum
QP
[hereafter
simul
quo et
j
iste
libros 1.7,
f.
Aristotelis
8rb:
indiffcrenter
conceptus
bene
"...
(Paris: est
bene
concipimus est
posterior
1509, rpr. universale
plures illis
res
rebus
causatus."
paper on the account of universal cognition in QDA issue at some length in QP 1.7 (ff. 7vb-10ra). See as well
this
50rb-52rb).
o
See Peter King, "Jean Buridan s Theory of Individuation", forthcoming in an anthology on the problem of individuation in the High Middle Ages, edited by Jorge E. Gracia.
QM
VII. 17, f. 52va, Utrum in substantiis differentiam substantialem aut accidentalem :
"...
species contrahitur ad ista contractio non est
individuum
per
quantum ad
res
John Buridan on Abstraction and Universal Cognition
395
the contraction is not with respect to the things signified, ... leaving concepts aside, since a man or animal or body or substance, exists singularly in this way, just like Socrates or Plato, etc., because nothing other than Socrates or Plato Jor some other individual] is a man. Since, then, a man or an animal would be a thing existing singularly, it is obvious, even with everything else left aside, that no contraction would be needed in order for it to exist singularly. One must say, then, that contractions of this kind have to be understood with respect to concepts or terms be significative of things ... And so a term which is a species would said to be contracted to a singular term by the addition of a differentia restricting the specific term to suppositing for that thing alone for which the singular term supposits.
Buridan
is
claiming here that the way to understand contraction
by imagining a
common
somehow squeezed
or specific nature as
term, the reference of which
is
term by
restricted to that of a singular
the addition of a differentia. For example, the reference of horse
general sentence,
The
horse
addition of the differentia if
Brunellus, is
is
a quadruped
oldest
an
common
by construing the specific nature as a specific or
individual, but
not
is
into
in the
could be restricted by the
,
-
to pick out a single individual
say,
Brunellus happens to be the oldest horse. Again, contraction
no longer a metaphysical question about the
restriction of essence or
commonality, but a semantic question about the restriction of reference.
Buridan wants to deny that the universality from any intrinsic property of concepts,
stems
in
universal
since
cognition
would be
this
tantamount to the admission of conceptual universals. What makes a thought universal rather,
is
not any property belonging to the concept
structural
certain
properties
it
possesses
as
a
term
itself,
in
but
mental
10
language:
circumscriptis conceptibus, quia ita singulariter existit homo vel animal aut corpus aut substantia etc., sicut Socrates et Plato, quia nihil aliud est homo quam Socrates vel Plato. Cum ergo homo vel animal sit res singulariter exsistens, etiam si omnia alia essent circumscripta, manifestum est quod non indiget aliqua contractione ad hoc quod singulariter exsistat. Oportet ergo dicere quod huiusmodi contractiones habent intelligi quantum ad conceptus sive terminos significativos rerum ... Ita etiam terminus qui est species diceretur contrahi ad terminum singularem per additionem differentiae restringentis terminum specificum ad supponendum pro illo solo pro quo supponit terminus singularis." significatas,
Tractatus de suppositionibus III: Maria Elena Reina, "Giovanni Buridano: Tractatus de suppositionibus in Rivista critica di storia della filosofia XII (1957): Sed ... notandum [est] quod, cum universalia, sccundum praedicationem principaliter ",
dicta,
non
sint
praeter
indifferenter concipit
animam,
plures res,
ista ut,
non sunt
quia
nisi
conceptus
omnes homnes
animae
quibus
anima
indifferenter concipit conceptu
396
Zupko But ... it should be noted that since universals in the predication mentioned principally [i.e. Man is running do not exist outside the soul, they do not exist except as concepts of the soul by which the soul indifferently conceives more than one thing, as for instance, because it conceives all men indifferently by some concept, the name man is imposed, and likewise for the concept of animal as regards animals. Therefore, since species and genera are universals in predication, it is apparent that species and genera are such concepts of the soul; it is true that spoken terms are consequently also colled genera and species (such as the utterances man and animal ), but they are not called universals or genera or ]
species principally, but rather significatively, in attribution to those universal [concepts], because in them they are imposed to signify other things ...
man
mental particular, it can function as a universal in propositional contexts, such as when I am Man is a rational animal where it refers to no man in thinking
Thus,
my
although
concept
itself
is
a
,
particular but to
men
all
indifferently.
Buridan spends most of Question 8 giving the psychological under pinnings of this semantic approach. He begins by saying that one reason, not
although
sufficient
even
universally,
universally
a
reason,
the
why
nor
understood not on account of the
fact
understand
can
intellect
though the things it understands are themselves universals, is that
neither "...
things
exist
are
that they are in the intellect, but
because their species, which arc representative likenesses of them, are in 11 the intellect." Furthermore, he holds (1) that this likeness-relation has a
natural
the
in
namely,
cause,
nature
their
or
likeness
a
fact
same
outside the soul belonging to the
essential
nomcn homo
that
"...
things
species or the
agreement
existing
singularly
same genus have greater
than
in
those
de conceptu animalis quantum ad animalia. secundum praedicationem, apparel quod species et genera sunt tales conceptus animae; verum est quod consequenter termini sed non vocales dicuntur etiam genera et species, ut istae voces homo et animal aliquo,
imponitur hoc
cum
Ideo
et
species
genera
,
ct
sic
universalia
sint
,
dicuntur
universalia
attributionem ad
vel
istos
significandum res alias
...
[conceptus] [p.
202,
species principaliter, immo significative, secundum universales, eo quod secundum eos impositi sunt ad
vel
genera 11.
65-76].
unam causam,
licet non sufficientem, quare intellectus potest intelligere universaliter, quamvis res intellectae nee universaliter existant nee universales sint, ego dico quod haec est causa: quia res intelliguntur non propter hoc
Si
ergo volumus assignare
quod ipsae
sint
in
intellectu,
sed
sentativae earum, sunt in intellectu.
quia species earum,
[QDA
quae sunt similitudines reprae-
210-216] [V ff.46rb-va]. Cf. QP 1.7: ... res intelliguntur non per hoc quod sunt apud intellectum, sed per suas similitudines existentes apud intellectum. [f.Svb]. III.8,
11.
John Buridan on Abstraction and Universal Cognition
397
12 and (2) that belonging to different species or different genera"; 13 In is transitive. or essential sort of property-likeness agreement
member
way, a likeness which the intellect acquires from one or genus will apply to indifferently.
all
For example, Buridan
agreement or likeness ex natura
rei,
same time
"...
ass
indifferently represent
asses have a mutual
all
when
that
by way
the intelligible
of likeness,
will at
it
my
Buridan contends,
all."
Plato or other men.
to
understands
intellect
"the
In the same way, any ass at from Socrates will not belong
abstracts
intellect
more than
Socrates any
which the name
man
is
taken.
And
this is to
when
the
contrary",
of the
namely, the concept from
understand
But where do these concepts come from? of Socrates begins
the
"On
men by means
all
representation indifferently, in a single concept,
thinking
of a species
of that species or genus
if
must be
this
14
the species-likeness to
says, it
some
species in the intellect represents
the
members
of the other
this
intellect
15 universally."
Buridan says that the
receives
species
thought of Socrates from a phantasm, making Socrates appear as
if
a
or
he
Tune accipimus quod res extra animam singulariter existentes de eadem specie vel eodem genere habent ex natura sui similitudinem seu convenientiam essentialem maiorem quam illae quae sunt diversarum specierum vel diversorum generum. [QDA 111.8,
de 11.
218-221] [V f.46va]. Cf.
QP
1.7:
convenientiam Postea
Res autem extra [animam] ex natura et simiiitudinem
D
est simili ipsi
et
ex essentia sua habent inter se
[f.Svb].
aliqua ad invicem similia, quidquid est invicem similia, ipsum est simile unicuique sint similia secundum albedinem quia sunt alba,
ego iterum suppono quod si eo in quo sunt duo
simile uni illorum, in illorum. Verbi gratia, sicut
...
si A, B et C A, oportet quod
sit
sint
in
consimili ipsi
B
et
C.
[QDA
111.8,
11.
243-247]
[V
f.46va]. Cf. 1.7:
Modo
QP
uni eorum,
Ideo
si
sit
quantum ad hoc si
omnes
asini
ita
in
ex
quod sint multa invicem similia, omne illud quod quo sunt similia, est simile unicuique aliomm. [f.Svb]. natura
rei
habent
ad
invicem
convenientiam
et
est simile
similitu
dinem, oportet quod quando species intelligibilis in intellectu repraesentabit per modum similitudinis aliquem asinum, ipsa simul indifferenter repraesentabit quemlibet asinum ...
[QP
1.7, f.Svb].
Ideo consequitur ex quo repraesentatio fit per similitudinem quod illud quod erat repraesentativum unius erit indifferenter repraesentativum aliorum, nisi aliud concurrat et obstet, sicut dicetur. Ex hoc finaliter infertur quod cum species et similitudo Sortis fuerit
apud intellectum
et
fuerit
abstracta a speciebus extraneorum,
ilia
non magis
erit
quam Platonis et aliorum hominum; nee intellectus per earn magis intelliget Sortem quam alios homines. Immo sic per earn omnes homines indifferenter homo Et hoc est intelintelliget uno conceptu, scilicet a quo sumitur hoc nomen ligere universaliter. [QDA III.8, 247-257] [V f.46va]. repraesentatio Sortis
.
11.
398
Zupko
were
the
in
someone cogni/ing him. 16 The phantasm
of
prospect
is
construed as a particular produced by the sensitive part of the soul, representing a bundle of undifferentiated properties. By means of this received species or thought, the intellect is said to understand Socrates in
a
mode.
singular
If
the
intellect
then
is
able
to
substance
whiteness
or
something which could
Socrates,
concept,
man.
exist
the
in
longer
as
perceived
someone cognizing him,
treats
way
this
of
product
substantial
the
of
process
required: the concept abstracted from
He
taken.
is
common
the
abstract
might
Socrates does not represent Socrates any
from which the name man
a concept of
it
concept. For example, from the singular
then
abstraction as universal in the
no
is
the prospect of
intellect
Buridan
Socrates
that
common
then there will be a concept,
so
the
differentiate
properties represented by the phantasm, and abstract from
more than
and
Plato,
it
is
that
adds that any power which can
17 perform this sort of abstraction can cogni/.e universally. But in what sense is the product of abstraction something nonuniversal? Buridan does not say very much about abstraction. Aristotle, as
we saw intellect
or
understands
above, distills
is
Aquinas
particular.
intellect
what
"bestows
abstraction
common has
a
the
as
or universal from what similar
determinate
is
the
that
claiming
explanation,
universality on understood forms
the
whereby
process
to the extent that
it
speaking, this is Buridan s account of how we cogni/e singular objects which we are not acquainted directly, hut only by means of a description. He holds that genuine singular cognition requires direct contact with the object in question [see QDA III.8, 11. 319-399]. There are some difficulties with the latter account which I do not have the space to discuss here: e.g. how the claim that some singular concepts are acquired by direct contact is compatible with the view that the intellect 1
Strictly
with
knows things by means of likenesses. Surely knowing degree of generality not present when it is said that we know
Tune ergo revertendo ad propositum,
dico
speciem vel intellectionem Sortis cum facientem apparere rem per modum existentis recipit
intelligit
ilium
abstrahere
modo
singulari.
Si
conceptum substantiae
modum
a
X
likeness
quod cum in
intellectus
confusione
tali
of
X
introduces
a
directly.
prospectu
a
phantasmate
magnitudinis cognoscentis,
et
situs,
intellectus
potest illam confusionem distinguere et albedinis a conceptu situs, ut non amplius res
intellectus vel
in prospectu cognoscentis, tune erit conceptus comconceptus Sortis abstracte a conceptibus albedinis et situs et aliorum accidentium vel extraneorum, ille non magis repraesentabit Sortem quam Platonem, et erit conceptus communis a quo sumitur hoc nomen homo Et quaecumque virtus potest facere huiusmodi abstractionem, sive ilia sit sensus sive
percipiatur
munis.
per
Unde cum
existentis
elicitus
fuerit
.
intellectus, ilia potest universaliter cognoscere.
[QDA
III. 8,
11.
347-360] [V f.47ra].
John Buridan on Abstraction and Universal Cognition
them from individuating material
abstracts
18
399
Buridan, however,
principles."
must be extremely cautious about adopting either of these explanations without qualification. Since he wants to maintain the particularity of the
mind
s
contents,
cannot be that the mind becomes or takes on a
it
it cognizes universally; it is not open to him to assert and object are formally identical in Aristotle s sense, for thought would seem to concede the existence of mental universals. So there
whenever
universal that that
must be another way of accounting
what the
for
intellect
does when
it
abstracts.
Buridan hints terminology.
He
a
at
representation of sense that understanding
is
from
a
shift
in
from a particular not a universal but a "commmon concept", and
what the
something
in
intellect
abstracts
accordance with a
amounts
that thinking universally
related Question
explanatory strategy with
different
says that
to.
19
his Questions
He
on
common
expands on
Aristotle s
this
"Physics",
is all
concept
remark in
in a
which he
says that the intellect can abstract the species or conception of a stone
from the species or conception of some location or other, and that every stone is understood by means of a common concept as being no more 20 here than there. But I m afraid he doesn t develop things much beyond he sometimes permits the old terminology to return in embarrassing ways by showing no aversion to speaking of the common concept as a kind of universal. In an effort to explain the relationship
this.
Indeed,
between a
common
concept and the singular concept from which
it
has
been abstracted, he says that each universal is tied to a corresponding vague singular, and that sense-conceptions of vague singulars immediately rise
give
to
intellective
conceptions of the corresponding universals, by
the abstraction of a conception of the thing from a conception of place. Finally,
18
he adds that that universal
Quaestiones de Anima, ed.
dicendum quod
intellectus dat
19
non eo quod
sit
unus
first
in
the
intellect
to
which
Robb (Toronto: PIMS, 1968), Q.2, p. 73: "Ad sextum formis intellectis universalitatem in quantum abstrahit cas
a principiis materialibus individuantibus." Cf. Q.3, p. 86, ad 8: "Sic igitur sua
universalis,
is
in
abstractione
omnibus, sed
in
quantum
intellectus est
facit
istam
unitatem
materialis."
See n.17. 1.7: Ideo intellectus poterit abstrahere speciem vel notitiam lapidis a specie vel huius situs vel alterius, et sic intelligitur lapis, vel quantum ad hoc intelligendo esse hie vel illic, et tune indifferenter omnis lapis intelligitur conceptu communi
QP
notitia
de non magis hie quam
ille.
[f.9ra].
400
Zupko
there corresponds the vague singular
first
in
the sense.
are unfortunate, given that Buridan has
universal
21
left
These uses of
means
us no
make
characterizing the product of abstraction which does not
it
of
into a
very good candidate for a universal. Might there be another way out of this difficulty?
Although Buridan has can
some
in
fill
little
to say about abstraction,
He
of the details for him.
believe
I
we
needs something metaphysically
much more
ordinary than the sort of abstraction suggested by Aristotle and Aquinas. Since he holds that the universality of thought is not a of
result
anything
of
virtue
in
possess
the
intellect
the
fact
but
does,
their
that
property which
a
thoughts
embodying singular concepts
naturally refer to sets of individuals in the world, he needs an account of
which
abstraction
stripped-down characterize
plays
singular
concept,
kind
a
as
it
up the
idea
that
while
of universal.
common
the
a
is
down any attempt
playing
As
concept
in
this
a to
direction,
I
aspects of cognitive processing
is
step
propose the following.
For Buridan, the singularity of contained
in
all
these three claims:
(1)
Intelligible things exist singularly outside the soul
(2)
Intelligible
things
are
to
represented
the
intellect
singularly
from the beginning Concepts
(3)
Buridan
s
all exist
account of
22
singularly.
how we
get from things outside the soul to concepts
the relata of which are depends upon the relation likenesses. Moreover, as we saw above, he assumes that:
of representation,
Likenesses have a natural cause
(4)
QP
1.7:
Modo
ultimo
considerandum
est
quod
unicuique
universal!
correspondet
unum
singulare vagum, et alteri universal! alterum singulare, ut homini/hic homo, animali/hoc animal, corpori/hoc corpus, et sic de aliis.* ... illud universale est prius apud intellectum cui correspondet singulare vagum prius
apud sensum. ... Sed unumquodque universale est propinquissimum et immediatum suo individuo aliud singulare vagum vago, statim enim et immediate ex notitia sensus secundum abstractionem notae consurgit notitia intellectiva secundum universale correspondens per rei a notitia situs, sicut
*Cf.
22
QDA
III.8,
Seenn.5-6.
11.
ante dictum
392-399;
fuit. [f.9vb].
V f.47rb.
John Buridan on Abstraction and Universal Cognition
From
and
(4)
(5),
An
some time
ass
of
side
of
representing
Buridan
some
s
ass
is,
all,
and
at
Now
we
if
the
this is the
the
claim
is
central
which
concept
of
virtue
at
and
(4)
(5)
the
to
does
the
above,
also
concept from which the term
construe abstraction as simply the filtering process by comes to have a representation, say, of Socrates
intellect
whiteness,
apart
is
Socrates
from
no prima
particular
sitting
down, being
in virtue of (4) all
feet
six
it
(call
properties
s-whiteness,
exhibited
and
(5)
it
for
abstracted
extension
of
things.
its
is
simply
by him. Moreover, s-whiteness is is a likeness of his whiteness. But
above, s-whiteness will also indifferently repre
general
property
corresponding predicate
The
it
then
short) separated from the
white things: not only Socrates, but Plato, Aristotle,
the
etc.,
tall,
facie reason to regard this as a universal;
whiteness
s
his
causally related to Socrates because
white
This
all.
an
rei,
same time
is
taken.
which the
sent
agree ex natura
of likeness
theory: in
asses
all
by way
representing any ass
representing any ass at
from
C
intellect
representing some
semantic
other
B
like
instantiation
indifferently
there
like
is
he infers
Recall his remark that because intellect
is
is
representing (i.e. having the likeness of) of natural property P is at the same indifferently representing all other P-instantiations.
(6)
ass
A A
Natural-kind likenesses are transitive, such that if in being white^ and B is like C being white, then in being white.
(5)
401
transitivity
of
s-whiteness, is
white
natural-kind
,
etc.;
we
that
is,
the
cognize
which ranges over
likenesses
ensures
that
should an intellect have instead abstracted p-whiteness (from Plato) or awhiteness (from Aristotle), it would still cognize by means of p-whiteness or a-whiteness something coextensional with what
is
cognized by means
of s-whiteness.
There
is
a certain pragmatism
attaching to this interpretation:
whiteness does not count as a universal because distilled
23 24
it
is
from the sensible representation of Socrates; but
Seenn.12-13.
See nn.14-15.
s-
Socrates whiteness, it
is
common
402
Zupko
25 enough, that the concept corresponding to it can be enough, or vague used to refer not only to Socrates but also to all other individuals k from which k-whiteness can be abstracted. No universal need be invoked
to explain the natural similarity of properties.
While
account
this
avoids
populating
mental
the
realm
with
and while there is something to be said for natural resemblance as the source of commonality, if not universality, let me add a proviso: it is not clear how Buridan might, using such an account, explain the important difference between having the concept s-whiteness universals,
and taking universally a vague
surely
this
concept to be true of other things besides
amounts
S. If
cognizing
to the recognition that the predicate corresponding to
common
concept refers to a set of individuals indifferently, then recognizing this would be another mental operation; that is,
abstracting
Another operation
be what
cannot
s-whiteness
needed
is
other individuals besides S
-
-
that
in
it
means
to
think
of taking s-whiteness
universally.
refer
to
to
order to grasp the universality of that
concept.
Buridan does speak
in his
common
Questions on Aristotle s
"De
anima"
about
under the guise of which things are concept being 26 but gives no details about how this works. Still, understood universally, we can reconstruct. Since concepts properly function as terms in mental the
that
language, most thinking will consist in our combining these concepts in
well-formed ways into mental language propositions. also will
holds that only be
in
is
it
it
actually
are refers
strictly
since Buridan
relevant.
presupposes
that
it
questions about the ontology
Using a concept
in
a
context
the user already has a fairly
firm grip on the signification of that concept.
concepts and come
And
propositional contexts that terms refer,
propositional contexts that
of thought-objects
where
only
in
Of
to appreciate their generality
is
course,
how we
learn
an important matter.
The very closest Buridan comes to something like the account I m sketching is in treatment of cognition in his Questions on Aristotle s "Physics", where he says that each universal is tied to a corresponding vague singular, and that sense-conceptions of vague singulars immediately give rise to intellective conceptions of the corresponding universals, by abstracting a conception of the thing from a conception of the place [see n. 21 above]. I think the vagueness of mental representations is exactly the notion his
Buridan needs to focus on if he wishes to avoid conceptual universals. A charcoal drawing of someone, for example, can be a vague representation of that person without being a universal, even though it depicts only some of his or her actual features. 26 See n.17 above.
John Buridan on Abstraction and Universal Cognition But here we
seem
to
reach
charitably be added to Buridan
In
reconciling
nominalistic
his
The
think universally. ability
to
cognize
of what
limits
can
reasonably and
original account.
s
Buridan
think
I
conclusion,
the
403
for
is
world-view with
task for the nominalist
without
universally
most the is
successful
part
problem
in
how we
of
to explain our evident
postulating
universals,
either
as
products of abstraction or thought-objects. Buridan endeavours to steer clear of both these obstacles by on the one hand stipulating that the species by which
we
entertain a universal
is
and on the
itself singular,
other by treating the universality of thought as a function of the
way
which
but
concepts
not
refer
And
to
abstract
concepts
or
entities,
in
to
account of concept-generation explains intellectual abstraction in such a way that its product still looks like a good candidate for a universal, we can tell a more suitable story individuals in the world.
without
much
difficulty.
At
although his
least
in
this
respcet,
Buridan
s
psychology
does not compromise his ontology.
Cornell University
27 I
wish to thank Calvin
earlier versions of this paper.
Normore and
especially
Norman Kretzmann
for
comments on
SECTION THREE
TRIVIUM
AND THE SCIENCES
E.J.
ASHWORTH
Paul of Venice on Obligations: The Sources for both the Logica and the Logica Parva Versions
on
Treatises
obligations
contribution
to
twelfth
late
insolubles.
but
century;
1
part
with
along
logic
consequences, and
formed
most
work presented the theory
the stage for
all
supposition
go back as early
theory,
far as the
treatise
was the
of Walter Burley, which dates from around
Tractatus de Obligationibus 1302. This
may
important
medieval
specifically
on
treatises
Their history
the
the
of
Magna
in a fully
subsequent discussion. For
my
developed form, and
set
purposes, the next leading
figure was Roger Swyneshed, who probably wrote between 1330 and 1335, and who held controversial views about the treatment of conjunctions and
His
disjunctions.
were
doctrines
Martinus Anglicus, 2
Robert
in a favourable light by and Richard Lavenham, 3 but were
presented
Fland
otherwise generally rejected. Richard Billingham,
who became
a fellow of
Merton College, Oxford, in 1344, wrote a text on obligations which formed part of the Logica Oxoniensis, a loose collection of logic treatises which was popular in the fifteenth century, and which was printed in 4
Another Englishman, Ralph Strode, who was a fellow of Merton 1359-1360, wrote a treatise which was especially popular
England as
late as 1530.
For general Obligations: A. History
discussion
of
and further references, see E. Stump, obligations to the early fourteenth century in The Cambridge edited by N. Kretzmann, A. Kenny and J. Pinborg
From the beginning of Later Medical Philosophy,
(Cambridge
Cambridge University Press, 1982), pp. 315-334; and Developments in the fourteenth century ibid., pp. 335-341.
etc.:
Obligations: B.
P.V.
Spade,
,
See E.J. Ashworth, after English Obligationes Texts Roger Swyneshed: The Tracts beginning "Obligatio est quaedam in The Rise of British Logic, edited by P. Osmund Lewry, O.P. (Toronto: Pontifical Institute of Mediaeval Studies, 1985), pp.311-312. ars"
See Spade, op.cit., pp.334-338. Martinus Anglicus and Robert Fland.
There
4
are
some
striking
similarities
between
For Billingham s Ars Obligatoria and the subsequent manuscript tradition, see For the Logica Oxoniensis, see L.M. de Rijk, Ashworth, English Obligationes Texts Logica Oxoniensis: An Attempt to Reconstruct a Fifteenth Century Oxford Manual of Logic Medioevo 3 (1977), pp.121-164; and E.J. Ashworth, The "Libelli Sophistarum" and the Use of Medieval Logic Texts at Oxford and Cambridge in the Early Sixteenth Century Vivarium 17 (1979), pp.134-158. .
,
,
Ashworth
408 5
in
At
Italy.
Paris,
we
Albert
find
6
of
Saxony,
whose discussion of
was
Logica particularly influential for the 7 1360 treatise of the Dutchman William Buser. In turn, Buser s treatise in
obligations
his
Perutilis
8
was heavily used in the treatise by his pupil, Marsilius of Inghen. Two Italian authors must also be mentioned. Peter of Candia, later Pope Alexander V, wrote an obligations treatise perhaps between 1370 and 1380
9
Peter of Mantua, writing between 1384 and 1392, included a long
.
on obligations
section
Logical This
his
in
the background
is
against
which Paul of Venice must be considered.
Four independent
logic treatises
have been attributed to Paul: the
12
the Quadratura; and the Sophismata Logica Parva-^ the Logica Magna; Aurea. The first two are general texts, each of which contains a section
on obligations. There but
I
shall not consider
some
also
is
it
here.
13
relevant material in the Quadratura,
Francesco Bottin has given reasons for
dating the Logica Parva 1395-96 and for dating the Logica
am
I
edition
presently preparing an edition of this text of the rest of Strode s Logica. References in
Obligationcs, in Consequentie Strodi ^
Albert
of
Olms, 1974),
Saxony, va
fol.46
Perutilis
-fol.51
etc.
in
(Venice,
.are
-fol.93
(Venetiis, 1517), fol.78
Logica
paper
to
1397-
Maieru
s
Ralph Strode,
.
Hildesheim,
1522;
A.
with
conjunction
this
Magna
New
York:
Georg
.
ra
7
For have used Oxford, Bodleian Library MS Canon.Class.Lat. 278, fol.72 -fol.78 discussion of Buser, see C.H. Kneepkens, The Mysterious Buser Again: William Buser of Heusden and the Obligationes Tract Ob Rogatum in English Logic in Italy in the 14th and 15th Centuries, edited by A. Maieru (Napoli: Bibliopolis, 1982), pp.147-166. I
.
r
8 I
r
MS 2602, fol.70 -fol.!01 MS Canon.Class.Lat. 278,
have used Cracow, Biblioteka Jagielloriska
.
vb ra For fo!.65 -fol.69 have used Oxford, Bodleian Library the date, I have used Green-Pedersen s conjecture about the date of Peter of Candia s
9
I
Consequentiae: see N.J. Green-Pedersen, The Rise of British Logic, p.307.
Early
British
Treatises
.
on Consequences
G
G
in
viii For ii I have used Peter of Mantua, Logica (Venice, 1492), sig. -sig. the dating of his logical works, see T.E. James, Peter Alboini of Mantua: PhilosopherHumanist Journal of the History of Philosophy 12 (1974), pp.161-170. .
,
Venetus, Logica (Venice, 1472; Hildesheim, New York: Georg Olms, For a translation of this edition, see A.R. Perreiah, Paulus Venetus. Logica Parva (Miinchen, Wien: Philosophia Verlag, 1984). I shall use the citation LP, with page references to the 1472 edition. These references are included in Perreiah s translation. Paulus
1970).
Paulus Venetus, Logica Magna (Venetiis, 1499); E.J. Ashworth, editor and translator, Venice. Logica Magna. Pan II. Fascicule 8. Tractatus de Obligationibus (printed
Paul of
Academy by the Oxford University Press, 1988). I shall use the citation with folio references to the 1499 edition. These references are included in my edition.
for the British
LM,
Paulus
Dubium
Venetus,
Quadratura
tertium, cap.6, cap.23, cap.29.
(Venetiis,
1493):
see
Dubium
secundum,
cap.ll;
Paul of Venice on Obligations 98.
14
409
is some controversy about the relationship between has even been asked whether Paul was the author of
However, there
these works; and both.
15
it
In this paper
the Logica
the Logica
on
treatise
Magna
light of what
shall first give a brief survey of the sources for
I
obligations;
have discovered, there
I
Magna and
is
and
shall then argue that, in reason to attribute both good I
same
the Logica Parva tracts on obligations to the
author.
The
first
thing to notice about the Logica
Magna
is
that despite
its
heavy dependence on other sources, it is an integrated and interesting work. It contains useful clarification of such matters as the frequent
function
of
in
ordering
16
obligational
abundance of new sophisms. For sophisms for positio seem to appear completely new
obligatio
instance, in
and
with
a
in
statement,
respondent, or a preface to
the
or
literature.
an
there
of
twenty-seven
no other source. 18
Instead or
action,
an
an
is
the
sixty
There are two
innovations. First, Paul offers a definition of
doctrinal
seems
disputations;
which
obligatio
of
of binding
act
an
identifying
some statement showing how
the
should be
it
he preferred to define an obligatio as a relation which arose when the opponent s positum was admitted by the respondent. Second, treated,
Paul
offers
suppositio,
a
somewhat novel
positio,
and
division
tripartite I
depositio.
of
obligationes
somewhat
say
novel
,
F. Bottin, Logica e filosofia naturale nelle opere di Paolo Veneto Filosofia all Universita di Padova nel Quattrocento, edited by A. Poppi alia Storia dell Universita di Padova 15. Trieste: Lint, 1983), pp.87-93.
e
into
because
in
Scienza
(Contributi
See F. del Punta and M.M. Adams, edition and translation, Paul of Venice. Logica Magna. Part II. Fascicule 6. Tractatus de Veritate et Falsitate Propositionis et Tractatus de Significato Propositionis (Published for the British Academy by the Oxford University Press, 1978), p.xiii: ...while the common authorship of the Logica Magna, the Logica Parva, the Sophismata, and the Quadratura is highly probable, it has not been proved with certainty.... We have found that the teachings of the Logica Parva are in any event often inconsistent with those of the Logica Magna. Perreiah, op.cit., pp.327-343, gives the strong impression that he doubts common authorship of the
Logica Parva and the Logica Magna.
For some discussion see in
Obligational Disputations: pp. 175-193.
E.J.
Some
Ashworth, The Problems of Relevance and Order Late Fourteenth Century Views Medioevo 1 (1981), ,
ra
17
These sophisms are found LM fol.l81 -fol.l89 the fourth sophism directed against the second rule), 4.6,
4.7,
4.8,
5.2,
supplementary sophism), 18
19
6.2,
6.1,
6.3,
8.1,
12.1, 12.2, 12.4.
LM foUTT*"^. LM fol.!78va -fol.l79 ra
.
8.3,
vt>
9.3,
The new sophisms
.
3.1,
9.4,
3.2,
9.5,
3.4,
10.3,
3.5,
3.7,
10.4,
are:
2.4
(i.e.
4.2,
4.3,
4.4,
10.4A
(i.e.
a
Ashworth
410
references
Mantua;
to
20
casus in Burley and
make
found
are
suppositio
Ockham.
21
Nor
the as
situation
The main
true.
to
agreed
respondent
background of assumed
fact.
is
links with that of
accept
a
set
to
obligatio in
of
description
would then be
obligatio
was
a category of which Paul
it
was a kind of preliminary
real use. Briefly, suppositio
which
Billingham, Strode and Peter of
in
and because the notion seems to have close
the
initial
against
this
22 However, Paul himself wrote:
In what follows, I shall not discuss the first species of obligatio, unless perhaps accidentally in the context of a positio or depositio, nor are since it is not a sentence used to test logical skills <
>,
misleading disputations produced through the Logica
In
Magna Paul combines
it.
discussion with long
original
paraphrases or even straightforward quotations from earlier sources, a technique which doubtless enabled him to produce a work so enormously 23
However,
long.
is
certainty
the
Albert of Saxony.
24
Burley and Swyneshcd
figures as
To some
extent the situation
source
direct
earliest
can
with
establish
the material which relates to such
All
also found in Albert, Buser or Strode.
is
the
is
one
same with
respect to Billingham and
the Logica Oxoniensis, but here there are a few places in which Paul uses 25 examples found only in some version of the Logica Oxoniensis. William Buser is an important source, especially for the discussion of
rules or
26
sophisms; 20
G
suppositio
Library
MS
is
Ralph Strode. This
Billingham, Ars faObligatoria, Salamanca University v Strode has the word suppono op.cit., sig.
Richard
of Mantua,
word
but the most important overall
appears
Canon. misc.219,
.
in
at
one
least
fol.37
of
the
v
MS ,
1735,
foLg9
op.cit.,
fol.78
see
Oxford,
manuscripts:
is
,
so
Peter
;
but the Bodleian
.
21
For Burley, see Stump, op.cit., p.322. Tor Ockham, see William Ockham, Summa I. St. Bonaventure, Logicae, edited by P. Boehner, G. Gal, S. Brown (Opera Philosophica N.Y.: Franciscan Institute, 1974), pp.735-736. ra 22 This is my translation of LM, fol.!79 .
For 24 II.
25
Cf.
full details,
Punta
Del
Fascicule
I
refer the reader to s
notes on
my
forthcoming edition: see note
sources
the
for
12.
Paul of Venice. Logica Magna.
Part
6.
V
is found in ) Oxford, in examples on LM fol.lgl in fol.22 of two relation to the third rule for dissimilars are reminiscent ibid., sophisms
For
instance,
the
Library
MS
Bodleian
tenth
rule
Lat.misc.e
for
79,
depositio r
fol.23
;
(LM
and
fol.!91
the
.
26
Given
the
similarities
between
Buser
and
Marsilius
of
Inghen,
one
might
Kneepkens offers reasons for thinking that Paul followed Buser: Kneepkens, op.cit., pp. 161-164. Kneepkens view is borne out by my own observations. For instance, Paul nowhere mentions Marsilius characteristic division of obligatio into positio, depositio, and dubie positio; and in at least one place where Marsilius and Buser offer different solutions to a sophism, it is Buser whom Paul
wonder whether Paul had used
Marsilius.
Paul of Venice on Obligations with
not
respect
Of
themselves.
the thirty-three sophisms for positio
the
to
sophisms I have
whose sources
and of these, eight are found only
traced, nineteen are found in Strode, 27
but
discussion
theoretical
to
only
41 1
Of five sophisms for both Peter and Paul, Peter provides the only source I know for three. 28 Moreover, of Paul s twelve rules for depositio, all but in
Strode.
Peter of Candia was another source.
positio found
in
two are found
29
Paul has largely adopted of the and and three rules, Paul s rules seven, wording examples; eight and nine, are unique to Peter of Candia. Finally, there is Peter of Mantua. He was not a strong influence; but there are various passages in Peter
Peter of Candia.
explicitly in
s
which Paul seems to be drawing on his text. 30 Let us now turn to the Logica Parva. At obvious feature of the Logica Parva
Like
Oxoniensis.
the
on various
treatises
31
Parva and
Oxoniensis,
in the
loose
a
is
it
was
as
32
collection
of
particularly striking, at least with
is
In the Logica Oxoniensis the standard
follows:
1.
Introductory
definitions of key terms. 2. Rules for positio. 3.
Sophisms and rules Interchangeable
for
for
6.
conjunctions
and
including
for positio. 4.
Sophisms and disjunctions.
5.
and dissimilar propositions. 7. Paul of Venice omits the section on
Similar
for depositio.
disjunctions,
outline exactly. This does not
section,
conjunctions
posited
propositions.
Sophisms and rules posited
most
in
Logica Oxoniensis
contents
of
the
logical topics,
summulae
respect to the table of contents. list
blush,
and like the Logica Oxoniensis it opens which terms, propositions and syllogisms are The resemblance between the obligations tracts in the Logica
with a brief discussed.
Logica
first
close relationship to the Logica
its
is
but
he
otherwise
mean, however,
follows
this
that the contents of each
section are the same. In fact, there are considerable differences.
The
first
difference concerns the introduction. Paul has substituted
Albert of Saxony
follows: see
27 28 o O zv
The
The
LM
LM
definition of
s
obligatio
ra
fol.l90
Marsilius, op.cit., fol.94 in
Strode are
Peter of Candia,
in
Billingham
1 ;
2.2, 2.3, 3.3,
three found only in Peter of Candia are v3 -vfl ;
found
r ;
eight found only
fol.191
for that
Buser,
3.5A, 5.3, 10.1, 10.2,
3.6, 5.4,
op.cit., fol.69
op.cit., fol.77
and
*.
and
12.3.
9.2.
ra -vh .
LM
For instance, foi.178 draws on Peter of Mantua, op.cit., sig. the distinction between concedenda participialiter and concedenda nominaliter
.
31
LPpp.[l]-[30].
32
For some reason
I
denied
this in
English Obligationes Texts
,
p.317.
G
ii
for
Ashworth
412
and the Logica Oxoniensis. Moreover, unlike Billingham, who mentioned both impositio and suppositio, but like all the other versions of the Logica Oxoniensis, Paul gives just two kinds of obligatio, namely positio and depositio. In both these respects the Logica Parva is unlike the Logica Magna where, as I have already pointed out, we find a completely
new
and where suppositio as a type of obligatio is Alan Perreiah finds these differences length.
definition of obligatio,
discussed
some
at 34
significant,
but
mere
six lines,
such
relatively
do
I
and
not.
this
The Logica Parva
marginal
notions
as
is
very brief, a
Furthermore,
suppositio.
Magna was written
believe, the Logica
introduction
alone would preclude the paying of attention to
after the
why Paul should not have changed his mind about appropriate way of defining obligatio. Instead of continuing Albert of Saxony, he developed his own view of the matter. reason
When one
as
if,
Logica Parva, there the to
is
I
no
most follow
turns to the sets of rules and sophisms, one again finds
between the Logica Parva and the Logica Oxoniensis On considerable, though I shall not pause to demonstrate this here. Parva and the the between the the other hand, Logica Logica relationship that the difference is
Magna
is
basis of his
very close.
This relationship was noted by Perreiah, on the
comparison of the rules.
He
wrote:
The treatment
of obligations in the two works thus reveals a close Apart from the initial definition and typology of obligations which are markedly different in the two works, the rules of obligation including the examples used to illustrate them are strikingly close. Because the Logica Parva expressions are normally simpler and briefer and because of a reduction of the number of to rules in several groups, the Logica Parva account would appear derive either from the Logica Magna treatment or more likely from a source which both works nave in common. kinship.
I
have two points to make about Perreiah s claims. First, if Bottin is Magna is later than the Logica Parva and there is hence
right, the Logica
no question of the former serving
as
source for the
latter.
Second, an
Magna and the Logica be absurd to explain by
investigation of the sources for both the Logica
Parva 33
reveals
a
Albert of Saxony,
situation
op.cit.,
which
^1.46^; LP
it
would
p.[118].
Perreiah, op.cit., pp.340-341.
The
material
relevant
Obligationes Texts
.
36 Perreiah, op.cit., p.343.
for
making
a
comparison
is
found
in
Ashworth,
English
Paul of Venice on Obligations
413
some as yet unknown intermediate source. mean by looking at each section of the Logica Parva
I
postulating
what
I
there are the rules for positio.
First,
are nine; in the Logica
Magna
31
shall
illustrate
in turn.
In the Logica Parva there
there are twelve. Rules three and five of
the Logica
Magna
are both included in rule three of the Logica Parva and
rules four
and
of the Logica
six
Magna
are both included in rule four of
the Logica Parva. Rule ten of the Logica
Magna appears
as a corollary to
rule seven of the Logica Parva. However, the ordering of the rules is otherwise exactly the same. This is significant, because I know of no
other source with just that ordering.
38
Moreover, rule one
to the effect that every possible proposition should
normally put forward as a
though
it
both works,
be admitted, was not
was a generally acknowledged
and rule
ten, the corollary to rule seven in the 39 not a standard rule either. It comes from Ralph Strode.
principle;
was
rule,
in
Logica Parva,
Second, there are the sophisms for positio. There are just ten of these
in
the
40
Nine of the ten are found
Magna.
Logica Parva,
as
compared in the
to
the
of the Logica
sixty
Logica Magna.
Of
these nine,
three are popular sophisms found in most sources; three are found
Strode and is
most one other source; one
at
closely related to a sophism of Strode
s;
is
found
and one
in
Strode alone; one
is
only in the Logica
Magna. The remaining sophism is very close to one found Candia, another of the known sources for the Logica Magna. Third, there 37
is
ra
LM
fol.l79
in
the section on interchangeable propositions.
ra
-fol.!80
;
LP
is
Peter of
41
There
pp.
">0
Perreiah, op.cit., p.341, points out that the Logica Parva rules omit the phrase He believes this to be important, but I scitum esse tale infra tempus obligationis think it could be explained by the brevity of the text. In the Logica Magna s treatment .
of sophisms 39 Strode,
The
little
seems to hinge on the presence or absence of the phrase
op.cit.,
fol.VS^.
relations are as follows:
Sophism
1
(LP
p.[122])
is
of Mantua. Sophism 2 (LP p.[123]) (following Strode) Peter ra Candia, op.cit., fol.67 Sophism 3 (LP p.[124]) is
LM
.
Sophism 4 (LP
in question.
LM
and found
LM is
found in Strode and one in Peter of found in Strode alone.
1.1,
similar to
3.3,
a variety of sources. Sophism 5 7.1 and found in a variety of sources. Sophism 6 (LP p.[126]) is p.[125]) is 9.1 and is found in Albert of Saxony and Strode. Sophism 7 (LP p. [127]) is
LM
found found
in
p.[125])
is
4.1
in
Strode and the Logica Oxoniensis. Sophism 8 (LP p.[128])
LM
is
LM LM 11.1
(LP 8.2
and and
Sophism 9 (LP p.[128]) is LM 12.1 and is similar to a sophism in Strode. Sophism 10 (LP p.[129]) is LM 12.2. For full references, see my edition cited in note 12. In the case of sophism 3, Perreiah s punctuation (op.cit., pp.218-219) obscures the sense. It should read: I posit to you this proposition: "You run and You do not run is to be conceded by you". 41
in
LP
a variety of sources.
pp.[129]-[134].
Ashworth
414
is
Logica Magna, and the
in the
no such separate section
six rules
found
in Logica Parva are not in the Logica Magna. Nor do they feature in here a case have so we I that authors know, may any of the other which Paul included new material in the Logica Parva, only to change his in the
mind about
its
Be
value before he wrote the Logica Magna.
may, the bulk of the section on interchangeable propositions the discussion of one sophism, I posit to you: "There is a
human being
is
a
donkey
are
interchangeable".
is
that as
it
devoted to
God and A
This sophism
is
discussed
in three separate places in the Logica Magna, and the third discussion, which owes a great deal to the long and elaborate discussion found in
extremely long and elaborate, occupying one whole page in 42 the 1499 edition. My hunch is that Buser inspired Paul s interest in the is itself
Buser,
this interest in the
sophism, that Paul indulged
worked
The fully
more
through the material yet fourth section
discussed
is
fully in
on similars and
is
dissimilars.
also discussed in the Logica
the sophism mentioned previously,
it
Logica Parva, and that he
the Logica
Magna
Magna. 43
The one sophism
at length and,
like
44
The
derives from William Buser.
the Logica package of rules is the same in both the Logica Parva and in any of be found is to no such and neatly organized package Magna; the other sources that I know.
The
final section
is
on
45
Here the Logica Parva has
depositio.
five
where the Logica Magna has twelve. Of the Logica Magna rules, the first two appear as general principles rather than as rules in the sources. Rule three of the Logica Magna is rule one of the Logica Parva. Rules rules
four and ten of the Logica
Magna
are included in rule two of the Logica
Parva; rules five and six are included in rule three; and rules seven and nine in rule four. Most of rule twelve is captured by rule five of the in Logica Parva. Rule eight of the Logica Magna, which also appears of Peter of Candia, does not appear in the Logica Parva .^ Rule eleven
the Logica
Magna appears
a definition given after the rules in the
as
Logica Parva. Apart from the placing of the Logica twelve, the content and ordering is virtually the
LM foLlTB*;
1
1
foI.lSO"
*; fol.lSS va
LP
pp.[134]-[138];
44
LP
fol.76 pp.[134]-[135]; Buser, op.cit.,
45
46
fol.l90
Buser, rb
"*;
43
LM
same
-fol.!91
-fol.75
op.cit., fol.74
.
vb
ra
-fol.77
LM foLWl^-foUM*; LP pp.[138]-[142]. LM 01.191^; Peter of Candia, op.cit.,
;
LM
va fol.!90
"
.
rules ten
in
va
va
3
"
42
Magna
.
and
both cases.
Paul of Venice on Obligations
While
415
have already argued that Peter of Candia was the main source for the Logica Magna rules, he was not responsible for their ordering. I
depositio.
are
there
Finally,
One
four
sophisms
the Logica Parva
in
section
on
of these features in the Logica Oxoniensis but not in the
A
47
second is given a different wording in the Logica but the discussion, which largely derives from Peter of Candia, is
Magna
Logica
Magna
,
same. 48 The remaining two sophisms appear 49 Magna, and they both come from Strode. exactly the
To sum
up: the pattern of sources for the Logica Parva
of obligations
Magna
Logica
in
is
s
the
exactly
same
We
treatment.
as
the
pattern
the Logica
treatment
s
of sources
for
the
find Albert of Saxony, Buser, the Logica
The rules given are generally standard rules, but their organization is idiosyncratic, and common to both the Logica Magna and the Logica Parva. The sophisms in the Logica Oxoniensis, Strode and Peter of Candia.
Parva are nearly all found in the Logica Magna. Given these facts, I would be astounded to discover that the same man had not compiled both treatises. Whether similar conclusions can be drawn for other parts of the Logica Parva remains to be seen.
University of Waterloo
47
Antichristus
non
est
albus
Oxoniensis, see English restored to the text found there.
Logica 48
Tu
homo
es
est
homo
animal
:
vel
tu
49
Aliquae op.cit.,
fol.192
fol.89 ;
propositiones .
Tu
es
et
Antichristus
Romae
es
LM fol.191
vel
Obligationes
-fol.192
:
.
LP
Strode, op.cit., fol.89
.
tibi
,
p.326.
pp.[139]-[140];
Peter of Candia,
non sunt simul verae
omne
coloratus
est
Texts
depositum
:
est
LP
:
Tu
LP a
non
should be
Romae
es
va
op.cit., fol.69
For the
p.[140].
The word
vel
aliquis
.
ra
LM
p.[140]; te negandum
fol.192 :
LP
;
Strode,
p.[141];
LM
NAIDA ANNA BACCIN
Homerus
estpoeta:
un caso
di prcdicazionc
secundum accidens
Con del
distinzione tra predicazione
la
CLVOLL
verbo
il
passo
Kcttf
21 a 25-28
auTO De
ancor oggi un oggetto di complesse discussioni. Non voglio addentrarmi nel problcma
Kara
e
del
Interpretatione
dell interpretazione
costituisce
del testo
la traduzione boeziana, della quale si greco, ma mi limitero a proporne awalgono commentatori medievali: Verum autem dicere de aliquo et simpliciter, ut quendam hominem hominem aut quendam alburn hominem album; non semper autem, sed quando in adiecto quidem aliquid oppositorum inest quae consequitur sed falsum est, ut mortuum hominem contradictiq, non verum hominem dicere, quando autem non inest, verum. Vel etiam quando inest quidem semper non verum, quando vero non inest, non semper verum, ut Homerus est aliquid. ut poeta. ergo etiam est an non? secundum accidens enim praedicatur esse de poeto est, sed non secundum se, Homcro; quoniam praedicatur de Homero quoniam est. i
<enim>
Nella prima parte del capitolo undicesimo del De Interpretatione si sono delineate le condizioni d inferenza da un enunciate con predicazione disiunctim
da e si
al
corrispondenteco/im/icf/w: est
"Socrates
da
inferire:
L inferenza non
si
per esempio, da
dato infenire
coniunctim
1
Per
la
posteriore
a
pu6
est
inverso,
est
homo
albus".
tuttavia generalizzare, senza
"Socrates
est
bonus"
bonus
ossia
e da
"Socrates
veda
in
opportune est
restrizioni:
citharedus"
non e
citharedus".
d inferenza
quello
una disiunctim, presenta analoghe
difficolta si
albus"
"Socrates
"Socrates
caso
II
est
"Socrates
puo
homo"
CLVOLL degli usi di e particolare: S. Knuuttila in
da
una
restrizioni.
predicazione L inferenza
e nella tradizione filosofica Hintikka, The Logic of Being, Reidel:
Aristotele J.
Dordrecht 1986. 2
Cfr.
A.M.S. Boetii Commentarii
Meiser, Lipsiae 1877, pp. 370, 373.
in
librum Aristotelis
ITepc Epfrnvet occ;,
II
ed.,
rec.
Un caso non e
una qualche forma
ci sia
quando
valida,
-
della predicazione
componenti
secundum accidens
di predicazione
oppositio
opposizione tra
di
le parti
-
adiecto
in
417
-
oppure quando passi da una predicazione
si parafrasando con una terminologia moderna con il verbo esse in accezione puramente copulativa -
sua accezione
alia
esistenziale.
testo
II
due
dunque
complesse come dall accezione
inferenza
(ossia
da
A
est
sua scia
sulla
B
A
ad
in
Nel
est).
di
et C,
De
De
del
ossia
esse
A
ergo
est
convinzioni
da
inferenza
A
et
est C, e
sua forma esistenziale
alia
Sophisticis Elenchis*
nuovo accomunati e
i
due schemi
classificati
come
4
tende
si
Interpretation
1
B
accomuna
-
nostre
le
differenti:
B
di
tardo-antica
dall esegesi
undicesimo
est
secundum quid et simpliciter.
casi $\ fallacia
Fin
A
medievale
esegesi
secondo
che,
copulativa
d inferenza vengono
validi
1
sostanzialmente
appaiono
predicazioni
non
e
d inferenza,
tipi
semantiche,
1
-
greco
alia
connettere
a
il
secundum
fallacia
passo et
quid
simpliciter degli Elenchi, secondo una linea, che tende a sviluppare una
tradizione
comune
Nel medioevo da
due opere.5
alle I
esempio
"Homerus est
spiega con la contaminazione tra
Ci6 forse
si
forniti nel
De
"Quod
non
poeta"
che e ricondotto a
"Homerus est in opinione",
est, est opinabile,
di "Homerus est
ergo
i
est poeta,
"Homerus
Interpretatione:
6
In ogni
est".
viene a volte sostituito
"Homerus est opinabilis".
due seguenti esempi, ergo
modo
una maggiore uniformita nella trattazione dei due valida o fallacia secundum quid. Sembra infatti che
in
entrambi
natura della determinazione, che funge da predicato
o
da
*
predicato
De Sophisticis Elenchis Occam
c.5,
("est
homo
mortuus"),
a
e
("est
i
ad
non
di inferenza
tipi
la
parte
est"
trasformazione
in "Homerus est in opinione/opinabilis" porta
poeta"
del
Homerus la
casi sia
opinabilis")
condizionare
la
167a sgg.
la necessita di precisare che la fallacia secundum quid et due modi: un modo, per cui si passa da est tertium adiacens ad est secundum adiacens; un secondo modo, per cui parte eiusdem extremi, vel a compositione sumpta cum determinatione, arguitur ab aliquo sumpto cum addito ad ipsummet sumptum sine addito". (Si veda: Guillelmi de Ockham, Expositio super libros Elenchorum in: Opera Philosophica et Theologica, III, ed. F. del Punta, St. Bonaventure
Tuttavia gia
simpliciter
si
sente
articola in
"a
University 1979, p. 54). 5
Cfr. S. Ebbesen, "The dead man is alive", Commentators and Commentaries on Aristotle s
in:
Synthese,
40 (1979),
Sophistici Elenchi,
v.L,
p. 43 e idem, Leiden 1981, p.
171. 1
L esempio
di
inferenza
dato talvolta nella versione:
non
valida
"Chimera
"Quod
non
est opinabilis,
ergo
est, est".
est
opinabile,
ergo
est"
viene
Baccin
418
era piuttosto
poeta"
ad
inferenze coniunctim-disitmctim
di
possibilita
1
in
(mentre
est
"Homerus
uso contestuale a decidcre del senso da annettere
est).
entrano in gioco nella spiegazione dei due tipi non di e diminuens di detenninatio d inferenza: quella quella
Due validi
nozioni
detrahens
determinatio
come
mortuus
dcterminazione
homo
alter!
"Socrates
(distraint]
mentre
il
L
distrahens.
comunemente,
piu
o,
fondamentale e che in espressioni
homo
est
come
mortuus",
la
termine
del
significato
idea
est
in
determinazione attenui (diminuit) o indebolisca il grado opinione", essere espresso dalla copula. Si ammette infatti che il verbo esse,
di
-
delerminato
,
in
espressioni
"Homerus
la
in
almeno presenza di certa determinazioni, pcrda importo esistenziale - e che di indebolito un a nel senso di esse extra grado designare passi -
1
essere, quale
A
comportino uniscono.
8
1
Se
accetta la
si
e
Vimpositio assai
irripetibile
problematico
cui
per
secolo,
("voces
acccttare
,
il
significato
per
che,
dei
dei
suis
csempio,
su
ossia
cui
termini,
diffusa nella
non cadunt a
-
poiche pare che esse
significato
comunemente
tesi,
9
tredicesimo
del
distrahentes
-
adiccto
in
sostanziale
alterazionc
e soprattutto dalle quaestiones,
determinazioni
sulle
focalizzata
e
tuttavia,
che implicano un oppositio
quelle
del
commenti
giudicare dai
attenzione
1
essere mcntale, quello immaginato e cosi via.
1
si
seconda meta
termini
6
fisso
significatis"),
e
diventa
neU espressione
homo
- manca - "Homerus est una predicazione, che rimandi poeta" esempio originate mentale o che esprima una qualchc no/.ione di modalita, e dunque li si di Boezio, secondo cui cio di cui si asserisce prcferisce mantencre la spiegazione cssere non e quanto e designate dal soggctto, ma dal predicate poeta). In altri commenti c e una netta distinzione tra il caso di oppositio in adiecto e quello di classificati come casi di predicazione predicazione accidentale, poiche entrambi vcngono con una nozione diminuens: come opinibalis diminuisce il senso di est in "Chimera est cosi fa mortuus nei riguardi di homo o pictus rispetto ad homo o ad animal opinabilis", Tractatus Called Afterwards Summule Logicales, ed. L.M. de Rijk, Petrus
Ncll
al
piano
1
Hispanus,
(cfr.
Assen 1972,
p. 158.
1
S.
9
Ebbesen,
Cfr.
History
J.
"The
dead man
Pinborg,
of
is
alive",
op.
cit.,
pp. 43-7.
Problems of Semantic Representation in Medieval Logic", in H. Parrel, Thought and Contemporary Linguistics a cura di
"Some
Linguistic
Berlino-New York 1976. Idem, Ebbesen,
"The
contributions in
a
English
"The
to
sophisma"
dead the in:
contribution man",
cit.;
discussion
the
to
H.A.G.
on univocal
Medieval Semantics and
Logic",
Synthese
Braakhuis,
40
"Kilwardby
(1979),
versus
pp.
Bacon?
19^2;
The
of being and non-being found de Metaphysics. Studies Dedicated to L.M.
signification
et Niimega, 1985; A. de Libera, "Roger Bacon and Semantics from the End of the 12th Century to the time of Ockham and Burleigh. Acts of the 4th European 1981. Symposium on Mediaeval Logic and Semantics, a cura di Braakhuis, Niimega
Rijk, a cura di Bos, Artistarium Suppl. 2,
le
probleme de Tappellatio
univoca",
in:
English Logic
Un caso mortuus
vivum
-
congiunzione con
in
sccundum accidens
perda
mantenere una
nell impossibilita di di esse
homo
termine
il
di predicazione
suo
il
419
originario
significato,
delle sue proprieta essenziali
la
-
quella
determinazione mortuum.
Se dunque si condivide la tesi della fissita del significato, occorre individuare un interpretazione semantica, capace di render conto di cio che awiene in espressioni come homo mortuus ed anche, in diversa misura, di cio che determina
come
est
"Homerus
Tra
opinione".
i
sostenitori
della
tesi
"radicale"
trovano alcuni esponenti di quella che permanenza in particolare Pietro d Alvernia e ha chiamato modista: Pinborg logica del significato
della J.
in
accezione indebolita di esse in espressioni,
1
Simone
di
si
Faversham.
mi occupero delPargomento relativamente ad alcune di Pietro d Alvernia; ricorrero anche ad un questioni In Perihermeneias In questa sede
passo, tratto dal
commento
di
Tommaso
Erfurt In Perihermeneias
di
Infme attraverso alcune delle argomentazioni
1
a
individuare
potra
di
esigenza
secondo
il
linee
larghe le
garantire
modello degli Analitici
una nuova
si
semantiche
e
scelte
Posteriori.
secundum quid o con oppositio
in adiecto
riflessione sulla teoria del singificato?
e che considerare
fatto
le
e plausibile chiedersi: perche la presenza nel linguaggio di
Ordunque
II
tra
da Rodolfo Brito 12
condizioni fondamentali del sapere scientifico,
predicazioni con determinazioni esige
nesso
il
tratte
n .
sostanzialemente
differente in
significato di
il
un termine quale homo
un espressione come
"x
est
homo
mortuus"
da quello in espressioni del tipo est homo" equivale ad ammettere che un cambiamento contestuale - quale la presenza della determinazione mortuum - o un mutamento di referenza - nel caso di est homo "x
"x
variabile
la
mortuus"
come
x
varia su
un dominio
di
enti
-
nel passato
non
solo, aspetta, possano cambiare le condizioni di verita, ma la stessa struttura semantica dei termini. Cio viola la tesi della fissita del ci
si
significato dei termini
nozioni di
tempo o
ed anche quella della
di modalita,
totale indifferenza dei
come insegna
il
nomi a
secondo capitolo del De
Interpretatione^
Si sono esaminati il Ms. F = Firenze, Ms. P = Paris BN lat. 16170.
11
12
Ms. L = Ms.
UB Leipzig
Vat. lat.
Cfr.
communi
distribuat
Ms.
B
Laur. S.Croce Plut. XII Sin.3 e
il
1356.
2141 e Ms. Vat.
Pietro
il
d Alvernia,
lat.
3061.
"Utrum quaestio signum universale additum ipsum pro suppositis presentibus, preteritis et futuris" (Ms.
terminis F,
f.lOrb
Baccin
420
Una
soluzione praticabilc potrcbbc consistere ncl mantencre
dell immutabilita
del
termini
significato,
delle
e
della suppositio
ratione
essendi.
logica
terministica
a
sviluppando,
loro
mezzi della
ai
una
volta,
di
logica
tipo dalla
costituita
appunto portante connotazione dei termini e non dalla loro funzione denotativa. intensionale,
Cio comporta che certe
espressioni,
verbo esse vada cercata
La nozione, termini
cui
piano dei
si
fa
-
analoghi:
tanto
di
I
ed
i
che cio che
pictus
prius-posterius e
&3\Vimpositio
est similis
-
rientra,
di
una
est
mortuus":
est
gia
(Homo termine
il
significati
secondari sussiste sempre una
mette
quondam
attributionern): nel caso
una relazione
in
di
continuita
fuit
materia
homini
sulla
la
"
La relazione
hominis".
tra
pura somiglianza pittorica
vero").
conta,
piu
cosi
dire,
nel
tale
relazione
"programma
un opportuna determinazione o nell atto
inscritta
quod terminus communis
la
e
fissata
del
semantico" -
nel caso del
funzione significativa,
dell imposizione,
substantialis
sicut
homo
che
in
non
ratione
nullum".
"Die Logik der Modistae", Studio Meditwistyczne, 16 (1975), pp.39-97; idem, Problems of Semantic Representation in Medieval Logic", cit., pp.263-4.
Pietro d Alvernia, q. Si sequatur: Sor f.lOva 20-1.
a
analoghi sono regolati secondo una relazione
per
di
uniti
secondario
significalo ("Homo
un opportune contesto modifica
regola,
"Intelligendum
sua tempus includit
vivus);
un
a
mentre
vivus che a quello di cadaver).
che
cio
e,
La presenza
verbo esserc
rimandano
homo
fonda invece
si
significati dei termini
secondo
un
di
tipi
verbo esse) vanno
il
infatti
homo
a
del
dei referenti.
analogia. Alcuni
vivo con quella di cadaverc sia la materia:
quod
pictus,
termine.
essi
se,
ad
concetto di
al
enim de cadavere quod
homo ed homo
55-6):
per
somiglianza (secundum
homo sembra nozione di uomo di
("Homo
non
di
"aberrante"
occorrenze
certe
di
di
quella
cadaver), oppure ad entrambi
qualche forma
di
di
presi
significato primario
dicitur
e
homo rimanda
homo rimanda il
significati e
ricorso
primario (es.: determinazioni rimandano
certe
Tra
predicativa,
sul
significato
mortuus
o
termini di sostanze corruttibili ed
i
(tutti
considerati
spiegazione del comportamento
la
funzione
in
de
diminutio
di
e
struttura
la tesi
tecnica
la
espressioni con
le
nozioni
sembrano rinunciare
modisti
i
14
cui
la
temiinonim
contenenti
comunque
Tuttavia
attraverso
nell analizzare
altre proprieties
o
distrahentes
c
est
homo
mortuus, ergo Sor
est
"Some
homo, Ms.
F,
Un caso dunque
implica
mutamento
il
sccundum accidens
di predicazionc
del
e
significato
421
reversibilita
la
dell impositio.
La nozione
di analogia
trattazione uniforme
adiecto
e
di
nell oppositio
il
in
di
tipo
adiecto
un
offre
altro vantaggio:
riconduce ad una
different! casi di predicazione
predicazione e
predicazioni
due
i
secundwn
chc
termine,
e
quid.
Cio
viene
con oppositio in nelle due
muta
che
interessato
dall analogia:
sempre un nome, che entra a comporre
il
predicate, ad essere analogo (homo), mentre nella predicazione accidentale
e analogo
il
verbo esse.
Occorre precisare che la soluzione, che si awale del criterio di come vedremo analogia, non e adottata da tutti i modisti: mentre alcuni nel caso di Rodolfo Brito
-
da quello esposto,
come
altri,
Paccolgono,
ma di
Sigieri
commento boeziano. 16 Tommaso
in
senso notevolmente diverse
Courtrai,
ripetono
il
vecchio
Erfurt riporta tanto la spiegazione
di
boeziana che quella fondata sull analogia e dell invenzione di quest ultima 17 attribuisce il merito ad Ammonio. Non e possibile in questa sede esaminare tutte le conseguenze di quest uso della nozione di analogia 1 ^;
mi limitero ad alcune considerazioni. verbo
esse,
del
usi
gli
ha
il
vantaggio
verbo;
di garantire
ambiti,
gli
per
interessata da nozioni di modalita di
seconda intenzione
II
modello analogico, applicato
una pur tenue forma
esempio,
in
("Chimera est
cui
la
di unita tra
predicazione
opinabilis")
("Homerus est in opinione")
al
e
o da termini
vengono esaminati
alia
luce dei significati secondari del verbo esse, che rappresentano, per cosi
che vuol dire che, per esempio, la di "Chimera est opinabilis, ergo Chimera non e dovuta alia netta separazione tra un uso puramente copulative ed uno esistenziale di gradi indeboliti
dire,
di
essere.
II
falsita
esse,
est"
ma
al
passaggio illegittimo da un grado forte d esistenza ad uno
debole.
Sigieri di Courtrai inserisce
comunque a qucsto proposito un rimando ad Ammonio. van Kortrijk, Commentator van Perihermeneias. Inleidende studie en tekstuitgave door C. Verhaak S.J. Verhandelingen von de koninklijke vlaamse academic voor wetenschappen, letteren en schone kunsten van Belgie. Klasse der Letteren. Cfr.
Zeger
Jaargang XXVI, 1964, n.52. Brussel 1964, p.143. 17
Ms.
18
L, f.26ra 80.
Va anche
nei testi del
Inoltre part. -
an.
detto che non dodicesimo secolo.
nelle
640b
si
tratta
di
un idea totalmente originale: era gia presente
opere biologiche di Aristotele (De gen. 726b 24, 734b 25, 735a 8; De 412b 14; ma anche: Meteor. IV, c.12 389b 31) si trovano alcuni passi
36,
del resto citati dai modisti
-
sull
equivocita dei termini di sostanze corruttibili.
Baccin
422
La
non
teoria
comunque
priva
di
di
esse,
che
viene
extra!
E
e
primario
significato
esse
dall espressione
in
re
ambiguita.
infatti
il
indicate
genericamente
suo importo
il
Qual e
csisten/.iale
(esse
in
oppure il suo riferimcnto ad essenze in atto? Alcuni passi della lettcratura modista sembrano attribuirc al significato primario di esse un
effectu}
csistcnziale.
importo
che
ritiene
il
ncll esscre
19
Tuttavia
significato
o
pcnsato
immaginato
contrapposizione
al significato
Pcrtanto
extra
Vesse
non
ma
secundum adiacens,
proposito della
fallacia
sia
(cs.:
ncl
csaurisi
dell analogia,
che
qucllo est
"Chimera 1
come
"Homcrus
in
est
esse
come
Tommaso
opinione,
in
cssere extramentale.
puro
chc
csistere
consistc
opinabilis"),
esistenziale
va intcso nclla sua contrapposizione
vicne confermata da un passo di
ipotesi
dottrina
la
esse
di
primario, chc dcsigna
puo
mcntali o fantastichc, tanto
L
sosticnc
chi
sccondario
essere di
o
entita
allc
dell essenza.
Erfurt,
che,
ergo Homerus
a
est",
afferma:
Omne ...
enim
Et ratio
verbum
"est"
effectu
et
quocumque In ogni
che
oppinione diminuit de ratione essendi absoluta subiecti est ista: quod secundum quod dicit Armonius hoc est terminus analocus, quia prius supponit pro esse in essentie el per consequens pro esse in anima et pro in
alia
modo
rinviare
1
le
secundum e
alio esse.
fa applicazione del concetto di analogia al verbo esse non tradizionali difficolta, che sussistono nel rapporto tra
tertium adiacens, alle
nuove nozioni
di significato
primario e
secondario del verbo esse. Notevoli pcrplessita affiorano anche nell applicazione dcWanalogia termini di sostanza corruttibile, di
mondo
sostanze fisiche del
significato,
different!
ma
anche
^ J.
Si
veda
Pinborg,
pp.260 sgg. 20
Ms.
21
la
distinzione
L espressione
ai
nomi
perche sussiste un etcrogeneita profonda tra termine homo annovera, per esempio, secondo suoi significati secondari, individui, che sono in
i
umane (homo
"Bezeichnung
i
sublunare verrebbero a possedere piu di un
potenza uomini, individui nel passato
sembianze
tutti
i
11
analogati.
Pietro d Alvernia, tra
come homo: non solo perche
21
pictus).
= (
cadaveri),
Ordunque,
ma
in
due accezioni di esse in effectu nella q. 56 In An.Pr. in der Logik des XIII. Jahrhunderts", Misc. Med., 8 (1971),
tra in
anche immagini e che modo, se non
ricorrc piu volte nella letteratura modista.
L, f.26rb 20-3.
Pietro d Alvernia, Ms. F, f.lOva 17-20.
Un caso puramentc equivoce statua?
si
di predicazione
sccundum accidens
di
puo parlarc
per un immagine o una
"uomo"
22
La quanto
scelta
di
di
tradurre
in
una
trovare
potrebbe
estensionale
problcmi di teoria del significato anche sua comoda interpretazione a livello
Alcuni tra
modisti non accettano
i
mantenendo
concetto
il
di
con
fmisce
terminonim,
proprieties
significato di aspetti difficilmente riconducibili
pur
conseguenze della
le
Uno
della logica terministica.
materiale (id
quod
della
permanenza
risulti
de
significatur),
proprio quello
sermonis
virtute
una semantica, che
ottiene
egli
di analogia.
nettamente due accezioni
significant,
Rodolfo Brito. Distinguendo nella (significatum ut significatum) ed uno
che uno dei concetti, che
pro
e,
agli sviluppi consueti
una continua reimposizione dei nomi, ma che dei supposita una condizione imprescindibile per la verita quindi naturale
radicale
tesi
ratio
necessita di
e
il
di questi e
un elemento formale
significatio
caricare
il
ad unita.
sviluppando una semantica per certi versi piu affine
Ed
423
Nella
q.
eius
primario
si
degli enunciati.
trova
a ridiscutere
Utrum terminus analogus 2^ Autore
significato
terminus analogus: una,
di
evita la
fa dell esistenza
1
stet
separa
come
nel caso di
termine ha piu significati, ma secondo una relazione di sanus, prius-posterius; la seconda e quella dei termini come homo, che hanno un in cui
solo
il
significato
e
che
impropriamente
sono
impiegati
per
designare
o semplici immagini. Questa seconda non e una vera e propria analogia, ma solo una certa forma di similitudo o di attributio, che viene delta analogia solo in senso lato e che non ne possiede le individui morti
caratteristiche.
permettere espressioni fare con
homo
con
"programmato"
linguistico,
il
una vaga idea
solo
di
linguistico
come homo
un
coincide
Pertanto
alPuso
homo
pictus o
deminutus.
Si
nell imposizione; il
si
somiglianza in re
termini
di
homo
Pietro
homo
come
mortuus, dove in verita
badi che questo
secondario
significato
che non intacca
impiegare
di
si
homo
in
ha a che
deminutus non d Alvernia,
tratta piuttosto del risultato di
significato di
puo
preso di per
se,
gia
un atto
ma
che
La regola sui termini analoghi pone qualche difficolta a Pietro d Alvernia. Nella q. Utrum sequatur est homo mortuus, ergo est homo (Ms. F, f.lOra 71-2) il magister accetta che ex usu auctorum un qualsiasi termine analogo, preso per se, rimandi solo al suo primo significato. Precisa tuttavia che cio non awiene de virtute sermonis: infatti secondo la natura del linguaggio un termine analogo pone tanto il suo significato primario che quello secondario. Parzialmente edita da Ebbesen,
"The
dead
man...",
pp.60-1.
424
Baccin
piega
a
espressione
1
designate
in
cui
di
cio,
passato
termine era
il
un esse secundum quid e non un esse simpliciter. L insistenza con cui PAutore ribadisce che un nome di sostanza
predicabile, ossia
puo essere usato
corruttibile la
solo equivoce per riferirsi agli individui
dopo
loro corruzione, evidenzia la sua convinzione che, al fine di confutare
semantica radicale, occorra ricondurre
la tesi
termini a quello che realmente sono: cui
in
luogo sofisma
dove
Sorte non existente,
due
intrecciano
si
fa
risalire
1
sit
quella
significative:
consueta
status
sullo
E
esistenti, poiche nel in
homo teoria
della
semantico all
tratta
si
Sortes est
vera:
II
del 25 ",
del
asserti
degli
autorita di Aristotele
idea della fondamentale equivocita dei
secundum Philosophum
Item,
non
nomi
riferiti
De animalibus si dice che: De animalibus, membrum mortuum
membrum, nisi equivoce, sicut diceret aliquis statuam regis hominem vel etiam ymaginem hominis esse hominem et non est
est
esse
equivoce.
Una
dottrina semantica, che leghi se
referenza,
e
primari
tematiche:
epistemologica
ad individui non piu
nisi
ista
presunti usi analogic! dei equivocita dei termini.
di
e
e sulla validita di alcune scicnze.
scientifici
egli
una
e
significato
che
questa
ripete
"Utrum,
casi
osservazione
i
secondari, al
ambiguita
da un lato
scientifico.
rischia
linguaggio: se
Infatti,
libera
si
e
tuttavia
non solo
nelle
il
dalla
scien/e
significato alia sussistenza della
proliferazione dei significati in
di
a
conferire
quello
una
ordinario,
biologiche
i
nomi
fondamentale
ma di
a
quello
sostanze
godono sempre di referenza, secondo quanto dice Aristotele, awiene per la scienza contenuta nel Meteorologica. In che modo
corruttibili
non
cosi
possono fare dunque asserzioni scicntifiche su fenomeni transeunti, come un eclissi, la pioggia o il tuono? 27 Nella q. Utrum rebus corruptis, corrumpatur scientia de rebus 2^ Rodolfo Brito si awale di una soluzione molto articolata, che nasce da si
presupposti gnoseologici
e
semantici ben
precisi.
usare nomi in completa assenza di referenza e
che
attraverso
Ci6
si
Radulphi 25
26
Ms.
i
phantasmata
supplisce
Ci6 che permette
la facolta della
all attualita
della
in
Vat. lat. 3061, f.44ra.
Ibidem, f.44ra, 35 sgg. Cfr. T.K. Scott,
"J.
Buridan on the Objects of Demonstrative
Science",
(1965), pp.666-7.
28
percezione:
nella questione Utrum sequatur homo mortuus, ergo homo, Quaestiones in artem veterem, ed. Venezia 1499, f.lSvb.
puo constatare
Briti
di
memoria,
Rodolfo Brito, Quaestiones In An. Po., Ms.
Vat. lat. 2141, f.205ra-206ra.
Speculum 40
Un caso condizione passato:
semantico
la
che
dell
di scienza;
A
cio
sul
corrisponde
elemento formale del
La duplice natura
425
awenuta una percezione
sia
esse.
nel
piano
dunque un sussistenza di un
significato:
rimane garantito almeno dalla
pluvia
significato formale.
modello
solo
habuerit
prius
permanenza
come
termine
e
indispensabile
dummodo
secundum accidens
di pre dicazione
un duplice
del significato permette
primo esige, accanto al significato formale, anche da una scienza qua scitur res esse et ex quibus
il
Pattualita dei referenti e
L altro
causis passiones sibi insunt.
formali
del
significato,
modello
si
costituisce sui soli element!
prescindendo dal problema della sussistenza
di
e la scienza qua scitur ex quibus causis res potest esse et ex
referenti:
29 Questa scienza studia le possunt inesse. condizioni del verificarsi dei fatti scientifici, senza presumerne 1 esistenza,
quibus causis passiones
ma si
sibi
richiede una condizione minimale d esistenza: che dei fenomeni studiati
modo da
dato un qualche caso nel passato, in
sia
nella
averne un immagine
memoria.
La
struttura
logico-grammaticale degli asserti
relativi
scientifici,
al
secondo modello, deve essere probabilmente espressa in forma implicitamente ipotetica e non categorica: sappiamo infatti che un asserto del tipo "Homo
est
sarebbe falso per Rodolfo Brito, se non esistesse piu
animal"
alcun uomo;
31
modificato in
"Si
est
homo, homo
est
animal",
esso risulta
invece sempre vero.
Quest interpretazione
Cum
dicitur:
ci
viene suggerita da un altro passo: se
que per
insunt de omni,
insunt,
quacumque
yerum
est,
sicut
differentia
temporis ponitur pro subiectum, ponitur etiam predicatum, sicut Philosophus exponit, si verum est cucere esse hominem, verum est dicere esse animal. Et si intelligendo:
pro
verum
est dicere mine esse hominem, verum est dicere nunc esse animal. Ista est sua intentio: pro quocumque tempore ponitur homo, ponitur et animal.
Pertanto un asserto generale su fenomeni transeunti, e sempre costituito nel
29 30
primo modello Ibidem, f.205rb 45-va
di scienza
da una proposizione, che
risulta essere
per
5.
Ibidem, f.205va 2-28:
"Dico
quod, corrupta
re,
non corrumpitur
scientia
de
re,
qua
scitur ex quibus et qualibus causis res potest esse et passiones sibi possunt inesse ... si res non sit, dummodo prius habuerit esse, potest esse scientia de ipsa, qua scitur ex quibus et qualibus causis possit esse."
Rodolfo Brito, Quaestiones "Sor
32
est
homo",
f.!89vb 13-5.
Ibidem, f.!98vb 22 sgg.
in
An. Po., Ms.
Vat.
lat.
2141, q.
Utrum
ista
sit
per
se:
Baccin
426
se,
ma non sempre
A
vera.
sempre
conclusione
ci
a
sottesa
semantica,
mentre ncl sccondo modello e
vera,
proposizione per se e
potrebbe chiedere quali sia la questo secondo modello di scienza.
senso
modo
riappaia
come
termini,
li
poiche
lato,
la
nozione
tonitms,
E
di analogia
eclipsis,
pluvia
mia
presa in
etc.,
ma
senza alcuna relazione a\Vesse actuate del fenomeno,
usati
struttura
si
convinzione che in qualche
da una
costituito
33
sono
solo
in
relazione alia loro possibilita d esscrc. Inoltre la condizione gnoseologica,
che rende possibile,
il
sapere scientifico su insiemi di oggetti, che non
siano sempre esistenti, e data dalla presenza dei phantasmata: e Rodolfo
anima
Brito osserva che Yesse in et
secundum
Detto
quid.
subiscono un ampliazione, possibili:
La
altrimcnti,
nel
i
stare per supposita
non
ma
attuali, 34
e questo e per Rodolfo Brito un uso analogice del linguaggio.
formale e materiale - della funzionc componenti dei termini rende comunque plausibile la teoria dei due
duplicita delle
significativa
modelli di scienza, anche se -
attuale dei referenti, pare libro
modo da
in
sempre un esse deminutum secondo modello termini
delle cose e
degli
Analytica di
"ipotetico";
universalita,
di
fatto
il
tipo di scienza, che
1
in osserva nza al capitolo iniziale del
postcriora
pero
presuppone
e
rispetto
privilegiato
quest ultimo
a
garantire
i
al
esistenza
secondo modello
caratteri
di
necessita e di onnitemporalita, che sono tipici del sapere
scientifico.
Universita
Una "Zur
"La
Sapienza"
di
Roma
J. Pinborg, posizione per certi versi affine e quclla di Boezio di Dacia: si veda 15 des Boethius de Dacia: ein Uberblick", Studio Mediewistyczne
Philosophic
,
(1974), pp.165-85. Cfr.
ratione cit.,
In
pro
pp.274-75.
Topica, suppositis
q.
6
Utrum
praesentibus,
terminus praeteritis
communis et
futuris,
distribuat in:
aequaliter
Pinborg,
et
unica
"Bezeichnung",
JOEL BIARD
Vcrbes
de
cognitifs ct appellation
la
forme
selon Albert de Saxe
Les Sophismata
de Saxe contiennent plusieurs sophismes, au
d Albert
demeurant classiques dans leur formulation, qui comprennent dans leur enonce le verbe savoir. De maniere generate, ces sophismes sont traites
la distinction
du sens compose
appel systematiquement pour resoudre
fait
la
grace a
troisieme
partie
du
recueil.
et
les
du sens
sophismes 20,
1
propositions modales, par exemple dans
II
n
1 .
32
Albert y
33 de
et
Bien evidemment, cette distinction
familiere a tous ses contemporains. Jean Buridan
Mais
divise
le
livre
est
evoque a propos des des Consequently
2 .
pour autant mise en rapport avec 1 etude des propositions comportant un verbe cognitif. Lorsqu il examine les problemes semantiques souleves par des verbes signifiant des actes de 1 esprit, Jean elle
est
pas
Buridan retrouve bien
n en
la division
du sens compose
et
du sens
divise,
pas principal moyen de resolution des difficultes; pour ce faire un concept forge a cet effet: Pappellation de raison. le
fait
il
mais
utilise
Curieusement pour quelqu un qui a etudie puis enseigne a Paris a Pepoque de Buridan, Albert n evoque pas cette notion, pourtant promise a un certain succes. En revanche, il fait un usage qui au premier abord peut paraitre curieux de
appellation de la
l
forme.
C est
pour tenter de
determiner ce qu il entend par cette expression, et pour preciser a travers comment Albert se situe par rapport a ses predecesseurs ou a ses eme contemporains que je voudrais etudier ici le sophisme 34 de la IH cela
Sortes patrem
partie:
On
suppose que
marche a quatre
Hoc
suum le
pattes.
credit esse
asinum.
pere de Socrate
Le sophisme
est revetu
d une peau d ane et
se prouve de la maniere suivante:
Sortes credit esse asinum, hoc est pater suus, ergo patrem
suum
Cf. J. Biard, Les sophismes du savoir. Albert de Saxe entre Jean Buridan et Guillaume Heytesbury, a paraitre dans Vivarium. Albert de Saxe, Sophismata, Paris, eme eme 1490, sophismes 33, 34 et 47 de la II partie, et sophismes 20, 32 et 33 de la
m
partie.
Cf.
Louvain
Jean -
Buridan,
Tractatus
Paris, 1976, pp. 56-57.
de consequents,
livre
II,
chapitre
2,
ed.
H.
Hubien,
Biard
428
asinum
csse
credit
3
L improbatio,
.
c est-a-dire
demonstration de
la
la
faussete de la proposition, procede quant a elle de la maniere suivante: Sortcs patrcm suum credit esse asinum, ergo Sortes credit quod pater
suus est asinus; hoc est falsum; la
faussete de
la
du consequent. Mais
faussete
refutee
est
Vimprobatio
infercrait le sens
le
a
grace
la
compose du sens
1
anteccdent resulterait de tenu
est
sophisme
pour
vrai,
et
d une consequence qui Dans son principe, le mode de
non-validite
divise.
resolution propose par Albert de Saxe est identique a celui
qu
il
a mis en
oeuvre pour les sophismes contenant le verbe savoir: il repose sur la these selon laquclle on ne peut pas systematiquement convertir 1 une en 1
une
autre
memes
les
comportant
sens
au
prise
proposition
mais
termes,
et
compose au
prise
sens
une
proposition
divise
longuement devcloppe par Guillaumc Heytesbury Un sophisme semblable est examine par Jean Buridan:
principe
.
esse asinum
accentue
Car
si
est
un
5 .
le
un ane, est
c est parce
voisine
de
c est-a-dirc
tu ne crois pas
est plus cxpeditive:
ctait
la
que -
vraie
que
celle
sais que tu n cs pas un ane. Mais la resolution differe. Tout d abord,
tu
elle
tu es
que
La probatio
ane.
Vimprobatio
que
credis te
paradoxe,
tu crois
voisins,
Tu
un peu differente qui En depit d une formulation le casus permet de rapprocher les deux sophismes. initiate
proposition initiale est
tu crois
que ton pere par
proposee
un ane parce
tu es
que
Albert.
les
sophismes paraissent sophisme doit etre nie, fausse, alors que chez Albert si
le
ce qui est une difference notable. Sans doute est-ce a
Vimprobatio tellc qu elle a etc ici formulee, immediate du savoir de soi et de sa propre nature humaine. Reste alors a refuter la probatio. En admettant le casus, on peut Pour quelle a conceder: aller patrem meum credo esse asinum
de
cause
1
evidence
reposant sur
1
de
intuition
jusqu raison? Jean
.
Buridan
reste
ici
asse/
elliptique:
quia
patrem
meum
meus credebam esse asinum, sed non secundum hanc propositionem Ainsi, contrairement a est asinus" scd secundum istam "Hoc est asinus". sens compose et du du distinction la a il ne fait aucunement appel "Pater
Albert,
sens divise, qui aurait pu etre 3 4
Albert de Saxe, Sophismata,
5
Guillaume
Jean Buridan, Sophismata, IV,
p. 73.
6
sign,
pertinente.
m
II
II
est vrai
Id., ibid., p. 81.
11,
ed.
qu
il
n explicite
vb.
Heytesbury, Tractalus de sensu composite P 2ra et f Bra. Sophismatibus, Venise, 1494, en part.
Cf.
cum
XXXIV,
ici
et
dn-iso,
Regule eiusdem
Th. K. Scott, Stuttgart -Bad Cannstatt, 1977,
Appellation de la forme selon Albert de Saxe
son
guere
raisonnement,
mais
de
suffit
il
429
dans son
celui-ci
replacer
contexte pour Peclairer.
Pour resoudre toute
la
serie
prend place, Jean Buridan juge nomme Pappellation de raison
de sophismes dans laquelle celui-ci de faire appel a ce qu il Cette derniere, resultant de la
necessaire .
presence de verbes comme comprendre, connaitre, savoir, ne doit etre prise en compte que si le terme suit un tel verbe. Selon la theorie
credo patrem le
proposition,
difference entre
la
buridanienne,
meum
patrem
esse asinum
vient
meum du
terme patrem n appelle pas
comme
individu est compris et signifie
fait
credo esse asinum
que dans
la
et
premiere
raison selon laquelle cet
la -
pour que la proposition soit vraie, il suffit done que je croie que ceci, de maniere indeterminee, est un ane - tandis que dans la seconde proposition, le terme appelle sa Par
raison.
la
s eclaire
la
que c etait un ane, non pas selon mais selon la proposition est un "ceci
Rien de parait bien
autre chose.
s
de
formulation buridanienne:
croyais ane"
pere
la
proposition
mon
"mon
pere, je
pere est un
ane".
ne se retrouve chez Albert de Saxe. Le sophisme 33 approcher de cette idee, mais il s y agit en verite de tout
tel
A
1
argumentation qui a ete presentee plus haut,
auteur
1
ajoute ceci: li a sequitur hoc verbum scit, appellat suam formam. Et ideo hec est falsa a Sortes scit esse idem ipsi a. Quando enim precedit hoc verbum scit, tune non appellat suam formam. Et ideo nee bene conceditur: Sortes a ipsi a scit esse idem
Quando enim
.
Puisque cette appellation de la forme vient de ce qu une expression suit un verbe intentionnel, on pourrait au premier abord faire Phypothese qu il s agit
d une reformulation de
alors attribuer a Albert
la
doctrine buridanienne. Mais
il
faudrait
un grossier contresens, revenant a confondre ce
que precisement Jean Buridan differencie, a savoir Pappellation d un terme - c est-a-dire le renvoi d un terme, dans une proposition, a pour sa forme Propter ista sophisma sciendum est quod ista verba huiusmodi, de quibus post dicemus, et participia et nomina inde descendentia [...] faciunt in terminis cum quibus construuntur quosdam modos speciales appellationum. [...] Talia verba faciunt terminos cum quibus construuntur appellare rationes secundum quas imposita sunt nomina ad significandum, et non solum res cognitas ad extra, sicut faciunt alia verba; a propos de cette notion, cf. J. Biard, Le cheval de Buridan. Logique et philosophic du langage dans analyse Cf.
id.,
intelligo
,
ibid.,
pp.
cognosce
,
73-74:
scio
et
1
d un verbe intentionnel, in Die Philosophic irn 14. und 15. Jahrhundert, in memoriam K. - ou Ton trouvera Michalski, O. Pluta, ed., Amsterdam, 1988, pp. 119-137 egalement des references a de nombreux articles anterieurs sur le meme sujet. 8
Albert de Saxe, Sophismata,
XXXIV,
sign. m.II. va.
Biard
430
ce qu -
et
connote, done
il
1
Bethune,
ne suppose pas selon le maitre de
pour quoi cependant
de raison qui seule
appellation les
9
signifie, et
caracterise,
verbes signifiant des actes de
1
il
On
esprit.
peut avancer une
hypothese differente. L exemple n est pas necessairement emprunte a Buridan, car il ne est pas propre et la formulation d Albert est un peu differente. revanche, on trouve une fois de plus
meme
le
lui
En
enonce chez Guillaume
mode de division et Heytesbury, parmi tuum credis esse Patrem de composition: asinum, igitur credis patrem les
tuum
esse asinum
sens
le
La
fait
de
1
appellations.
le
encore, Heytesbury se contente d opposer
ici
sens
divise.
II
done a expliquer
reste
1
usage
appcllation.
Perutilis
L
Mais
.
et
compose
qu Albert
10
exemples relevant du huitieme
un
comprend
logica
existence
d un
tel
sur
portant
chapitre
les
chapitre, dans un oeuvre a bien des logicac de Guillaume d Ockham, traduit
egards tres proche de la Summa la place prise par ce concept d appellation dans au milieu parisien, et 1 importance nouvelle qui
les
discussions propres
lui
a etc conferee par
Jean Buridan. Mais en ce qui concerne le contenu du chapitre, Albert s ecarte de son maitre. En vertu du vieil adage selon lequel le predicat appellation est presentee comme une propricte du appelle sa forme, 1
predicat.
Mais
il
ne
s agit
ni
de reduire immediatement
1
appellation a
une espece de la supposition (comme le faisait Guillaume d Ockham), ni de nommer appellation tout renvoi a des choses que le terme signifie et pour lesquelles il ne suppose pas (comme die/ Jean Buridan), ni a plus raison
forte
penser par
(comme
la le
c etait
le
cas
avec
Guillaume de Sherwood), de
commune. Que
renvoi a une forme
le
predicat appelle sa
simplement que dans la forme mentale ou vocale selon se trouve predique dans une proposition, il peut se un terme laquelle verifier, dans une autre proposition au present, du pronom demonstratif
forme
signifie
qui renvoie a ce pour quoi suppose si
dit,
animal
qu
il
est
un animal
en montrant un homme,
est le
vraie,
11
premiere
peux
dire
.
Autrement
ceci
predicat devant conserver la
M.
est
un
forme
par ex. Jean Buridan, Summulae dialecticac, IV (Tractatus de suppositionibus), V, E. Reina in Rivista critica di storia delta Filosofta, 1957, fasc. II III, p. 343.
&
Guillaume Heytesbury, Tractatus de sensu composito 11
je
la
a dans la proposition initiale.
Cf.
ed.
Phomme
de
le sujet
Cf. Albert
de Saxe,
Perutilis logica, Venise, 1522,
F
et diviso,
16rb.
F
3va.
Appellation de la forme selon Albert de Saxe
Ceci
tres
est
des
proche
ou
passages
Le
allusion a cette formule traditionnelle.
431
Ockham
Guillaume d
fait
evoque a trois reprises dans la Somme de logique. Le plus important de ces passages se trouve dans le chapitre 72 de la premiere partie. II vient a la d un
suite
developpement
contenant,
exemple,
par
a
qui
un
Venerabilis Inceptor
au
une
dans
que
precise
verbe
proposition
introduire
faut
il
passe,
1
une
terme suppose pour des choses qui existent ou que pour des choses qui ont existe. Mais, ajoute 1 auteur, cette distinction ne concerne que le terme qui est sujet et non pas celui qui est predicat distinction selon
le
puisque
d
le
A
12
appelle sa forme
predicat
.
occasion, Guillaume
cette
Ockham explique comment il comprend cette formule: Quod est sic intelligendum: non quod supponat
pro se vel pro
conceptu, sed quod per talem propositionem denotatur quod propositio in qua ipsummet praedicatum sub propria forma, hoc est ipsummet et non aliud, praedicatur de illo pro quo subiectum supponit fuit vera, si tails propositio sit de praeterito; vel quod erit vera si talis propositio sit de ruturo; vel quod sit possibilis si prima propositio sit de possibili... .
Apres avoir ecarte une hypothese selon laquelle 1 appellation de la forme serait le renvoi au terme lui-meme ou au concept (done la supposition
ou simple), Guillaume propose quelques elements d
materielle
En
premier
Autrement expliciter
le
lieu,
dans
dit,
cette
terme les
propositions
on
appellation,
bien que
chose,
si
terme
lui-meme,
morphologic du
la
et
signifiant.
sub
considere
Ton
que
va
explication.
forma. reformuler pour propria
trouver ce terme et non pas autre
doit
forme au
etre
doit
nous oriente chef
premier
En meme
ici
vers
du
ou
la
configuration
est indique
il
temps,
vers la materialitd
la
par
la
qu une
proposition dans laquelle ce terme est predique, sous cette forme propre,
de
ce
pour
quoi
proposition initiate 1
suppose le sujet, a ete est au passe; autrement
vraie, dit,
si
appellation de la forme par le predicat implique qu
sub propria forma, temporalites
ou
Sortes est albus modalites.
Par
-
et
verbe
le
si
Sortes il
fuit
fut vrai
de
la
albus, de dire,
pareillement pour les autres
consequent,
cette
formule
implique
egalement une relation semantique, qui se traduit comme c est souvent le cas par une predication, ainsi que le respect des temporalites, le privilege
donne
au
present
dans
la
formulation
predication/supposition se traduisant par 12
Cf.
Guillaume d Ockham,
13 Id., ibid., p.
216,
1.
61-68.
Summa logicae,
I,
de
la
relation
une indexation temporelle de
chap.72, p. 216.
de la
432
Biard
de
valcur
de
verite
la
DCS considerations semblables
proposition.
retrouvent dans les deux autres passages de allusion a
1
appellation de la forme par
le
Somme
la
se
de logique qui font
14
predicat
.
Tous ces elements sont bien ceux par Icsqucls Albert de Saxe explique appellation de la forme par le predicat dans son chapitre 1
lequel toutefois est 1
beaucoup plus complet sur
1
appellation que ne
1
etait
oeuvre ockhamiste.
Jean Buridan, le
lequel
il
evoque lui aussi enonce commun selon 15 sa forme Mais en depit de certaines
vrai,
appelle
predicat
convergences,
est
1
.
interpretation de cet adage
1
pas vrai au sens propre des mots
16
-
Si
le
dont
-
il
precise
qu
n
il
est
est quelque peu differente. II se propose d analyser les causes de verite de propositions comportant des termes appellatifs, qui signifient ou cosignifient des choses pour
lesquelles
ils
ne supposent pas.
terme en question
est
sujet,
il
chose, selon auteur, non seulement en appelle expression de relation au temps du verbe mais selon une disjonction de ce temps et du temps present. Par exemple, le blanc qu appelle le terme album lorsqu il sa
est
sujet
1
d une
1
au
proposition
futur,
peut
etre
signifie
comme
etant
presentemcnt ou dans un temps futur adjacent au suppot. On pcut ainsi considerer comme equivalente a album erit nigrum, la disjonction quod est vel erit album erit nigrum. Pour qu une proposition au futur soil il
vraie,
n est
pas requis que dans
futur
le
la
proposition
au present
simplement qu une certaine reduction au s Mais dans ce cas, present puisse operer. appellation doit disparaitre et le sujet doit etre transforme en terme non appellatif. II suffira en effet correspondante
soit vraie.
faut
II
1
qu
il
ait
etc vrai de dire
hoc
est
album, en montrant
proposition actuelle, qui a ce moment-la sera noir.
pour
le
predicat car celui-ci appellant
sa chose
II
le
sujet
de
la
en va diffdremment
en relation determinee
au temps du verbe de la proposition, il doit toujours, si Ton de telles transformations ou reductions, conserver la meme forme: opere 17 ... debet manere in propria forma quantum ad appellationes On et exclusive
.
retrouve ainsi Pambivalence de cette notion de
terme doit rester 14
16
17
le
meme
quant
Cf.
id., ibid., II,
Cf.
Jean Buridan, Sophismata, chap. IV,
Id., ibid., p. 64. Id., ibid., p. 63.
chap.
7, p.
a
la
materialite
271; et III-l, chap. 43, p. 473. p. 64.
forme
qui indique que le
du
signifiant,
mais
433
Appellation de la forme selon Albert de Saxe
comporte en meme temps une indeniable composante semantique puisque la forme est aussi Pobjet meme de appellation telle que 1 a definie Buridan. 1
De
la resulte
forme
1
interpretation que Buridan propose de
tout terme, des lors
realite
et ceci vaut
qu
le sujet;
egalement pour
la
adage classique: en
comme
mais
exclusivement en relation au temps du verbe,
dans
1
par definition sa
est appellatif, appelle
il
formulation des causes de verite, qu
il
n
est
il
ne Pappelle pas
pas indispensable,
reste sub propria
forma 18 que ce doit etre le cas du predicat Dans ces d6veloppements de Buridan, on retrouve des questions evoquees par Albert, puisqu il s y agit, identiquement, des termes
cum
il
appellatione, alors
appellatifs.
.
De meme, on
peut deceler une facon identique de designer
la
du terme. Cependant, le developpement de Buridan insere sans equivoque dans une conception de 1 appellation de la forme
forme propre s
(comme
type de renvoi signifiant contredistingue de la supposition) qui est
absente de Pexpos6 d Albert. En revanche celui-ci met sur le meme plan questions liees aux determinations temporelles et leur effet sur le
les
predicat d une part et les problemes particuliers suscites par des verbes intentionnels d autre part, avec
comme
denominateur
commun une
idee de
qu indiquait deja Guillaume d Ockham. Si done les deux champs que Buridan traite a 1 aide des notions d appellation de forme et d appellation de raison sont de ce fait rassembles, il ne s agit forme
reduite au seul aspect
pas pour autant de confondre indument les deux concepts buridaniens; s agit
plutot de les remplacer par
d une certaine
qui,
la
vague que usage ockhamiste. avoir enumere des apres
qui est plus proche de
En
un concept d appellation de
est plus
fac,on,
effet,
la
il
forme
notion buridanienne et
1
regies
qui
concernent
appellation dans une proposition au present, au passe, au futur puis a la modalite du possible, Albert ajoute une cinquieme regie qui prend en compte les verbes tels qu intelligo, scio, cognosco. Us sont caracterises
1
que lorsqu ils sont suivis d une complexio, et non pas seulement d un adjectif ou seulement d un substantif, 1 adjectif n appelle le
par
fait
pas seulement sa forme
egalement sa complexio substantif.
Ce n
Par exemple, cette
il
est
proposition
18 Id., ibid., p.64.
pas
est vrai
-
au sens qui a etc precise plus haul - mais ici son union, sa conjonction - avec un
done
le cas,
que
6quivaut
en revanche,
Deum a
si
trinum et
hoc
le
terme precede
unum
cognovit
le
verbe.
cognovit Aristoteles;
Aristoteles,
ou
hoc
Biard
434
Mais
renverrait a Dieu.
Deum unum
Aristoteles cognovit
trinum
et
est
faux, parce que impliqucrait quo non sculement le Philosophe ait connu Dieu, ce qui etait le cas, mais encore qu il 1 ait connu comme un et 19 On retrouve encore une fois des trine, ce qui n etait pas le cas
cela
.
voisins de ceux qui etaient etudies par Jean Buridan.
phenomenes
Albert se garde d introduire Pidee d appellation de raison,
Mais
meme
la
ou
Buridan y faisait appel, par exemple a propos de Penonce canonique, d inspiration aristotelicienne, Sortem venientem tu cognoscis. Cette demarche s etend aux cas ou la complexio qui suit le verbe est
une proposition. Supposons par exemple que a signifie la proposition Deus est mais que tu 1 ignores. a scis esse verum doit etre tenue pour hoc scias esse verum, hoc renvoyant au vraie: il suffit pour cela que sujet
de
la
a
proposition
scis esse
vcrum. En
revanche, d aucune chose
hypothese tu ignores que Deus est la proposition a. On pcut done estimer que dans les cas ou la est proposition suit le verbe, elle appelle sa forme, ce qui a Pevidence
vraie tu ne
sais
c est a, puisque par
que
croyance porte sur la proposition Deus est elle-meme, ou plus prdcisement que on sache que a signifie Deus est. La forme n est done pas simplement ici Pidentitc a soi materielle du
que
ici
implique
le
ou
savoir
la
1
bien
terme,
qu
elle
qui
specifique,
etre
devrait
un
ni
impliquc,
I
renvoi
des
distingue
de supposition, mais Pidentite du terme simple ou complexe.
qu
il
soil
Meme
dans
si
concernant
Perutilis
logica,
signifiant
eclairer
suffit
de
comme
de Saxe rcste assez
Albert
cela
dernier
ce
type
habituelles
relations
signification et tel,
d un
semantique
allusif
les
quelques pour exemple, phrases des Sophismata qui avaient initialement retenu notre attention. Le
sophisme XXXIII precise: 20 appellat suam formam universali patrem suum
forma
et
in
-,
Socrate a ce
un
;
particular!. est
un
..
mais d apres
moment
En
homme est
le
li
hominem sed
effet,
-
il
Socrate
tient,
casus, la
ceci est
individu qui est son pere, alors
Id., ibid.,
m
II,
vb.
ignorat
sail
qu
le il
pronom
hoc
in
propria
cette
proposition
la
croyance de
ceci
renvoyant a
ignore cette identite.
meme
"scit",
de maniere generate
forme propre de
un ane,
meme
verbum
Sortes in dicto casu in
a juste litre,
On peut noter au passage qu on trouve le Heytesbury, attribue a Averroes. 20 Albert de Saxe, Sophismata, XXXIII, sign, m II, va. 21
a sequitur hoc
sophisme XXXIV:
esse
scit
21
que son pere pour vraie
Quando enim et le
exemple
chez
Toute
Guillaume
Appellation de la forme selon Albert de Saxe
proposition qui suit
fonde
la
peu qu est
ou
croire
appelle sa forme, ce qui
savoir
non-substituabilite d expressions de reference equivalente, pour
elles soient
assez
ratio
verbe
le
435
de
forme
differente.
Le sens
exact de cette notion
a preciser mais elle est sensiblement differente de
difficile
Non seulement
buridanienne.
la
concerne aussi bien des termes
elle
mentaux que des termes vocaux, mais elle implique a la fois le respect de la litteralite du terme et une portee semantique qui peut se traduire par des propositions du genre s agit
pas
d une
simple
ceci est
confusion
un x.
II
entre
en tout cas qu il ne deux types d appellation
est clair
les
distingues par Jean Buridan. Albert cherche a elaborer, en integrant les
phenomenes semantiques que son aine raison,
de
1
done
les
appellation
demarque
ainsi
expliquait grace a Pappellation de
problemes suscites par qui
s
appuie
sur
consciemment de
Centre National de
la
Recherche
la
les
seule
la theorie
verbes cognitifs, une theorie notion de forme, et il se
buridanienne.
Scientifique, Paris
IVAN BOH
Medieval Rules of Consequences and the Idea of Demonstrative Science
Introduction. Medieval logic rules.
The
inferential for
truth,
rules
in
question
moves are such
are
been
basically a logic of
indicating what
devices
metalinguistic
help us in our rational search
that they will
such that they
i.e.,
said to have
may be
never lead from truth to
will
falsity;
and
seemingly correct inferential moves are faulty, e.i., of the sort which can lead from truth to falsity. While truth of propositions was correctness of inferences, the rules of sharply distinguished from
what
consequence were nevertheless conceived scmantically and, in the case of obligational and epistcmic logic, they essentially involved a pragmatic relation or reference to a user of language signs.
was
Logic specifically
characterized
always
one
as it
of
one
as
listed
sermocinal
of
arts.
the
and
arts
liberal
But
medieval
authors
would make a
as a science. Occasionally, they
more also
distinction
between logica utens and logica doccns, the former concept stressing the nature of logic as an ars and the latter suggesting the nature of logic as a system of correct principles which can be learned so as to enable us
speak
"to
enables us
Obviously,
truly".
"to
speak
the
congruously"
In their investigations
relation
of
was never quite
on the nature of
logic
to
grammar which
coincidental.
logic medievals
were led
to
two related questions. One was primarily ontological: If logic is a science in the sense of an enterprise of formulating a set of true propositions, it must have its proper object. But then, what is this object? Philosophers
who
spoke
of
second-intentional
being
were
Acknowledgements: The author gratefully acknowledges State
University
&
for
granting
him
the
sabbatical
year
his
ontologically
inclined
indebtedness to the Ohio
1986/87,
to
the
International
Exchange Board (I.R.E.X.), and to the U.S. Department of Education for their research grants to the German Democratic Republic and to Poland during the same academic year. Most special personal thanks are due to Dr. Gunther Schenk of the Martin Luther University (Halle) who always found ample time to share his views on the history and philosophy of logic. Research
Rules of Consequences and Demonstrative Science philosophers of logic
who
answer
tried to
this first question.
437
The
present
paper does not concern itself with this line of discussion. The second question in the discussion of the nature of logic became prominent soon after the recovery in the Latin West of Aristotle s Posterior
Analytics
the
in
translated into Latin by
half
first
demonstration?
limited
to
If
categorical
so,
syllogistics?
1
century
meet the Aristotelian requirements of
what
in
when it was The question now was: Does
twelfth
James of Venice.
logic itself conceived as a science strict
of
It
sense? is
the
demonstrative
Is
science
impact of the recovery of
on the conception of logic that interests us in this The has two parts. The first one deals with the rules of study. paper consequence considered as the very core of medieval logic. The second
Posterior Analytics
part
relates
the
systems of consequences to the idea of demonstrative
knowledge as formulated
in the Posterior Analytics.
A
concluding section
summari/.es the findings.
Pan One. Some of
history
years of progressively intensified research in the
sixty
medieval
logic,
from
pioneering
work of H.
Scholz,
I.M.
Boehner, through the studies and editions by EA. J. Pinborg, S. Ebbesen, N. Kretzmann, A. Maieru, V.Munoz Delgado, E.J. Ashworth, etc., and through a long and expanding list of other prominent investigators and editors, there can be no doubt Bocheriski,
and
Moody, L.M. De
about
the
P.
Rijk,
centrality
medieval logical
of
treatise.
rules
of
consequence
in
any
Nor can there be any doubt
comprehensive
that the idea of
consequence itself and of its types developed significantly through the centuries from the seeds found in Aristotle s Topics and Prior Analytics
and possibly from other sources. One can also observe a progressive extension of areas brought under the umbrella of a comprehensive system of rules
of consequence,
culminating,
perhaps,
in
the
treatise
entitled
Conscquentiae by Ralph Strode. This English logician collected rather eclectically, twenty four general rules of consequence among which one could find rules of prepositional logic, of alethic modal logic, of a "logic
of
quality",
of obligational disputations,
and of epistemic and doxastic
Cf. E. Serene, "Demonstrative Science", in The Cambridge History of Later Philosophy. Ed. N. Kretzmann et al., Cambridge: University Press, 1982, pp. 496-517.
Medie\>al
Boh
438
The only notable absence from
logic.
axiological rules.
The
the
set
and
of deontic
that
is
2
earlier systems of
consequences such as that of Walter Burley,
system of John Buridan
s Consequentiae developed in the 3 mid-1300s on the Continent, were indeed more perfect than the system of Strode if we consider them simply as quasi-axiomatic structures. There
or the
is
"mature"
made
a clear distinction
in
Burley and Buridan between the principal
and the derived rules of prepositional logic and the proofs of the latter from the former are consciously and carefully worked out; while in Strode all
24 general rules seem to be treated as
of
them are shown
be
to
"reducible"
"principal",
even though some
to another. This shows, of course,
independent and that from a strictly axiomatic point of view Strode could have done with fewer than 24 principal rules. Strode s that they are not
admirers
and
critics
such
as
Alexander
logicians such as Peter of
work by
raising
many
Paul
Sermoneta,
Cajetan of Thiene, and Frachantianus of Vicenza,
of
Pergula,
as well as other great
Mantua and Paul of Venice continued Strode
interesting
questions
about
various
s
problematic
points of his text.
The medieval correctly be
rules
of consequence
are
done and what should be avoided
relations in various areas of discourse. This in the controversies
of what
descriptive in
can
considering inferential
comes out
especially vividly
over the definition of consequence and in the implied
or even explicit attitude toward certain problematic rules. Everyone, of course, agreed that no consequence could be sound unless
it
rules out the
case where the antecedent obtains but the consequent not. While keeping in
mind the
distinction
between the so-called material implication,
implication, and relevant entailment, and
This
is
not
to say that medievals did
have
stipulating
a
strict
new symbol
not pursue deontic logic at
all,
=>
but only that
been
integrated into a comprehensive quasi-axiomatic system. For developments in this area, see the pioneering work of Simo Knuuttila: "The Emergence of Deontic Logic in the Fourteenth Century", in New Studies in Deontic M. Logic. Ed. R. Hilpinen, Dordrecht: D. Reidel 1981, pp. 225-248; and S. Knuuttila
deontic
rules
not
yet
&
Yrjonsuuri, "Norms and Action in Obligational Disputations", in Die Philosophic im 14. and 15. Jahrhundert (Bochum Studien zur Philosophic 10). Ed. O. Pluta, Amsterdam: B.R. Griiner, 1988, pp. 191-202. Cf.
Tractatus de Consequentiis. Ed. H. Hubien (Philosophes Medievaux 16). Louvain,
1976.
For relevant texts, see Consequentiae Strodi cum commento Alexandri Sermonetae, Gaetani in easdem Consequentias, Dubia Magistri Pauli Pergulensis,
Declarationes
Obligationes eiusdem Strodi ... Quaestiones in Frachantiani Vicentini. Venice 1517.
Consequentias Strodi perutiles
...
Antonii
Rules of Consequences and Demonstrative Science
439
ergo ) to represent systematically-ambiguously all the consequential structures of medievals, we can say that everyone agreed that if P Q is (read
=>
to
be sound, then
satisfied
as
at least
necessary
~(P & ~Q)
~O(P & ~Q)
must be
Whether these conditions were
conditions.
soundness of
sufficient conditions for
not even
if
P
=*
Q
seems
matter of some dispute throughout the ages. The
Ex
to have
also
remained a
impossibili quodlibet
and the Ex falso quodlibet rules which come along with the acceptance of ~(P & ~Q) or ~O(P & ~Q) as sufficient conditions for the soundness of
P
=>
Q also remained a source of perplexity. We should stress that medieval rules
when
there
is
a
question
of
the
of
whole
of the intellectual structures (or
"constitutive"
not formally constitute them in the
way
consequence,
system
of
"games"):
especially
them, that
is,
not
are
they do
in which, say, the rules of chess
may be said to constitute the game of chess, or in the way in which the formation rules and definitions may be said to constitute certain systems. Rather, they take the intellectual structures or
as already given.
"games"
They merely bring out explicitly the most general features inherent in or and they help to organize and tacitly assumed in those structures, possibly
the
reorganize
framework
materials.
They
also
a
provide
theoretical
comparison and contrast of various deductive fields. the mutual Thus, consequential rule which in fact allows us to use P Q and ~Q =$~P interchangeably may be seen to be operative in the system of alethic modalities, e.g., allowing for interchange of OP nQ and for the
=>
=>
~OQ
=>
of
system
CP [P
=>
~OP,
with
the
obligational
possible
proviso
disputation
and
e.g.,
that
allowing
N%Q =*N%P The general consequential rules, such as Q] and known by a to be sound [Ka (P =>C^0
n(P
(with the proviso that If =>
=>
and
Q));
for
in
interchange
the of
Ka (P=* Q)). a consequence Q)], then
is
sound
P is to be [CQ]\ should if
conceded by a [C%P], then Q must also be conceded by a not be confused with constitutive rules of the game of obligation such as the following three rules from Paul of Pergula
which
s
Obligationes:
Everything
possible and posited to you and known by you to be such must be admitted by you Everything which is possible and posited to you, is
;
and admitted by you
be conceded by you for as long as the Everything which follows from what has been posited and admitted from it alone or from it together with some thing which has
obligatio lasts
is
to
;
been conceded, or some things which have been conceded, is to be conceded The constitutive rules are sufficient to play the game, while .
Boh
440
the general rules of consequence help to explicate the logical force of
to-be-conceded, to-be-denied,
and to understand the conceptual or
etc.,
theoretical underpinnings of various types of obligationes.
Mutatis mutandis, one could
make
remarks about the rules of
parallel
a consequence is sound such as Strode s Rule 13, then if he knows the it to be sound [K (P = and a knows Q)], [P Q] a antecedent [K^], then he also knows the consequent [Ka Q]\ in relation to our first order knowledge, opinion, and justification claims in various If
epistemic logic, =>
areas of
human
We
Part Two. in
logic
will
now
some medieval views on
explore
general and of the theory of consequence
demonstrative
of
ideal
endeavor.
science
as
in
expressed
in
the
the relation of
particular to the
newly
recovered
Posterior Analytics.
As
already noted, the medievals since Boethius characterized logic loosely as both art and science. It was cultivated together with grammar, rhetoric
opposed
and other to
the
liberal
"real"
arts
-
as
opposed
and
sciences,
to mechanical arts, i.e.
The recovery
sophy, metaphysics, and theology.
and also as
mathematics, natural philo of Posterior Analytics in
the mid-twelfth century changed greatly the discussions of the nature of these disciplines. Arguments were set up to establish the status of
demonstrative science for
all
these disciplines,
-
a status which
seems
have become a high desideratum. As for logic, two remarkable phenomena should be observed.
On
to
the
one hand there was a progressive development by logicians such as Abelard, Peter of Spain, and others, of certain ideas on inference found Aristotle
in
Megaric
s
Prior Analytics
tradition),
culminating
systems of consequences.
development,
the
5
On
appeared
in
(and possibly in the Stoicformulation of quasi-axiomatic
Topics a
the other hand, and concomitantly with this -
under
the
influence
of
the
Posterior
a rising tendency to claim for logic itself the status of a demonstrative science. This tendency became especially strong by first half of the 13th century when Robert Grosseteste wrote a
Analytics strict
there
and
On
-
the relation of topics to consequence see E. Stump, Topics: their development Later Medieval Philos consequences", in The Cambridge History of
and absorption into
Kretzmann et al., Cambridge: University Press, 1982, pp. 273-299. See also Green-Pedersen, The Tradition of Topics in the Middle Ages, Miinchen: Philosophia
ophy. Ed. N. N.J.
Verlag, 1984.
441
Rules of Consequences and Demonstrative Science
detailed
commentary on every aspect of the
particular on
central concept,
its
The requirements
of
i.e.,
Prior Analytics,
and
in
that of scientific demonstration.
demonstration
scientific
as
understood
by
medievals were rather restrictive and stringent. Scientific knowledge was supposed to consist of syllogisms in Barbara whose premisses are true, universal,
better to
and necessary, as well as immediate, and more certain and the conclusion to be demonstrated. While restrictions
known than
seem
have been incorporated into the very of science and while scientific demonstration was originally syllogism
categorical
definition
to
phenomena and
thought to be a model to explain natural
certain metaphysical propositions, the concept of science
demonstration was
extended
soon
geometry and arithmetic, as well as
to
cover
other
grammar and
to establish
and of
disciplines
scientific
such
as
logic.
But although the criteria of demonstrative science were in a sense relaxed, there were still some definite criteria to be met. Thus, the
anonymous author of a mid-14th century Petri
I-III
Hispani
rules,
in logic
"for
treatise Quaestiones in tractatus
emphatically denies that logic requisites of
all
its
is
a
mere
being a science are
collection of found".
The
requisites he listed are three, viz.
the subject of which a property
which
(dignitas} means or
More
is
being demonstrated, the property
been demonstrated of the
has
subject,
and the principle
known
proposition which serves as demonstration that the property belongs to that subject.
or
the per se
the
concretely,
logic has a subject, such as syllogism ... it also has properties, such as demonstrative probable and^ apparent (as are the enthymeme, the induction, and many other things). Moreover, it has principles (dignitates), e.g. if that which appears less to inhere inheres, then that whicn appears more [to inhere] also inheres , or to whatever fits the defimens, the deiiniendum also , and many others, as is evident from Topics and from the fifth treatise of this book [i.e., Summulae Petri Hispani}. ,
Several
centuries
later,
John Versor
question of whether logic can
He
first
"analysis",
points
and
out
that
is
the
"first
material principles of syllogism,
Cf.
Jan Pinborg,
"Anonymi
(1982), pp. 1-170; pp. 12f.
means
Quaestiones
Analytics
"resolutio".
resolution"
i.e.
concerned with the same
claim to be a demonstrative science.
(etymologically)
that in Latin this
explain that there
1
itself
is
when one
have to
do with
Then he goes on
to
points out both the
terms and propositions, as well as the
in
Tractatus Petri Hispani
I-III",
CIMAGL
41
Boh
442
formal principles, i.e., the mode and figure and the regulative principles, i.e. the dictum de omni and the dictum de nullo. But after this first there
resolution
the
is
second
one
which
is
a
of
resolution
the
consequent or of the thing concluded into the principles and causes of that consequent, these causes being signified
remarked
be
and of
circularity his
Vcrsor
that
commentary on
infinite
is
fully
regress,
Prior Analytics
as seen
where he
of
It
premisses."
the
from the
initial
should
charge
possible
of
paragraph of
says:
of a conclusion acquired by a syllogism; therefore, if there be knowledge of syllogism, it too must be through syllogism. Thus, such a syllogism is either known or not known. Not the first, because then it would be known by another syllogism, and that one by another, and so there would be a process in infinitum. Nor could one say the second, because then there would he no principle on the basis of which to come to knowledge of syllogism.
Every science
demonstration;
Versor consists
possession
now demonstration
is
escape from both circularity and the recourse to the distinction between the
s
in
a
is
firm
aware
by the
a
knowledge by resolution There is no doubt
infinite
.
were
that medieval authors
fully
conscious of the
significance of the structure of their systems of consequences
procedures of deriving
regress
two senses of
some
rules
and of the
from others. Four cases should
suffice
to illustrate the point. [1]
puritate [i.e.,
rules
with
De
Walter Burley (12757-1345?), explaining artis
logicae:
Tractatus
regulis generalibus
longior,
he
consequentiarum
his
says: ]
in the
procedures "In
are laid
the
first
down
which ought to be assumed as the principles in this the rejection of incorrect rules which lead to the
De
chapter
the general
art",
together
fallacy
of
second chapter Dc modo arguendi enthymematice consequent ...; in conditionalibus ] it will be explained in what way one ought to argue on the basis of these rules in the realm of enthymematic consequences. in the
[
John Buridan (1295/1300 Consequentiae, states his aim as
[2]
of his
d.after 1358), in the
opening sentence
follows:
In this book I wish to discuss consequences, dealing as much as I can with their causes, about which many things have sufficiently been proved by others in an a posteriori manner, although perhaps they were not reduced [by them] to the first causes in virtue of
Cf.
8
Johannes Dorp, Super omnes
Ed. P. Boehner,
p. 60.
libros
nove
logice,
Koln, 1503, a2 rA.
Rules of Consequences and Demonstrative Science
Now
which they are saki to hold.
it
443
will
be necessary to put forward
his
discussion
some assumptions. Johannes
[3]
Dorp
sciences,
points out that,
of other sciences at
in
(fl.c.1400),
whether logic can establish
its
first
own
of
principles logic
all,
but only shows
all,
of the
question
or only those
of other
does not establish principles
how one can
correctly derive
conclusions from premisses in any science. Having said that, that
"in
principles,
from
its
Dorp adds its own
sense logic also provides a method in respect of
this
because
own
it
teaches 10
principles]."
how
form argumentation from these
to
The use
[i.e.
of logic in a deduction of derived
from the principal ones in closely analogous to the deduction of conclusions from principles of particular sciences.
rules
[4]
Alexander Sermoneta (d.1486),
on Strode tract
on
s
in the
Prologue to his commentary
Consequentiae, speculates on the proper location which a
on consequences should have
in a systematically
ordered textbook
logic:
say that this book [Consequentiae] is the most universal part of the Prior Analytics, or else is introductory to it; and therefore it should be placed immediately after the De Interpretatione, and before the Topics, Sophistical Refutations, and Posterior Analytics. This order is evident, because this book is concerned with consequence as its subject, and this is more universal than any kind of argumentation or syllogism, with which the Prior special Analytics is concerned. I
Conclusion. Medieval rules of consequence can be seen as metalinguistic
formulations of the logic of propositions and also of the most general principles of particular sub-branches of logic. The principal rules are
analogous to axiom-rules, and the derived rules are analogous to theorems in our natural deduction systems. The function of the rules of
consequence was not only to provide a logical tool for reasoning in any subject-matter and in all sciences and speculative arts, but also to make explicit
The
the most general logical presuppositions in any inferential area.
recovery
of
the
Posterior
Analytics
stimulated
the
subsequent
n
Ed. H. Hubien, p. 17. Cf. also P. King, Jean Buridan s Logic: Supposition; The Treatise on Consequences. Dordrecht: D. Reidel, 1985.
The
Treatise
on
Johannes Dorp, Commentary on Buridan s Dialectica; quoted in E.A. Moody, Truth in Mediaeval Logic. Amsterdam: North-Holland, 1953, pp. 14f.
and Consequence
Alexander Sermoneta, 1493.
in
the Prologue to his
Commentary on Strode
s
Consequences,
Boh
444
discussions that logic
on the nature of is
because they
The Ohio
itself
logic
itself.
Medievals did come to believe
a demonstrative knowledge, but this was possible only
in fact re-defined
State University
and extended the concept of science.
HARTMUT BRANDS
Die zweifache Einteilung dcr formalen Supposition bei William of Sherwood
Von den Anfangen
bis
heute hat
man
die verschiedenen Einteilungen der
Arten und Unterarten durch sogenannte porphyriaSupposition nische Baume darzustellen versucht. Es verdient eine gewisse Beachtung, in
daB
ein
ihre
solches,
Unternehmen
im
und
triviales
Prinzip
auch
unproblematisches
von William of Sherwood gegebene Einteilung bis heute nicht adaquat gelungen ist. Der Grund hierfiir ist ohne Zweifel, daB William
of
fur die
Sherwood
bei
der
formalen
Supposition
Einteilung vornimmt. Diese wird namlich einerseits personale, andererseits in die diskrete
Es
und allgemeine
eine
zweifache
in die einfache
und
eingeteilt.
gibt zwei Modelle, diese zweifache Einteilung in die
stammbaum-
artige Darstellung zu integrieren. Das erste findet sich bereits als Marginalie in der Pariser Handschrift und faBt die zweifache Einteilung selbst als eine Zweiteilung auf.
Dies hat zur Konsequenz, daB aus zwei
Zweiteilungen eine Vierteilung wird. Da das genannte Schema in keiner der beiden Editionen 1 der Introductions in logicam des William of
Sherwood enthalten
ist,
fiihre ich es hier an:
2
Die Introductiones in logicam des Wilhelm von Shyreswood. Einleitung und Textausgabe von Martin Grabmann, Miinchen 1937. William of Sherwood, Introductiones in logicam: Critical Text. By with Peter Kunze and Bernhard Mussler. New York 1983. (Edition Lohr)
2
MS Paris
Bibliotheque Nationale,
lat.
16617,
fol. 14r.
Literarhistorische
Charles
H.
Lohr
Brands
446
Die weitcren Einteilungcn schlieBcn an die personale Supposition an und sollen hier iibergangen wcrden. Im Prin/.ip gleiche Darstellungcn finden sich in
3 4 neueren Arbeiten bei Enders und Marenbon
Modell
Das zweite
.
denkbar einfach: die Einteilung der formalen
ist
Supposition in eine diskrete und allgemeine wird weggelassen. Dieser Umstand wird von Kneale/Kneale allerdings angemerkt: "Apart from one
be noticed
pair to
later,
all
the varieties of suppositio distinguished by
6 5 William of Shyreswood are shown in the (...) table." Bei de Rijk und 7 Heyer die wohl auf Kneale/Kneale /uriickgreifen, wird die Unvollstandigkeit des Schemas indessen nicht vermerkt. Moglicherweise ist das Schema ,
bei
deshalb
Kneale/Kneale
Verhaltnis
der
denn
erschien,
one distinction
sie is
Zweiteilung monieren: he docs not explain
in
"...
allerdings,
ihnen
das
anderen nicht hinreichnend klar
/,ur
related to the
meine
Ich
weil
geblieben,
unvollstiindig
einen
how
detail
the
8 other."
daB William of Sherwood dieses Verhaltnis
keineswegs ganzlich uncrklart liiBt, merkt er doch eigens an, daB es sich bei beiden Einteilungen um vollstandige Disjunktionen handelt. nota, totaliter sub se divisionum suppositionem, comprehcndit quod utraqiie "Et
formalem
Omnis cnim
dico.
Aut
Item.
discreta.
accipitur
suppositio, out pro re defcrente
muB man
Jacobi
10
supponens out
dictio
pro forma significata
formam
et
tune est
communis
est et
aut
tune est simplex 9
personalis."
Insofern
zustimmen, daB mil dieser zwcifachen Einteilung der
formalen Supposition eigentlich eine Kreu/.klassifikation vorliege, wenn er
H.
Enders,
Munchen J.
5
Sprachlogische
Traktate
des
Mittelalters
und
der
Semantikbegriff,
1975, S. 81.
Marenbon, Later Medie\-al Philosophy, Ixmdon/Ncw York
W. Kncale and M. Kneale, The of
Peter
Spain,
Tractatus.
De\<elopment
First
1987, S. 44.
of Logic, Oxford 1962,
Critical
Edition
S. 253.
from the LXXVIII.
(Kneale/Kneale)
Manuscripts
with
an
Introduction by L.M. de Rijk, Asscn 1972. Introduction, S. in: Peter of Spain, Tractatus K. Jacobi, Rez. von Philosophise he Vgl. hierzu: dem Diagramm, das de Rijk von der Rundschau 22 (1976), S. 48 - 64; bes. S. 58: ,
"In
bei
Einteilung
communis
-
Wilhelm
von
Shyreswood
discreta gar nicht vor. Dies
ist
gibt,
jedoch
kommt
G. Heyer, Generische Kennzeichnungen, Munchen 1987, 8
(Kneale/Kneale), 9 K.
Jacobi,
Unterteilung
suppositio
S. 68.
S. 256.
S. 266.
(Edition Lohr), 1
die
unrichtig."
in den Die Ai Modalbegriffe - Koln 1980, S. 414, Anm. 127.
Shyreswood, Leiden
logischen
Schriften
des
Wilhelm
von
Die Einteilung der formalen Supposition bci William of Sherwood
auch bei
schematischen
der
11
447
von dieser Einsicht
Darstcllung
keinen
Gebrauch macht. Alle genannten
Darstellungen der
William of Sherwood
in
der Supposition des
Einteilung
Stammbaumform
miissen als wesentlich unvoll-
angesehen werden, weil keine von ihnen die von William of
standig
Sherwood eigens hervorgehobene und thematisierte suppositio simplex discreta
AuBerdem wird Williams
enthalt.
Einteilung
schematische ausgesetzt
anderen
mit
ist,
aus
diesen
den
Darstellung,
die
hatte folgende
Form:
kritischer
Schemata
nicht
vorgebrachten
seiner
Vergleich verstandlich.
Eine
Einwanden
nicht
suppositio formalis
communis
discreta
L
I
simplex
simplex
personalis
personalis
Hierauf bezogen wird unmittelbar verstandlich, was William of Sherwood an anderen Einteilungen verwirft, und es erscheint die Annahme gerechtfertigt,
daB William of Sherwood
Supposition gerade wegen hat. sit
"Volunt
divisio
discreta
die zweifache Einteilung der formalen der suppositio simplex discreta vorgenommen
enim quidam, quod haec
communis
suppositionis,
divisio, alia simplex, alia personalis,
non
quia
cadit
haec
diversitas
in
12 suppositione."
Fur diese diskrete und einfache Supposition
gibt
William of Sherwood
einen Beispielsatz, zu dessen Verstandnis es sinnvoll erscheint, zunachst
kommenden
die hier in Betracht
Definitionen der einzelnen Suppositions-
arten durchzugehen. Ein formal supponierender Terminus supponiert
immer
signifikativ. Supponiert er einfach, so supponiert er unmittelbar fur sein
Signifikat
(und
nicht,
wie bei der personalen Supposition, mittelbar fur GemaB der Definition von significatio,
eine unter dieses fallende Sache).
worunter William of Sherwood die begriffliche Vergegenwartigung bzw. Darstellung einer Form versteht, bedeutet einfach zu supponieren auch,
Form - pro forma significata enim nomen significat solam formam
fur
11
12
eine
K. Jacobi, a.a.O., S. 163.
(Edition Lohr), S. 267.
13
(Edition Lohr),
S. 268.
-
zu supponieren. Denn: 13
,.."
"Omne
Diskret schlieBlich supponiert
Brands
448
um
ein Terminus, sofern es sich
handelt wie Sokrates oder dieser
aus
Das
sich
der
Kreuzklassifikation
Mensch
Problem
stellcnde
hier
einen diskreten bzw. singularen Terminus .
offensichtlich
sich
ergibt
beiden
der
Einteilungen
gerade formalen
der
Supposition, d.h. speziell aus der Kombination von einfachcr und diskreter Supposition.
Was
soil
daB ein singularer
darunter verstanden wcrden,
Terminus, insbesondere ein Eigenname eine Form bezeichnetl Genau namlich eine Form zu bezeichnen, behauptet William of Sherwood Sokrates
Subject
seines
und
einfache
die
fiir
diskrete
dies,
vom
Supposition
gcgebenen Beispielsatzes. "Cum dico Socrates est praedicabile de uno 14 Dem Verstandnis solo respicitur pro forma significata per nomen." ,
Eigenname cine Form bezeichnct, kommt man wohl ein Stuck naher, wcnn man sich um ein Verstandnis des von William of Sherwood angefiihrten Beispielsatzes bcmuht. dessen, was es heiBt, daB ein
Kneale/Kneale erscheint
Sherwood
offensichtlich
sowohl die von William of
postuliertc suppositio simplex discreta
und
die damit
Annahme, daB singulare Termini eine Form bezeichnen, Beispielsatz abwegig:
be
said
to
a
signify
suppositio.
As
substance,
Socrates
he
"...
example means anything Socrates Socrates
is is
and
rightly
not
is
at
that
this
remarked
predicable all,
verbundene
auch Williams
name can
very strangely that a proper
insists
form
Aristotle
als
it
of
is
in
essential
to
doctrine
his
anything.
If
its
having
of
primary William s last
must mean either that being-called-
one thing or that being-identical-withpredicable predicable of only one thing, and in neither case is a form of of only
1
Socraticity
Die
involved."
kritische
Interpretation von Kneale/Kneale leuchtet ein,
man das esse praedicabile als Wenn Aristoteles sagt, daB erste
Pradikat-(in
einem Urteil)-sein
Substanzen weder
in
wenn
auffaBt.
etwas sind noch von
etwas ausgesagt werden, so besagt dies in logischer Terminologie, daB singulare Termini in einer Aussage niemals an Pradikatsstelle stehen
konnen. Folglich rekonstruieren Kneale/Kneale
Sokrates
als
einen auf
genau ein Objekt zutreffenden allgemeinen Terminus, und zwar in Form einer Relation zu Sokrates (als Person) bzw. zu Sokrates (als Namen), in der
nur Sokrates selbst
steht.
DaB
Sokrates
nur von einem
einzigen
ausgesagt wird, besagt dann, daB die als offene Schemata dargestellten 14
(Edition Lohr), S. 267.
15
(Kneale/Kneale),
S. 257.
Die Einteilung derformalen Supposition bei William of Sherwood Pradikate
x
x wird
bzw.
identisch mil Sokrates
1st
Sokrates
nur von einem einem einzigen Objekt, namlich Sokrates
449
genannt
selbst,
erfiillt
werden.
Es
mir
erscheint
Intention Williams
ob
zweifelhaft,
Es
wird.
getroffen
mit
dieser sich
bietet
die
Interpretation
namlich ein anderes
Verstandnis des esse praedicabile und damit auch des von William of Sherwood gegebenen Beispielsatzes an, da der Ausdruck esse praedicabile de uno solo als Defmiens im Pradikabilien-Kapitel der Introductiones
vorkommt, und zwar
als
Defmiens des Definiendums Individuum
individuum, quod de uno solo
:
est
"Et
nomen proprium
est praedicabile, ut est
et
pronomen et dictio communis cum pronomine. Dicitur enim individuum, eo 1 quod non dividitur in partes subiectivas." Die Erlauterungen, die William of Sherwood der Definition hinzufiigt, *
erleichtern zunachst das Verstandnis des Satzes nicht.
einen Schritt sichtlich
in
kommen: Der
weiter
den
Socrates
aquivalenten
Form
angefiihrte
Dennoch kann man
individuum
est
darf offen-
Beispielsatz
transformiert
von Kneale/Kneale keine Parallele zu Aussagen wie eine Ansatzpunkte mehr. Ferner ergibt sich Homo est species insofern species zu sein bedeutet, daB homo von werden. In dieser
bietet er fur die Kritik
,
mehreren ausgesagt werden kann. "Species autem est, quod praedicatur de 17 Weiterhin kann gesagt werden, daB wegen der angefiihrten pluribus ,.."
Socrates
innerhalb des transformierten Beispielsatzes vorliegt. Historisch
und systematisch
Wenn nun
in
einfach
von Interesse, daB W. Burleigh im gleichen praedicatur de pluribus und Socrates est
hier
ist
Homo
Kontext die Beispielsatze 18 individuum verwendet.
Socrates
der einfachen Supposition auch im Falle von
Modus
Parallele der erste
dem
Satz
Socrates est individuum
supponieren
soil,
so
kann er nicht
der Eigenname fur
die
Person
Sokrates supponieren. Folglich kann individuum nicht als solcher Begriff verstanden werden, der auf Personon zutrifft. Die Erlauterung ut est
nomen proprium sonst
Socrates
William
of
...
kann aber auch
material
Sherwood
nicht wortlich
(Edition Lohr),
17 (Edition Lohr),
W. St.
Burleigh,
weil
supponieren wiirde. Vorlaufig bleibt der von
fur
die
suppositio
simplex
Beispielsatz in beiden Versionen problematisch. 16
genommen werden, discreta
angefiihrte
Zur Vorbereitung eines
S. 237. S. 238.
De
puritate
Bonaventure, N.Y., 1955,
S.
17
artis u. 19.
logicae
tractates
longior,
edited
by Ph.
Boehner,
Brands
450
angemessenen Verstandnisses gehe vorlaufig zu dcr Frage zuriick, was cine
Form
es heiBt,
und kehre
Umweg
daB ein diskreter Terminus
bczeichnct.
Wort
Ein
ich einen kleinen
(material) noch
wenn
einfach,
supponiert
es
weder
fur
sich
selbst
Gegenstande (personal) supponiert. Dasjenige, was von etwas ausgesagt wird, sind nun aber auch weder Worter ( Sokrates ) noch entgegen der bei Aristoteles iiblichen Ausdruckweise Gegenstande fiir
(Sokrates). Ausgesagt werden in der Regel Eigenschaften bzw. Begriffe. Beide sind Kandidaten fiir dasjenige, was als Bedeutung eines Terminus im
Unterschied zu seiner Referenz Sokrates
Es
ist
Betracht gezogen wird. Die Person
das Referenzobjekt des Eigennamens Sokrates
als
Supposition
.
keine groBen Schwierigkeiten bereiten, die Theorie der
diirfte
Sherwood
in
Referenztheorie
cine
aufzufassen.
19
Fiir
William
of
wcitergehende Auffassung, daB die Referenz eines Terminus ausschliefllich eine Sache seiner Supposition sei. offensichtlich
gilt
die
Hiervon zu trennen
ist die Signifikation: die Bezcichnungsfunktion eines Terminus ist die Darstellung einer Form. So auch des singularen jeden kann sich auch durch den jeweiligen Satzkontext immer nur die -
d.h.
Supposition
20
Signifikation.
konscquent
Referenz
Was
Terminus wandeln,
eines
nicht
aber
wir somit bci William of Sherwood vorfinden,
durchgefiihrte,
die
d.h.
singularen
Termini
seine
ist
eine
einbeziehende
Semantiken sind uns
in der Gegenwarts"Wenn wir die Trennung zwischen Bedeutung wohl vertraut. philosophie und Referenz richtig beachten, spaltcn sich die Probleme dessen, was so
dualistische Semantik. Derartige
leichthin
Semantik genannt wird,
verschieden sind, daB
sic
Wir konnen von der
Tfieorie dcr
21
(
denn
Eigennamen
er
trennt
in
Namen
nicht
so fundamental
mehr
verdienen.
Bedeutung und der Tfieorie der Referenz kommt William of Sherwood sehr
ubercinstimmend
Sache
der
die
signiflcatio
)
an,
dann
muB
singulare
Termini,
speziell
eine Entitat benannt werden, die als Bedeutung
P.V. Spade, The Semantics of Medie\ al Philosophy, Cambridge 1982, theory of reference."
"71
die
Gebiete,
von der suppositio ( Referenz ). Wcndet man diesen Dualismus auf
Bedeutung
20
zwei
Dieser modernen Sicht
sprechen."
nahe,
in
einen gemeinsamen
in:
Terms",
S.
192:
The
The
Cambridge
History
of Later
theory of supposition proper
is
a
Vgl. (Edition Lohr), S. 267 (1. Dubitatio); ferner: (Kneale/Kneale), S. 254.
W.V.O. Quine,
"Anmerkungen
zur
logischen Standpunkt, Frankfurt 1979, S. 125.
Theorie
der
Referenz",
in:
ders.,
Von einem
Die Einteilung derformalen Supposition bei William of Sherwood
451
Unterschied zu ihrer Referenz fungiert. Hierbei so vermute ich, um dicjenigen Entitaten, die nur von
singularer Termini in:
handelt es sich,
einem einzigen ausgesagt werden konnen: die Individua. Diesen mochte ich mich nun in Form eines kleinen Exkurses in die Semantik der
Gegenwart zuwenden. Von den verschiedenen dualistischen Semantiken der 22 Gegenwart wahle ich die von R. Carnap in Bedeutung und Notwendigkeit entwickelte Theorie von Extension und Intension.
Carnap
semantischen Begriffe der Extension und Intension
fiihrt die
per Abstraktion ein. Dabei handelt es sich um das prazisierende Verfahren der Begriffsexplikation, bezogen auf bekannte Begriffspaare wie Umfang
oder Freges Bedeutung und Sinn Der Begriff der Intension wird vor allem im Hinblick auf die Modallogik eingefiihrt und ist nicht
und
Inhalt
.
identisch mit
dem umfassenden
Begriff der Bedeutung in
Abgrenzung zur
Referenz. Nicht nur aus diesem Grunde sind Analogisierungen zwischen
der significatio bei William of Sherwood und dem der 23 iiberhaupt nur cum grano salis zulassig. Bevor Wesenheiten gesucht werden, die als Extension bzw. Intension
dem
Begriff
Intension
wenn
Frage kommen, wird die Gleichheit, bzw. allgemein die Aquivalenz von Extension und Intension festgelegt. Ich beschranke mich hier auf die von auf die singularen d.h. Carnap so genannten Individuenausdriicke in
,
Termini. Zwei Individuenausdriicke sind extensionsgleich gdw. der Satz a = b wahr ist; sie sind intensionsgleich gdw. dieser L-wahr ist. Ein Satz
L-wahr
soil
heiBen,
Tatsachenwissen kann.
Da
wenn
seine
iiber
Wahrheit
unabhangig
von
aufgrund semantischer Regeln entschieden werden a = b genau dann wahr ist, wenn a und b auf
allein
der Satz
dasselbe Objekt referieren,
kommt
als
Extension eines singularen Terminus
nur das jeweilige Referenzobjekt in Frage. Der Begriff der L- Wahrheit ist an sich umstritten. Davon unabhangig bereitet es gewisse Schwierigkeiten, sich einen L-wahren Satz der Form a=b
vorzustellen, vor
sollen.
allem
wenn
Dementsprechend bieten
sich
a
und
b
echte
Eigennamen
sein
auch keine Wesenheiten unmittelbar
an, die als Intensionen singularer Termini in Frage
kamen. Das hiermit
angedeutete Problem scheint mir demjenigen analog zu sein, welches sich als Frage nach der durch einen singularen Terminus bezeichneten Form darstellte.
7? R. 1
und
23
Da
bei den anderen Designatoren als jeweilige Intensionen sich
Carnap, Bedeutung und Notwendigkeit,
9.
Vgl. P.V. Spade, a.a.O., S. 188.
Wien
-
New
York,
1972,
insbes.
Kap.
Brands
452
solche Wesenhcitcn ergaben, die gewohnlich als Bedcutungen odcr Begriffe
bezeichnet wcrden, Individuenbegriff
Terminus
fuhrt
zur
Carnap
Entsprechung dazu den Ausdruck
in
der
Bezeichnung
Intension
eines
singularen
ein.
In Ansehung der Analogic, aber auch im BewuBtsein der Differenzen zwischen den dualistischen Semantiken William s of Sherwood und R.
Carnaps mochte ich vorschlagen, den von William of Sherwood eindurch Individuum Terminus Individuenbegriff im Sinne gefiihrten Carnaps zu iibersetzen. Williams Erlauterung ware danach wie folgt zu verstehen: Ein Individuenbegriff ist dasjenigc, was nur von einem einzigen ausgesagt werden kann, wie dies bei der Verwendung singularer Termini der
Fall
werden
Sie
weil
sie
(im Unterschied zu Allgemeinbegriffen) keine untcrgeordneten Begriffe haben. Entsprechend ware species in dem Satz homo est species durch ist.
Individuenbegriffe
genannt,
24
Artbegriff wiederzugeben.
von
Die
hiermit
der
durch
vorgcschlagene Interpretation, welche ihren Ausgang William of Sherwood eingefiihrten suppositio simplex
kann selbstverstandlich nicht ohne Folgen fur ein Verstandnis der suppositio simplex im allgcmeinen bleiben. Es hat den
discreta
genommen
hat,
Anschein angesichts der verschiedenen, Beispielsatze,
angefiihrten
wenn
als
supponierende Termini Suppositionsart auch ganz
fur einfach
diese
verschiedene Gebrauchsweisen von Termini abdecken wiirde, welche der
personalen oder materialen Supposition nicht zugeordnet werden konnen. Feststeht, daB ein an Subjektstelle einfach supponierender Terminus durch ein bestimmtes Pradikat determiniert sein muB, und daB unter
diesem Subjektterminus ein descensus ad singularia generell nicht moglich ist. Die Griinde fiir die Unmoglichkeit eines Descensus sind allerdings andere
als bei
der immobilen Supposition.
Angesichts der Frage nach
dem
quantitativen Status von Satzen mit
einfach supponierendem Subjekt, weist William of
Sherwood
die Auffas-
sung, derartige Satze seien singular, deshalb zuriick, weil sie eine mit Semantik unvereinbare Deutung der einfachen dualistischen seiner
Supposition voraussetzt. Diese faBt namlich species
als
Eigennamen
muB fiir William Terminus homo indem
Interpretation
der
24
,
So
z.B. Kant, Logik,
A
150.
homo
in
dem
Satz
homo
est
einer Art auf, also als singularen Terminus. Diese
of er
Sherwood unakzeptabel erscheinen, weil nicht mehr als konkreter allgemeiner
Die Einteilung derfortnalen Supposition bei William of Sherwood
Terminus sondern
abstraktcr singularer Terminus 25 fungieren wiirde,
als
seine Signifikation andern wiirde.
personal und
Dann
homo ohne
aber wiirde
Zweifel
supponieren. Die gleiche Konsequenz ergabe sich einen material supponierenden Terminus durch
diskret
wenn man
iibrigens,
453
Hinzufiigen von Anfiihrungszeichen modifizieren wiirde.
Es
den
hat
wiirden
Kneale/Kneale die einfache Supposition als miBliche Folge des Umstands verstehn, daB wir zwischen abstrakten, singularen und konkreten, allgemeinen Termini im gewohnals
Anschein,
lichen Sprachgebrauch nicht hinreichend scharf unterscheiden:
use the
new
word homo
as a substitute for the
But William refuses to admit
sense.
account
incoherent
two
of
kinds
we
word humanitas, we give it a this, and produces instead an 26
of
if
"For
suppositio."
Da
dieses
sich
Verstandnis der einfachen Supposition offensichtlich mit der dualistischen
Semantik
Williams
vereinbaren
nicht
la Bt,
man
konnte
andere
eine
erwagen, welche den Vorzug hat, daB sie sich aus unserer Interpretation von Williams semantischem Dualismus ergibt und zugleich erklart, warum ein derart einfach supponierender Subjektterminus keinen Descensus zula Bt.
Wenn
es so
ist,
daB ein Terminus
nach unserer Interpretation
Signifikat,
in einfacher fiir
Supposition
sein
fiir
einen Begriff steht und dies
durch den spezifischen Charakter des Pradikats bewirkt wird, dann liegt es nahe, derartige Pradikate im Sinne Freges als Begriffe zweiter Stufe aufzufassen.
Individuum,
solche Begriffe, welche
species,
und praedicabile de uno solo
immer nur auf andere
Begriffe zutreffen.
sinde
Nun
sind
allerdings die durch solche Begriffe zweiter Stufe Begriffen erster Stufe
zugesprochenen Eigenschaften nicht auch schon deshalb Eigenschaften der unter diese fallenden Gegenstande. Das ist der Grund dafiir, daB ein
Descensus
diesem Fall nicht moglich
in
ist.
Die Beziehung der Unter-
ordnung eines Begriffs unter einen andcren, wie animal
,
ist
transitiv,
anderen, wie in
Zum FaBt
25
diejenige
Satz
homo
AbschluB mochte
man,
wie
Zweiteilungen auf,
dem
erhalt
Vgl. hierzu:
man
Fallens
est species
,
ist
(Kneale/Kneale),
dem
Satz
Begriffs
homo
unter
est
einen
dies nicht.
noch auf ein Problem
am Rande
die
W.V.O. Quine, Grundzuge der Logik, Frankfurt
26
in
eines
hinweisen.
Ausfiihrungen Williams nahelegen, beide formalen Supposition als vollstandige Disjunktionen einen Stammbaum der Arten und Unterarten der
dies
der
ich
des
S. 255.
1969, S. 262
f.
Brands
454
Supposition,
dcr den
Intentioncn von William
of
Sherwood zumindest
dahingehend entspricht,
daB
Nun
daB William dann auch die suppositio personalis
ist
es zweifellos so,
schon
discreta
einfiihren
die suppositio
simplex discreta
fiihrt
Zweiteilung
der
Supposition
personalen
determinierte und eine konfuse. Konfuse Supposition dictio
27
supponit pro
diskreten nicht fur
Ich
enthalt.
Abgrenzungsgriinden, wie das Schema ausweist, aber zu Schwierigkeiten mil der nachfolgend
aus
muB. Das
vorgcnommenen
er
multis".
Supposition sein,
liegt
vor,
in
cine
"quando
Dies kann aber keine echte Unterart der
da ein diskreter Terminus per defmitionem
mehreres supponieren kann. hoffe
gezeigt
zu
haben,
daB
die
zweifache
Einteilung
der
formalen Supposition bei William of Sherwood mil einer Reihe nicht nur formaler Probleme verbunden ist. Die Einbe/iehung der modernen Semantik hatte nicht nur den Sinn, diese Probleme besser zu verstehen, sondern
auch zu zeigen, wie modern William of Sherwood
Universitat Diisseldorf
27
(Edition Lohr), S. 266.
ist.
MARCIA L. COLISH
Mathematics, the Monad, and John the Scot
The importance
s
Conception ofNihil
of John the Scot in the history of medieval thought has
always rested squarely on his transmission and use of Neoplatonism.
1
To
the extent that scholars have sought to bring the Latin school tradition
bear on their assessment of John
to
the
as
logic,
discipline
conceptual tool. his
2
There
which he is,
philosophy they have turned to applied the most consistently as a s
however, a key juncture in John s thought, 3, at which he distances
analysis of the term nihil in Periphyseon
himself both from the Neoplatonic tradition and from the discipline of
As
logic.
with
other
medieval
authors
confronted
with
the
task
of
explaining the idea of creation ex nihilo, John canvasses the liberal arts
and the philosophy available to him for assistance. But, in this case, he finds the help he seeks in the science of arithmetic, as it had come down to him in the works of Boethius and Martianus Capella, whom John and his
studied
associates
appeals
to
school
foundation of
all
and glossed. The
arithmetic
is
the
critical
point
at
of monad,
definition
which John the
abstract
numbers. Can the monad be equated with the deity, as Can the monad be defined as nihil!
the later Neoplatonists had argued?
I
would
like
to
acknowledge the support of the
Princeton, where this paper was written
The
in
Institute
for
Advanced Study,
1987.
conspectus on John and his relation to his Neoplatonic sources is Gersh, From lamblichus to Eriugena: An Investigation of the ftehistory and Evolution of the Pseudo-Dionysian Tradition (Leiden, 1978) and Middle Platonism and Neoplatonism: The Latin Tradition, 2 vols. (Notre Dame, 1986). For
provided
best
by
overall
Stephen
see Marcia L. Colish, "John the Scot s Christology and Soteriology in Relation to His Greek Sources," Downside Re\ icw, 100 (1982), 138-51. For the influence of Marius Victorinus in particular see Gustavo A. Piemonte, expression quae sunt et 6 Jean Scot et Marius Victorinus," Jean Scot ecrivain: Actes du IV quae non sunt 28 aout-2 ed. G.-H. Allard international, Montreal, 1983, colloque septembre earlier literature
"L
:
Vita in omnia pervenit El vitalismo eriugeniano y Mario Victorino," Patristica et Mediae\>alia 1 (1986), 3-48. I would like thank Dr. Piemonte for making offprints of these two papers available to me. "
(Montreal/Paris, 1986), pp. 81-113; la
to
influencia de
:
}
John Marenbon, From the Circle of Alcuin to the School of Auxerre: Theology and Philosophy in the Early Middle Ages (Cambridge, 1981); Gangolf Schrimpf, Das Werk des Johannes Scottus Eriugena im Rahmcn des Wissenschafts\<erstdndnisses seiner Zeit: Eine Hinfuhrung zu Periphyseon, Beitrage zur Geschichte der Philosophic und Theologie des Mittelalters, n.F. 23 (Miinster, 1982). See, especially,
Logic,
456
Colish
Can it
nihil
be viewed as the privation of essence, species, or habitusl Can logical opposite of aliquid, which it excludes? All of
be defined as the
these
contemporary
Carolingian
patristic sources.
grounds It
more
and
possibilities
3
had
been well
as
masters,
In the Periphyseon
John
and
as
by
rejects
all
their
ancient
and
these options and
argument instead on the arithmetical notion of the monad. should be noted that Periphyseon 3 is not the only place where
prologue to
John
St.
argument, and one
s
nihil.
He
does so as well
in his
all
things. Further,
coeternal and coessential with the Trinity. Since the
was not made
line
of
tune with the Boethian logic of opposition. In ipso factum est nichil
"Sine
quod factum
observes that nothing was created except through the includes
homily on the
Gospel, where he uses a much simpler
fully in
explicating the line
that
earlier
his
John addresses the idea of
Word
by
ventilated
Word is the in Him and
Word
est,"
John
because the
is
impossible to envision anything
Word
except the other Persons of the
it
logos of creation, 4
"nothing
Nihil here
at
all
remains
nihil
omnino, through of omnia in and at the the created all, nothing conceptual opposite through the Word, which omnia logically negates. The Boethian logic of Him."
is
mutually exclusive opposites is sufficient for John s task in this homily, is not the case in Periphyseon 3, where he sets for himself a much more complicated assignment. For it is here that John develops his
but this
doctrine of the primordial
causes.
It
invokes the mathematical idea of the
Periphyseon
is
largely for this reason that
monad
in his
he
handling of nihil in
3.
Before we
proceed to the Periphyseon it must be stressed that ancient Greek mathematicians had developed a standard notion of the later Neoplatonists rang their own changes. The mathematical definition of the monad as the abstract substratum of all
monad, on which the numbers, to which the
all
numbers can be reduced, was
first
formulated by
Pythagoreans. While the Pythagoreans were not averse to number
symbolism in other areas, their treatment of the monad was straight forward and strictly mathematical. This perspective was continued by the
Neopythagorean
A
mathematicians,
detailed investigation focusing
provided by Marcia L. Colish, Theological
Method,"
whose most
influential
exponent was
on Fredegisus of Tours and Ratramnus of Corbie Debates over Nihil and Tenebrae: A Study
"Carolingian
is
in
Speculum, 59 (1984), 757-95.
John the Scot, Homelie sur le Prologue de Jean 8, ed. Edouard Jeauneau, Sources chretiennes, 151 (Paris, 1969), p. 240: "nichil omnino relinquit quod in ipso et per ipsum factum For the whole argument see pp. 238-40. sit."
Mathematics, the Monad, and John the Scot
Nicomachus of Gerasa. Written remained the
teaching and
Nicomachus
debt
the
to
conception of the monad.
5
main currents of Neopythagorean
the
textbook in the
classic
Pythagoreans
can be
centuries.
for
field
seen especially
in
his
Eschewing any cosmological applications of the
he treats number as the structure of
idea,
457
Conception c/Nihil
the second century A.D., his Intro
in
summed up
duction to Arithmetic
s
reality.
The monad and
the
and dyad, the two most primitive elements of number, refer not to as actual numbers but to the metaphysical principles of unity and alterity underlying them. According to Nicomachus, all actual numbers "one"
"two"
monad, which is a pure intelligible simple, and alone incomposite, and
derive their essential natures from the
mind
the
in
constituted
"in
When textbooks
it
of
God,
primary,
accordance with
6 itself."
Boethius was preparing his translations of the quadrivium was to Nicomachus that he turned as the authority on
arithmetic. His treatment of the
aequalitas in Latin,
the
preserves
not by any other but by
itself,
monad, which he renders
more abbreviated than
is
of
essentials
Nicomachus
as unitas or
Nicomachus, but he
that of
Boethius
Numbers,
teaching.
agrees, are diverse in themselves. They can be reduced to the concepts of "odd number" and "even number," which in turn "come forth from one 7 source."
This source
is
equality,
from which
all
inequalities are derived
8
With these definitions in hand, in which they are all resolved. Boethius propels the strictly mathematical Neopythagorean view of the monad firmly on its course in the Latin school tradition. and
The
later
Neopythagorean handling of Plato For their
part,
they sought
were
however,
Neoplatonists,
to
with
dissatisfied
this
doctrine of the one and the many.
s
explore
broader metaphysical and
the
On Nicomachus and his place in the arithmetical tradition see Frank Egleston Robbins and Louis Charles Karpinski, "Studies in Greek Mathematics," the intro. to Nicomachus of Gerasa, Introduction to Arithmetic, trans. Martin Luther d Ooge (New York,
1926),
16-17,
pp.
35,
37-38,
99-102;
Nicomachus of Gerasa, Introduction arithmetique 1
Dernier,
Nicomachus
trans.
of Gerasa, Introduction to Arithmetic d Ooge, pp. 190, 192, 211-12. The quotation is at 1.6.4,
De
Boethius, 13:
Janine
"ex
Number
institutione arithmetica
una tamen genitura Theory:
A
profluunt."
Translation
of the
to
intro.
her
trans,
of
(Paris, 1978), pp. 16, 24-25. 1.7.1,
1.6.1-4,
1.16.9-10,
2.1.1,
p. 190.
Godofredus Friedlein (Leipzig, 1867), p. a translation by Michael Masi, Boethian De institutione arithmetica (Amsterdam, 1983), p. 1.2,
ed.
There
is
76.
o
De
arith.
inst.
aequalitate
2.1,
processerit.
componuntur,
The same point
et is
in
p.
77:
Tota
inaequalitatis
Sed quae rerum elementa
eadem
rursus resolutione facta
also found at 1.32, p. 66.
substantia sunt,
a
principe
ex hisdem
solvuntur."
The
sui
generis
principaliter translation is
omnia mine.
Colish
458
monad
monad,
concern we can document
a
Proclus and Dionysius the Areopagitc. Since they saw the
in
especially
of the
implications
cosmological
as the opposite of
Neoplatonists held
plurality, these
all
be
to
it
even as identical with, a higher hypostasis of being. analogous Proclus envisions each order of being, not merely numbers, as starting from a monad and as being reducible to the monad at the top of its or
to,
He
particular order of being.
the deity.
and
is
9
A
similar view
docs not hesitate to equate the monad with found widely among the late Neoplatonists,
further elaborated by Dionysius. Recasting the
and the many
in
above
creation,
each order of being to the
all
the archetypes.
or
directly
Creation
simple and beings that are composite.
monad "Every
the
number it
is is
unified in the
monad,
distinguished
and
number
of
in
its
whole. In Stephen Gcrsh
monad
in
relation
Neoplatonists gave
monad
But
the
God
to this
s
more
10
restricted
sense
idea a
is
the
all
unity levels
are
that
As Dionysius it
puts
it,
proceeds from
having transferred the to
the
11 number."
warm welcome,
of
beings
creation
words, Dionysius has also recast
which creation
status
alone shares with the
but inasmuch as
multiplied,"
its
supreme
monad
contains
the quality of radical and indivisible unicity.
monad
concept
level of the
God becomes
indirectly.
problem of the one
monad up from
numerical terms, he moves the
as the archetype of that stands
of
is
God
as
as
a
"the
Other Christian
treating the deity as the
and physical worlds. They sei/cd on this notion as a useful way of conceptuali/ing the emanation of plurality from unity that harmoni/ed with the additions and revisions they imported into in relation to the angelic
the pagan Ncoplatonic view of the spiritual order.
are
12
While the Neoplatonic and Neopythagorean theories of the monad manifestly different, they were sometimes combined by authors in
Proclus, Theologia Platonis 138, 231, ed. H.D. Saffcy and I,.G. Wcstcrink (Paris, 1968- ); In Timaeum 3.106.1-17, cd. E. Dichl (Ixipzig, 1903-06); Institutio theologica 24.1-3, 2nd cd., cd. E.R. Dodds (Oxford, 1965). On this whole development sec Gcrsh, to Eriugena, pp. 63, 99, 141 n. 81, to whom this account is much A.C. Lloyd, "The later Neoplatonists." The Cambridge History of Later Greek and Early Mcdic\ al Philosophy, ed. A.H. Armstrong (Cambridge, 1970), p. 307; Philip Merlan, "Zur Zahlenlehre im Platonismus (Neuplatonismus) und im Sefer Yezira," Journal of the History of Philosophy, 3 (1965), 175-76.
From lamblichus indebted;
also
Dionysius the Areopagite, De divinis nominihus 5.6, ed. B. Cordier, PG, 821A. The trans, is that of Gersh, From lamblichus to Eriugena, p. 140. Gersh, From lamblichus to Eriugena, p. Neoplatonists more generally see ibid., pp. 140-41. 12
Ibid., pp. 175-77.
140.
On
Dionysius
and
3:
820D-
other
late
Mathematics, the Monad, and John the Scot
s
459
Conception o/Nihil
Favonius Eulogius, a pupil of Augustine, produced a de Somnio Scipionis in the late fourth century which reflects a Disputatio blend of this sort. On the one hand, Favonius describes the monad as an late
antiquity.
which generates
indivisible unity
and
first
numbers 13 and, on the
all
causes manifested as God,
final
14
mind,
15
other, as the
or soul.
16
As
with
monad can be viewed as the deity The reasons leading mind or soul are far from clear. A much
Dionysius later on, he thinks that the
because of
him
primordial incapacity to suffer division.
to extend this idea to the
more
influential
commentator on the dream of
Scipio, Macrobius, follows
Consistent with his generally Neoplatonic outlook, Macrobius defines
suit.
the
its
monad
as that
"which
is
the beginning and end of
knows neither beginning nor end, distinguishes our understanding of
is
to
applied
Him from
the
all
things but itself
highest
God and
the plurality of things and
17 But, in the same passage, Macrobius goes powers subsequent to Him." on to say that the monad can also be found in the ranks of creatures
below
God,
He
which
innumerable forms of
generates,
including
intellect,
soul,
and
the
1
things.
Also open to some confusion is an author even more central than Macrobius to the educational enterprise of John the Scot and his Martianus Capella. In the seventh book of his Marriage of Mercury and Philology, devoted to arithmetic, Martianus offers both the associates,
Neopythagorean
unambiguous,
crisp,
which they return, creator
God,
Favonius
in
15 16
and a Neoplatonic
contrast with matter in
Eulogius,
Scarpa (Padova, 1974). 14
19
of
definition
principle of numbers, the source from which
all
the
monad
definition of the
a state
monad
of generation.
de Somnio Scipionis 3.1, 4.1-2, 5.12, author see Gersh, Middle Platonism, 2:739.
Disputatio
On
this
the
as
numbers proceed and
as the
20
6.1-2,
to
Even
ed.
L.
Disp. 5.4. Ibid. 6.3, 7.3.
Ibid. 5.2.
Somnium Scipionis 1.6.8, ed. JA. Willis (Leipzig, 1963), 2:19: "Haec finisque omnium, neque ipsa principii aut finis sciens, ad summum refertur deum eiusque intellectum a sequentium numero rerum et potestatum sequestrat, nee in inferiore post deum gradu frustra earn desideraveris." The translation is that of Macrobius, In
monas
initium
Gersh, Middle Platonism, 2:525. 18
In Som. Scip. 1.6.8-9, Willis, 2:19-20.
Martianus Capella, De nuptiis Philologiae Willis (Leipzig, 1983), pp. 263, 269, 270. 20
Ibid. 7.733, p. 264.
et
Mercurii
7.732,
7.743,
7.745,
cd.
J.A.
Colish
460
more problematic
is
the speech of Arithmetica which opens Book
together in
Before
all
things,
let
monad be
the
disparate notions
these
way Martianus lumps
the
7:
numbers coming
called sacred;
have taught that before everything the monad is the original quickener. For if form is an accident 01 to that anything that exists, and if that which numbers is prior which is numbered, it is fitting to venerate the monad before that which has been called the beginning. Then too, I shall not neglect to point out to those who examine the matter that because the monad is unity, it is alone self-sufficient. From it other things are is generated; it alone is the seminal force of all numbers; it alone the measure and cause of increases and the extent of losses. The monad is everywhere a part, and everywhere the whole; it endures through all things. For that which is prior to things existing and which does not disappear when they pass away, must be eternal. and Jove - a conclusion Rightly is the monad called Father of All, corroborated by the causative force of its ideal and intelligible form. have called the monad Concord, others Piety or Friendship, ... Some because it is so compact that it is not cut into parts. But more and father of the properly is it called Jupiter, because it is the head after
and associated with
it
it
gods.
Richard Johnson and E.R.
Burge,
their
in
commentary on Martianus
acknowledge the eclectic character of his treatment of the monad. But, they stress, despite his comparisons between the monad, the in practice Martianus tends to deity, and various benevolent attitudes,
arithmetic,
confine
his
application
of the
function of undergirding
all
monad more
rigorously
to
the
numbers, from the dyad on down,
abstract
in the less
rhapsodic manner of the Neopythagoreans.
Given
this
array
of
possibilities,
Neopythagorean mathematical approaches, how did John the Scot come literalism
from
Neoplatonic
to texts that freely
use
as
it
a
strictly
mathematical
to
mingle these
monad? Was he of the monad and
to grips with the
able to dismiss as an allegorical fancy the theologi/.ing to
theology
concept,
or
did
he
tread
the
monas esto, quam ante Quae si species est accidens cuilibet extantium primo, priusque est quod numeral quam illud numerandum, rite earn ante ipsum, quem principem dixere, veneramur. Nee dissimulabo ex eo, quod monas, retractantibus unum solum ipsam esse ab eaque cetera procreari omniumque numerorum solam seminarium esse solamque mcnsuram et incrementorum causam statumdum per cuncta perque detrimentorum. Quae tamen ubique pars est, ubique totum, Ibid.
cuncta
7.731,
vibrantem
pp.
262-63:
sociati
"Prae
cunctis
igitur
postmodum numeri
affata
principia
sacra
docuerunt.
non absconditur, neque enim, quae est ante extantia et quae post absumpta omnium lovem rite esse nominatam, quod potest non esse perpetua. Hanc igitur patrem testatur. ... Hanc quoque alii quidem idealis illius intellectualisque speciei vis causativa in Concordiam, hanc Pietatem Amicitiamque dixere, quod ita nectatur, ut non secetur sit idem caput ac pater deorum." The partes; tamen rectius luppitur nuncupatur, quod William H. Stahl et al., Martianus Capclla and the Seven Liberal Arts translation is petua;
by
(New York,
1977), 2:276-77.
Mathematics, the Monad, and John the Scot
Ncoplatonic path, equating the
monad
s
Conception o/Nihil
with the deity? John
s
461
work both
as
pedagogue and as a philosopher affords an unambiguous answer. In Periphyseon 3 he adheres expressly to the Neopythagorean concept of the monad. As was suggested earlier, his inspiration here was the need a
to
distinguish
came
causes from God. But even before John
the primordial
to address that problem,
he and
had taken
his circle of educators
a solidly Neopythagorean stand on the
monad
in their
commentaries on
Martianus Capella.
There
some
is
commentaries and
on the relationships among these is not likely to be resolved
scholarly debate
their
authorship, which
a complete critical edition of all the known manuscripts has been made. 22 None the less, a scholarly consensus has been achieved on two until
main
points:
systematic
First,
study
of
while the
who
was Alcuin
it
liberal
whose
in
arts,
first
out
mapped
service
the
Martianus
the
were produced, the program was not activated until the middle of the ninth century under the leadership of Martin of Laon, John the Scot,
glosses
and other Hiberno-Latin masters. Second, while the
literary
form of the
commentary is by nature somewhat fluid, making attribution within a group of scholars joined in a common pedagogical pursuit rather difficult, it
is
agreed that the glosses contained
in a Paris
manuscript published by and those preserved in an Oxford manuscript, Book 1 of has been published by Edouard Jeauneau, 24 may be read as 23
Cora Lutz, which
authentic
brought
indices to
the
to text
the
learning,
and the point of view, which John
of Martianus. 25
In
the
addition,
continental
first
On the status of this question and the scholarly literature pertaining to it, see Gersh, Middle Platonism, 2:799 n. 100; Michael Ilcrren, "The. Commentary on Martianus Attributed to John Scottus: Its Hiberno-I^tin Background," Jean Scot ecrivain, pp. 26571; Claudio Leonardi, "Martianus Capella et Jean Scot: Nouvelle presentation d un vieux ibid.,
probleme,"
21-23,
35-36,
pp.
37-48,
"Martianus Lutz, Kristeller and F.E.
196-207; Schrimpf, 133-34. Authors not
Capella,"
Catalogus
Das Wcrk discussed
des Johannes Scottus Eriugena, pp. by these scholars include Cora E.
Translationum
Commentariorum
et
ed.
,
P.O.
Cranz (Washington, 1971), 2:367-78, who at that point attributed to Martin of Laon the commentary she had earlier published and assigned to Dunchad; and M.L.W. Laistner, "Martianus Capella and His Ninth-Century Commentators," Bulletin of the John Rylands Library, 9 (1925), 130-38, who attributes to Martin the Paris MS. 12960 which was later edited by Lutz and which subsequent scholars have agreed in assigning to John.
John
the
Scot,
Annotationes
in
Marcianum,
ed.
Cora E. Lutz (Cambridge,
MA,
1939).
Edouard Jeauneau, Quatre themes
erigeniens (Montreal/Paris, 1978), pp. 91-166.
Commentary on Martianus," Das Werk des Johannes Scottus Eriugena, pp. Herren,
"The
pp.
269,
21-23,
271,
35-36,
272,
37-48,
274,
285;
133-34;
Schrimpf,
"Zur
Frage
Colish
462
master to gloss Martianus, Remigius of Auxcrrc, shows a close dependence 26
and, on both the Paris and the Oxford stages of the Eriugenian project, as we will see, he shares and expands on John s treatment of the monad in particular.
One
now
of the leading scholars
Leonard!, has argued that this outlook
made
asserts,
to
recover
however,
the
decidedly Neoplatonic. John, he
guide to Martianus, in whose work he sought 27 With respect to the monad, cast of mind.
Platonic
exactly
is
Claudio
texts,
his
Dionysius
the
work on these
at
reverse
is
the
Not only does John avoid speech that would have allowed
case.
lemmatizing the portion of Arithmctica
s
on the Neoplatonic description of the monad as the line dependent on Boethius deity, he also takes a strictly Neopythagorcan He proceeds in a nomonad. the discuss he does in those glosses where
him
to
expatiate
nonsense and non-metaphorical manner. The monad, he states, is the mathematical substratum underlying all numbers, and abstract 28 Whatever their capacity for subdivision and of all numbers."
"the
principle
he
composition,
continues,
numbers are
"all
likewise
reducible
29 Finally, he notes, "once monad, which alone is irreducible." have been reduced, the monad endures ... because above
nothing, since the end of the
In
may be
line
that lies
numbers
all
constituted in
is
there
it
is
it."-
cited
time John had moved
translations,
more
to consider
dcr Authentizitat unscrcr Tcxtc von Johannes Scottus J.J.
By the work he had had the
the Periphyseon.
Platonic theory of the
and he was able
ed.
in
to the composition of that
opportunity to acquire a
Mind of Eriugena,
the
John does not speculate on what the nihil above the monad, or how they are related. This theme is last
one to which he devotes extended attention
Greek
to
numbers
all
O Meara
and
its
monad thanks
to his
merits side by side
Annotationcs
Ludwig Biclcr (Dublin,
in
Martianum,
1973),
pp.
The
125-39;
Scottus Eriugena und die Re/.cption dcs Martianus Capella im karolingischen ed. W. Beicrwaltes (Heidelberg, Eriugena: Studien zu scincn Qncllen,
"Johannes
Bildungswcsen,"
1980), pp. 135-48.
26
27 28
Herren,
The Commentary on
I^eonardi,
John
"Martianus
the
Scot,
numerorum
"omnium
Martianus," p.
Capella et
Annotations principium."
Jean
Scot,"
272.
pp. 202-03.
in Marcianurn, Musica 490.14, ed. Lut/., p. 202: Similarly Arithmctica 366.20, 367.18; Musica 490.15, pp.
155, 202.
2^ Ibid.,
Arithmctica 367.13,
quae non potest 30 Ibid.,
remanet
...
p.
155:
"quando
rcsolvuntur numeri ad
monadem
pcrvenitur
resolvi."
Arithmetica
367.15,
quia supra earn nihil
p.
155:
est,
quia
"postquam
finis
omnium
omnes numeri consummantur, monas in
ea
constat."
Mathematics, the Monad, and John the Scot
s
monad which he
with the Neopythagorean understanding of the
463
Conception o/ Nihil
reflects in
Martianus glosses. In Periphyseon 2, the first point in the work where 31 he holds up these two alternatives almost as he refers to the monad, of the monad as the cause and end of all the notion He cites parallels. his
numbers
one instance of the general philosophical maxim
as
cause can have
effects.
many
32
He
also quotes Dionysius
mathematical understanding of the monad to the 33 and Maximus Confessor s similar analysis in cause,
that a single
yoking of the
monad
as
the
first
commentary on monadic teaching
Gregory Nazianzus, whom Maximus reports as principle that no difference should be admitted into the
Book
not until
is
It
his
"the
First
34 Cause."
3 of the Periphyseon, in the context of defining
and explaining creation ex nihilo, that John makes a preclusive choice between these contrasting approaches. His ultimate goal in this section of the work is to dismiss one Neoplatonic conception of nihil in
nihil
As he
poses the question of nihil, he asks "whether it is the complete privation of essence or substance or accident, 3 or the excellence of the divine superessentiality." The Neoplatonism of of another.
favor
initially
*
both the
which he doctrine
which John supports, and of the privative theory, has been noted by previous commentators on John s
latter position,
rejects,
of nihil,
as
well
as
the
fact
Carolingian discussions of the subject
Cf.
Greek
I.
P.
Sheldon-Williams,
monad and
identifies
it
Philosophy, with God as
which, however, does not mention the
Hiberniae, 9 (Dublin, 1972),
Ibid.
2.618B-C,
p.
Eriugena, p. 140 n. 76. 34 Periphyseon 2.615B, introducatur."
The
trans,
p.
202:
is
responding to recent
addition to older debates.
Eriugena,"
36
What
Cambridge History of Later
522, who claims that John the first cause in Periphyseon
adverts 1.1,
a
to
the
passage
at all.
ed.
and
trans.
I.
P.
Sheldon-Williams, Scriptores
p. 174.
210. This passage
is
he
p.
monad
John the Scot, Periphyseon 2.602B, Ixitini
Scottus
"Johannes
and Early Medieval
in
that
"de
has been noted by Gersh,
monade rationcm
ut
Prom lamblichus
non separatio
in
primo
to
causali
at p. 203.
3.634B, ed. and trans. I. P. Sheldon-Williams and Ludwig Bieler, Scriptores Hiberniae, 11 (Dublin, 1981), p. 60: "utrum privatio totius essentiae vel substantiae vel accidentis an divinae superessentialitatis excellentia." The trans, is at p. 61. Ibid.
I^atini
36
The
fullest
A. Piemonte,
study to date of John s doctrine of nihil in the Periphyseon is Gustavo sobre la creatio ex nihilo en Juan Escoto Eriugena," Sapientia, 23
"Notas
Donald F. Duclow, "Divine Nothingness and Self-Creation in John Journal of Religion, 57 (1977), 110-15 and Sheldon-Williams, intro. to his ed. of Periphyseon 3, pp. 5-11. Briefer accounts are given by Henry Belt, Johannes Scotus Eriugena: A Study in Medie\>al Philosophy (New York, 1964 [repr. of 1925 ed.]), (1968), 37-58; see also
Scotus
Eriugena,"
97 and Maieul Cappuyns, Jean Scot Erigene: Sa vie, son oeuwe, sa pensee (Bruxelles, 1964 [repr. of 1933 ed.]), pp. 344-50. The first scholar to note that John was respond-
p.
Colish
464
has not been appreciated
his use of the
is
Neopythagorean view of the
to exclude the Neoplatonic identification of the
monad
monad
with the
nihil, preserving nihil as a denomination for his handling of nihil in his Johannine homily, with God alone. In contrast where he treats it as the opposite of omnia, in Periphyseon 3 John
and the monad with
deity
of aliquid, here equates the divine nihil with omnia, seen as the opposite with omnia and nihil superessence. In identifying aliquid with essence and arriving at
that
John also has
destination,
to
define the nature of the
which remain eternal in primordial causes, which are created by God and themselves God. For not which are but the mind of God once created, this
purpose
as
the
well,
strictly
supplies him with conceptual
tools
notion
mathematical that
help him
of
the
monad
to obtain the desired
result.
John presents the idea of
as
nihil
the privation of being as the
major traditional position he needs to refute, including under this heading nihil as the absence of species, accidents, and habitus as well as the absence of essence
He
itself.
insists
that
there
is
between
a difference
the privation of being, on the one hand, and the apophatic method as an to the latter, he epistemic approach to God, on the other. With respect reflect appropriate to predicate negations of God, for they not denote do and our awareness of His transcendence any privation they
agrees,
is
it
of substance
means the view, says
already
37
on His
Nihil,
part.
however,
is
when
not acceptable
it
or aptitude of being. Such a privation of being or any function from a being of something it removal John, would involve the
possesses.
the
But,
nihil
that
before the
requires
when
explanation
there were
is
the
no created
creation, nothingness present of their essences or of beings yet in existence that could be deprived 38 second definition of nihil which John rejects, although anything else.
A
the exegetical tradition than he claims, is the identification of nihil with unformed matter. "For He Who made the
there
less
is
support for
it
in
and contemporaries and not just to a remoter past ing to his Carolingian predecessors J.A. Endres, Forschungen zur Gescluchte der fruhmittelalterlichen Philosophic, zur Geschichte der Philosophic des Mittelalters, 17:2-3 (Miinster, 1915), pp. 12-
was
Beitrage 13,
although this forerunner
is
not acknowledged by Piemonte,
"Notas,"
pp.
4M2
n.
6.
Carolingian background see Colish, "Carolingian Debates," scholars mentioned above has noticed the Speculum, 59 (1984), 757-95. None of the mathematical and anti-Neoplatonic aspects of John s treatment of nihil.
For more
37 38
details
on
the
128. Periphyseon 3.634C-D, 3.663C, pp. 60-62, Ibid.
3.634C-D, 3.686A-687B, pp. 60-62, 178-80.
Mathematics, the Monad, and John the Scot
all,"
he plainly
backing up
states,
idea with a
this
465
Conception o/Nihil
made unformed matter
world out of unformed matter 39
s
out of nothing at
number of
familiar
40
arguments.
Having cleared the decks of these alternatives, John turns to two other theories, one of which he plans to refute and the other of which he intends to support. The
equated with
In the
nihil.
first
the
is
section of
idea
that
monad can be
the
Book 3 where he
considers this
John does not mention Martianus
specially, although he cites Boethius as an authority on arithmetic, summarizing and applying the Boethian doctrine of the monad, which we also find in the Martianus
possibility
41
Numbers, John notes, are themselves pure concepts, which can be reduced to the monad, the monad ... is the beginning and the middle and the end of all numbers."42 While they may explain the nature of changeable realities in act and operation, numbers remain eternal in glosses.
"for
their condition as
pure
intelligibles
and share,
in the
monad,
attribute
its
of abstract unity and indivisibility. Given that status, can the
monad be
regarded as the nihil out of which number was created and, through number, the phenomenal world that number can describe? After due consideration,
monad
the
John
with the
monad
reflected
it
any attempt to equate
cause. In thus de-Neoplatonizing the
first
John may well have had in mind nihil lies above the monad. This the
and with
rejects this idea,
remark
his
in the
monad,
Martianus gloss that
clear decision to bring his doctrine of
into line with a purely mathematical understanding of
and
more
still
it
is
commentary on
in
pointedly, Remigius Remigius expressly abandons the philosophical, that is, the 43 Neoplatonic, monad in favor of the exclusively mathematical monad. later,
Martianus.
39
Ibid.
3.636D, p. 66:
materiam de omnino 40
Ibid.
"Qui "
nihil.
The
enim
fecit
trans,
is
mundum
de materia informi ipse
fecit
informem
at p. 67.
3.637C-638C, 3.650B-651A, pp. 68-70, 98-100.
For the whole passage see
3.652B-663A, pp. 102-10. References to Boethius in have been noted by Goulven Madec, "Jean Scot et ses Scot ecrivain, p. 166, who emphasizes the fact that John cites Boethius auteurs," Jean primarily as a mathematician; and Alison White, "Boethius in the Medieval Quadrivium," Boethius: His Life, Thought and Influence, ed. Margaret Gibson (Oxford, 1981), pp. 169, this
section of the Periphyseon
195
n.
51,
arith. 1.32
who emphasizes John
and
Periphyseon
3.652C,
monas."
The
367.7,
quotations from Boethius on the
102: "est enim p. trans, is at p. 103.
Remigius of Auxerre, 367.6,
s
monad
at
De
inst.
2.1.
42
numerorum
ibid.
367.9,
367.13,
Commentum 367.15,
376.9,
in
principium
et
medium
Manianum Capellam,
377.10,
et
365.9, 377.18, 378.5, 378.12, ed.
finis
omnium
365.15,
367.4,
Cora A. Lutz
Colish
466
But John
for that choice.
Remigius offers no reasons
s
reasons for making
He has two aims in mind. First, Periphyseon are quite specific. of any unique metaphysical status by he wants to deprive the monad causes. And second, he wants to use treating it as one of the primordial for the monad as a model for explaining the primordial causes and in the
it
showing why they are not
The primordial
nihil either.
causes,
John agrees, are
eternal,
and they are the 44
Word brings all things into being. agents through which the are not nihil and they are not identical with God Himself. ,
several limitations.
creation
causes
to
They have
While they are eternal once created, they are created. causes have the capacity to be and not to be,
Hence, the primordial which is not true either of the
Yet, they
God
or of nihil. Further, before
God
ordained
phenomenal world, the capacity of the primordial 45 The actualizing of this causes was only potential.
of the
act
as
their own autonomous power but through a capacity occurred not through 46 Thus, the seminal force (vis seminalis) implanted in them by God.
called nihil. Nor, since they are created, are primordial causes cannot be dwell in the mind of God. The they identical with God, even though they nihil out of
which the world was created
Word, John
in the
says,
must be
no creature can possess, even consubstantial with the Word, those causes that occupy the second, or created and creative, subdivision a status that
of nature.
47
With
this
reasoning in place, John arrives
at
his positive definition of nihil as the superessential
aliquid,
the nihil-as-omnia
that
denotes
God
s
his
final
conclusion,
God, the opposite of
superabundant goodness.
that is infra-real but Nihil-as-omnia, John stresses, refers not to a being that are to a being that is hyper-real, "beyond all things that are and 48 In John s terms the divine nothingness is the direct antithesis of not."
the idea of
omnino
nihil,
and
it
is
the only conceivable nihil out of which
196-99. At 367.16-368.18, pp. 182-84, Remigius 1962-65), 2:177, 178, 180-82, the association of the monad with Jupiter by Martianus, and argues vigorously no way are to be under that his remarks here are merely allegorical and that they in
(Leiden, tackles
stood
44 45
46 47 48
literally.
Periphyseon 3.641C-D,
p. 78.
Ibid.
3.642C-644A, 3.663B-670D, pp. 80-82, 126-44.
Ibid.
3.672A-C, 3.679B-C, pp. 146-48, 162-64.
Ibid.
3.679C-680B,
p. 164.
Ibid. 3.681C, p. 168:
"ultra
omnia quae sunt
et
quae non
sunt."
The
trans,
is
at p. 169.
Mathematics, the Monad, and John the Scot s Conception o/ Nihil the world can have been created.
As
the
name
of God, nihil
is
467
thus an
accurate denotation of a divine nature that admits of no privations and
an adequate reflection of the divine transcendence which makes the negativa apposite to the deity.
This
conclusion
is
via
49
of
is,
course,
compatible
perfectly
with
the
Neoplatonic theology which John derived from his Greek sources. But, as paper has sought to show, in the argument John develops enroute to
this
that
conclusion he displays a willingness to dissociate himself from the
Neoplatonic tradition, not only by rejecting a privative view of nihil but also by detaching himself from the Neoplatonic doctrine of the monad.
For
it
he substitutes the Neopythagorean understanding of the monad, by Nicomachus, Boethius, and the Latin transmitters and
mediated
accepted by John himself as a way of teasing the purely mathematical idea
of
monad
arithmetic.
out
of the
tangled
how
After
eclecticism
he
of Martianus this
observing applies metaphysical problems he addresses in Periphyseon conclusions
of our
own.
First,
3,
Capella to
principle
s
the
we may draw two
John was no mere imitator or passive
conduit of his Greek Neoplatonic sources; rather, he wields them with
independence and discrimination. Second, in investigating the intellectual principles that informed John s philosophy, we need to widen our perspective to include the science of school arithmetic, which at
work
in the case just
examined.
Oberlin College
49
Ibid.
3.684C-685A, pp. 174-76.
is
clearly
ANGEL D ORS
On Stump s Interpretation of Barley s De obligationibus
her
In
contribution
valuable
the
to
History of Later Medieval Philosophy
1
important reader Jlie Cambridge Eleonore Stump has looked into
the doctrine on obligations according to Walter Burley (ca. 1275-1344/5)
2
one of the apparently paradoxical examples analyzed In her work, E. Stump the which present paper will focus upon. by Burley does the following: a) tend to the interpretation of two texts by Burley which he respectively formulates and solves the paradox); b) reject and
specifically into
(in
offered by Burley;
solution
the
paradox. In
new
the
my
and
c)
propose a new solution to the
of Burley opinion, both the rejection
s
solution as well as
solution proposed by Stump come about by means of an incorrect of Burley s texts. Burley s solution can be defended. This is
interpretation
of the object of this paper, and along with it a greater comprehension be in my view, the nature and history of the doctrine on obligations can,
obtained.
1.
On
The
the Interpretation of Burley s texts
texts
which Stump tends are the following: ex posito et opposite Item, probatur quod non omne sequens es Romae vel bene negati sit concedendum. Et ponatur ista:
by Burley
321-
to
"tu
A. From the beginning to the early fourteenth century", in J. Pinborg (eds.), The Cambridge History of Later Medieval 315-334. E. Stump has also gathered together a large Philosophy, Cambridge, 1982, pp. Logic of carried out in this work in a later work: the of analyses part 63 (1985), pp. 355-374, in Walter Burley s Treatise on obligations", Synthese disputation to which we can apply everything said in this paper. 1
E.
Stump,
"Obligations:
N. Kretzmann, A.
Kenny
&
"ITie
2
Burley
Treatise
s
unpublished,
by
R.
DC
of a doctoral dissertation, as yet obligationibus is the topic to at the Catholic University of Louvain: An Introduction
Green
texts of William of Sherwood (?) been able to consult this work and texts I have stuck exclusively to the texts therefore s life and works see Una offered in Stump s work. For a complete reference of Burley cultural de Walter Burley, Biblioteca Contexto XIV. del La siglo Juarez, A., Filosofia Ciudad de Dios", Real Monasterio del Escorial, Madrid, 1978.
the
and
"La
Treatise
logical
Walter
De
obligationibus. I
With
have
Burley. Unfortunately for the analysis of Burley s
critical
not
Stump on Burley s De
469
obligationibus
Romae
te esse
est concedendum". Deinde, esse prpponatur: est concedendum". Haec est falsa et impertinens, igitur
Romae
"te
Deinde,
neganda.
proponatur:
posito et opposito bene negati". conditionahs est necessaria:
"si
Romae
concedendum, sed
est
cedendum,
igitur tu es Romae".
Romae
esse
"te
ex haec
sequitur
Haec
est necessaria, quia tu es vel te te esse non est Concessa ista te esse
Romae Romae
esse
con
Romae
"
sequitur ex posito et opposito bene negati", proponatur ista: esse Romae est concedendum". Si concedas, idem concessisti et negasti, igitur male. Si neges, cedat tempus, negasti sequens per regulam. Quia si regula sit bona, tune sequitur: te esse Romae sequitur ex posito et opposito bene negati, igitur "te
"
Romae
te esse
quod haec
Dicitur
3.22:
est concedendum". "
est
te
neganda:
esse
Romae
sequitur ex
opposito bene negati". Nee haec est necessaria. Et, si sit necessanum te esse Romae sequi ex disiunctiva, quae ponitur cum opposito alterius partis, tamen non est necesposito et t
sarium istam disiunctivam poni. E.
Stump
formulated
-
analyzes
the
in the following terms:
Oponens
Romae
est
conce-
dendum
which
the
paradox
is
Ratio
(la)
T
(2a)
F
(Ib) estpositum
(2b) est falsa et imperti-
nens
Romae sequitur e posito et opposito bene negati
(3) te esse
Romae
est
(3a)
conce-
The paradox concede
(4)
T
(3b) (3) follows from the truth of (1) and the falsity of (2)
(4a) ?
dendum
either
in
Respondens
Romae vel te esse Romae est concedendum
(4) te esse
-
3
(1) tu es
(2) te esse
text
first
resides in the fact that the respondent can not in (4a)
because
it
is
the
same proposition
(2)
which he has
already denied, or deny (4) because from (3) which has been conceded there follows the truth of (4). In
my
opinion, in this analysis
incorrect interpretation which
paradox. This
we can
already find the root of the
Stump makes of Burley
s
treatment of
this
so for at least three reasons:
first, because she analyzes the answers given by the respondent in terms of truth (T) and falsehood whereas in the text are in terms of concession and (F) they presented is
negation; second, because (3b) does not constitute an adequate analysis of
P. 323. In the presentation of these analyses I have recuperated of the enunciations translated into English by E. Stump.
the
Latin version
D
470
0rs
the concession of (3); the reason explicitly given in this text in favor of third column and third, because by introducing within the analysis as a the
reasons
given
inadequately in
my
favor
in
opinion
-
respondent s answers, it seems as though these reasons come to be part of of
-
the
the respondent. By the dialogue maintained between the opponent and in her analysis the concession of (3) in terms of truth (T), interpreting is then taken to interpret the negation of (3), which Burley
Stump
the paradox, as a declaration of the falsehood proposes as the solution to what I believe to be Hurley s intention. On the other (F) of (3), against in his text in favor of the concession of hand, the reason Burley gives the not the one to be found in Stump s analysis, but rather is (3)
conditional proposition whose consequent is not necessity of a determined in the first part of the disjunctive (1). If we analy/.e (1) (3) but rather text in the ultimate the form of (pvq), the reason alleged in Burley s the conditional instance in favor of (3) is the necessity (validity) of the of in favor reasons the given Finally, (((pvq)A-iq)^p).
not be interpreted as part of the dialogue respondent s answers must which is initially maintained between the opponent and the respondent of a metadialogue which both maintain around the but rather as part
if the respondent has rules of the the not does obey answered correctly or not and which
initial
dialogue
but
obligations
with
the
rather
object
strict
of
determining
considerations
of
truth
or
falsehood;
the
be even more urgent when and a the very initial dialogue bears upon the conditions of the dialogue, the as same enunciation can be presented as a proposed enunciation and as in the reason for one of the respondent s answers in that dialogue, distinction
between either dialogue
paradoxical
case being analy/ed
is
in
made
to
which an enunciation which
in
the
true is denied in the dialogue metadialogue would be recogni/ed as being has its of repugnance with regard to what in spite of its truth by reason
The relevance of these three observations will previously been conceded. of be made more clearly manifest when we analy/c Stump s interpretation the solution offered by Burley.
Stump
offers
two interpretations of the second
text in
which Burley
to formulates his solution to the paradox: one, more immediate, according and a which Burley s solution would be, in her opinion, extravagant, her opinion, also second more elaborated solution which is, according to
Stump on Burley s DC
4 inadequate although apparently more reasonable. According to of these two interpretations, Burlcy would have maintained in
logically
the
471
obligationibus
first
text that the answer given to (3) is incorrect given that (3) must not be conceded but rather denied and this by virtue of the fact that (3) is not necessary, a fact which according to Stump Burley would have this
concluded by is
is
derived,
text
s
Burley
completely
such a solution would effectively be, as Stump points out, 6 extravagant and completely do away with doctrine on
But what
obligations.
In
virtue, in turn, of the fact that premise (1), from which (3) not necessary. 5 If this happened to really be the meaning of
the
face
is
Stump attempts
leads,
the textual fundament of this
of the
extravagance
to
which
first
interpretation?
this
first
interpretation
a second interpretation which allows a reasonable
meaning to Burley s solution, but this interpretation, in her opinion, makes an important confusion to become manifest. 7 This interpretation is based upon a new analysis of the paradox in the following terms: 8
Oponens
Respondent (1 a)
T
(2
)
q
(2 a)
F
(3
)
p
seqiiitur ex posito et opposito bene negati
(3 a)
T
Ratio
(3 b) (3) follows from the truth of (1) and the falsity
The Stump,
9
previously mentioned confusion would be found, according to it is p and not (3 ) what follows from the truth of (! ) and
that
the falsehood of (2 favor
),
10
"On
8 9
has
to
);
be
sustained in (3 b) as the reason in
such a case, according to Stump s considered as impertinent and, in
the face of
premisses
7
(3)
is
in
Pp. 324-325. it, then, Burley is saying that (3) is to be denied because it is not reason for claiming that (3) is not necessary is that one of the derived from, namely (1), is not necessary" (p.324).
and
necessary,
6
against what
or the concession of (3
interpretation, 4
of (2)
it
is
his
P. 324. P. 324. P. 324. P. 324. "Suppose
we then consider
(3)
irrelevant
and judge
it
on
own
its
merits.
According
Burley, we ought to judge it false. If (3) had read That you are in Rome follows from the conjunction of this disjunction - namely, "You are in Rome or that you are in Rome is to be granted" - with the denial of the second disjunct then Burlcy would, I to
,
D
472
Ors
agreement with Stump s reading of Burley, to be considered as false. This es Romae" follows requires that we do not interpret (3) as if meant "(u
from
Romae
es
"tu
vel
le
Romae non
est
concede
but rather in
1
(3),
concedendum
would not
"ex
posito"
be
false and, in
its
,
my
necessarily refer to the
opinion,
I fail
meaning
my
opinion,
not say that (3)
disjunctive
Stump
s
(1),
esse
te
(3)
would
interpretation, (3)
two interpretations
of Burley
texts.
s
As
three confusions previously mentioned.
we
"
to understand).
of these
neither
and
concedendum"
agreement with Burley as to
ascertaining the true
if
est
which case Burley would have to sense in which case the expression
in
literal
has to be denied (for what reason In
Romae
esse
capable of both are the Underlying is
for the first interpretation, in
meaning of the texts, Burley docs must be denied because (3) is not necessary, but rather stick
to the literal
he says that (3) has to be denied and that (3) is not necessary; neither does he say that (3) is not necessary because premise (1), from which (3)
alleged
not
is
derives,
in
favor
of
(3),
and
to
necessity
necessary,
the this
but
concession is
so
rather because the (metadialogue
positum is not necessary because (1) should be posited.
As grasp
-
for the
since
I
rather
not s) it
of
that
the
(3)
does
because
(1)
necessary not is
not
enunciation which says that (1) is
in
its
necessary but is
the
contingent that such an enunciation
second interpretation, whose meaning I fail to completely fail to understand, as I have already stated, the value and
meaning of the alleged reason in favor of the falsehood of (3) said,
proposition
communicate
-
it
can be
opinion and for reasons I shall soon put forth, that Burley try to defend that (3) should be impertinent and false but
my
docs not
on the contrary, and here is the key to the solution proposed by him, that in the metadialogue from the moment that (2) is denied both (3) and (4) are true but repugnant with regard to the opposite of the rather,
enunciation (2) already negated; for this in the dialogue by virtue of rule 2 of the obligations (omne repugnans opposito bene negati est negandum), although they are true they must be negated. The reason for which
Burley has recourse to the non-necessary nature of (3)
is
not the defense
think, agree that (3) had to be granted. But (3) does not read that way; and if we are considering (3) as it stands, on its own merits, then Burley seems to think we should deny it because the phrase from the positum need not refer to the particular disjunction which just happens to be the positum in this particular case of obligations.
other positum; but unless it refers to It could refer to some Therefore, on Burley s view, it is a mistake to grant (pp. 324-325). (3)"
this
one,
(3)
is
false.
Stump on Barley s De of the falsehood of (3), but rather of in
order for
to
it
because what
is
its
contingency, a needed condition
be repugnant with regard
necessary
is
473
obligationibus
to
some other
From whence
not repugnant to anything.
not necessary) and should be (since
enunciation, (3)
repugnant to In the the opposite of (2)) negated. proposed interpretations it can be seen how by virtue of the inadequate analysis of the reason alleged in favor of (3) there is no adequate separation of the conditions of the can (because
it
is
it
is
dialogue and of the conditions of the metadialogue, and that there comes about an undue transposition of questions relative to the concession or the negation of enunciations in the dialogue to questions relative to the truth or falsehood of enunciations in the metadialogue.
In
opinion, in order to adequately
my
comprehend Burley
need to tend to the global meaning of the stated question: -
pretended with the paradox is to the absurd which furthermore is
is
11
s texts
that
we
which
by means of a procedure of reduction a dialogue
-
to
make problematic
the
value of one of the parts of rule 1 of the obligations: quicquid sequitur ex posito
et
opposite bene negati
est
concedendum, which can also be
expressed in the following terms:
Ax(x sequitur ex posito
etc.
->
x est concedendum),
which has the form of a universal enunciation, one of whose singulars is:
(p sequitur ex posito etc.
->
p
est
The argument around which ponendo ponens (which
Rl
I
shall call
(3)
(p sequitur ex posito etc. p sequitur ex posito etc.
(4)
p
est
from which follows
from
it
concedendum). the question revolves
is
the elemental
argument Al): ->
p
est
concedendum)
concedendum is
(3)
argued (an argument I shall call A2) that given that (4) and Rl, and that (3) has been conceded, if Rl were and
admissible rule (4) would have to be conceded (by virtue of the other part of this same Rule 1 which states: quicquid sequitur ex posito et
concedendum); now, since (4) is the same enunciation (2) which before has been denied we can now not concede it but rather we
concesso
est
to the question in a global manner and this is probably the root of her incomprehension; even in the English translation which she offers of Burley s texts she omits the initial enunciation in which the main question is
E.
what
is
Stump does not tend at
formulated
(p. 323).
D
474
must negate
it
Ors
and therefore we either have
an admissible rule (which
to conclude that (3) should
what Burley concludes) or that Rl what the objection pretends), and since
not have been conceded (this is
is
not
is
(3)
is
(supposedly) necessary and therefore must be conceded, it is concluded that Rl is not an admissible rule. Both arguments, Al and A2, are in my
opinion logically impeccable.
The key
to
s
Burley
solution,
has been
as
denial of the supposed necessity of (3) which
indicated,
lies
the
in
held in the final part of
is
argument A2. Now, why does Burley deny the necessity of (3)? In the paradox, the argument put forth in favor of the concession of (3)
and the argument put
necessity
following argument (which
of
favor
in
its
necessity
its
is is
the
argument Bl): ct
nq
opposite benc ncgati
argumented (an argument I shall call B2) that given that true and necessary since the conditional (((pvq)A-iq) ^p) in
is
(3 b)
ct
p sequitur exposito
)
from which
which
shall call
p sequitur ex (p vq)
(3 b) (3
I
forth
it
fundamenled
is
it
is
necessary, and given
is
that
Burley rejects argument
(3
Bl:
necessary )
is
the
(3
(valid),
necessary,
(3
)
is
)
has
to
true
also
does not follow from
conclusion
and
be conceded. this
premise only but rather requires two complementary premises; argument
Bl must be transformed
into the following
argument (which
I
shall call
argument Cl): p sequitur ex (p v q)
(3 b)
-iq est
ii)
(3
from which
-iq
oppositum bcne ncgali
p sequitur ex posito
)
ct
(P vcl) est positum
i)
it
is
ct
opposito benc ncgati
argumented (an argument
the three premises are true, the conclusion (3 b)
is
necessary given that both
contingent,
we can
not
i)
and
conclude that
shall call
I
is
ii)
(3
)
C2) that given that
also true but that although
are not necessary but rather is
necessary and
is
in
fact
contingent.
This
is,
in
my
opinion, the true
problem put forth by Burley. interpretation offered by in
meaning of the texts and of the is what lies beneath the second
Argument Bl
Stump but however
it
does not come to the fore
her interpretation because she does not approach the matter from the
theory of argumentation but rather from the theory of signification. She considers - incorrectly in my opinion - that (3 b) and (3 ) are two possible equivocal meanings of (3), and that Burley got
them confused
Stump on Burley s DC
475
obligationibus
understand the already mentioned confusion to which Stump alludes). But, in my opinion, this is not the analysis which Burley s text, completely removed from such a confusion, requires. Burley clearly distinguishes between (3 b) and (3 ) and he considers that both (only in this sense can
What Burley
are true. relation
I
denies
there should exist between the two a
is
and hence he denies the truth of the second
of consequence
premise and therefore the truth of the conclusion of argument B2.
2.
Critique of Burley s Solution
Whatever the meaning of Burley
s texts,
whatever his reasons for denying
Stump maintains
(3) as the solution of the paradox,
that Burley s solution does not solve the paradox since the paradox reproduces itself regardless of (3), in spite of the negation of (3), because with just (1) and (2) we would be obliged to concede (4). 12 Her argument (which I shall call Dl) in favor of this thesis is the following:
conceded we also have is
to
concede
Burley has accepted that
(4), that is (4)
if
(3)
follows from (3); and
is it
a condition, in order to admit this, that one also admit the following
argument (which
I
shall call
D2):
P
p
est
concedendum
and, for the
p
est
p E.
est
same
reason, the following argumentation as well:
concedendum concedendum
Stump
est
concedendum.
further considers that there are reasons within the art of
obligations in order to admit this argumentation and she presupposes that 13
Burley admits it. the enunciation p
conceded, and
if
In this manner,
later
if
instead of (3)
we were
to
propose
enunciation would have had to be Romae), we were to propose (4) once more, in virtue of D2,
(tu es
this
seems to have in mind the mistaken notion that if (a) is false, (c) is false hence we can deny (4) and the paradox is solved. But of course, he has not solved the paradox by such means since (c) can be true even if (a) is false. Furthermore, if Burley is willing to accept the inference from (a) to (c), we can show him that on his own views (c) must be true" (p. 325). (a) is here enunciation (3) and (c) enunciation (4). "lie
inference from (a) to (c) depends on accepting as valid the inference from (b) Rome to (c) That you arc in Rome must be granted and there is some reason for accepting the inference from (b) to (c) in an obligations disputation" (p. 325). "The
You
are in
;
D
476
it
would also have
Ors
be conceded, with the resulting reproduction of the
to
14 paradox regardless of the primitive enunciation (3).
There
however here a
is
follows from I
argument
clear
error.
If
Burley admits that
(4)
argument Dl, it is only by virtue of the have called Al whose first premise, for being precisely a rule (3)
as
said in
is
presupposed and whose fundament is none other than ponendo ponens. Why would argumentation D2 also have to be admitted? On the contrary, there are very good reasons making us think
of obligations,
is
the
D2
that
is
an inadmissible argument within the framework of obligations. in the strict sense, would lead us to absolutely concede all
To admit D2,
on obligations not only allow us but even force us to deny true enunciations which are repugnant with regard to previously conceded enunciations or with regard to the opposite of
true enunciations,
and the
rules
previously denied enunciations.
paradox
3.
is
D2
not reproduced. Burley
s
can not be admitted and therefore the solution, therefore, can
be defended.
Stump s Solution
E.
the supposition that the paradox put forth by Burley happens to
Upon
not be solved by him and that
reproduces itself regardless of (3), in argument D2, Stump proposes her own personal solution to the paradox. In order to do this she relies on both argumentation D2 as well it
virtue of
as
on
its
p
inverse (which
est
I
shall call
D3):
concedendum
P
from which she concludes the equivalency of both parts, p and disjunctive (1) which for the same reason would be equivalent
q,
of the
to
(pvq)
or to (qvq) and, in virtue of the idempotency of the disjunctive, also to
"Even
with the denial of
(3),
however, from the truth of (1) and the
Rome. And
falsity
of (2),
given the validity of the inference from (b) Rome it follows that You are in Rome is to be granted. Hence even with the denial of (3), we are committed, on Burley s own views, to the truth of (4). And so, even if we give Burley all he wants, the falsity of (3) and the validity of the inference from (a) to (c), we can demonstrate that the paradox remains. follows that you are in to (c), from You are in it
The respondent
is
same proposition
at
committed (2a)"
to
the
(pp. 325-326).
so,
truth of (4) although
he has correctly denied the
Stump on Barley s DC
p,
or to q.
15
In such a case,
with respect
q,
clear that p (or q) are not impertinent
(pvq) but rather pertinent, equivalents, and that they and therefore (2), which is none other than
to
follow from
is
it
477
obligationibus
that disjunction
insofar as
follows from (1), should not have been denied but rather
it
conceded. This not only would have solved the paradox but indeed it 16 This is Stump s proposed would have impeded its very apparition. Obviously, once D2 is rejected, and for analogous reasons D3 the art of obligations allows to concede something which is false (since
solution.
it follows from something already conceded), we can no longer admit such an equivalency between the parts of the disjunctive, nor can
when
we admit Stump
proposed solution. Burley
s
s
my
solution, in
opinion,
is
the only admissible solution, given the general rules on obligations.
4.
Conclusion
Having seen the foregoing analyses, of
insufficiencies
believe to have clearly
I
of Burley
s
s
texts
shown the
and to have
Stump interpretation come closer to the real meaning of those texts. As a result I do believe that some of the consequences to which Stump comes from her analysis of the nature of the rules on obligations within Burley
would require
revised, but such a task
a
more
s
work have
to
be
detailed study of the whole
work and of course goes beyond the scope of this paper. These analyses, however, do not merely pretend to rectify the
of Burley
s
made by Stump concerning these all, to shed some light on the
interpretations
rather hope, above
on
the doctrine
In
obligations.
my
opinion,
texts
by Burley, but
nature and history of
the distinctions established
between the dialogue and the metadialogue, between the conditions of truth and falsehood in the metadialogue and the conditions of concession and negation in the dialogue, which allow us to deny in the dialogue an enunciation which in the metadialogue
is
recognized as true,
lies
at
the
"And we can also show the converse, that if q is true, p is true. If you grant q, you are granting that p is to be granted. But if you grant that p must be granted, you cannot consistently deny p, and so you must also grant p. Hence, if q is true, so is p. Consequently, p and q are equivalent" (p. 326).
"Hence,
irrelevant.
in
In
between p and really
solved;
place"
(p. 326).
this fact,
q.
or,
case, it
And more
it
is
a
from
mistake
to
consider
(2)
in
the
schematisation
as
the positum and the implicit logical relationship so (2) ought to be granted. In this way, I think, the paradox is accurately, in this way the paradox fails to arise in the first
follows
D
478
Ors
"revolution" brought about by Swyneshed within the rules of P.V. which and Spade speaks of in his contribution to the obligations
root of the
17 same reader.
University of Navarra
17
P.V.
335-341.
Spade,
"Obligations:
B.
Developments
in
the
fourteenth
century",
op.
cit.,
pp.
ALVIN
P.
DOBSEVAGE
DC Guillclmi Occamcnsis dialcctica
Salvete
domini
omncs,
dominacquc,
philosophiae et certe sodales
litteris
professores,
fovendis
latinis.
Hodie argumenta rcnovare volo utrum nominalista sit
studiorum
cultores
aut conccptualista
noster Inceptor Venerabilis.
esse
Et responsum facile in mcntcm evenit. Sunt qui aiunt Guillclmum antcccdentem illorum Rcnati Descartes et Emmanualis Kant et
Summam
delatorem philosophiae scholasticae. Est nobis tigare ad haec omnia noscenda.
Cum nisi
de tempore
et loco
compositions
Summae
Logicae inves-
Logicae non habeamus
coniecturam... Londinii in Anglia fuisse compositam (notat G. Gal). Ibi
amicos Chatton
et
Wodeham
ciae Angliae habuit. Et
Londiniensis. Chatton
Sed
in
"Prologo"
ex ordine Fratrum
Ockham
ct
Wodeham
Summam
Logicae
Summae
Logicae
legit
Minorem
erant
(Gal
et socios
Provin-
socii
Custodiae
Adam
de Anglia
quoque
p. 55-56).
fratris et magistri
notatur:
Quam magnos
veritatis
sectatoribus
afferat
fructus
sermocinalis
scientia, quam logicam dicimus, multorum peritorum docet auctoritas, ratioque et experientia liquido cpmprobat et convincit. Unde Aristoteles, auctor praecipuus huius scientiae, nunc introductoriam
methodum, nunc viam
sciendi
modum, nunc dans
scientiam omnibus
communcm
nulli ad Averroes sapientiam patet accessus nisi in quoque, Aristotelis interpres, in Physicis dialectam dicit esse "instrumentum discernendi verum a falso". Ipsa namque cuncta dubia definit, cunctas Scripturarum difficultates dissolvit et penetrat, ut testatur doctor egregius Augustinus.
et
Et deinde
in
veritatis
"Epistola
Logica enim
appellat,
Prooemialis"
ex
his intellegere quod scientia logica erudito.
Ockham
ipse notat:
omnium
artium aptissimum instrumentum, sine qua potest, quae non more materialism instrumentorum usu crebro consumitur, sed per cuiuslibct alterius scientiae studipsum exercitium continuum recipit incrementum. Sicut enim mechanicus sui instrument! perfecta carens notitia utendo epdem recipit pleniorem, sic in solidis logicae principiis eruditus dum aliis scientns operam impendit sollicite simul istius artis maiorem in logica labilis ars adquirit periliam. Unde illud vulgare solis sapientiale studium negligentibus locum reputo obtinere. nulla
est
scientia
perfecte
sciri
"ars
est"
480
Dobsevage
eorum Swincshcad, Hcytcsbury, Gcrson
In scriptis cst
nominalista
cum
ct
conditorcm
d
ct
suae
scholac
Ailly,
crcdunt.
Ockham Ockham
ct hanc male venit partim Avicennae. Porphyrius quoque partim Augustini, partim huius problematis erat. In libcllo suo Isagogc (sive introductione in Catcgorias Aristotelis) notat Porphyrius a. Genera et species suntne
Aristotclcm a Scotistis male interpretari credit ex auctoritate
St.
substantia aut mentis notioncs? b.
corporalia vel incorporalia?
Si
c.
Si,
modo
fortassc, in se constant, suntne vel
sunt incorporalia, suntne in rebus
sensibus percipi vel eis rebus separata?
Ens horum disputationum Medii Acvi scientiae
mctaphysicam
per
Ockham scqucns
philosophiam
Aristotelem
logicam
e
erat ct
logicam
ct
theologiam
metaphysica
doctrinam
interpretari.
philosophia
et
e
theologia disiungere inccpit.
Primum de
divisione
terminorum
scribit,
subordinata conceptibus scu intentionibus
et
notat
animae".
"voces
esse signa
In cap. 4 ad
metam
venit dicens:
quia terminorum quidam sunt categorcmatici, quidem syncategoTermini categorcmatici finitam et certam habent significationem, sicut hoc nomcn homo significat omnes homines et noc nomcn animal omnia animalia, et hoc nomcn albedo omnes albedincs.... Termini autem syncatcgorcmatici, cuiusmodi sunt tales tantum totus nullus omnis inquantum et aliquis practer huiusmodi, non habent finitam significationem et certam, nee significant aliquas res distinctas a rebus significatis per categoremata. (p. 25) ...
rematici.
,
,
Per se
omnis
,
nihil significat,
sed ante
,
,
,
nomcn hominem
est classis
omnium hominum. Hie videtur logica esse instrumentum ad philosophiam naturalem fovendam. Philosophia naturalis est de rebus. Logica est de sententiis
de terminis universalibus. Et
mentis, est
de multis praedicabilc.
Ockham numquam
Cum
omne
univcrsale est
de scientia humana loquitur universalia apud
sunt individualia. Et logica universali post
rem
refert.
universalia non sunt res extra animam. Propter quod non sunt de csscntia rerum nee partes rerum extra, sed sunt quaedam entia in anima, distincta inter se et a rebus extra, quarum aliqua sunt signa rerum extra, aliqua sunt signa illorum signorum. Sicut hoc nomen universale est commune ad omnia universalia, et per conscqucns est signum omnium aliorum universalium a se. Et ideo potest concedi quod illud universale quod est pracdicabile de quinque universalibus, non tamen pro se sed pro universalibus, est genus ad universalia; sicut aliqua dictio praedicabilis de omnibus dictionibus est nomen, et ...
non verbum, nee participium, nee coniunctio Qui
vult
pleniorem
notitiam
de
universalibus
etc. (p.
et
83)
proprietatibus
habere, legere poterit Porphyrii librum. Sed Porphyrius duabus
eorum
sellis
sedet
De
Guillelmi Occamensis dialectica
ut notat Bocthius. Est inter et
Ockham
alii
scripsisse
Platonem logicam
481
Aristotclcm. Dicit Pater Boehner
ct
Aristoteleam
reapse
formalem
et
universe certam.
Ex
(signum universale) et ex haeccitate (signum individuale), aut connotatione et denotatione, ut hodie dicimus, Duns Scotus viam ad nominalisticam philosophiam logicam discipulo suo Ockham offert.
Et
quidditate
animo
in
illius
Ecclesiae Catholicae movit.
modo
Ockham est omnia eum contra Papam
in et
quaestionem vocare. Amor et Philippo et Ludovico
pro
Logicus erat qui salutem Ecclesiae promovere voluit. Sed hoc contra Papam et pro regibus ille ex ordine fratrum minorum optavit.
Praecepta Ecclesiae Catholicae in toto per fidem, non per philo sophiam noscuntur. Creatio ex nihilo non demonstratur sed sentitur.
Multum de rebus audimus
externis individualibus quas videmus, tangimus, olfacimus,
gustamus ut res particulares notantur. Universalia sunt signa mentis, sunt nomina. Benigne Guillelmo Ockham et Scoto philosophia scholastica fracta et
est.
Ockham fundamentum logicae modernae mathematicae incepit cum terminis syncategorematicis. Necesse esset hoc
Et fortasse formulare
ratum facere per logicos huius temporis ut Quine, Hiz, et al. (Aliquid de theoria Occamensi et quantificationis terminorum et propositionum de modali notatur ab Alfredo J. Freddoso: Ockhatris quoque logica TJieory
hodie
of Propositions. Part unus qui logicam
est
II
of the
Summa
Occamensem
Logicae, pp.
terminis
logicae
19-28.
Ille
hodiernae
investigat et describit.)
Hoc
loco necesse
sit,
credo, tacere. Sed
non
sine
mentione horum
logicorum hodiernorum et eruditorum historiae philosophiae naturalis qui non multum de Venerabilis Inceptoris scriptis logicis investigant. Satinest, si
vobis
quiretis?
acroasin meam ita dedi expolitam, ut improbare non multum De me quidem vestrum erit iudicium. Valete et plaudite.
Western Ct State University
482
Dobscvage
Bibliographia:
Guillelmi de
Cura
Ockham
s
Ockham. Summa
Theory of Propositions. Introduction ab Alfred
Univ of Notre Philotheus
Boehncr G. Gal, Bonavcnturc Univ. N.Y. 1974.
logicae. Ed. P.
Instituti Franciscan!. St.
Dame
J.
S.
Brown.
Freddoso.
Press, Indiana, 46556. 1980.
Boehner. Collected Articles Bonaventure, N.Y. 1858.
on
Ockham.
Institute. St.
Ernest A. Moody. The Logic of Ockham.
New York.
1935.
Ed.
Franciscan
SILVIA
Ancora una volta
DONATI
sulla
nozione di quantitas
materiae in Egidio
II
tema
di
elaborata attirato la si
1
questa
comunicazione
e
Romano*
nozione
la
di
quantitas
materiae
da Egidio Romano. La dottrina egidiana ha gia in passato attenzione degli studiosi; A. Maier fu la prima a sottolineare che
nozione quantitativa introdotta da Egidio, distinguendosi dall estensione, awicina al concetto moderno di massa. 1 II merito di Egidio starebbe
nell aver
fatto
e
analisi
di
oggetto
riconosciuto
quantitative una nozione che, come vedremo, anche
e
presuppongono
utilizzano
loro
nella
come altri
descrizione
un
concetto
autori medievali
dei
mutamenti
pero darne una precisa definizione. stato anche osservato che le maggiori innovazioni medievali sulla
quantitativi senza
E nozione alle
di quantita si
numerose
Un altra
sono avute
discussioni
occasione
di
in
un contesto
connesse
riflessione
per
con i
il
2
teologico;
problema
pensatori
basti pensare
delPEucarestia.
medievali e costituita
dalla questione della creazione di Eva, questione che viene affrontata in
genere nel corso dei commenti
appunto
problema
dell applicazione
della
creazione
al
secondo
libro
delle Sentenze. Ora, e
della nozione egidiana di quantitas materiae al di
Eva che intendiamo occuparci
in
questa
comunicazione.
Questo articolo e il frutto delle ricerche condotte grazie ad una borsa di studio Alexander von Humboldt-Stiftung (Bonn). Intendo ritornare su questo tema in uno studio piu ampio attualmente in corso di preparazione. della
Cfr. 14.
Problem der quantitas materiae", in- Die Vorldufer Galileis im Edizioni di Storia e Letteratura, 1966 p.26-52; cfr. inoltre, J.A. Concept of Matter in Fourteenth Century Science", in: The Concept of
A. Maier,
"Das
Roma,
Jahrhundert,
Weisheipl, The Matter in Greek
,
and Medieval Philosophy, E. McMullin ed., Notre Dame, Indiana, The University of Notre Dame Press, 1963, p.147-169; E. Sylla, "Godfrey of Fontaines on Motion with Respect to Quantity of the Eucharist", in: Studi sul XIV secolo in memoria di Anneliese Maier, a cura di A. Maieru e A. Paravicini Bagliani, Roma, Edizioni di Storia e Letteratura, 1981, p.105-141. 2
Cfr. E. Sylla,
"Godfrey
of
Fontaines...",
p.107.
484
Donati
Secondo di
Adamo.
la
Bibbia? Eva
Pietro
un interpretazione sola
dalla
lettcralc:
costola,
4
secondo
libro dellc Sentenze,
Eva
intcro corpo di
si
fu
attiene a a partire
prodotto senza alcuna aggiunta cstrinscca. In caso contrario, 1
dovrebbe dire che Eva
infatti, si
da Dio a partire da una costola
fu prodotta
ncl
Lombardo,
anche a partire dal materiale
fu prodotta
teorico che
problema pone teologi successivi e dunque qucllo di un aumento non accompagnato da nessuna aggiunta. Parlando di un aumento non dovuto ad alcuna addizione, teologi II
aggiunto.
ai
si
i
medievali vogliono escludere
sia
ipotesi che la materia aggiunta esistcsse
1
precedenza sotto altra forma, sia ipotesi che essa venga creata ex novo da Dio, giacche anche nel caso della creazione di nuova materia il in
1
Eva contcrrebbc
di
corpo
In
costola.
trasformare
la
formazione
di
intero
in
una costola
umano
corpo
Eva rappresenta
non era contenuta
che
discussione
della
materia contenuta
un
a
sufficiente
materia
della
nocciolo
il
effetti,
senza
e
proprio
una quantita
in
creare
un caso limite
allora
se
altra
nella
Dio puo di
materia
materia.
di
La
in
aumento, cui, una ccrta quantita di materia, senza alcuna addizione estrinseca, gra/ie a una sorta di espansione, cresce fino a diventare una quantita maggiore. Per
riformulare
medievali,
porzione
di
la
nei
questionc
termini
adottati
tecnici
dagli
autori
un aumento quantitativo da parte di una ccrta materia che in se stessa rimane sostanzialmentc idcntica.
si
tratta
di
Questo processo appare chiaramente in contrasto con le norme che regolano Paumento in natura. Nella filosofia della natura medievale vengono
distinti
rarefazione. Ora, gli
due
base
della
Nell
aumento
coppia
nozione
la
comunque
autori medievali
aumento, Paumcnto vcro e propria e
di
tipi
di quantita di
sembrano distinguere di
concetti
i
quantita
due di
tipi
di
mutamento
materia
variazione
la
la
materia venga intcsa,
e
delle
sulla
estensione
dimensioni
.
e
propriamcnte intcso, accompagnata da un aumento della quantita di materia. La rarefazione, cstensione aumenta, la invece, non e un aumento reale, giacche, se materia rimane invariata. Ora, aumento reale in natura e sempre un 1
I
aumento per additionem; 3
1
agente
naturale,
che
non ha
il
potere
di
Cfr. Genesi, Lib.I, cap.2, w.21-22. Cfr.
logiae
Lombardi Sententiarum
Petri
cursus
completus,
series
libri
secunda
quatuor, Lib. II, dist. XVIII, cap.5, in: Patroaccurante J.P. Migne, t.192, Parisiis,
(latina),
1880, col.688. Sulla
distinzione
Fontaines...",
medievale
p.105-107.
tra
i
due
tipi
di
aumento
cfr.
E.
Sylla,
"Godfrey
of
La nozione
di quantitas matcriae in Egidio
Romano
485
trasformare poca materia in molta ne di creare nuova materia, puo far crescere un corpo solo aggiungendo dclla materia gia esistente sotto altra
forma. Sulla
possibilita
da parte
Dio
di
causare un tipo di aumento
di
diverse sia dall addizione che dalla rarefazione, un
registrano
aumenta
materia
di
quantita
tredicesimo
nel
S.Tommaso escludono questo sibile e di
senza
secolo
conseguenza respingono
1
la
possibilita di
rarefactione in natura, lo
un
aggiunta
discordant!.
opinioni
cio6 in cui la estrinseca,
Pensatori
si
come
aumento come teoricamente impos-
tipo di
interpretazione letterale della Genesi
data da Pietro Lombardo. Altri autori,
pur negando
alcuna
aumento
come per esempio Egidio Romano,
tipo di
aumento
sine additione et sine
ritengono possibile per Dio.
problema viene chiaramente impostato da S.Tommaso. Nel commento al secondo libro delle Sentenze egli respinge la posizione di II
Pietro
Lombardo defmendola
inintelligibile.
S.Tommaso
distingue due
modi
materia puo aumentare: o secundum quantitatem tantum oppure secundum essentiam. Nel caso di un aumento solo secundum quantitatem, in cui la
una certa materia, numericamente ad un certo momento avra una data estensione e in seguito
cioe relative soltanto alle dimensioni, identica,
acquistera un estensione maggiore. Ora, questo tipo di mutamento, che
comporta soltanto
la
variazione
delle
processo di rarefazione. Se invece essentiam, allora nel corpo, quella
che c era
materia,
alPinizio.
non importa
dopo In
1
la
aumento,
altri
se creata ex
dimensioni,
non e
altro
che un
materia aumenta anche secundum
termini,
novo o
ci
sara altra materia oltre a
sara
stata
preesistente.
aggiunta
Un
nuova
terzo tipo di
6 aumento, diverse da questi due per S.Tommaso non e possibile. Questo passo rappresenta un tipico esempio del modo di procedere che si e menzionato prima: se da una parte S.Tommaso distingue un
Cfr.
Thomas Aquinas,
In
II
dist. XVIII, q.l, a.l, in: Scriptum super libros M.F. Moos, Parisiis, Lethielleux, 1929-1947, vol.11, enim per multiplicationem materiae hoc factum dicant, oportet multiplicatiop.448: nem hanc aut secundum quantitatem tantum attendi, aut secundum essentiam materiae. Si primo modo, sic oportet ut eadem materia numero quae fuit primo sub parvis dimensionibus, postmodum majores dimensiones recipiat: hoc autem idem est quod rarefieri... Si vero multiplicatio essentiam materiae attingat, cum nihil aliud sit multiplicari quam aliquid fieri quod prius non erat, oportet quod aliquid materiae sit sub forma corporis mulieris quod prius sub forma costae non erat...". Cfr. inoltre Summa Theologiae, Pars
Sententiarum,
ed.
P.
Mandonnet
Sent., -
"Si
I,
q.92, a.3,
Taurini-Romae, Marietti, 1952, p.452.
Donati
486
aumcnto
da un aumcnto della quantita
dclla sola estensione
di materia,
7
non introduce alcun concetto quantitative divcrso da quello aumento della quantita di materia Tommaso di estensione. Per descrivere essentiam materiae, usa cioe un concetto secundum di multiplicatio parla dall altra, egli
1
non quantitative. D altronde, poiche aumento della quantita di materia e in se concepito da S.Tommaso come una moltiplicazione della materia 1
come
stessa e
sostrato, e evidente che
1
idea di una
medesima porzione
di
materia che aumcnta quantitativamente pur rimanendo sostanzialmcnte identica
gli
A
volte.
piu
appare
problema
II
inintelligibile.
della creazione di
questo argomento e
Quodlibet; piu tardi al
secondo
il
problema vicne
libro delle Scntcnze.
dottrinale:
continuita
Eva viene discusso da Egidio Romano dedicata una questione del secondo
8
trattato
nuovamente
polemica con S.Tommaso,
in
accetta
egli
pretazione di Pietro Lombardo. La soluzione del problema
un applicazione
della
nozione
egidiana
di
quantitas
commento
nel
una sostanziale
In questi testi troviamo
si
materiae.
1
inter-
fonda su Infatti,
e
proprio grazie a un concetto quantitative diverse da quello di estensione che Egidio puo difcndere 1 idea di un tipo di aumento diverse sia
addizione che dalla rarefazione.
dall
Considcriamo brevemente
Come
e
noto,
Egidio,
la
accanto
nozione egidiana alia
introduce una nozione non spaziale
di quantita.
di quantitas
nozione
tradizionale
di
materiae. estensione,
Egli distingue la quantita
occupa un certo spazio dalla quantita in molta o poca. Infatti, se la medesima quale materia, in condizioni diverse, puo assumere volumi differenti, estensione e quantitas materiae sono carattcristiche diverse. In che cosa consiste la novita di Egidio? Osservando che nella descrizione dci mutamenti in
virtu
dclla quale la materia
della
virtu
la
materia
nozione
quantitative, accanto alia
A
questo
cd.cit.,
8
proposito
cfr.
e
anche
di
volume, compaiono anche espressioni
Thomas Aquinas,
In
II
Sent.,
dist.XXX,
q.2,
a.l,
p.778-779.
anast. rist. Acgidii Columnae Romani Quodlibcta, II, q.ll, Lovanii, 1646, Frankfurt a.M., 1966, p.76-79; In If Sent., dist. XVIII, q.l, a.3, in: Aegidii Columnae Romani In secundum Libmm Sent. Quaestiones, Venctiis, 1581, vol.11, rist. anast. Minerva, Frankfurt a.M., 1968, p.68-73. questi due testi puo essere aggiunto un Cfr.
Minen/a,
A
terzo documento, gentilmente segnalatoci dal. Dr.R. Wielockx (Alhcrtus Magnus-Institut, Sentenze di Egidio Bonn), cioe una prima versione del commento al secondo libro delle tramandataci da Goffredo di Fontaines nel ms. Paris, Bibl.Nat., lat. 15819, f.311ra-312ra (la
questione
sulla
creazione
di
Aegidii
Romani Apologia, Edition
Omnia,
III, 1),
et
Eva si trova al f.311va-b). Su questi estratti cfr. commentaire par R. Wielockx (Aegidii Romani Opera
Firenze, Olschki, 1985, p. 13, nota n.35, p.75-76, nota n.3.
Sulla dottrina egidiana cfr. le opere citate alia nota n.l.
La nozione
Romano
487
Egidio, a differenza di
S.Tommaso
di quantitas matcriae in Egidio
come molta materia o poca matcria
,
e di altri autori, cerca di analizzarle. Egli sottolinea, quindi, che
molto all
si
1
altro
di
tipo 1
giustifica
uso
quantita
come
Egidio, sine
non
che
varia
variare
al
molto e poco questo nuovo concetto
di termini quali
L introduzione et
termini
i
riconducono a determinazioni quantitative. Accanto poco esistenza di un estensione, allora, si deve presupporre nella materia e
di
rarefactione
1
ipotesi di
commento
Nel
.
e
che
.
e detto, di salvare
si
dell estensione
secondo
al
consente
quantitative
a
un aumento sine additione libro
delle
Sentenze,
trattando del problema della creazione di Eva, egli riporta la posizione di
S.Tommaso. La conclusione un tipo
di
di
S.Tommaso, secondo
aumento diverse
dalla
il
o
rarefazione
quale non e possibile
i
quali
non possono trasformare poca materia
quale motive? La ragione risiede nel Essi agiscono tramite
naturali.
possono mutare condensazione,
volume
il
ma non a
di
di
1
modo
in
e
il
proprio degli agenti
moto;
un corpo tramite process!
possono modificare
differenza
la
agenti naturali,
gli
molta o viceversa. 10 Per
di agire
alterazione
osserva
dall aggiunta,
Egidio, e perfettamente corretta per quanto riguarola
di
conseguenza,
di rarefazione e di
quantita di materia; questo
inerisce alia materia piu quantita, intrinsecamente di qualsiasi qualita e della stessa forma sostanziale, oltre 11 la quale 1 azione degli agenti naturali non puo cstendersi. tipo
Non
pero alcuna ragione
esiste
impossibile un tipo di
L aver
dell estensione,
ricondotto
per
aumento quale quello
caratteristiche
molto
quali
come logicamente da Pietro Lombardo.
escludere descritto
e
nell
poco
ambito
quantitative ne fa anche delle determinazioni accidentali della materia: la
materia non e tanta o poca in virtu della propria essenza, della
quantita.
diventi
da
Allora,
poca
molta
nulla
vieta
che
una certa porzione
rimanendo
pur
sostanzialmente
ma
in virtu
di
materia
identica.
La
conclusione di S.Tommaso, sottolinea ancora Egidio, sarebbe corretta se la materia fosse tanta o poca in virtu della sua essenza, osservazione che
sembra una precisa allusione
all
idea tomista di una multiplicatio
secundum
Cfr. Aeg. Rom., In II Sent., p.69: "Scd quidam hoc dictum Magistri et etiam Hugonis, tamquam impossibile et contradictionem implicans reputantes, improbant... Sed isti optime concludunt de actione naturali creaturae...".
Ibidem, p.70: "Ergo, nullum agens creatum potest agere nisi localiter movendo vel quale faciendo. Et quia qualitas supponit quantitatem per quam materia est multa vel pauca et motus localis etiam hoc supponit, quia per motum localem non potest de materia parum fieri multum nee e converse, nullum agens naturale de poterit
materia facere multam nee e
converse".
Cfr. inoltre
Quodl.U, q.ll, p.77-78.
pauca
Donati
488
essentiam materiae. In qucsto caso,
infatti,
aumcnto o
1
la
diminuzione
materia comportcrebbero nccessariamente un cambiamcnto dclla materia in se stessa c come sostrata, consicche in ogni caso di dclla quantita di
dovrebbe effettivamente postulare un aggiunta o materia. Ma poiche la quantita e una determinazione
variazione quantitativa
una sottrazione della
estrinseca
di
si
materia,
qualsiasi quantita. Se
la
montagna fossero considerate forma, esse non differirebbero una quantita maggiore che stessa
la
viceversa.
materia,
se
in 1
un grano
una
all altra.
stesse,
facendo astrazione da ogni
dall altra e all una non competerebbe Di conseguenza, Dio, che a differenza
sostanzialmente
diventi
identica,
da
puo poca
far
che
si
o
molta
12
La posizione tuttavia
di
agire direttamente sulla materia,
puo
degli agenti naturali,
porzione di materia e in potenza a di miglio e la materia di una
qualsiasi
materia
di
Egidio sul rapporto tra materia e quantita presenta lato la quantita viene vista come
una certa ambivalenza. Se da un
una determinazione accidentale
della
materia,
quando viene
dall altro,
considerata nel suo ruolo di principio di individuazione, essa acquista carattere stesso
di
una determinazione
Egidio,
sostanzialmente
quando
la
in
un
certo
differenti,
intrinseca.
senso,
cosi
parti
come
lo
Infatti,
di
come
materia
sono individui
sottolinea
differenti diversi.
il
lo
sono
Allora,
materia aumcnta quantitavamente, ex consequent! essa viene ad
essere moltiplicata anche in se stessa, sebbene solo per accidens.
13
Ora,
queste considerazioni servono a Egidio per dimostrare ancora una volta che gli agenti naturali, non potendo agire sull essenza della materia, non
possono agire nemmeno sulla sua quantita. Sulla base di questo argomento materia egli puo concludere che la facolta di agire sulla quantita della
compete solo all agente che ha 14 materia medesima. Tuttavia, considerando
le
la
gli
Rom., In
si
potrebbe
cose sotto questo punto di
netta la distinzione tra variazione
Aeg.
capacita di creare e di annichilare la
II
Sent.,
p.71:
vista,
forse
"Miramur
Aeg.
Rom., Quodl.ll,
q.ll,
di
enim de dicentibus quod oporteat creare
materiae de se esset multa vel pauca, tune abscinderetur vel annihilaretur aliquid de ipsa materia...". !
che,
puramente quantitativa e creazione
novum subiectum sive novam materiam vel addi aliquid ipsi materiae virtute divina quodcumque sit illud ad quod essentia materiae est in essentia
obiettare
non appare piu molto
forte
ut suscipiatur ibi potentia. Si enim
non posset minorari
nisi
soprattutto p.78: "...quantitas autem, licet per se non essentia materiae per se diversificari non potest,
diversified
essentiam
diversificat
tamen ipsam per accidens. Vel, ut clarius loquamur, licet materia secundum sit diversa, est tamen alia ct alia sub diversis partibus quantitatis".
essentiam non 14
Ibidem,
p. 77.
materiae,
quia
La nozione
di quantitas matcriae in Egidio
Romano
489
15 In nuova materia.
di
effetti, in questa prospcttiva, 1 idea di una porzione materia che varia quantitativamente pur rimanendo sostanzialmente
non sembra esente da
identica
Puo non
materiae
quantitas
teoricamente altri
autori
difficolta.
essere privo di interesse osservare che, se la nozione di
1
e
idea
che
chiave
la
consente
a
Egidio
un aumento sine additione
di
non giungono
alia stessa conclusione.
Un
et
di
sine
giustificare
rarefactione,
esempio e
costituito
da Giovanni Quidort. Quidort e uno dei pochi a far propria la distinzione 16 distinzione che sembra suscitare tra egidiana tra i due tipi di quantita, 17 Nell adottare Egidio piu critiche che consensi. dottrina egidiana, Quidort conia anzi un nuovo termine per designare concetto di quantita di materia egli distingue, infatti, 1 estensione e
i
di
contemporanei
;
la il
la
sottolineando cosi la differenza tra un concetto spaziale e un
tantalitas,
18 concetto non spaziale di quantita.
Ora, Quidort concede, con Egidio, che Dio, a differenza degli agenti
ha
naturali,
la
di
capacita lui
questo significa per
quantita di materia senza contraddittoria cosi
La ragione la tantalitas,
concepita
come
di
1
quantita
della
L idea
di
materia,
tuttavia,
un aumento
della
aggiunta di alcuna materia e per questo autore
lo era per
S.Tommaso. 19
questa posizione? Essa sembra risiedere nel fatto che
pur essendo una proprieta distinta dalla materia, tuttavia e proprieta per se di questa. Per Quidort, allora, una
come una
data porzione di materia, non quantita, anzi, essa
puo
sulla
agire
creare nuova materia.
modificarla.
e,
come per
Egidio, indifferente a qualsiasi
ha una quantita certa e
fissa,
cosicche
nemmeno Dio
20
Egidio sembra prendere
in
esame un obiezione
di
questo genere
in In II Sent., p.71.
16
Cfr. In II Sent., dist.XVIII, q.2 e q.4, in: Jean de Paris (Quidort) O.P., Commentaire sur les Sentences. Reportation, Livre II, ed. J.P. Muller (Studia Anselmiana, LII), Roma,
Herder, 1964, p.144-148, 149-151. Sulle "Godfrey
18
Cfr.
critiche
of
alia
dottrina
egidiana,
A.
cfr.
Maier,
"Das
Problem...";
E.
Sylla,
Fontaines...".
Jean de Paris, In II Sent., p.150.
19
Ibidem, p.146-147.
non determinat sibi aliquem gradum maior et minor... Ad aliud dico quod differunt quantitas materiae et dimensio, quia materia habet certam quantitatem, qua non est maior quantitas vel qua non est minor, et haec, sive materia accipiatur totius Ibidem, p.144,
quantitatis.
147-148:
"Item,
materia prima
Ergo sine mutatione sua potest
mundi sive aliqua determinata materia, secundum se...".
fieri
scilicet
materia partis. Et
ista
quantitas inest ei
Donati
490
in
nozione
di
duzione
della
innovatrice
in
moderna,
realta,
Una
metafisica.
ccrti
per
e,
L intro-
conclusione un ultima considcrazione.
Ci sia consentita
quantitas
rispondc
materiac, a
vicina
vcrsi,
nozione
concetti
che appare
utilizzati
dalla
cosi
scienza
Egidio a un esigenza eminentemente
per
fungono da principi-guida nella metafisica
delle idee che
egidiana e che ritroviamo anche al fondo di questa dottrina e quella della assoluta
che
materia
della
potenzialita
materia
della
potenzialita
E
prima.
siamo
causa
a
a
indotti
assoluta
della
postulare
una
suo essere molta o poca, giustifichi cosi come dobbiamo postulare una determinazione quantitativa per spiegare la sua estensione: in se stessa la materia non e ne molta ne poca cosi
determinazione quantitativa che
come non ha un
il
estensionc maggiore o minore.
Ed
indifferenza rispetto a qualsiasi quantita che una
e grazie a questa sua
medesima porzione
di
materia, di per se, e capace di assumere quantita diverse.
dunque, in questa dottrina una strategia tipica di tendenza a liberare la nozione di materia prima da ogni
Ritroviamo, Egidio,
la
determinazione
senso
della
S.Tommaso
luce
critica
e
ne
che
fisica,
potenzialita. Alia
di
queste
rivolta
da
fisica",
"troppo
metterebbe
in
considcrazioni,
Egidio
a
giacche,
Passoluta
pericolo
risulta
chiaro
anche
S.Tommaso. La posizione parlando
di
il
di
multiplicationem
secundum essentiam matcriae, fa di una caratteristica puramente fisica come la quantita una determinazione intrinseca alia materia. Ora, degno di nota e
anche
il
fatto
che questa e una
S.Tommaso S.Tommaso non
che Egidio rivolge a
Sembra quasi che, per Egidio, formulare una nozione autenticamente metafisica
in altre occasion!.
sia riuscito a
critica
21
di
materia
prima.
Pisa
Egidio adotta la stessa strategia a proposito della materia dei corpi celesti; anche incorretibilita di questi corpi questo caso respinge la posizione tomista, che spiega sulla base della natura della loro materia, in nome dell assoluta potenzialita della dottrina di Egidio Romano sulla materia prima. Cfr. a questo proposito S.Donati, materia dei corpi celesti. Discussioni sulla natura dei corpi celesti alia fine del tredicesimo secolo", in Medioe\*o 12 (1986), p. 229-280. in
1
"La
LEILA
HAAPARANTA
A Frcgcan Perspective into Ockham s Method
1
.
Ockham
For
Conceptual Order
s
William
of
Ockham,
the
is
logic
of
study
the
acts
of intellect
considered as signs which constitute a mental language. In contrast to the
Ockham
conventional spoken and written words,
signify
spoken and written words logicae, the first part of which I
they
signify
naturally what
conventionally.
In his
Summa
that
natural;
is,
regards mental signs as
mainly discuss in this paper, Ockham calls the acts of the parts of mental propositions, intentions of the soul.
shall is,
of
the
soul
something something else (SL I, 12). A not itself an intention of the second
intention
species,
property,
intention.
of
Terms
Ockham
s
the
in
is
is
a
first
tertn
universal,
a
that
is
capable
An
intention
of
signifying
intention signifies something that
soul,
of
sign
soul
intellect, that
e.g.,
first
man,
intention.
and proposition
is
while a
this
man, etc., For example, genus, are terms of second
of second intention belong to the conceptual machinery
logic,
by means of which
Ockham
studies the terms of
first
intention (ibid.).
In the
Summa
logicae,
Ockham
asks whether the units which he
considers to be mental signs are representations in the
mind which would
between
mental acts and the individual objects which are signified, or whether they are acts of knowing themselves. He answers that logic is fall
interested
in
those acts of knowing themselves, and hence, that
we do
not need any intermediate images of objects between mental acts and objects.
As Ockham
from postulating
puts
it,
all
the theoretical advantages that derive
from
acts of understanding can be had without making such a distinction, for an act of understanding can signify something and can supposit for something just as well as any sign (SL I, 12).
Ockham
model so
entities distinct
thus seems to think that because he builds his logical
that he takes the mental units to be signs of a mental language,
he does not have to assume that the mental units are something more than acts. Hence, Ockham does not postulate any images in the mind,
492
Haaparanta acts. Nor does he postulate any ideal which logic would be interested in. thoughts
which would be contents of those objects like propositions or
2. Tfie
Materiality of Logic
The aim
of this paper
logic
through
logic
as
the
in
appears
it
predecessors.
logic,
and
in
considered,
was
which
s
logic
which were made
Frege
Superficially
psychologistic
Ockham
to consider
is
distinctions
and philosophy of nineteenth century
in
contemporaries and closest Ockham s view comes close to his
a
by
represented
number
great
of
nineteenth century logicians such as Beneke (1820, 1842), Sigwart (1873),
Wundt
Erdmann
(1880),
criticized
Gottlob
by
(1892),
and Lipps (1893). Those logicians were
and
Frege
other
Psychologists
antipsychologists.
human thought. Some of them believed that the rules of logic concerning how we ought to think have their origin in psychological laws of association concerning how regarded logical laws as psychological laws of
people
in
fact
Others
think.
our
took
logical
concepts of plurality, relation and possibility, to analyzing the
material,
the nineteenth century that
in
logicians
that
that
is,
logic
speaks is
about
all
metaphysical
reality,
human thought, objects. Of course
logicians different
the
who
realm
of
abstract
considered
branches
within
material logical
psychologists belonged to those
and
logic
studies.
who argued
or the
phenomenal were also
there logic
Frege
and
to
even
if
anti-
that logic mirrors the
realm
a
specific
logical
objectified the transcendental structure of
of abstract
1
is
parallel
distinct from, sense-perception.
By acknowledging
distinction
be two
other
of abstract objects and that our logical source of knowledge to,
basically
represents
the psychological
formal
1
is
logic
something
world, the transcendental conditions of or
the
was one version of the doctrine upheld by a
logic
something, whether that something
realm,
as
human mind.
Psychologistic
number of
such
concepts,
become understood by
objects
among
called
thoughts.
In
source
human
this
way,
of knowledge, Frege thought into the forms
he came to make a
three realms. For Frege, there were the realm of the
See Haaparanta (19885).
A Fregean Perspective into Ockham s Method
493
objects of sense experience, the realm of psychological events, and the 2 realm of logical objects, which provides us with logical concepts. Even if Frege acknowledged the realm of abstract objects, he took
for
it
that
granted
knowledge of analysis.
its
objectivity
structure. This
its
By means
acknowledgements
of this of
the
is
did not prevent us from having because he relied on the method of
method we truth
of
constitutive components of thoughts.
we have
of reason, to which
handle by our methodological
start
with judgements, which are
and
thoughts, 3
direct
Frege
s
come up with
the
logical objects are objects
we
access and which
are able to
tools.
we construe Ockham s procedure in Fregean terms, we notice that for Ockham we neither have direct access to our minds nor to any realm of abstract objects, because there is no such realm for Ockham. If
Ockham
believes in the conceptual priority of ordinary languages. This
belief manifests
itself
For what Ockham thought,
he
which
as a methodological choice in his logical studies.
when he
has at his disposal calls
the
mental
studies the structure of
language,
are
the
grammatical
concepts which pertain to overt languages.
we find George Boole, whose work has a number of traces from Ockham s and other medieval nominalists thought. He even comments on some of their tenets in his more philosophical considerations. He states that if a
Among
the pioneers of
modern
logic in the nineteenth century
by symbols, he would thereby take a step towards a philosophical language. However, he does not recommend the view represented by extreme nominalists which logician should succeed in expressing logical propositions
makes
dependent on language (Boole, 1965, p. 5). What idea resemble the ideas endorsed by Ockham is the fact
logic entirely
makes Boole
s
logical symbols to be founded on the laws of mental processes which they represent (ibid.). Boole s philosophy of logic is a version of psychologistic logic, for he ties
that
Boole takes the laws of the combinations of
the
mechanism of reasoning
to
the
laws
and the constitution of the
intellect. He presumes that if this constitution were changed, our would also turn out to be different from the present one (ibid., p.
human logic
2
See
GLA,
85,
Erkenntnisquellen
GGA der
XXIV, Der Gedanke (1918), KS, p. 353, and I, pp. XVIII Mathematik und der mathematischen Naturwissenschaften
(1924/25), NS, p. 286. 3
See Frege,
Frege,
Was
ist
Uber den Zweck der
Begriffsschrift
eine Funktion? (1904), KS, p. 273.
(1883),
Frege (1964),
p.
101,
and
494
Haaparanta In this peculiar sense, Boole
6).
but
Hence, what Boole of
construction
the
a
is
algebra
not an empty calculus,
medieval nominalists
in
criticizes
we do
the conviction that
s logical
and the mechanisms of the human mind.
structure
the
reflects
it
views
is
precisely
not have direct access to our minds but that
which
language
logical
language takes place by means
mental
the
represents
of the tools received from the study of
overt languages.
Like Boole
s
logic,
Ockham
s
is
his
material in the sense that
is
it
a language which speaks about the realm of the objects of
is
logic
logic
realm. Frege, for his part, assumes that
interested in the psychological
sense experience and the realm of abstract objects, and that
it
is
also
transcendental, for it gives us the structure of thought in general. Frege wants to give us a new language which is not a representation of overt languages but which is a direct symbolic representation of the forms of
Ockham
thought.
and
s
secondarily
notation
model
of
is
the
primarily a
mental,
model of overt languages
whereas
model of the realm of thoughts and
a
is
model
logical
a
Frege
s
conceptual
a representation of the
4
That is, Frege s universal language is be a language of thought itself. What this means is that Frege s and Ockham s interests and objects of study are crucially different. transcendental forms of thought.
meant
3.
to
Ockham
s
and Frege
first-order
Fregean
considered
are
constituted
is
characterized
framework
the
concepts
empirical negation,
conditionality,
Ockham
Models
language
in
by
s
generality,
of
by the idea that objects
Judgements
judgements.
and
by
logical
and
existence,
functions
identity.
Even
are like if
model does not represent the same object as that of Frege s, it Frege s model provided by a conceptual machinery which distinguishes between the material and the formal constituents of is
s
like
propositions.
That
is
because
Ockham makes
categorematic and syncatcgorematic
signs.
such expressions as every, no, some and
both
signification,
which
is
its
context, and supposition, which
For arguments (1985).
in
favour
of
this
a
distinction
Syncategorematic signs include all. A categorematic sign has
meaning independently of a is
between
sentential
a property of a term in a proposition.
interpretation
of
Frege
s
logic,
see
Haaparanta
A Ockham
proposition supposits (SL
a
s
Method
subject
495
a
or
predicate
of a
63).
I,
of three kinds, personal, material, and simple
may be
Supposition
be
can
whatever
that
states
Ockham
Fregean Perspective into
A
term supposits personally when it supposits for the thing which it signifies and when it is significant in suppositing. A term has material supposition when it does not supposit significatively but supposits 64).
(ibid.,
spoken or a written word.
for a
an
for
supposits
significatively.
of
intention
The term man
in
A
term has simple supposition when it the soul and is not functioning "Man"
material supposition, and the term
example of simple supposition. In the intention
species
has
intention of the soul
Accordingly, contains
terms
personal
man which overt
the
of
first
syncategorematic signs.
it
Man
in
latter
is
a
is
an example of species is an
example, the term of second for
supposition,
it
supposits
for
the
signifies.
Ockham
which
language,
terms
intention,
A
name
a
is
man
of
second
interested
is
intention,
in,
and
part of this language, namely, terms of second
intention and syncategorematic signs, consists of the logical vocabulary of this
language.
By means
of this vocabulary
semantic model of the overt language the mental language.
Ockham
formulates a proper and secondarily a model of
itself
5
4. Tlie
Method of Analysis
In
two methodological recommendations were emphasized. grammatical concepts like subject and predicate must not be used
Fregean
First,
logic,
as basic conceptual tools.
out
must
of
method of composing judgements replaced by the method of analyzing
Secondly, the
be
concepts judgements. This is how Frege claims to have found the primitive logical 7 functions which constitute the judgements.
seems that from the Fregean point of view Ockham s logical ought to be criticized for not giving up grammatical tools but praised for adopting the method of analysis in the logical descent to It
studies
This
kind
of
reconstruction
of
Ockham
s
project
is
given
by
Moody
(1953),
on
p. 27.
6 7
See Frege (1964), pp. 2 See Frege,
(1988a, 19885).
-
3,
and Frege an Husserl (1906), BW,
Uber den Zweck der
Begriffsschrift
,
BS
p. 102.
(1964),
p.
101.
Cf.
Haaparanta
496
Haaparanta
when
individuals
Ockham common
terms
divides
Ockham
what
clarifying
having
personal
not
are
as
suppositing terms,
discrete
Ockham
(SL
supposition.
the proper
is
name
Common terms are such 70). Among common
I,
and
discrete
into
supposition
terms. In discrete supposition the term
object or a demonstrative pronoun.
terms
common
calls
of an
suppositing personally
then distinguishes between determinate, merely
confused and confused distributive supposition. A term has determinate supposition when it is possible to descend to particular objects by means of a disjunctive
This
man
man
runs, or that
when
supposition
For example,
proposition.
is
it
runs, or
possible
...
.
A man runs reduced to A term has merely confused is
descend
to
a
to
proposition
with
a
disjunctive predicate involving particulars. For example, Every man is an animal reduces to Every man is this animal or that animal or ... A .
common
term has confused distributive supposition when
descend
individuals
to
is
possible to
a conjunctive proposition. For by means an animal reduces to This man is an animal, and
of
example, Every man is that man is an animal, and
The
it
...
.
three rules of descent which correspond to the three forms of
The
supposition must be used in a certain order. is
supposition
applied
the
first,
rule
for
must be the second, and the
supposition
rule for determinate
confused rule
last
and
applied
distributive
that
is
for
merely confused supposition. For example, the proposition Every man is an animal receives the analysis This man is this animal or that animal or
...,
and
For a
that
man
is
this
animal or that animal or
uses a often
specific read as
symbol
some
.
v,
which behaves
When
for
,
y
= VX
solving
y
The
in
his
somewhere
introduce formulas like
syllogisms, Boole gives solution of the universal
is
.
solution of the universal negative proposition
No Xs
are
Ys
,
symbolically xy
= 0,
is
= v(\-x).
The corresponding forms
for particular affirmative
are
(3)
.
Broadie (1987), pp. 17-25 and pp. 90 - 96. the structure which Boole gives to propositions lies and Frege s analysis. Unlike Frcge, Boole does not
propositions of the forms A, E, I, and O. affirmative proposition All Ys are Xs symbolically v(l-A ) = 0, solutions
(2)
8 ...
that
quantifiers. However, he an existential quantifier
The
and
clarification of this idea, sec
may be noted between Ockham s It
(1)
...,
vx = vy,
meaning Some Xs are Ys
,
and particular negative propositions
A Fregean Perspective into Ockham s Method The very
may remind
of supposition
idea
us
497
of Frege
context
s
which the meanings of words must be looked for 9 contexts. Frege s logical analysis, which starts with
principle, according to
sentential
in
judgements and not with concepts
in isolation, is true to that principle.
10
And Ockham
s descent to individuals may resemble Frege s descent to which are put into the empty argument places of functions in his objects
conceptual notation. This is how things seem to be. But
what Ockham and Frege are doing, crucially different views of analysis.
there
a
is
different
ontological
more
consider
carefully
turn out that they endorse
their
For
doctrines.
we
if
will
Someone might argue
between
difference
great
it
logics,
example,
for
that of course
they
singular
represent
sentences
like
man
are considered by Frege to be compounded out of a refers to an object, and a function name, which which proper name, refers to a function. For Ockham, there are no functions like properties
Socrates
a
is
and relations
in the
world to be referred
to;
a
instead,
man
stands for
particular men.
However, the point which
want to make here
I
a difference between ontologies,
Ockham
not that there
is
is
being a nominalist and Frege
being a kind of Platonist. Instead, the difference which we find between their views from a logical vantage point is precisely due to a difference between the ways they use the method of analysis and thus a difference
between
their epistemologies.
Both Ockham and Frege propositions
Socrates
be a
to
reading
Socrates
as
identical with a
is
man and is
is
Socrates
the
reject
man man in a
.
That
of
such
they do not think
that
essentialist is,
the sense that Socrates
identical with his essence.
is
reading
based on a sharp distinction between the
essence
is
However, Frege s of identity and
is
and vx = v(l-y),
(4)
meaning Some Xs are not Ys (Boole, 1965, pp. 32
-
33).
These formulas bear
a
striking
similarity
to
the
basic
level
of
Ockham
s
analysis,
exception that Boole stops at the structure of propositions given by elective symbols, which serve as concepts, by the symbol v, which stands for the word some and by the symbol of identity. Ockham has only discrete terms, that is, proper names and demonstrative pronouns, and the symbol of
however,
with
the
not
unimportant ,
identity at the basic level.
9 See,
e.g.,
GLA, Vorwort
,
p.
X, and
For the interpretation of Frege 93.
60. s
context principle, see Haaparanta (1985), pp. 79
-
498
Haaparanta
the
of predication, and
is
takes the sentence to
it
11
mean
that Socrates
for his part, construes
under the concept ma/?. Ockham, and a man as names of one and the same object, that falls
is,
Socrates
as suppositing
for one and the same individual (SL I, 43). A apparently similar view is held by Bertrand Russell in Ttie Principles of Mathematics (1903). Russell
between two readings of the sentence Socrates is a man He assumes that one reading expresses a relation of Socrates to the .
distinguishes
man, while the other reading expresses the identity of Socrates with an ambiguous individual (Russell, 1950, pp. 54 55). Frege in the article in his view kind of criticizes this posthumous writings class-concept
there Logik in der Mathematik (1914). He characterizes it by saying that have been people who have held that concept-words are ambiguous names and that a man is hence a new name for Socrates (NS, pp. 230 - 231).
Frcge
criticism
s
meanings which
would not
Ockham
hit
Ockham
s
theory,
according to the
for
gives to such terms as univocity
and ambiguity
common names arc not ambiguous. The name man signifies several individuals equally, but it signifies them by one convention and it is subordinated to one single concept of the mental language,
view (SL
in
Ockham
s
17).
I,
is analysis of universal, particular and singular judgements Frege include which and between distinction based on the functions, objects
s
are concepts and relations. Proper identity statements and predications would remain kept apart in his logic in order that objects and concepts 12
Frege even connects his distinction between objects and concepts with Kant s distinction between intuitions and concepts, which are the apart.
13 two irreducible and indispensable components of our knowledge.
He
with bundles of argues that objects are not identical with concepts or statement. Proper concepts. Hence, Socrates is a man is not an identity statements like Venus is the Morning Star have a special identity
content for Frege.
They
are metalinguistic statements which claim that
two names refer to one and the same object but that they have different senses (Sinne), which they ascribe to the object named, that is, they
11
See, 12
168 13
This -
e.g., is
Frege,
Uber
168 Begriff und GegenstancT (1892), KS, pp.
strongly emphasized by Frege
169.
See GI
A
27, footnote.
in
his
Uber
-
169 and
p. 174.
Begriff und Gegenstand
,
KS, pp.
A Fregean Perspective into
Ockham
to think that the
for a
view,
form
what
signifies
he also claims that
43), but
I,
whiteness is
asserted
is
it
is
499
that
one nature
Socrates
is
it
to all
white
false to think that
sentence
in the
Method
Ockham argues common
express different aspects of the object.
name man
s
white
.
In
is
false
men (SL supposits
Ockham
s
which the subject stands is (ibid., 66), Hence, Ockham and
that the thing for
the thing for which the predicate stands
Frege agree in their criticism against essentialism, but they disagree in what they think of the basic level of analysis. In Ockham s procedure, analysis brings us to the level of individual objects, while Frege s analysis
stops at the level of individuals, concepts, and relations.
5. TJie
Two Epistemologies
But why does Frege stop
at
an earlier
level
treatment of a predicative judgement like allow
any reduction
Frege thinks that via
a
of concept-words
that
a
a sense,
via
is
it
name
a
than
Socrates
names of
to
Ockham? Frege
s
man
does not
objects.
Similarly,
a
is
conceptual component, and only
related
an
to
15
Hence, every mediated by a concept under which that object falls, and every judgement is construed as an expression of an act of knowledge which consists of conceptual components alone or together sense,
apprehension of an object
is
object.
is
with symbolic representations of individual objects.
Ockham, for his part, upholds the view that all terms, both discrete and common, stand in direct relation to individual objects and, moreover, that mental signs are on a par with overt signs, that is, that they also stand in direct relation to individual objects. proposition as a composition of
conceptual components like Frege s Sinne. Of course we might suggest that
between
Ockham
repeated
point
s
and
that
Frege
they put
s
basic
forward
disregarding this alleged difference
Ockham and Frege have Frege gives his main (1892), KS, pp. 143 144. This
remark
(1892), NS, p. 135.
is
crucially
argument for
made by Frege
Ockham
s
model construes a
two names without even a mentioning of
in
the levels
reason for of
different
analysis
the is
ontological
difference
the views.
often
But
and taking into account the fact that different aims in their logical studies,
this
his
tenet
in
his
Ausfiihrungen
Uber Sinn und Bedeutung fiber
Sinn
und Bedeutung
500
Haaparanta
we may formulate
the
answer
in
another
way.
Namely, Ockham is is committed to the
committed to his scarce basic level only so far as he view that his semantic model languages,
model
is
is
model of spoken and written sign-object relations, and that this
primarily a
thus consisting of simple
then automatically extended to the mental realm. if Ockham s mental language may appear to have the
Hence, even
same
constituents as Frege
close to constructing a
new
s
Ockham does not come What prevents Ockham from
conceptual notation,
logical language.
precisely the view upheld by him that the primary which the conceptual machinery of logic is applied are overt spoken and written languages. Surprisingly enough, this conviction brings
constructing
it
is
objects to
Ockham
to a number of logical developments of the twentieth what Ockham does, expressed in contemporary terms, is to century, give a semantic theory for natural languages and not to give a new
closer
for
universal language, which Frege
Academy
s
conceptual notation was meant to be.
of Finland,
University of Helsinki
References
F.E Erfahningsseclenlehre Siegfried Mittler, Berlin, 1820.
Beneke,
als
Beneke, F.E., System der Logik als Ferdinand Dummler, Berlin, 1842.
Grundlage Kunstlchre
alles
des
Wissens,
Denkens
I
Ernst
-
//,
Boole, G., Tlie Mathematical Analysis of Logic, being an essay towards a calculus of deductive reasoning (1847), Basil Blackwell, Oxford, 1965.
Broadie, A., Introduction
to
Medieval Logic, Clarendon Press, Oxford,
1987.
Erdmann, 1923
B.,
Logik (1892), Walter de Gruyter
&
Co., Berlin
und Leipzig,
(3. ed.)
Frege, G., Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Verlag von L. Nebert, Halle a.S., 1879; von I. repr. in G. Frege. Begriffsschrift und andere Aufsatze, hrsg. Angelelli, Georg Dims, Hildesheim, 1964. (Referred to as BS.) G., Die Gnmdlagen der Arithmetik: eine logisch mathematische Untersuchung uber den Begriff der Zahl, Verlag von W. Koebner,
Frege,
A Fregean Perspective into Ockham s Method
501
Breslau, 1884; repr. and transl. by J.L. Austin in Tfie Foundations of Arithmetic I Die Grundlagen der Arithmetik, Basil Blackwell, Oxford, 1968. (Referred to as
Frege,
GLA.) der Arithmetik,
Grundgesetze
G.,
begriffsschriftlich
Band, Verlag von H. Pohle, Jena, 1893. (Referred
to as
abgeleitet,
I.
GGA I.)
Frege, G., Kleine Schriften, hrsg. von I. Angelelli, Wissenschaftliche Buchgesellschaft, Darmstadt, und Georg Olms, Hildesheim, 1967. (Referred to as KS.) Frege, G., Nachgelassene Schriften, hrsg. von H. Hermes, F. Kambartel, und F. Kaulbach, Felix Meiner Verlag, Hamburg, 1969. Frege,
G.,
Wissenschaftliche
Hermes, F. Kambartel, C. Hamburg, 1976. Haaparanta,
L.,
Briefwechsel, hrsg. von G. Gabriel, H. Thiel, und A. Veraart, Felix Meiner Verlag,
Frege s Doctrine of Being,
Ada
Philosophica Fennica 39,
1985. L., Frege and His German Contemporaries on Alethic Moda (1988a), in S. Knuuttila (ed.), Modem Modalities: Studies of the History of Modal Theories from Medieval Nominalism to Logical Positivism, Kluwer Academic Publishers, Dordrecht, 1988, pp. 234 274.
Haaparanta, lities
L., Analysis as the Method of Logical Discovery: Some Remarks on Frege and HusserF (1988b), Synthese 11, 1988, pp. 73-
Haaparanta, 97.
Lipps, T., Grundzilge der Logik, Verlag von Leopold Voss, Leipzig, 1893.
Hamburg und
Moody, E.A., Truth and Consequence in Medieval Logic, North-Holland Publishing Company, Amsterdam, 1953.
Ockham. W. and
S.
of,
Summa
Brown,
Ockham, W.
of,
St.
Logicae (1323 1329), ed. by P. Boehner. G. Gal, Bonaventure, N.Y., 1974. (Referred to as SL.)
Ockham
transl.
and
Notre
Dame
s
Theory of Terms, Part 1 of the
Sigwart, C., Logik, Erster Band, Verlag der H. Tubingen, 1873. Russell, B.,
Summa Logicae, Dame Press,
by M.L. Loux, University or Notre and London, 1974.
intr.
Lauppschen Buchhandlung,
The Principles of Mathematics (1903), George Allen
&
Unwin
Ltd, London, 1950.
W,
Logik: Eine Untersuchung der Principien der Erkenntnis und der Methoden Wissenschaftlicher Forschung, Erster Band: Erkenntnis-
Wundt,
lehre,
Verlag von Ferdinand Enke, Stuttgart, 1880.
BRIAN HENDLEY
A New Look at John of Salisbury s Educational Theory
In recent years, there has life
been
and works of John of of John
edition
critical
s
a resurgence of scholarly interest in the
2
John
City, talks
and a
scholar,
at
appeared with an accompanying 1980, scholars from around the world
just
among
others.
3
Similar
an international Conference held
as well
interest
interdisciplinary
at Salisbury,
book
England, with Tfie
papers being published 4 Careful attention of Salisbury.
a
as to his activities as a student,
Church administrator,
in
later
of the
writings,
s
historian, a classicist, a philosopher,
of John
World
a
on John were given by a
literary
bulk
edition
of John
commemorate the octocentennial of at Fordham University in New York
was shown the
new
volume of
At the Conference held
death.
s
A
appeared.
English and Dutch translation. gathered at various conferences to In
the second
1979, 1
Letters
Maior and Minor has
Entheticus
In
Salisbury.
was
entitled,
paid
John
to
s
and inveterate traveller. Many of the papers challenged his and views argued for a revised interpretation of John and accepted political advisor,
work. It
is
the
in
spirit
of these
"John
of Salisbury
shall take a fresh look at his educational theory. article
Daniel
by
Metalogicon
of
McGarry,
John of
entitled 5
theory of knowledge John develops
what
at stake philosophically
is
I
Salisbury."
in
of Salisbury
s
Entheticus
(Leiden, Netherlands: E.J. 3
John
York 4
of
City,
Salisbury
October
Michael
Wilks
1984). Cf. also
5
my
take
shall
that
1
concentrate on an in
Theory
special
note
of
the the
the Metalogicon in order to see defense of the arts of the Trivium
in
his
W.J. Millor and C.N.L. Brooke (eds.), The Two: The Later Letters (1163-1180) (Oxford, 1979).
John
will
"Educational
1
2
I
revisionists"
Letters
Maior and Minor,
cd.
of John
Jan
of Salisbury,
van
Volume
3
vols.
University,
New
I^aarhoven,
Brill, 1987).
Octocentennial
Conference
held
at
Fordham
25, 1980. (ed.),
The
review of Wilks
of John of Salisbury (Oxford: Basil Speculum, 62 (January, 1987), pp. 220-222.
World in
Daniel D. McGarry, "Educational Theory Speculum, 23 (1948), pp. 659-675.
in
the Metalogicon
of John of
Blackwcll,
Salisbury,"
John of Salisbury s Educational Ttieory and show how
his defense
is
relevant to
some
503
of the educational problems
of today.
McGarry on John
s
article
McGarry s
Educational Ttieory
was
the
in
pivotal
sense
that
introduced
it
many
English-speaking readers to the cultural background and the philosophical foundation for John s defense of the Trivium. 6 John wrote the
Metalogicon as a defense of with
dealing
language:
grammar,
these
because
arts
and
rhetoric,
answer the attacks of those he called the of
broad sense of the three
in the
"logic"
of
their
7
belief
that
reasoning and verbal expression comes as the
fruit
study
He
logic.
"Cornificians"
it
to
decried the
"effective
facility
in
of natural talent and 8
exercise rather than as a product of formal
wrote
who
arts
teaching."
Like contemporary
proponents of education as job-training, the Cornificians were impatient with the time being spent studying great works of the past and dubious of the need to master the rules for effective speaking, clear writing, and
cogent argumentation. They would reduce the attention paid to the arts of the Trivium to a minimum in order to expedite the entry of students into lucrative occupations. They claimed that came as an innate eloquence gift
rather than as the result of formal study.
John was
eminently suited to answer this charge, according to because of his wide reading and love for the classics. 9 As a McGarry, There had been previous studies on John on a more popular level; cf., for example, Clement C.J. Webb, John of Salisbury (London: Methuen, 1932) and Reginald Lane Poole, Illustrations of the History of Medieval Thought and Learning (London, 1920). McGarry s translation of the Metalogicon did not appear until 1955. Scholars
when he
are
still
not
referred to the
Cornifician
motif
in
certain
which
"Cornificians".
John of Salisbury
Cf., s
had in particular individuals John for example, Rosemary Barton Tobin,
Metalogicon,"
History of Education,
13
mind "The
(1984),
pp. 1-6. o
McGarry, 9
This
op.
cit.,
view of John as a most notably by Janet Martin.
traditional
challenged,
p. 660.
lover Cf.
her
of
the
Classics
has
recently
of Salisbury and the interest are her articles,
"John
been
Classics"
dissertation. Harvard, 1968). Also of "John of Manuscripts of Frontinus and of Gellius," Journal of the Warburg and Courtauld Institutes, 40 (1977), pp. 1-26; "Uses of Tradition: Gellius, Petronius and John
(unpublished
Salisbury
of
s
Viator, 10 (1979), pp. 57-76; and "John of Salisbury as Classical Scholar," The World of John of Salisbury, op. cit., pp. 179-201. Further criticism of John s classical scholarship can be found in Peter Von Moos, "The Use of Exempla in the Policaticus of John of Salisbury," in The World of John of Salisbury, op. cit., pp. 207-261. in
Salisbury,"
504
Hcndley
student of the
"Christian
humanism"
of Chartres, he was able to
draw
with upon a deep knowledge of the writings of classical authors together 10 He the Bible and the works of the Church Fathers. proposes that schools adopt the educational
wherein at
"the
lectures,
11 activity."
learning process consists in reading, active attendance reflection, memorization, exercises in imitation and original recitations,
production,
method followed by Bernard of Chartres,
full
John
s
known statement
and review,
all
of which
indebtedness to Bernard to the effect that
is
"Bernard
further
further
stress
marked
student
in his well-
of Chartres used to
compare
us to [puny] dwarfs perched on the shoulders of giants. He pointed out that we see more and farther than our predecessors, not because we have
keener vision or greater height, but because we are
on
aloft
their gigantic
lifted
up and borne
12 stature."
Having traced the intellectual lineage of John s thought, McGarry is the foundation for goes on to say that "John s philosophy of education his whole pedagogical theory, and the key to his philosophy of education 13 This philosophy sees knowledge as based on is his philosophy." general
Reason frees us opinions derived from the senses and imagination. hidden natures to the access us and from deception by opinion gain helps and causes of things. Education seeks to develop reason through the fallible
study of the
arts,
which are
of experience:
light
"efficacious
tools, fashioned
by reason
in the
results expeditious short-cuts to the achievement of
10
R.W. Southern has claimed that there never was a distinctive School of Chartres with its own brand of Christian humanism. Cf. his The Schools of Paris and The School of Chartres," in Robert L. Benson and Giles Constable (eds.) Renaissance
and Renewal "Humanism
in
and
the
the
and his Century (Oxford: Clarendon Press, 1982), p. 113; of Chartres," in Medie\ al Humanism and Other Studies the issue is far from 1970), p. 74. Southern does admit that
Twelfth
School
(Oxford: Basil Blackwell, settled and he refers to criticisms of his view by Nikolaus M. Haring, "Chartres and Paris Revisited," in J. Reginald O Donncll (ed.), Essays in Honour of Anton Charles Peter Dronke, "New Approaches to the School of Pegis (Toronto, 1974), pp. 268-329; de estudios medie\ ales, 6 (1971), p. 117-140; and Robert Giacone, Chartres," Anuario Books and Library at Chartres According to the Cartularies of Notre-Dame "Masters, and Saint-Pere," Vivarium, 12 (1974), pp. 30-51. Also of interest on the topic is J.O. on Cicero s De Inventione by Thierry of Chartres Date of the "The
Commentary
Ward, (ca.
1095-1160?) and the Cornifician Attack on the Liberal
Arts,"
Viator,
3 (1972), pp.
219-273. 11
Ibid., p. 673.
12
The Metalogicon of John of Salisbury, trans. Daniel D. McGarry (Berkeley/Los this remark is commonly attributed to Angeles, 1955, reprinted 1962), p. 167. Although Bernard of Chartres, Raymond Klibansky claims that the original statement comes from 147-149. Priscian; cf. "Standing on the Shoulders of Giants," Isis, 26 (1936), pp. 13
McGarry,
op.
cit.,
p. 664.
John of Salisbury s Educational Theory
would
which
be
otherwise
development of reason
is
too
or
difficult
505
unattainable."
14
The
complemented by acquiring eloquence through
study of the verbal arts. Eloquence enables us to accumulate and
the
what we know by thinking correctly, accurately comprehending what we hear and read, and effectively expressing ourselves in speech distribute
and
15
writing.
have no quarrel with this since I too am a firm supporter of the 16 view that the concerns of wisdom and eloquence are mutual for John. What I cannot fathom is McGarry s attempt to connect John to presentI
day educational thinkers by labelling to
McGarry, According between several of the
"There
in
fact,
advocated
views
of an
his theory as that
exists,
"Idealist".
a remarkable parallelism in
the
Metalogicon
and
corresponding propositions presented by R.M. Hutchins of the University of Chicago in his ... [book] Higher Learning in America, and Hutchins is
an
considered
Idealist
.
Tragmatist or Materialist
The comparison not
there
...
is
no
John was no
that
question
17 ."
of John of Salisbury to Robert
Maynard Hutchins
an apt one. Hutchins was a staunch follower of Aristotle and
Thomas Aquinas. He be
could
clearly
is
St.
believed that the aims and content of education
once
delineated
we recognized
the
importance
of
metaphysics. Metaphysics gives us knowledge of the ordering principles
and causes of order
of
distinction
some as
reality
studies
in
which provide the underlying framework for the education. Even the sceptic must presuppose a
between knowledge and opinion, says Hutchins.
certain, clear knowledge. If there
such,
and
it
be
which there
in
disciplines
should
beginning of our
curriculum."
taught is
is
first.
knowledge, Let us then it
certainty and
let
us
"There
must be
should be taught
enumerate the
place
them
at
the
18
The key idea is that of order. The rational order of the universe can be known and it should be mirrored by the order of studies in school.
14 15
In
a
simplistic
but
oft-quoted statement, Hutchins puts
it
this
Ibid., p. 668.
Ibid., p. 675.
A
1
New Interpretation Cf., for example, Brian Hendley, "Wisdom and Eloquence: of the Metalogicon of John of Salisbury" (unpublished dissertation, Yale, 1967). McGarry, 18
Robert
op.
M.
cit.,
p. 665.
Hutchins,
(November, 1936),
p. 588.
"A
Reply
to
Professor
Whitehead,"
Atlantic
Monthly,
158
506
Hendley
way:
"Education
implies teaching. Teaching implies knowledge.
Knowledge
everywhere the same. Hence education should be 19 Practical applications of ideas have no place in same." the everywhere the proper order of higher education. What can be learned at the is
The
truth.
truth
is
university are general principles, fundamental propositions, the theory of
any discipline, unhampered by any concern for
The university own sake. The role of
results.
their
with
"true
of
"models
as the
rules
"means
for
reasoning
excellence".
scheme
and
is
to supply us
logic are singled out
Grammar, rhetoric, how excellence is achieved". Thus,
of determining classical
speaking, is
the classics in this
of writing,
rules
demonstrative."
rigorously
20
for
pressure
to study things for
is
says Hutchins,
spirit",
or
utility
"conditions
there are
under which
The culmination of
the whole
programme of studies should be metaphysics. Indeed, Hutchins asserts that we can revitalize metaphysics and restore it to its proper place in the higher learning, we may be able to establish rational order in the modern "If
world as well as It
is
21 university."
to reconcile this view of education with that of
difficult
of Salisbury.
who
in the
For one
thing,
John
a
is
self-professed
sceptic
"in
Whether such propositions may be 22
probable certitude." guide our way in
judgements effective
John
matters that are Metalogicon with the disclaimer that to a wise man, I cannot swear to the truth of what I say.
begins his
doubtful
Academic
use
experiences,
of
of
or
false,
I
am
satisfied
with
For John, there are no metaphysical certainties
Human knowledge
education.
sensation
language.
clarify
true
and
and
imagination.
We
learn
critici/e
to
It
begins
to
fallible
advances
communicate
our opinions,
with
through the our ideas and
argue with one another
about the meaning of things. The truths that Hutchins would start from in education are the ideal end or goal that John would have us strive towards, with no guarantee of success.
The
difference between the two
approaches to knowledge can be highlighted by recalling John of universals and his
commentary on Aristotle
s
s
treatment
Organon.
Although he acknowledges Aristotle as the master on the question of universals, John stops short of fully endorsing his position. For Robert Maynard Hutchins, The Higher University Press, 1936, reprinted, 1965), p. 66. 20
Learning
Ibid., p. S3.
21
Ibid., p. 105.
The Metalogicon of John of Salisbury,
op.
cit., p. 6.
in
America
(New Haven: Yale
John of Salisbury s Educational
507
Tiieory
knowledge of the universal was knowledge of sensible things
Aristotle,
under the aspect of their formal cause. The mind is able to abstract a content from particular sense perceptions and use this as a basis for scientific knowledge. For John, we have no such knowledge of universal
the formal aspects of individual things because
seemingly melts
when confronted by
the
strength of reason
"the
principles of
[first]
The
things."
our grasp and we must make do it (figmenta) which reason devises
real nature of sensible things exceeds
with universals which are delves deeper in
"fictions"
of learning, John assures us, their
"as
investigation and explanation of
its
All branches
things."
devise fictions to expedite
"unhesitatingly
23 investigations."
This
reluctance
reality
claim
to
certainty
John
in
our knowledge of sensible
apparent commentary on the Organon. toward Aristotle s Posterior Analytics which
also
is
in
s
relatively
with methods of logical demonstration. Such methods
mathematics,
and
especially
truths; but they are not of
geometry where we
scientific
knowledge
of what
is
may be
deal
is
deals
of use in
with
necessary use in our investigation of sensible
much
Strictly speaking, says John,
reality.
He
indifferent
"there
can be no necessary proof or
corruptible",
so
that
the
demonstrator
should leave
all topics that are not necessary to the dialectician and the seek only probability. John strongly prefers Aristotle s Topics which aids our investigation of probabilities by accounting for the mutual
orator
who
connection of things and words and provides us with an abundance of
to
24
Once
through language that we will advance, if not mathematical (or metaphysical) certainty, then to higher degrees of
reasons.
again
is
it
probability.
McGarry was
complementarity of wisdom and eloquence in John s educational theory. What he failed to appreciate was that John sees the efficacious use of language as our chief means to achieve wisdom. is
advantageous
wisdom."
Ibid.,
of
25
pp.
Universals,"
to
right
"Fluency "only
note the
does not always merit
when
it
is
oriented
Through reading and learning
praise,"
to
facilitated
[the
John
acquisition
by the
130, 135; cf. also Brian Hendley, "John of Salisbury and Journal of the History of Philosophy, 8 (1970), pp. 289-302.
24
tells us;
it
of]
arts
of the
the
Problem
pp. 212, 215, 201. Cf. also Brian Hendley, "John of Salisbury s Defense of the Arts Liberaux et Philosophic au Moyen Age. IVe Congres international de philosophic medievale. Montreal, 1967 (Paris, 1969), pp. 753-762. Ibid.,
Trivium,"
The Metalogicon of John of Salisbury,
op.
cit.,
pp. 91-92.
508
Hendley
we can
Trivium,
an intuitive understanding
attain
help,
Such
into the real nature of things.
(intellectus)
it
or meditative insight
must be learned.
speaking and writing correctly in order to gain comprehensibility in the use of words. We must also learn for
in
disserendi)
(ratio
reasoning"
distinguish the true from the false and what 26
impossible.
Finally,
we must
is
order
science of
be
to
able
disprove
proposed It
in
is
that
learn the art of disputation
either
is
doubtful,
to
necessary from what
or
or
denied,
something 27 one way or another by alleging reasons." precisely because John does not think we
can
underlying principles and causes of things with our natural
is
whereby we
can persuade others of the likelihood of our assertions and seek to or
and
clarity
"the
argumentative
s
language does not come We must master
facility in
naturally, as the Cornificians contend;
rules
God
eventually get beyond fallible opinions and, with
"prove
[simply]
the
grasp
abilities that
he advocates the study of the Trivium. His defense of the verbal arts does not stem from a so-called Christian humanism which values the study of the classics for like
Hutchins who
of
reality
its
own
sake; nor
is
it
the outlook of
someone
patterns the content of education on the rational order
disclosed
to
us
through
It
metaphysics.
rather
is
the
theory sceptic whose scepticism is tempered by an abiding faith in language as the means to overcome the limits of our knowledge and draw closer to the truth. This can be seen in the of
educational
a
he poses for the Cornificians: "Can the secret and hidden recesses [cuniculos] of nature be charted by one who is utterly ignorant questions
of
all
philosophy?
Can
they be understood by one
to speak correctly, nor to
Almost
as
comprehend what
surprising
as
theory with that of Hutchins
his
is
is
attempt
McGarry
s
who knows
written or to
neither
how
28 spoken?"
link
John
disavowal of
s
educational
"Pragmatism"
as
an alternative description of what John is up to. Various scholars have commented on the pragmatic turn to John s thought. According to Peter
Von Moos, fancies
and
for
effective ideas.
26
example, John had
abstract conceptions 29
It
Ibid., p. IS.
Ibid.,p.80.
29
Ibid., p. 18-19.
Peter
Von Moos,
op.
an aversion to felt
purely
theoretical
that the only valid ideas
were
has also been noted by Michael Wilks that the lack
27 28
and
cit.,
p. 209.
509
John of Salisbury s Educational Theory
outcome of ideas was seen by John as the source of bad government as well as bad philosophy. The verbal jugglers of concern for the practical
Metalogicon are the philosophical counterparts of the nonsense minstrels and prince-pleasers he attacks in the Policraticus:
he
criticizes in the
"the
of the
universalists
This
curialium."^
the
is
he espouses a naive
that sort
the
promoted by in its
same nonsense
of the
the nugae
courtiers,
not to suggest that John was anti-intellectual, nor
is
"learning
by
Cornificians.
doing"
I
approach to education of the
think
his
overall
viewpoint
is
and that
scepticism, and
combination of
faith, fallibility, pragmatic bears strong similarities to the thought of the founder of American
it
pragmatism, Charles Sanders Peirce (1839-1914).
John and Peirce
Much
has been written about Peirce
s interest in
Duns
Scotus.
31
It
should
be noted that he read and appreciated other Medieval philosophers, of Salisbury whom he called elegant writer and
also
among them John accurate
"the
32
Peirce
thinker."
specifically
refers to the Metalogicon
men
fitting since both
approaches to the
intellect
alone",
number of
While John admits
because
35
a
s
works
times.
34
and he
This seems
share a healthy scepticism which rejects infallible
truth.
attain necessary truth
the
owned and read John
we
that in
deal only with
mathematics we can
"concepts
he would agree with Peirce that
perceptible by in
regard
to
Michael Wilks, "John of Salisbury and the Tyranny of Nonsense," in The World of John of Salisbury, op. tit., p. 276. For a good sample of John s impatience with verbal jugglers cf. his remarks in the Policraticus, VII, 12, trans, by Joseph B. Pike as Frivolities of Courtiers and Footprints of Philosophers (Minneapolis: University of Baldwin archdeacon of Totnes," Minnesota Press, 1938), p. 261, and his Letter 238, in The Letters of John of Salisbury, Volume Two, op. cit., pp. 450-451. "To
21
for example, John F. Boler, Charles Peirce and Scholastic Realism: A Cf., Study of Peirce s Relation to Duns Scotus (Seattle: University of Washington Press, 1963). 32 Charles S. Peirce, "Letters to Lady Welby," in Philip P. Wiener (ed.), Values in a Universe of Chance (New York: Doubleday Anchor Books, 1958), p. 403.
33
Peirce owned a copy of John s Metalogicon (Paris, 1610) and Opera (Oxford, 1848), according to Max Fisch (personal correspondence, March 6, 1967).
and
Omnia
Weiss (eds.), Collected Papers of Charles Sanders Harvard University Press, second printing, 1960), 1.560. Specific references to the Metalogicon can be found in 2.317, n.l, 2.364, 2.391, n.3, 2.434, and 8.378. Charles
Peirce
Hartshorne
(Cambridge,
Paul
Massachusetts:
The Metalogicon of John of Salisbury,
op.
cit.,
p. 250.
510
Hendley
knowledge is never absolute but always swims 36 continuum of uncertainty and indeterminacy."
sensible reality
Peirce sees the
of
fallibility
human
in a
...
"our
opinion leading to an irritation
of doubt which acts as a stimulus to inquiry, the sole object of which
settlement
the
and
of
the
fixation
of
belief.
37
This
will
is
be
opinion achieved in the long run by the efforts of a community of inquirers using common methods of investigation. Such methods should have a public and
and be directed
self-corrective character
to a
38
common
Although he would substitute an empirical, experimental method for John s more linguistic approach to finding the truth, Peirce would support John s belief that
common methods
through
reach the truth. According to Peirce,
of investigation "all
goal.
we can
ultimately
the followers of science are
animated by a cheerful hope that the processes of investigation, if only pushed far enough, will give one certain solution to each question to 39 This "cheerful hope" of science is an abiding which they apply that we can eventually ascertain by reasoning how things really and it."
faith
truly
are.
In
much
grammar,
the
rhetoric,
same way, John argues and
logic will
that
mastery of the arts of
enable us to rise above the limitations
of the senses and reach an intuitive understanding of the exact nature of
By taking advantage of the stature of the classical authors whose we read and study, we can see more and farther than our predecessors. By learning how to communicate effectively and argue cogently, we can also, in Peirce s sense of community inquiry, stand on things.
works
one another in
Peirce
s
s
shoulder. This similarity of outlook
description
investigators
of the
and
cooperate
of the
procedure "stand
one
upon
is
brought out strikingly
natural sciences
another
communicating observations, examining hypotheses, and against
experience.
The
subject to further testing.
final
results
only
shoulders"
in
testing predictions
provisionally
accepted,
40
Collected Papers of Charles Sanders Peirce, op.
37
are
s
where
cit.
,
1.171.
Ibid., 5.375.
A
good treatment of Peirce s view of community inquiry can be found in John The Spirit of American Philosophy (New York: Oxford University Press, 1966), and in his article, "Community and Reality," in Richard J. Bernstein (ed.), Perspectives on Peirce (New Haven: Yale University Press, 1965), pp. 92-119. E. Smith,
Collected Papers of Charles Sanders Peirce, op.
40
Ibid., 5.413.
cit.,
5.407.
John of Salisbury
s
Educational Theory
511
Such an open-minded approach to the pursuit of truth seems much more in line with John s thought than do the dogmatic pronouncements of 41 Hutchins. McGarry directs By mis-labelling John s position as "Idealist",
most interesting features: the recognition of of human knowledge and the concomitant distrust of claims
our attention away from the
fallibility
its
to certainty, the distaste for intellectual exercises that lead
the
properly trained in
hidden
nowhere, plus powers of reason and the capacity of men, the arts of language, to help one another toward the
in
faith
ongoing
the
truth
we
all
in
the
sense
pragmatic
seek.
This
that
it
is
a
claims
view
would
I
do count
ideas
that
characterize
and
as
that
community inquiry can be an effective means to the truth. It forms the core of an educational theory that still has something to say to us today, faced as we are by challenges to liberal education from contemporary
who
Cornificians truth,
disdain study of the past, seek quick shortcuts to the
and see education as a means of
satisfying
immediate vocational
wants rather than meeting long-range needs. John serves to remind us that we must not neglect our cultural heritage for we have much to learn
from the
"giants"
need some
who
tried to
make
sense out of
life
We
before us.
also
expression and logical thinking, so that we can share and compare our ideas and talk with rather than at or about one another. Above all, we should maintain a sceptical attitude towards discipline in verbal
matters doubtful to a wise man. These are the elements in John
s
defense
of the liberal arts that are worth recalling today.
University of Waterloo
One Hutchins
could
draw
similar
made by another
"Rationality
in
Education,"
parallels
between
John
s
views
leading American pragmatist, John Social Frontier, 3 (December, 1936),
Hutchins Proposals to Remake Higher Education," Ibid. and The Higher Learning in America," Ibid. (March,
and
the
Dewey. pp.
criticisms Cf.
71-73;
Dewey
of s,
"President
1937), pp. 103-104; 1937), pp. 167-169. Also of education to ultimate first principles
interest is Dewey s objection to subordinating derived from Aristotle and St. Thomas; cf. Experience Books, 1963 [1938]).
(January,
and Education (London:
Collier
CHRISTOPH KANN
Zur Suppositionsthcoric Alberts von Sachscn
Die Suppositionstheorie Alberts von Sachscn wird zumeist vordergriindig als
ockhamistisch angcschen und
1st
in
ihrcr
eigenstandigen Bedcutung
umstrittcn. Wcnnglcich Alberts Eintcilung der Supposition mit derjenigen seines Vorgangers William of Ockham ubercinstimmt, so sind doch bei der
einzelner
Behandlung einfacher,
und
personalcr
am
insbesondere
von
Bcispicl
welche
deutlich,
Supposition
Abweichungen
grundlcgcnde Unterscheidung von materialer Supposition betrcffen. Dies wird
welche bereits die
festzustcllen,
wesentliche
Suppositionsartcn
in
erstc,
Alberts ihren
der
Behandlung
iiber
Differenzierungen
materialcn
Ockhams
Modell hinausgeht. Die vorliegende Untersuchung zu Alberts Suppositions sich dahcr auf cine Analyse seiner Behandlung der
theorie bcschrankt
materialen Supposition und
stellt
cinen Bc/.ug zur heutigen Unterscheidung
von Gcbrauch und Erwahnung eines Sprachzeichens her. Albert
materiale
definiert
Supposition
als
eines
Verwendung
"die
Terminus, der fur sich selbst (pro sc) oder eincn ihm entsprcchenden (sibi verwendet wird, welcher simili) odcr nicht cntsprechenden (sibi dissimiii)
modo) oder anders
auf dieselbe Weise (eodcm
welchcm
nicht /ur
cr
(alitcr)
supponiert, und
Be/eichnung beigelcgt ist, und der das, wofiir er r Wcise bezeichnet" (PL 1 ll ).
supponiert, nicht in eigentlicher natiirlicher
,
Alberts Analyse der materialen Supposition geht bereits in der Definition iiber
Ockhams Bestimmung "wenn
vorliegt,
ein
dann
hinaus, nach der materiale Supposition
Terminus
nicht
sondern
signifikativ,
fur
ein
2
gesprochenes oder geschriebenes Wort supponiert" (SL 1,64). Die letzten beiden Teilbestimmungen der Definition Alberts, nach ,
welchen ein material supponierender Terminus seinem Suppositum nicht signifikativ
beigelegt
bezeichnet,
kommen
Albertus (y.itiert in
2
Saxonia,
und
es
nicht
in
eigentlicher
natiirlicher
Weise
material supponierenden Termini generell zu. Die
Perutilis
Logica,
Vencdig
1522,
repr.
Hildesheim
1974;
eigcner Ubersetzung).
William
Hamburg
de
ist
of
1984.
Ockham,
Summe
der
Logik
Uber
die
Termini,
ed.
P.
Kunze,
Zur Suppositionstheorie Alberts von Sachsen iibrigen
Teilbestimmungen lassen sich wie
513
disjunktiv
folgt
gegeniiber-
stellen:
acceptio termini
pro se
pro aliquo I
sibi simili
sibi dissimili
I
eodem modo
supponente
(1)
supponente
(2)
Als
Terminus
eodem modo
aliter
supponente
Beispiel
aliter
supponente
(3)
materialer
Supposition
fur sich selbst nennt Albert die
als
(4)
der
Aussage
Verwendung
"Homo
est
eines
disyllabum".
Den Teilbestimmungen der materialen Supposition als Verwendung eines Terminus fur einen anderen Terminus lassen sich Alberts Beispiele wie folgt in einer Kreuzklassifikation
zuordnen:
pro aliquo
pro aliquo
sibi simili
sibi dissimili
(1)
(3)
Sortes:"Homo est
disyllabum. (supp. materialis)
eodem modo supponente
Plato:
"Homo
est
terminus
prolatus a Sorte." (supp. materialis) (2)
(4)
Sortes:
"Homo
est
animal."
(supp. personalis) Plato: aliter
"Homo
est
terminus
prolatus a Sorte." (supp. materialis)
Homo est animal, (supp. personalis)
Animal praedicatur de homme.
(supp. materialis)
supponente
Amo deum. (supp. personalis)
Amo est verbum. (supp. materialis)
Sortes currit. (supp. personalis)
Sortem currere verum.
est
(supp. materialis)
Kann
514
(1)
Angenommen,
"Homo
Sokratcs sagt
terminus prolatus a
est
"Homo
Sorte",
den ihm entsprechendcn Terminus Weise, namlich material. (2) est
Angenommen,
Sokrates sagt
terminus prolatus a
der
mil
Plato
est
und supponiert
"Homo
"homo"
den
fur
anderer Weise,
in
personal supponiert.
is
"Men
a
3
noun
schlagt als Beispiel vor:
the
in
plural"
bezieht sich
Aussage "Man is uttered in the plural", so fiir den von ihm verschiedenen Terminus
der
steht
und
"men"
namlich material. Auf die Problematik
derselben Weise,
in
fur
derselben
sagt
"man"
supponiert
sagt
"homo"
in
und Plato
animal"
kein Beispiel. Boehner
auf die Aussage
Angenommen, Terminus
hierfiir
und supponiert
so steht der Terminus
"homo"
"homo"
(3) Albert gibt
und Plato
disyllabum",
so steht der Terminus
"homo"
"Homo
Sorte",
ihm entsprechenden Terminus namlich material, wahrend
est
dieses Beispielcs wird im folgenden noch eingegangen. (4)
auf die Aussage
Angenommen,
"Homo
est
wird durch die
animal"
Aussage "Animal praedicatur de hominc" Be/.ug genommen, so Terminus "homine" fur den von ihm verschiedenen Terminus supponiert in anderer Weise, namlich material, wahrend
steht der
und
"homo"
"homo"
personal
supponiert.
Ockhams demgegeniiber
Differenzicrung lediglich
die
matcrialen
der
Unterscheidung
Supposition
vor,
daB
ein
sieht
material
ihm selbst supponierender Terminus fiir sich selbst oder fiir eincn von verschiedenen Terminus steht (SL 1,67). Eine Entsprechung zu Alberts Fallen (1) und (2) weist Ockhams Modell nicht auf. Die Teilbestimmung, nach der ein material supponierender Terminus seinem Suppositum nicht signifikativ beigelegt ist, erlautert Albert anhand Die Aussage "Vox est monosyllaba" legt eines Beispiel wie folgt (PL 11 ): zunachst die Auffassung nahe, daB hier ein Fall mctasprachlicher Bezugnahme und damit materiale Supposition vorliege. Indessen handelt es sich
nach Albert
um
personale Supposition, da
"vox"
selbst
sich
signifikativ
Entsprechend argumentiert er in Bezug auf den vierten beigelegt ra von hypothetischen Zweifel (PL 12 ) hinsichtlich der Supposition auch hier einerseits innerhalb der Aussage "Vox est sonus". Zwar scheint sei.
"vox"
der Terminus
"vox"
material zu supponieren, da er
andererseits aber personal, da er (sich
selbst)
fiir
signifikativ beigelegt
Albert spricht in der Widerlegung dcs Zweifels (PL 12 3
Ph.
Boehner,
(1958), S. 240-289.
"A
Medieval
Theory
of
Supposition",
sich selbst steht,
in:
va )
ist.
dem Terminus
Franciscan
Studies
18
Zur Suppositionstheorie Alberts von Sachsen personale Supposition zu, was so zu erklaren
"vox"
ist:
515
Fur sich
selbst
zu
zwar eine mogliche, jedoch weder eine notwendige noch eine hinreichende Bedingung fiir materiale Supposition. Das Stehen eines stehen
ist
Terminus
fiir
Umgekehrt
sich selbst impliziert also nicht seine materiale Supposition.
impliziert jedoch die signifikative
Verwendung
seine personale Supposition, da signifikative
eines
Terminus
bei materialer
Verwendung und einfacher Supposition per defmitionem ausgeschlossen ist. Hieraus wird klar, daB in der Aussage "Vox est monosyllaba" das Subjekt fiir sich und personal, in der Aussage "Homo selbst und material supponiert. Wahrend
selbst
sich fiir
in
est
disyllabum"
dagegen
der ersten Aussage
in
fiir
"vox"
sein urspriingliches Signifikat, d.h. einen Stimmlaut, steht, supponiert
der zweiten Aussage
"homo"
offensichtlich
nicht
fiir
seine urspriing-
Menschen, sondern fiir ein Sprachzeichen. Teilbestimmung, nach der ein material supponierender
lichen Signifikate, d.h.
Die
letzte
Terminus dasjenige, wofiir er supponiert, nicht Weise bezeichnet, betrifft mentale Termini,
in eigentlicher natiirlicher d.h.
nicht
die
Termini,
aufgrund von Beilegung, sondern natiirlicherweise etwas bezeichnen. Einem mentalen Terminus, z.B. "Mensch", kommen zwei mogliche Verweisungsfunktionen
zu:
dasjenige bezeichnen,
Terminus bezeichnet;
er
in
eigentlicher
natiirlicher
Weise
was er vermittels eines konventionell beigelegten dieser Weise bezeichnet der mentale Terminus
in
Menschen und supponiert personal. Andererseits kann allgemeiner natiirlicher Weise dasjenige bezeichnen, was er ohne
"Mensch"
er in
kann
Einerseits
einzelne
Vermittlung eines konventionell beigelegten Terminus bezeichnet; er bezeichnet dann sich selbst bzw. ihm entsprechende Termini und supponiert material, wie z.B. in der mentalen Aussage "Mensch ist ein mentaler Terminus". Der mentale Terminus "Mensch" supponiert also nur
dann
material,
natiirlicher
wenn
Im Rahmen unterscheidet diskrete
er
fiir
dasjenige
was
steht,
er
in
allgemeiner
Weise bezeichnet. einer Aufstellung von
Albert
und eine
hinsichtlich
der
Suppositionsregeln
materialen
(b) determinierte Supposition,
der komplementaren Suppositionsarten
-
was
folgendes
(PL 12
Supposition -
eine
f.)
(a)
unter Einbeziehung
Schema
ergibt:
Kann
516
Bcmcrkenswcrt
daB
ist,
es sich hicrbci
um
cine Untcrscheidung handelt,
die in Alberts urspriinglicher Eintcilung dcr Supposition
bei
Ockham und den
ra (PL ll ) sowie
bekanntcn Autoren dieser Tradition
iibrigen
lediglich
Differenzierung der personalen Supposition vorkommt. Als die ersten beiden Suppositionsregeln (PL 12 ) gibt Albert an, daB das Subjekt einer als
singularen Aussage, z.B.
"Sortcs
currit",
"Isle
homo
currit",
immer
diskret,
Aussage, z.B. "Homo est animal", aber Subjekt determiniert supponiere. Im AnschluB an die zweite Regel merkt Albert ausdriicklich an, daB die genannten Regeln neben der personalen auch die das
indefiniten
einer
materiale
betrcffen.
Supposition
Albert
nennt
Supposition
die
Als
Aussage
materiale
diskrete
fur
Beispiel
est
"Sortes
nomen",
fur
determinierte materiale Supposition die Aussage "Homo est nomen". Die Unterscheidung einer diskreten und einer determinierten materialen 4 Supposition hebt Boehner als einen besonders interessanten Aspekt in der in der Suppositionseintcilung Alberts hervor und merkt hierzu an, daB
Penttilis
Logica dieses
Aussagen
in
disyllabum",
keine
Stelle
Typs der
zu
fmden
thematisiert
der
also
sei,
wlirden,
an
der
etwa
Subjcktterminus
auch
"Omne
(c)
universelle
homo
est
konfus-distributiv
supponierte. Boehner venveist auf cine anonyme Handschrift des friihen 15. Jahrhunderts in der Wiener Dominikanerbibliothek, in der eben diese
Aussage mit material supponierendem und allquantifiziertem Subjekt vorkommt. Indessen ist hervorzuhebcn, daB der genannte Aussage-Typ durchaus auch bei Albert erwahnt wird. Im Kontext der personalen Supposition
fiihrt
Albert anhand des Beispiels
"Homo
est
disyllabum",
in
genereller Terminus material supponiert, eine allgemeine materiale Supposition ein und nennt im AnschluB an die Frage, wie diese
welchem
ein
Aussage
universalisiert
disyllabum"
(PL
ll
va ).
werden konne, das Beispiel
DaB
das distributive Zeichen
4
Ph. Boehner, Medieval Manchester 1952, S. 103f.
Logic.
An
Outline
of
its
"Omne
"omne"
Development
homo
est
hierbei nicht
from
1250-1400,
Zur Suppositionstheorie Alberts von Sachsen
dem grammatischen
Geschlecht von homo,
immer material supponiert
ein
1st
hat,
maskulinum, angeglichen Wort, welches auch
i.e.
wird, begriindet Albert mit folgender Regel:
517
"Jedes
und undeklinierbares
neutrales
Nomen."
Aufgrund dieser Regel liegt den Fallen (3) und
zwischen
ausdriicklich
fur
differenziert,
Beispielsatz angibt.
Denn
die Moglichkeit nahe,
materialen
der
(4)
Fall
nicht
(3)
ein undeklinierbarer
daB Albert, der nicht
Supposition
keinen
zufalligerweise
Terminus kann eben nicht
von seiner urspriinglichen Form abweichen, urn fur einen dann von ihm verschiedenen Terminus material zu supponieren. Hieraus ergabe sich, daB das von Boehner angefiihrte Beispiel fiir Fall (3) inadaquat ware, denn von "Men
is
a
noun
in the
zu
plural"
"Man
is
uttered in the
wird der
plural"
material supponierende Subjekt-Terminus verandert. Ein in Analogic zu Fall
(4)
konstruiertes Beispiel
Nimmt man
auf
die
grammatisch
"Homo
Aussage
unkorrekte
Fall (3) verdeutlicht die Problematik:
fiir
-
est
"Homo
disyllabum"
durch
est
Aussage disyllabum Bezug, so wird dies zwar der Regel gerecht, nach der hier die material
supponierenden komplexen Terminus
gleichbleibt,
Nimmt man
jedoch trifft die Bestimmung aber auf die Aussage "Homo est
"pro
die
est
est
"Homo
sibi
-
verum"
Form
des
disyllabum"
dissimili"
nicht
zu.
durch die Aussage "Hominem esse disyllabum est verum" Bezug, so ergibt sich zwar einerseits eine grammatisch korrekte - Aussage nach dem Muster von Alberts Beispiel
"Sortem
currere est
genannte Regel verstoBen.
verum",
Denn
Terminus "Hominem
"Hominem
"hominem"
zwei-, sondern
"homo"
esse disyllabum est
abgewandelt
esse disyllabum est
"Homo
est
disyllabum"
darf nach ihr nicht zu verum"
werden.
verum"
aber wird gegen die
andererseits
der in der Aussage
material supponierende Terminus
der Aussage
disyllabum"
falsch,
dem
in
material supponierenden
Zudem denn
ist
die
"hominem"
Aussage ist
nicht
dreisilbig.
Die Unterscheidung von materialer und personaler Supposition wird ha ufig mit der heutigen Unterscheidung von Gebrauch und Erwahnung bzw. use und mention eines Sprachzeichens in Verbindung gebracht. Die genannte Parallelisierung ist insofern naheliegend, als das grundsatzliche
Motiv der
mittelalterlichen
und
der
modernen Unterscheidung
darin
dem Bezug von Sprachzeichen auf Dinge, d.h. gewohnlichen Signifikate, und dem Bezug von Sprachzeichen auf Sprachzeichen zu differenzieren. Dennoch ist die Gleichsetzung von iibereinstimmt, zwischen ihre
personaler
Supposition
mit
dem Gebrauch
eines
Sprachzeichens
und
Kann
518
materialer
Supposition
dcr
mil
Erwahnung
cines
Sprachzeichens
bei
gcnauer Betrachtung inadaquat.
Mensch ist ein Lebcwesen", so man die Aussage liber eincn Menschen zu sprechen. um Wort man das Mensch, gcbraucht Von dem Wort Mensch ist in dieser Aussage nicht die Rede. Spricht man Mensch ist ein Lebewesen", indem man andererseits iiber die Aussage /..B. sagt, daB in ihr das Wort Mensch vorkommt, oder bildet man die Aussage "Mensch ist einsilbig", so gebraucht man das Wort Mensch nicht, Bildet
"Ein
"Ein
sondern erwahnt
es.
Hierzu bemerkt Tarski:
In Verallgemeinerung dicscr Ansicht hatten wir dann hinzunehmen, daB jedes Wort bisweilen als sein eigener Name auftreten kann; in der T erminologie der mittelalterlichen Logik hieBe das, daB das bctreffende Wort in Suppositio materialis verwendet wird und nicht d.h. in seiner gewohnlichen Bedeutung. Die in Suppositio formalis ,
Konsequenz hiervon ware, daB jedes Wort der gewohnlichen oder wissenschaftlichen Sprachc mindestens zwei Bedeutungen hatte, und nian brauchte Beispiele fiir Situationen nicht von weither zu holen, in denen ernste Zweifel auftriiten, welche Bedeutung gerade gemeint Mit dieser Konsequenz wollen wir uns nicht abfinden und es ist. lieber zur Regel macnen, daB jeder Ausdruck (wenigstens in dcr SchriftspracheJ von seinem Namen unterschieden werde. Damit entsteht das Problem, wie man allgemein Namen von Wortern und Ausdriicken bilden soil. Hierfiir gibt es mehrere Moglichkciten. Die einfachste von ihnen besteht in der Vcrabredung, den Namen eines Ausdrucks dadurch zu gewinnen, daB man den Ausdruck in
Anfiihrungszeichen
Wesentlich hierbei
ist
setzt.
nun, daB Mensch ein genereller Terminus,
"Mensch"
aufgrund der Anfiihrungszeichen als sogenannten namendagegen bildcndem Funktor - ein singuliirer Terminus ist, den wir gebrauchen, um
den urspriinglichen Ausdruck ohne Anfiihrungszeichen zu reden, bzw. ihn zu erwahnen. Nach der Konvcntion der Anfiihrungszeichen steht also iiber
der Ausdruck
"Mensch"
(mil Anfiihrungszeichen) nicmals
fiir
den Ausdruck
"Mensch" (mit Anfiihrungszeichen), sondern immer nur fiir den Ausdruck Mensch (ohne Anfiihrungszeichen). Ein mit Anfiihrungszeichen gekennzeichneter Terminus steht also als solcher niemals fiir sich selbst.
Infolge der Gleichsetzung mit der
Erwahnung
eines Sprachzeichens
werden haufig Beispiele fiir material supponierende Termini in Texteditionen und Schriften zur mittelalterlichen Logik durch Anfiihrungs zeichen gekennzeichnet. Dies
ist
zunachst schon deshalb inadaquat, weil
materiale Supposition die Moglichkcit der
A.
Tarski,
"Suppositio
Einfuhnmg
formalis"
ist
in
die
Verwendung
mathcmatisclie
nach verschiedencn Autoren
zu personaler und einfacher Supposition.
Logik, (u.a.
W.
eines Terminus
Gottingen
1966,
S.
fiir
71;
of Sherwood) Oberbegriff
Zur Suppositionstheorie Alberts von Sachsen sich
selbst
(pro
wie
was,
vorsieht,
se)
Rahmen Zudcm legt
im
erwahnt,
Vcrwendung von Anfiihrungszeichen ausgeschlossen
519
1st.
der die
Definition sowohl der personalen als auch der materialen Supposition als einer bestimmten
Terminus nahe,
(acceptio seu usus) eines
Verwendung
daB die Erwahnung von Sprachzeichen im heutigen Sinne innerhalb der Suppositionstheorie eher als eine besondere Weise ihres Gebrauchs aufgefaBt wird. Fur die Suppositionstheorie
ist
daB
wesentlich,
metasprachliche Bezugnahme gerade ohne die Bildung von Sprachzeichen ermoglicht und sich hiermit sogar wechselseitig
eine
sie
Namen
fur
ausschlieBt.
Die Unterscheidung
in
personale und materiale Supposition miiBte ihren
wenn
in
der Aussage
Sinn verlieren,
materiale Supposition der Terminus wiirde,
denn
Terminus
"Mensch
Mensch
ist
in
als Beispiel fiir
einsilbig"
Anfiihrungszeichen gesetzt
(mit Anfiihrungszeichen) supponiert als singularer
"Mensch"
und personal. Die Teilbestimmung Alberts, nach der ein material supponierender Terminus fiir einen ihm nicht entsprechenden Terminus stehen kann, signifikativ, d.h. diskret
schlieBt zusatzlich eine Parallelisierung mit der
zeichens aus, da nach Alberts wie auch nach
wie
eine A.c.I.-Konstruktion
currere est
"Sortem
supponieren
kann. in
Subjektterminus
verum"
dem oben genannten
material
der
In
in
Erwahnung eines SprachOckhams Auffassung z.B.
"Sortem
currere
est
Anfiihrungszeichen zu setzen, ware
Konvention sicherlich
falsch.
Zudem
ist,
der Weise, wie
wie
z.B.:
Sokrates
ist
sie
Subjektstelle
determiniert
Pradikat
6
hinweist,
Bezugnahme
durch die Iterierung von Anfiihrungszeichen moglich benennt Sokrates Sokrates benennt Sokrates. .
Grieche."
AbschlieBend an
den
nach moderner
ermoglicht, worauf King
""Sokrates"
ein
(4)
verum"
die materiale Supposition keine mehrstufige metasprachliche in
fiir
Verbform
eine Aussage mit finiter
fiir
Aussage
Beispiel
sei
einer
wird.
angemerkt, daB die Suppositionsart eines Terminus Aussage durch das auf ihn bezogene Pradikat
Z.B. wird
"Lebewesen"
der
Subjektterminus
"Mensch"
auf personale, durch das Pradikat
durch das
"einsilbig"
aber
auf materiale Supposition festgelegt. Die jeweilige Suppositionsart eines
Terminus Relation.
ist
also
Satzzusammenhang
Ausdruck
zugleich
Ein Ausdruck
in
isoliert
P.
King,
Jean
Buridan
s
Consequences, Dordrecht 1985,
Logic S. 40.
bestimmten
syntaktischen
Anfiihrungszeichen jedoch kann aus seinem werden und ist insofern von einer syntak
tischen Relation unabhangig.
1
einer
Diejenige Eigenschaft eines Terminus, die
-
The
Treatise
on
Supposition
/
The
Treatise
on
Kann
520
ist nach Auffassung der mittelaltcrlichen Scmantik kontextunabhangig 1st, der seine Signifikation. Bereits William of Sherwood erklart beziiglich
Unterscheidung von
Supposition
und
Signifikation:
beziehen sich allein auf eine AuBerung
"Manche
oder ein Wort,
Pradikate
manche auf
ein
Dies andert jedoch nicht die Signifikation. Denn so wie ein Wort ein Wort ist, bevor es in einen Satz eingeordnet wird, so hat es zu auch vorher eine Signifikation, und nicht aufgrund einer Zuordnung
Signifikat.
7
Da
anderem."
ein
ohne
Ausdrucks
Anfuhrungszeichen als Anfuhrungszeichen nicht im Sinne
Ausdruck
in
Name
desselben
eines
material
bedeutet das Setzen von
supponierenden Terminus kontextabhangig ist, Anfuhrungszeichen offenbar einen Unterschied
nicht
der
Supposition,
sondern der Signifikation.
Dusseldorf
7
William
of
zungsberichte
Sherwood,
(1937); (zitiert in
Introductions
Bayerischen Akademie eigener Ubersetzung).
der
in: in Logicam, ed. M. Grabmann, der Wissenschaften, Phil.-Hist. Abteilung
Sit1
GERHARD KRIEGER
*>Homo<
supponit simpliciter pro
natura"
Der Zusammenhang von Logik und Mctaphysik im spatmittelalterlichen Scotismus (Petrus Tartaretus)
Das
zwolfte Jahrhundert diskutiert im sogenannten Universalienstreit die
dem Zusammenhang
Frage nach
zwischen der logischen Eigenart des
und seiner Eignung, die zu begreifende Sache im Erkennen zu reprasentieren. Indem dieser Zusammenhang mil Blick auf jene BegriffBegriffs
thematisiert wird, die das Seiende in seinen allgemein-maBgeb-
lichkeit
lichen Strukturen erfaBt, erfahrt die Universaliendiskussion eine
Offnung
hin zur Kennzeichnung des Verhaltnisses von Logik und Metaphysik. Dies geschieht im Mittelalter infolge der Rezeption der arabischen Philosophic in
vollem
Umfang
Thomas von Aquin. 1
erstmals bei
Die im Folgenden dargestellte Bestimmung dieses Verhaltnisses
ist
maBgeblich gepragt durch das Scotische Verstandnis der distinctio formalis einer natura communis a parte rei und der damit verbundenen Gestalt der In
Metaphysik.
inquantum ens)
ihrer
Betrachtung
erfaBt
sie
jenen
des
"Seienden
schlechthin
als
Seienden"
einfachen Begriff,
der
(ens als
grundlegendes Moment seinerseits zu dieser Notwendigkeitsstruktur gehort, die das Faktisch-Wirkliche fundiert. SchlieBlich sei hier vorauswie
immer
es
um
die
ontologische Qualifizierung der intramentalen Realitat allgemeiner Entitaten durch Ockham stehen mag, 2
geschickt,
Vgl. begriffe
2
daB,
dazu und zum Folgenden W. Kluxen, "Bedeutung und Funktion der Allgemeinim thomistischen und scotistischen Denken", in De doctrina Joannis Duns Scoti
(Rom
229-240;
1968),
J.
Owens,
"Common
Thomistic and Scotistic
metaphysics",
Art.
in:
in:
A
nature.
Med. Stud.
19
point of comparison between
1-14; L. Honnefelder, Bd. VI, Sp. 494-504; zum Verstandnis der Universalien in der arabischen Philosophic G. Verbeke, "Introduction in: S. Van Riet doctrinale", (Ed.), Avicgnnq latinus, Liber de philosophia prima sive scientia divina, Louvain Leiden "Natura
communis",
1980, bes. 2 -19
Fur
HWP
(1957),
.
Entwicklung in Ockhams Denken von der sogenannten Fictum- zur oder Intellectio-Theorie hat sich zuerst P. The realistic Boehner, conceptualism of William of Ockham", ausgesprochen, in: Collected articles on Ockham, ed. by E.M. Buytaert, St. Bonaventure N.Y. 1958, 156-174. Darin ist ihm die weitere etwa V. Ockhams Entwicklung in der Forschung gefolgt, Richter, vgl. eine
Qualitas-
"Zu
Universalienfrage",
in:
Phil.
Jahrb.
82
(1975),
177-187.
Zu Ockhams Bestimmung
des
522
Kriegcr
aus seiner Kritik folgende Frage sich ergibt: Wie kann die begriffliche Vergcgenwartigung der Struktur und Einheit der Realitat im Erkennen die
iibcr
logisch-semantische
Funktionsbeschreibung
hinaus
fundicrt
von
wclchem
werdcn? im
werde
Ich
weiteren
niiher
erstens
beleuchten,
Ansatzpunkt aus das Vcrhaltnis von Logik und Metaphysik im spatmittelalterlichen Scotismus bestimmbar und wie hicr der ontologische Status der "allgemeinen Natur" charakterisiert und begriindet wird. Zweitens
gehc ich auf die Konsequen/ dieser Fundierung Metaphysik
Der
im
fur die
Begriindung der
ein.
des
Paris
ausgehenden
Jahrhunderts
15.
Philosoph und Scotist Petrus Tartaretus Status
ontologischen
allgemeiner
3
set/.t
Entitatcn
4
lehrende
Theologe,
der Kcnn/eichnung des
in
an
der
Stelle
an
an,
der
Ockham das Allgemeine von seiner Zeichen- und Pradikatfunktion her Ockhamsche die Tartaretus charakterisiert. greift Infolgedcssen Unterschcidung simplex auf.
5
/wischen
der
Tartaretus folgt
suppositio
Ockham
personalis
und der
siippositio
darin, mit Hilfe dieser
/.umichst
von I,ogik und Metaphysik vgl. J.P. Bcckmann, die Frage nach der Moglichkcit von Metaphysik bei Franz. Stud. 59 (1977), 1-14.
Vcrhaltnisses
"Das
Schcma und
Wilhclm von
in:
Ober iiber
sein
Lcbcn und Wcrk informicrcn:
Fran/.iskanerlehrer
des
15.
li.
Jahrhunderts",
Wegcrich, in:
Subjckt/PradikatOckham",
"Bio-bibliographische
Noti/.en
29
150-197;
Franz.
Stud.
(1942),
ferner C. Lohr, "Medieval latin Aristotle commentaries, Petrus Tartaretus", in: Traditio 28 (1972), 372-376. Den weiteren Ausfuhrungcn liegen folgende Ausgaben seiner Werke et Quodlibcta Scoti, Venedig 1583; zugrunde: Commentaria quattuor libros Sentcntianim In unwersam philosophiam opera omnia, Venedig 1621. Ich danke der Bayerischen Staatsbibliothek fur die freundliche Bercitstcllung dieser Tcxte.
4
des ontologischen Status theologisch bestimmte Ort dieser Kenn/.cichnung des Engels, aus der sich die Frage Natur nach der ist die Frage Entitaten allgemeiner nach dem Individuationsprin/ip ergibt: In lib. sent. II, d. 3, q. 1, Fol. 126b: Ecce ostensum est, ubi angeli fucrunt etc. ... Primo tamen tractat de distinctione personali
Der
angclorum. diversa
Secundo
dicunt
de
loco
de
distinguuntur et qualiter de omni 5
et cognitionibus illorum; et quia diversi videre idco oportet quomodo ipsorum, personali substantia quae est principium distinctionis.
operationibus
distinctione
"Ockham s theory of supposition Suppositionstheorie vgl. P. Bochncr, in: Collected articles a.a.O. of truth", (Anm. 2), 232-267; J.P. G. Lcibold, "Zu Interpretationsfragen der Schema"; Beckmann, "Das Subjekt/Pradikat Universalienlehre Ockhams", in: W. Kluxen u.a. (Hg.), Sprache und Erkenntnis im Akten des VI. International Kongresses fur mittelalterliche Philosophic Mittclalter.
Zu Ockhams
and
the
notion
Logik und Metaphysik im Scotismus
523
Unterschcidung iiber die Richtigkcit dcr Scotischen These von der fehlenden Singularitat und Individuality der natura communis entscheiden zu wollen. in
"homo"
Beide stimmen "personaler
iiberein, daB,
Denn
haec").
ist
sich aus
"einfacher
diese"
Supposition"
Denn dann
falsch.
Aussage hingegen
die
Termini
"natura"
und
("natura
hominis
de
est
Verwendung supponieren beide Termini fur ein
bei dieser
und diesselbe Sache. In
von
werden
gebraucht, es durchaus heiBen kann:
Supposition"
Natur des Menschen
"Die
se
6
verwandt,
eine solche
ist
Natur fur einen von der
steht die
hervorgebrachten mentalen Begriff und nicht fur eine singulare, extramentale Sache. Trotzdem glaubt Tartaretus, an der Scotischen
Seele
Auffassung von der natura communis festhalten zu konnen. Denn, so
fiihrt
er begriindend aus, der Terminus "Mensch" in einfacher Supposition verwandt, steht fur die Natur als solche gemaB dem, was sie an sich
und
selbst
ihrer positiven Indifferenz
in
sua
in
et
homo
ly
("quando
pro natura ipsa secundum se
stat
simpliciter,
ist
supponit
indifferentia").
Darin sieht Tartaretus die Moglichkeit der Vermittlung seiner sich 7 Nachfolge des Scotus begreifenden und der opinio nominalium
in der
.
Indem Tartaretus Ockham
Suppositionsweisen zustimmt, folgt
Allgemeinen
als
der genannten
in
Zeichen und Pradikat.
die suppositio simplex behauptet, der fur
Natur
die
Pradikation an.
ihm
er
selbst,
Denn
er
setzt
in
Wenn
in dieser
communis
natura
als
der S.I.E.P.M. in Bonn,
ihn
heiBt,
geschieht,
1.
Verwendung Prinzip
einen Terminus in seiner Pradikatfunktion
Pradikabilien naher zu kennzeichnen, wie es in der Aussage species"
Hbd. Berlin
im
New York
Sinne
(Mis.
der
er gleichzeitig mil Blick auf
Terminus stehe
die
Differenzierung
der Charakterisierung des
der
">Homo<
suppositio
Med. 13/1)
der
gema B den simplex
est
zu
1981, 459-464.
OT
Tartaretus bezieht sich auf folgende Ausfiihrungen Ockhams: Ord. I, d. 2, q. 6, 198: ista propositio natura hominis de se est haec est distinguenda ... eo quod natura hominis potest supponere simpliciter vel personaliter, hoc est eo, quod potest stare pro re extra animam vel pro se. Si secundo modo, sic est haec falsa natura lapidis est de se haec quia tune denotatur, quod conceptus mentis, qui est universalis, de se est hie lapis; et hoc est falsum ... Si accipiatur primo modo, sic est haec vera natura hominis de se est hie homo II
,
.
In
inceptor dicit,
sent.
lib.
ut
...
ly
II,
d.
3,
Concede
illam,
natura
lapidis
Fol.
1,
q.
127b:
Respondet
ad
istam
rationem
Venerabilis
natura lapidis supponit personaliter: nego tamen illam supponit simpliciter. Et cum ista solutione solvit omnia etiam diceremus nos, quod homo supponens personaliter est
ut
ly
argumenta Scoti. Hoc modo unum numero. Nam tune supponit pro Sorte, Platone etc. Secundo etiam concede. Nam natura est unus conceptus, quia natura hoc modo supponens, significat simpliciter quendam conceptum mentis fabricatum ab anima. Tamen secundum Scotum, quando ly
homo
supponit simpliciter, stat hie est briga inter nos et ipsos, et
pro natura ipsa secundum se et in sua indifferentia, conceptus est verificabilis de multis.
ille
et
524
Krieger 8
Und indem
gebrauchcn.
Tartarctus
communis zur
natura
die
dafiir
Voraussetzung macht, begrcift er sie als Prinzip dcr Pradikation. Diese pradikative Funktion der allgemcincn Natur fundiert Tartadurch
retus
ihren
Dazu
Status.
ontologischen
auf
er
grcift
jene
Unterscheidung des intramentalen Seins zuriick, die bei Ockham zu einem Wandel in der Auffassung iiber die Natur des Allgemeinen gefiihrt hat. Tartaretus erlautert sie in folgender Weise. subiective
Trager
in
intcllectu}
der
also
hat,
dispositionen und intellectuales,
sccunda
des
Begriff
intelligendi}?
also
intentio,
Im
den
das
Gebilde;
logischc
real sie
Verstandes-
intelligibilis,
ist
zum
Intellekt
die
Wesensgehaltes,
"Objektiv"
Sinne (esse
"subjektiven"
Realitat,
Erkenntnisaktc sclbst (species
die
actus
ctwas
besit/t
habitus
zum anderen aus
resultieren
die
jener
Erkenntnis, bei der sich der Intellekt auf Vorstellungen
vergleichcnden
bezieht, die gleichfalls
Das Resultat
10 "objektiv
einer
sind".
derartigen vergleichenden
Erkenntnis
somit
ist
Kcnnzeichnung allgemeiner Priidikate (universale in den Pradikabilien, bei der ein Terminus in der Weise der actu) gemaB das Allgemeine dabei fur die suppositio simplex gebraucht wird. Da nichts anderes als jene
8
Ockhams Diese Losung des Tartaretus kommt dcr Kritik F. Inciartes an "Die Suppositionsthcorie und die Anfange der Suppositionstheorie nahe, die dicser in: cxtcnsionalcn Semantik" vorgetragcn hat, in: A. /.immcrmann, Antiqui und Modcrni. und FortxhrUtsbewufitsein im spdten Mittelalter, (Mis. Med. 9) Yraditionsbcv;ufitsein Berlin New York 1974, 126-141. Systematisch gcsehen stimmen beide Kritiker Ockhams daB dcr mil dcsscn Auffassung verbundcnen Gefahr eincr rein darin iibcrein, Hilfe
extensionalcn mil werden konne. 9 In.
sent.
lib.
d.
II,
intensionalcn,
"bcdeutungstheoretischen"
131a:
Fol.
1,
q.
subiective
omnes
habitus
intelligibilcs,
3,
modo
Uno
dupiiciter.
eincr
habere esse in esse habcnt
aliquid
scilicet
...
actus intelligendi:
et
intellectuales
omnia
Logik
in
begegnet
intellectu,
intellectu ista
stat
species
habent ipsum
intellectum pro subiecto.
^
A.a.O.
Fol.
Ola:
esse
aliquid
in
sccundo modo, scilicet obiective, est obicctum in sua specie intelligibili, quae non proxima dispositione ad movendum intellectum.
intcllectu
dupiiciter. Uno modo habitualiter movet actualiter intellectum, sed est
sicut
Hoc modo
esse
...
etiam,
species
quod
de
rosa
esse
aliquid
dicitur
in
in
intellectu
in
intellectu
obiective
alicuius,
actualiter,
scilicet
potest
obiective.
Nota
adhuc
intelligendi esse actualiter
esse actualiter ante actum intelligendi. Alio modo Primo in intcllectu obiective et actualiter ante actum intelligendi. post vel natura universalis in actu in determinata potentia, intelligendi dicitur esse species Sed illud dicitur habere esse in intellectu habens esse in intellectu
Uno modo
dupiiciter.
actum
per
obiective
actualiter post
modo secundae intelligendi:
actum
intentiones sunt
speciem.
intelligendi, in
quod
intellectu;
capit
nam non
Auf die eingangs erwahnte derelinquitur ex actu comparative intellectus. nicht braucht habitualiter obiect we esse des eingegangen zu eigens wie sich /.eigen wird, unter der hier leitenden Frage nach dem sie, Status der natura communis mil der Moglichkeit des esse obiective
et
Moglichkeit werden, da ontologicshen
esse per actum intelligendi. Isto sunt nisi quamdiu manet actus
actualiter identisch
ist,
vgl.
dazu weiter unten
Anm.
15.
Logik und Mctaphysik im Scotismus
525
allgemcine Natur selbst steht, stellt sie jene Vorstellung dar, aufgrund deren der Intellekt zu dieser Erkenntnis gelangt. Die Bestimmung der Pradikatfunktion
Terminus
eines
sich
ergibt
indem der
also,
Intellekt
aufgrund eines Vergleichs zwischen verschiedenen "allgemeinen Naturen" etwa der hutnanitas und der animalitas - die Eigenart des Terminus als
"homo"
Artbegriff ein
als
Verwendung bezeichnet.
Diese
erkennt.
das
Pradikat,
Eigenart
konkretes
ein
Einzelseiendes
11
Im Kern
auf diese
trifft
ontologische Kennzeichnung allgemeiner
Entitaten allerdings noch Walter Chattons Kritik an als
Ockhams Fictum
das ein Allgemeines gleichfalls objektive Realitat besitzt.
Kritik
darauf
"lauft
zu
das
all
13
communis
der natura
A.a.O.
als esse obiective in
ut
relatio
quo
ilia
est
fundamentum
Fictum
ein
ist,
Ockham
genus
fundatur.
illius
vel
real
ist,
Fictum
das
die begriffliche
Uno modo modo non dicit nisi
dupliciter.
Sed universale pro fundamento est illud, in fundamento est duplex, quia duplex
universale pro scilicet
relationis,
fiihrt
Universale formaliter primo
species.
Unde
intellectu
quod universale capitur
etiam,
modo pro dcnominato.
rationis,
talis
uberfliissig
dessentwillen
"um
leisten,
Notandum
132a:
Fol.
formaliter. Alio
relationem
es
zu,
Chattons
Anders gewendet: Die Charakterisierung der Realitat
hatte."
eingefiihrt
daB
hinaus,
12
denn der Erkenntnisakt, der im subjektiven Sinne
anzunehmen";
vermag
seine
ermoglicht
fundamentum
proximum
et
fundamentum
remotum. Unde fundamentum est ipsa natura actualiter existens in pluribus, quae natura ut sic non est nata proxime dici vel praedicari de ipsis inferioribus. Sed universale pro fundamento proximo est ipsamet natura, inquantum ipsa actualiter per intellectum ab illis singularibus vel inferioribus, quia ut sic abstracta nata est praedi de pluribus. Tune dicitur universale in actu. Unde ad universale in actu duae conditiones requiruntur. Prima est, quod sit natura actualiter abstracta per intellectum a suis singularibus; et tune ilia natura licet sit una numero, tamen nata est dici de pluribus; et est unum obiectum numero: et tune dicitur esse in potentia proxima ad hoc, quod dicatur in pluribus. Secunda conditio est, quod in ipsa natura sit actualis attributio praedicationis ipsius ad ipsa inferiora. Nam si ilia natura esset abstracta per intellectum et non compararctur ab ipso eodem intellectu ad sua singularia in ratione communioris et praedicabilis de illis, iam non esset universale in actu, sed secundum abstrahitur cari
vel
dici
esse universale in potentia proxima. Primo modo quando scilicet ipsa natura abstrahitur per intellectum a suis singularibus et non comparatur actualiter ad ilia, est de
consideratione
comparatur sequitur,
tamen
et secundo modo quando est abstracta et actualiter metaphysici: tune est de consideratione logici; et dicitur universale in actu. Unde
quod universale
ipsa
naturam,
illo,
natura,
et sic patet,
ut
quod
in dixi;
actu
habet suam
quia
differentia
dabilis est natura
unitatem erat
communis
et
inter
entitatem ab
ipsum
intellectu
universale
et
non
ipsam
realis.
Vgl. zu dieser Kontroverse G. Gal, "Gualteri de Chatton et Guillelmi de Ockham controversia de natura conceptus universalis", in: Franc. Stud. 27 (1967), 191-212. C. Knudsen, Walter Chattons Kritik an Wilhclm von Ockhams Wissenschaftslehre (Diss.) ,
Bonn 13
1976, 37-50.
C. Knudsen, a.a.O. 40.
526
Krieger
zwar
Eigenart
auf
eine
auBerlogische,
abcr
doch
nur
psychologische
Realitat zuriick.
Tartaretus
communis
species
hinaus
dariibcr
daB
verweist,
in
diesem ein
intelligibilis
Begriindung
dcnn auch der Einheit und Realitat der natura
sucht
der
Fundament zu geben, indem er darauf das gegeben 1st, was in der
ein
Vorgcstclltscin esse
subiective
in
und
Eigenart
begrifflichen
intellectu
besitzt.
14
Pradizierbarkeit
Diese des
Allgemeinen macht im Unterschied zu Chattons Auffassung und dariiber hinaus die Intension nicht nur zu einer Seite des Begriffs, sondern zu jenem Fundament, welches seiner Extension, d.h. seiner Verwendung als
Zeichen vorausliegt. Demzufolge wird der Wesensbegriff als Begriff gemaB der Funktion der natura communis, die als notwendige Strukturbestimmtheit des Moglichen das Faktisch-Wirkliche fundiert, zum Inbegriff der Realitat.
Diese Konsequenz zieht Tartaretus in der Charakterisierung des Verhaltnisses von intramcntaler und extramentaler Realitat: Er begrenzt namlich das ens
anima auf
in
die
logischcn
Vorstellungen;
die
extra-
mentale Realitat bildet das, was unter die Kategorien fallt. Infolgedessen sowohl das, was subjektiv im Verstand ist, wie die objektiv
gewinnt
gegebene Verstandesvorstellung die Bedeutung eines ens In dicitur in
sent.
lib.
esse
Fol.
131a:
species vel
intellectu
Intellekt, vgl.
in
natura
intellectu
universalis
per speciem. Vgl. oben
oben Anm.
Anm.
objective
10;
et
actualiter
ante
actum
animam. 15
intelligendi
determinata potentia, habens esse die species ist ihrerseits subjektiv real im
actu
in
extra
in
9.
A.a.O. Fol. 131b: Secundum dictum ... sumitur ex quinto Metaphysicae. Ubi Philosophus distinguens ens in ens in anima et ens extra animam non capit ens in animo pro ente in anima subiective, nee pro ente in anima objective, actualiter vel habitualiter, ante actum intcllectus; sed Philosophus capit ens in anima pro ente habente esse actualiter objective post actum. Pro hoc dcclarando suppono unum, quod scilicet si probovero, quod unitas ilia, quae est minor unitate numerali, sit in re extra animam, quod etiam bene probabitur, quod ilia unitas cst rcalis. Tune declaratur hoc secundum dictum. ... Philosophus ... non capit ens in anima pro scientia vel habitibus intellectualibus, quae subiective tamen omnia habea(n)t esse in intellectu. Nam ibidem dicit,
animam ponitur
in
huiusmodi scientia non sunt entia
in
ens
Et
consequens virtutes, habitus vel Philosophus capit ibidem ens in anima. Nam dicit quomodo ilia ponuntur in genere qualitatis, ut patet, et sic non capit ens in anima subiective. Dixi etiam secundo, quod non capit ens in anima objective, vel actualiter vel habitualiter, ante actum intelligendi. Nam illud, quod habet esse isto modo in aliquo praedicamento. Etiam illud, quod in anima, scilicet objective, dicitur esse habet esse in intellectu objective actualiter ante actum; quia nihil ponitur in praedica mento praeter ista. Et ita dicuntur entia extra animam. Et hoc modo intelligence, quod scilicet ilia, quae ponuntur in praedicamento, non sunt termini, sed etiam entia extra animam. Et ita relinquitur, quod per ens in anima intelligit Philosophus illud, quod habet esse in anima objective, actualiter post actum intelligendi, cuiusmodi sunt secundae intentiones et relationes rationis. Relinquitur etiam, quod per ens extra
quod
extra
genere.
anima,
per
modo quo
Logik and Metaphysik im Scotismus
Die
im
Kennzeichnung eines Terminus
pradikative
527
Unterschied
zum
16 Eigennamen beruht somit auf einer extramentalen Realitat.
Tartaretus setzt also iiber als
der
Prinzip
Ockham hinausgehend
Pradizierbarkeit
ausschlieBlich ein esse in
Terminus
eines
communis Indem er ihr
die natura an.
zuerkennt, verfallt er nicht der Kritik
intellects,
Ockhams, nach der der denkunabhangige Status allgemeiner Entitaten sowohl die Identitat des singularen Gegenstandes 17 wie die Einheit und damit die Aussagbarkeit des Begriffs zerstort. 18 Freilich stellt sich hier die weitere Frage, wie diese MaBgeblichkeit des Begriffs zu vereinbaren ist mit der fur den Theologen Tartaretus durch den Schopfungsgedanken vermittelten
Einsicht
menschlichen
Intellekts.
in
die
Es
und Verganglichkeit auf der Hand, daB Tartaretus allein
Individuality
liegt
des
dem
Erkennen eine derart fundamental Bedeutung zuzusprechen so daB alle strukturellen Bestimmtheiten des Seienden in der vermag, Realitat dieses Denkens ihren Grund fmden: In seiner Antwort auf die gottlichen
19 verweist Tartaretus auf Frage nach der Unverganglichkeit des WiBbaren
animam
intelligit
A.a.O.
ens
illis
133a:
Fol.
duobus primis modis. Dico
nam
quod universale in actu habet fieri per naturam illam abstractam ab omnibus habitudine praedicationis, quae omnia talia debent fieri per
patet,
singularibus intellectum.
cum ilia actuali Secundum dictum.
rebus,
unde
hominem
vel
ideo
primo,
universale
dicit
Intellectus
faciens
illud
universale
in
rebus,
invenit
in
moveatur ad faciendum tale universale. Unde quod intellectus dicat asinum esse universale, hoc ideo est, quia in homine vel asino est aliquid,
unde conveniat intelligitur aliter esset
nunc
illud
intellectum,
istud praedicatum, scilicet universale.
sibi
sub
ratione
ratio
in
universalis,
se
non
dicendo,
falsa,
intelliguntur
homo
est
Unde quando homo vel animal modo illis repugnanti; nam
sub
universale,
animal est universale. Et
repent aliquid in ipsis, ratione cuius potest ilia concipere, isto modo ilia ratio est bona. Nam si intellectus non reperit in homine, quare debeat illi imponere hoc nomen universale vel species plusquam in ipso Sorte, non videretur ratio, quare non posset aeque bene ipsi Sorti attribuere ilia praedicata, scilicet species et universale. Et ideo oportet, quod ex parte rei moveatur. Unde quando homo supponit simpliciter, etiam secundum nominales, supponit pro quodam conceptu communi vel ergo ille conceptus dicit rationem in se falsam, et tune nulla esset disputatio. Si ergo non dicit rationem in se falsa, oportet dicere, quod intellectus non compararet unum ad aliud, attribuendo intellectus
unum
alteri
et
faciendo
illam
praedicationem,
homo
est
aliquo modo moveretur a re ipsa. 17 Ord. I, d. 2, q. 5, II 159. 18
Ord.
I,
d. 2, q. 6,
19
Diese universam
habemus
log.
scientiam,
sit
Fol.
vel
est
genus,
nisi
197.
Tartaretus in seinem Kommentar zu den An. post., In 205rb C: Dubitatur primo, utrum scibile, seu illud, de quo
diskutiert
Frage Arist.
OT OT II
species
aeternum
et
perpetuum
et incorruptible.
528
Krieger
dem
Unzerstorbarkeit
seine
Intellekts.
nach
Sein
als
Inhalt
des
gottlichen
20
Diese
Begriindung der Struktur des Seienden fiihrt zu einem Problem, das sich logisch fassen laBt als
ontologische ihrerseits
allcrdings
zwischen
Widerspruch
der
mittelalterlich
oder,
transkategorialen
gesprochen, der transzendentalen Bedeutung von
und
einerseits
"seiend"
der kategorialen Bestimmtheit des esse subiective in intellectu als Qualitat andererseits; oder anders gewendet:
Welche Konsequenz ergibt sich aus als ens diminutumr*
der Kennzeichnung der Realitat des Denkens selbst
Im Ergebnis, so
zum
ich
zweiten der
Einheit
laBt sich
in
Lehre der
Tartaretus
die
sich
dem MaBe
begriffliche
komme
FaBbarkeit
der
sicher, wie die Erfahrung des unbezweifelbar sein kann. Wie
als
Existierenden
aktuell
kontingenten,
erweist
Punkt,
Realitat
zusammenfassend sagen und damit
intuitiven Erkenntnis zeigt,
ist
allein die
Erfahrung
der Einheit der aktuellen Existenz des Erkennenden selbst von absoluter,
unbczweifelbarer Evidenz. Die Metaphysik griindet demzufolge GewiBheit der Erkenntnis des cxistierendcn Subjckts. d.h.
in
der
II.
Zu diesem die
rung,
fiihrt
Ergebnis
dem
Tartaretus
bezeichnenderweise die Analyse der Erlautefiir den univoken "Beweis"
ersten Scotischcn
F,t si quis quaerat dc scibili remote, scilicet de subiecto vel per subiectum conclusionis, utrum sit generabilc et corruptibile. Respondctur, quod quodlibet tale crcatum secundum proprium esse potest corrumpi et desinere esse: etiam quantum ad esse cognitum, quod habct in intellectu create est corruptibile, cum quilibet intellectus crealus possit desinere illud cognoscere, sed secundum esse
A.a.O. Pol. 205vb EF:
re
significata
cognitum, quod habet
non
intelligere
talia
in
mente divina numquam corrumpetur, impossible
scibilia
Unde per quam
remota.
res
cognita
participative
et
enim
Deum
obiective
habet
est
cognoscitur: sed cognitio Dei est aeterna et quale habet cognitio, ipse Deus, ideo talia scibilia participative dicuntur esse aeterna. tale
esse,
Zur Geschichte und Bedeutung note
on
its
origin
and
meaning",
dieses Begriffs vgl. A. Maurer, "Ens diminutum: a in: Mcd. Stud. 12 (1950), 216-222. Gema B der
esse intellectu" ergibt sich bei Tartaretus im communis Unterschied zur traditionellen Auffassung, daB nicht nur die intentio secunda, sondern auch die intentio prima ein ens diminutum darstellt: In libr. Arist. de anima I Fol. 246 ra-va DE: Ad hoc, quod res cognoscatur, non oportet, quod habeat aliquod verum esse
Fundierung der natura
reale
esse
...
res reponitur in
ab aeterno
fuit
"in
praedicamento secundum eius esse essentiae cognitum, cum tale ideo res ab aeterno fuerunt in praedicamento, saltern
cognitum,
natura ipsius Dei. ... Sequitur, ... quod esse cognitum praecedit non quaerat, an illud esse cognitum sit Deus. Respondetur, quod realiter est Deus, quia non est nisi ens diminutum ... Dicitur ulterius,
secundum cognitionem esse possibile. formaliter nee
quod non
...
Et
si
est intellectio, sed est res cognita,
quae terminat intellectioncm.
Logik und Metaphysik im Scotismus
529
Charakter des Begriffs des "Seienden gibt. Die Scotische Uberlegung besagt, daB dcr menschliche Verstand unter den Bedingungen dieser Welt aufgrund der Unterscheidung zwischen sicher und zweifelhaft GewuBtem erkennen kann, daB "Seiendes" erkannt werden kann, ohne es schon als
bestimmtes -
geschaffenes oder ungeschaffenes, endliches oder unendliches
-
Seiendes
Zum
konnen.
zu
identifizieren
einen
wird
also
in
der
Univozitatsthese die FaBbarkeit der Einheit aller Realitat im Begriff des "Seienden" behauptet. Indem diese Scotische Uberlegung die "Sicherheit" dieses Begriffs mit Hilfe der Unterscheidung von sicher
(certitudo)
GewuBtem
zweifelhaft
zu erweisen sucht, macht
und
begrifflichen Erkenntnis
ihrer Inhalte
zum
sie
und
die Erfahrung der
entscheidenen und, wie die
nahere Analyse der Scotischen Lehre gezeigt hat, auch zum einzigen positiven Argument fur den Aufweis der erkennenden Vergegenwartigung dieser
Weil
Einheit.
Tartaretus
der
infolge
strukturellen Bestimmtheiten des Seienden nur
fundierem
vermag,
Erfahrung und Aufweis fur die
mehr im
die
Intellekt selbst zu
Hinweis auf die begriffliche gerade Inhalte dazu, dariiber hinaus einen besonderen
fiihrt
ihrer
ihn
Ockhams
Kritik
der
dem Erkennen
vorausliegende Fundierung des Begriffs der
Einheit der Realitat zu verlangen.
Und
es erscheint nur folgerichtig,
daB
diesem Ausweis vor das Problem der ontologischen Fundierung des Kontradiktionsprinzips gestellt wird. Denn im Scotischen Konzept bestimmt er in
sich
primare Sinn von
der
Seiendes
ist
das,
dem
"seiend"
ja
mit Hilfe dieses Prinzips,
es nicht widerstreitet zu sein:
"ens
(est hoc,)
d.h.
cui
23 non repugnat Infolgedessen steht Tartaretus in seinem Bemiihen um den Aufweis der vorgangigen Fundiertheit des Begriffs der Einheit der Realitat im Seienden selbst vor der Aufgabe einer dem Erkennen vorausesse."
liegenden Begriindung des Kontradiktionsprinzips. Im Sinne also dieser Stellungnahme geht es Tartaretus in seiner
Erlauterung des genannten Scotischen Beweises darum, die "Sicherheit" des Begriffs des "Seienden" nachzuweisen, indem er ihn als subiectum des Kontradiktionsprinzips 22
Ord.
demzufolge
3, p. 1, qq. 1-2, ed. Vat. Bd. Ill, 18, 21, 26ff.; vgl. dazu und zum Honnefelder, Ens inquantum ens. Der Begriff des Seienden als solchen als der Metaphysik nach der Lehre des Johannes Duns Scoius, Miinster
L.
(BGPhThM NF
16) 1979, bes. 286-294, 339-343.
Ord. IV, d. "modalen
sich
d.
I,
Folgenden Gegenstand
Dieser Begriff erweist
aufzeigt.
q. 2, n. 8, ed. Viv.
1,
Interpretation
Metaphysik",
Intemationalis,
in:
des
Regnum Hominis
Rom
1978, 305ff.
XVI
Seienden"
et
109; vgl.
dazu und zu der damit verbundenen "Die Originalitat der Skotischen
W. Kluxen, Regnum Dei. Acta
Quarti
Congressus
Scotistici
530
Kricger
dadurch
daB auf seiner Grundlage erkennbar
als sicher, 24
oder nicht
Um
ist.
dies
nach/.uweisen,
erklart
GewuBtem
scheidung von sicher und zweifelhaft Unterschiedenes am Leitfaden der
ist,
ist
Unter-
soweit, wie sich derart
Ordnung
logischen
ob etwas
Tartaretus die
Die
ergibt.
Bezweifelbarkeit etwa einer Artbestimmtheit beruht auf der Sicherheit des
um
Wissens
die Gattungsbcstimmtheit. Dieser Leitfaden verliert jedoch
zum
einen seine Bedeutung untcrhalb der Artbestimmungen; die Sicherheit, mil der ein Eigenname gewuBt wird, ohne ihn ebenso sicher von bestimmten Individuen aussagen zu konnen, erlaubt nicht den SchluB auf seine Univozitat.
keine
Vor allem aber
Sicherheit
in
vermittelt der Leitfaden der logischen
auf
bezug
die
Bestimmtheit von
Ordnung
Da
"seiend".
es
dariiber hinaus keine sichere Erkenntnis geben kann, taucht das Problem auf,
ist
wie die Sicherheit dieses Begriffs gewahrlcistet werden kann. Aufgrund der eingeschrankten Realitat der logischen Vorstellungen das Wissen um das "Seiende" im Sinne der Erkenntnis realer
Bestimmtheit jedenfalls nicht hinreichend durch die Sicherheit verbiirgt, die der Leitfaden der logischen Ordnung bietet. Deswegen stellt Tartaretus einen
gemeinsamen
das ens rationis
fur
Begriff
und das ens
Frage, fordert ihn aber zugleich fur Gott und die Kreatur.
In
lib.
Probatur,
sent.
quia
I,
d.
3,
2,
q.
Fol.
primum principium
primum principium
vel
138b:
nulli
subiectum primi
Conceptus
potest
esse
principii.
reale
in
25
entis nulli potcst esse dubium. dubium. Sed conceptus entis est
Ergo conceptus
entis
nulli
potest esse
dubius.
A.a.O. Fol. 139a-b: Contra. Obiicitur contra maiorem.
quod hoc nomen Sortes univocus omnibus illis.
...
Scotus et
disputant
quod est univocum
Si
ipsa esset vera, sequeretur,
conceptus communis ... Item universalibus, isti duo habent conceptum de universal!, utrum sit ens reale vel ens rationis. Tune ens erit
univocum pluribus individuis et Item sequeretur, quod ista vox canis
esset
Occam de
ens, et sunt dubii, enti reali et enti rationis.
erit
esset univocum.
Sed consequcns est absurdum. Ergo etc. Pro solutione istorum supponuntur aliqua. Prima supponitur, quod a pluribus suppositis impossible est aliquem conceptum univocum suppositalcm abstrahi. Patet, quia conceptus Sortes non suppositalis est incommunicabilis, sicut suppositum. Ex quo sequitur, quod potest dicere conceptum communem et univocum isti Sorti et illi Sorti. Patet, quia
nomen suppositale. ... Ad secundam instantiam supponitur, quod proxima qua possunt habere conceptum univocum communem canis latribilis et piscis marini, est substantia, quia licet sint aequivoca in ratione canis, non tamen in ratione substantiae, corporis animati et animalis, immo univocantur in omnibus istis. Modo ad argumentum. Sum certus, quod canis movetur. Distinguo, aut ly canis est vox mere Sortes ratio,
est
in
aequivoca aut ut canis
dicit
non solum
dicit
rationem
in qua ista conveniunt, ut in animali. aliquo conceptu univoco, sed solum in cadit supra animal, non sic de ente, quia
rationem proximam,
Concedo primo modo, quod non conveniunt voce. Sed secundo modo dico, quod certitudo
communem,
in
sed conceptum.
tertiam instantiam supponitur, quia talis conceptus sit conceptus communis enti reali et enti rationis. Quaeritur, utrum est realis, et sic includeretur per se et quiditative in ente rationis, et sic ens rationis, ut secunda intentio, esset ens reale, secluso omni
Ad
Logik und Metaphysik im Scotismus Tartaretus
daB
fest,
531
denn auch zu Beginn seiner eigentlichen im Bereich des conceptus rationis, also allein
stellt
lediglich
der sichere
vom
solutio
der
in
zweifelhaften Begriff verschieden
sei. logischen Ordnung Deswegen verlangt er einen besonderen Ausweis (probare) dafiir, daB Gott und die Kreatur in einem univoken und "wirklichen Begriff (conceptus
iibereinkommen. 26 Dazu geht Tartaretus davon aus, daB das und "Nichtsein" Gott und (esse) als ein Glied der Kontradiktion von der Kreatur unabhangig von aller Vernunfterkenntnis zukommt. Soil jedoch
realis}
"Sein"
"Sein"
der univoke Begriff des
muB
bilden,
er
sich
"Seienden"
als
das subiectum
Grundlage
dieser
dieser Kontradiktion
Erkenntnis
erweisen.
Eine
Erkenntnis der beiden Glieder der Kontradiktion kann es
gleichzeitige
geben, weil ein und dasselbe nicht zugleich sein und nicht sein kann. Folglich bedarf diese Erkenntnis des Seins oder Nichtseins der nicht
der
Voraussetzung
Der univoken subiectum
des
von
Vorstellung
quiditativen Begriffs des
"Etwas
Begriff des
Bestand haben kann.
d.h.
des
erweist sich also deswegen als
"Seienden"
weil
Kontradiktionsprinzips,
Erkenntnis jenes Seins
iiberhaupt",
27 "Seienden".
er
die
Grundlage
der
darstellt, das nicht zugleich mit seinem Gegenteil
"Sein"
und
"Nichtsein"
bilden demzufolge die Glieder
der Kontradiktion, die ein bestimmtes Etwas identifizieren laBt, namlich Existierendes oder Nichtexistierendes. Soil die Realitat dieses Begriffs des
durch
"Seienden"
actu
ein
Gott
und
der
Kreatur
unabhangig
von jeder
ens rationis, tune ens reale esset ens rationis, quia includeret secundum Scotum, quod enti reali et enti rationis ens non conceptum aliquem communem, sed tantum vox est communis, non sic est de ente intellectus.
dicit
Si
esset
Ex quo
ens rationis.
sequitur
respectu Dei et creaturae.
A.a.O. Fol. 139a: Circa hanc rationem sunt aliquae difficultates, sed dantur primo ad earn solutiones. Prima solutio dicit. Concedo maiorem de conceptu rationis, nego de conceptu reali, ideo habes probare, quod Deus et creaturae conveniunt in conceptu aliquo univoco reali.
A.a.O.
139a:
Fol.
Contra.
In
quibuscumque
includitur
realiter
unum extremum
contradictionis, etiam in illis ponitur aliquis conceptus realis et univocus. Sed in Deo et creatura ponitur et includitur realiter unum extremum contradictionis. Igitur etc. Maior
patet
Tune non
Ad contradictionem requiritur non solum unitas nominis, sed simul. Probatur minor, ut esse, quod est unum extremum contradictionis. Vel esse convenit Deo et creaturae per opus intellectus tantum, et sic Deus
Elenchorum.
I.
nominis
et
sic.
erit
rei
ens
cessante
opere intellectus, quod est absurdum, vel secluso opere habeo propositum. Contra. Tua contradictoria veniunt in mentem. Dicit Philosophus, quod opiniones contrariae non possunt venire in mentem, quia extrema contradictionis non possunt venire in mentem, quia impossibile est idem esse et non esse simul. Ex quo concludit, quod esse et non esse sunt contradictoria. Ex quo sequitur, quod conceptus, de quo sum certus, est alius a conceptu, de quo est dubius intellectus,
et
sic
per hoc primum principium.
...
532
Krieger
Vernunftcrkenntnis zukommendes Scin begriindct sein, fragt es sich also, als realen kontingente, aktuell existierende Seiende
welches Begriff
"seiend"
erkennen
"sicher"
Die ErfaBbarkeit der Einheit der Realitat
laBt.
dem MaBe
erweist sich somit in
als sicher, als die
Erkenntnis von aktuell
Existierendem sicher und unbezweifelbar sein kann. Die Beantwortung dieser Frage fiihrt iiber die Betrachtung des Verhaltnisses von Logik und
Metaphysik hinaus zur Lehre von der cognitio intuitiva intellectualis, durch die das aktuell Existierende als solches erfaBt wird. Deswegen kann an dieser Stelle die betreffende Auffassung des Tartaretus nur erwahnt werden, ohne
im einzelnen darzustellen und zu analysieren.
sic
Tartaretus
kausalen
Ockham 28
folgt
des
Bedeutung
in
der
existicrenden
Einschrankung (auBeren)
der
effizient-
dessen
fiir
Objekts
29
Infolgedessen sind die entsprechenden kontingenten
Urteile iiber die
vom
Urteilenden selbst verschiedenen Objekte (aliquod
nur
von
intuitive Erkenntnis.
extrinsecum)
eingeschrankter
Evidenz
conditionatd).
(evidentia
Hingegen von absoluter Evidenz (evidentia absoluta}, also unbezweifelbar sind alle kontingenten Urteile, die den Urteilenden selbst in der Einheit seiner aktuellen Existenz betreffen
(ego sum, ego cognosco, ego v/vo).
SJQ
Grundlegung zu dieser of the
later
S.J. Day, Intuitive Bonaventure N.Y. 1947;
I^ehre
St.
scholastics,
Ens inquantum ens (Anm.
22), 218-267;
non-existents according to William of
29
In
lib.
sent.
I,
d.
3,
q.
4,
Fol.
zu
Ockham
Ockham", in:
cognition,
P.
Deus
the significance
to
Scotus L.
Boehncr,
Collected articles
163b: Quidquid
a key
ferner zu
"The
(Anm.
30
Honnefelder,
notitia intuitiva of 2),
268-300.
potcst mediante causa secunda
obiccto potest causare notitiam potest immediate et se solo potest. Sed Deus mediante intuitivam. Ergo sine obiecto, cum obiectum sit causa notitiae intuitivae effectiva ...
causa effectiva secunda praecise concurrat cum Deo alio modo concurrit obiectum, quia in ratione termini, vel alio modo sic negatur maior. Ad minorem, negatur minor praecise, ratione causae quia non sufficit, quod obiectum concurrat cum Deo praecise in
Respondetur, concede maiorem.
in
ratione
efficientis
ad
notitiam
termini attingitur, quia In aliquid
duplex
et
efficientis
non
Si
alio
intuitivam,
ibi est
modo. Sed
sed
concurrit
ultra
in
ratione
termini,
et
in
ratione
attingentia.
Arist. log. In An. post., Fol. 229vb-230ra II-B: Dubitatur prime, utrum evidenter possit a nobis cognosci. Pro cuius solutione supponitur primo, quod est evidentia primi principii, vel rcducibilis ad earn. Alia est conditionata vel
unwersam
solum de supposito dicitur primo, quod possibile est, nos non etiam de multis aliis veritatibus habere evidentiam absolutam: Dicitur secundo, ... quia aliter sequeretur omnes scientias perire, quod est inconveniens quod possibile est nos de multis veritatibus contingentibus habere evidentiam absolutam;
secundum primo
ut
quid.
principio:
Hoc immo
...
quod ego sum, quod ego cognosco, quod ego vivo
est, licet
nos
aliquod
extrinsecum
evidentia conditionata.
nobis
sensibile
...
evidenter
Dicitur tertio, quod impossibile cognoscere evidentia absoluta:
Logik und Metaphysik im Scotismus
Die
Metaphysik
also
griindet
letztlich
Erkenntnis des existierenden Subjekts.
in
der
533
Unbezweifelbarkeit
der
31
III.
durch Ockhams Kritik bedingte Frage, wie iiber die logischsemantische Funktionsbeschreibung der allgemeinen Begrifflichkeit hinaus die Erkenntnis der Struktur und Einheit der Realitat zu begriinden ist,
Die
sucht
der Pariser Scotist Petrus Tartaretus zu beantworten,
diese
Strukturbestimmtheiten
Freilich
vermag
als
Prinzipien
er ihre strukturelle
zu
subiective
in
intellectu
communis
ihr
eigentliches
der
Infolgedessen
hat
er
ansetzt.
Bedeutung nur mehr durch ein
fundieren.
die
esse
natura
Fundament im unverganglichen Erkenntnisakt
Die Begriindung der allgemeinen Begrifflichkeit vorausliegenden, Gott und die Kreatur umfassenden Realitat Gottes.
fur
indem
Pradikation
den menschlichen Verstand
allein auf
dem Weg
einer
hi ist
ihr
deswegen
iiber die unbezweifel-
bare Erkenntnis des aktuell Existierenden nachweisbar. Infolgedessen ist die Erkenntnis der Einheit der Realitat nur noch begriindbar aufgrund der absolut evidenten Selbsterkenntnis des existierenden Subjekts.
Wie immer man Metaphysik Infolge
der
die
Bedeutung dieses Begriindungsversuchs der
historisch beurteilen
mag, eins scheint mir jedenfalls
Ockhams wird
Kritik
der
denkunabhangige
geleugnet, und
ihr Realitatsgehalt
sicher:
Status
der
bedarf einer
allgemeinen Begrifflichkeit eigenen Begriindung. Diese Begriindung zeigt wiederum, dafi der Gedanke der Allmacht Gottes das theoretische Weltverhaltnis des Menschen nicht allein
32
pragmatisch,
sondern
durchaus
in
einer
absolut
evidenten
Erkenntnis des wirklichen und kontingenten Seienden fundieren lieB. Die im Gedanken der Allmacht Gottes motivierte Kritik Ockhams fiihrt somit
zwar dazu, daB das wirkliche und kontingente Seiende nicht weiterhin aufgrund seiner formal distinkt unterschiedenen washeitlichen Struktur31
Vgl. in der vorangegangenen
Anm.
die explizite
Betonung der evidenten Erkenntnis
des Urteilenden selbst als Grundlage der Wissenschaft. 32 In diesem Sinne charakterisiert H. Blumenberg, Frankfurt a.M. behauptung, theoretischen Weltverhaltnisses
Versuch,
die
Leistungsfahigkeit
1974,
229
das
Sdkularisierung
und
Selbst-
Verstandnis des der Neuzeit den einen Akt humaner
spatmittelalterliche sieht deswegen in
des Menschen. Er des theoretischen Vermogens
als
Selbstbehauptung gegeniiber dem "theologischen Absolutismus" zu entfalten, wie er im Allmachtsgedanken zum Ausdruck kommt. Ausfiihrlich seize ich mien in der in Anm. 34 genannten Habilitationsschrift Arbeit mil dieser These auseinander.
534
Krieger
momente vermag
das eigcntlichc
man
Fundament der Metaphysik ausmacht. Trotzdem an
weiterhin
der
theoretisch-wissenschaftlichen
Ver-
Welt im ganzen im Sinne der Tradition standigungsmoglichkeit uber die in der festzuhalten. Urn so mehr gewinnt die Frage an Gewicht, was mittelalterlichen Theologie und Philosophic selbst jenen Wandel ermoglicht hat,
der
in
der Neuzeit zu der bekannten Veranderung der Fragestellung
der Metaphysik fuhrte.
Diese Frage scheint mir also insbesondere wegen der Begrundung, Tartaretus die ihr Scotischer Entwurf infolge der Kritik Ockhams bei eher beantwortbar, wenn man den theologischcn Ort, naherhin den findet,
"praktischen"
dieser
Charakter
33
Theologie
berucksichtigt.
Unter dieser
das Problem, zu welchen Konsequenzen fur Perspektive ergibt sich namlich Theorie und Metaphysik der Versuch fiihrt, gegcniiber dieser "praktischen"
humaner Praxis und Theologie eine genuin philosophische Bestimmung 34 ihrcs Verhaltnisses zur Theorie zu gebcn.
Univcrsitat
33
Bonn
bei Scotus, das auch Tartaretus in der Honnefelder, Ens inquantum ens (Anm. 22),
Zu diesem Verstandnis der Theologie
Nachfolge des Scotus stehend J.H.J.
Einleitung, bes. 22-29; Bonn, 1986, 357^03.
teilt,
vgl.
Schneider,
L.
Thomas Hobbes und
die Spatscholastik,
34
(Diss.)
die theologische Kennzeichnung In diesem Sinne, als philosophische "Antwort" auf dazu meinen der Praxis bei Scotus erweist sich die Ethik des Johannes Buridanus, vgl. bei Johannes Buridanus", Ethik der und philosophischen Bedeutung Beitrag: "Die Stellung dieser Antwort fur Theorie und Metaphysik Den 12 in:
Medioevo
gehe
ich weiter
Auswirkungen
(1986).
nach
in
der
z.
Zt. in
Vorbereitung befindlichen Habilitationsschrift.
MARIA LEONOR LAMAS DE OLIVEIRA XAVIER
Trivium et Philosophic:
Dans une
Le De Maestro de
ou Pheritage des
culture
arts
Saint Augustin
liberaux etait transmis chez le
rheteur, grammaticus que Ton a plus tard appele le Triuium n etait pas seulement 1 ensemble des sciences du langage, mais
chez
et
ce
le
c etait surtout le cycle des disciplines qui pourvoyaient a la
Phomme, 1
suivant
modele de
le
modele
influence de ce
et
il
1
orateur. Augustin
meme
en a
est
formation de
ne
cru sous
et
reproduit les valeurs,
comme
1 professeur de rhetorique. Toutefois, chez Peminente autorite en oratoire Ciceron - Augustin s est eveille pour la valeur philosophique classique
de
la sagesse.
2
De
puise
devenait vitale dans
de
n avait pas oublie le nom du Christ, qu il avail 3 Monique. L union de la sagesse avec le Christ
plus,
chez sa mere
Pauteur
il
developpement de Confessionum, mais il
des
le
la
personnalite et de la pensee
du patir la mediation du il ou a rencontre le nom du Christ, mais pas trop de manicheisme, 4 et du neoplatonisme, ou il a trouve de la sagesse, mais sagesse pas le a
,
Christ, c est a dire, Pincarnation
d Augustin ou le
du Verbe. 5 Le
s est
expressement scellee Palliance entre chretien, par Punite de la sagesse de Dieu et de
Christ.
ideal
Saint
Cf. H.-I. Marrou, Premiere Partie. Cf.
3
4 5
Pouvrage
philosophe
et
personne du
Confessionum
III,
4,
Augustin
7-8
(texte
et
de
la
la
1
revision critique
Fin
ed.
de
M.
la
Culture
Skutella,
homme
et,
en
du modele de son
Antique,
Paris,
1938,
Bibliotheque Augustinienne
372-376).
Cf. Conf. Ill, 4, 8. Cf. Conf. Ill, 6, 10.
Cf. Conf. VII, 9, 13 "Ille
id
la
de sagesse demandait un nouvel
consequence, obligeait Augustin a
13, pp.
le
est
6
Mais ce nouvel
2
De Maestro
est
-
14.
autem qui consulitur docet, qui in interiore homine habitare dictus est Christus, incommutabilis Dei atque sempiterna sapientia." De Magistro, 11, 38 (texte du CC
rev. et cor.,
BA
6, p. 136).
Lamas De
536
Oliveira Xavier
education, ainsi que des valeurs qu
meme. La
rhetorique
emportait, entre lesquelles ressort la
il
retractation d Augustin rheteur a etc aussi profonde,
qu elle a merite, de lui, abandon de la profession et, posterieurement, dans ses ecrits, les references les plus ameres et desapprouvantes a son 1
ancien
m6tier.
Dans
ecartee.
7
Neanmoins, la rhetorique n a pas et6 defmitivement livre IV du De Doctrina Christiana, lequcl rend chretien
le
de
eloquence, Saint Augustin revient aux trois finalites de
1
art classique
1
oratoire scion Ciceron
1
-
imposant un ordre axiologique
mots
est
la
et flectere
8
mais en leur
-
tres net: la valeur essentielle
se
laquelle
de
comme
soumettcnt, 9
Get
1
usage des
des moyens
ordre
denonce,
bon usage des mots ne vaut pas autant par
ses effets
delectation
la
le
que
surtout,
a
pedagogic,
circonstanciels,
delectare
docere,
et
la
persuasion.
personne d autrui. En 10 vcritd, la pedagogic ne se justifie point par Pefficacite de Phomme. Cependant, evidence de ce fait n est pas aussi immediate, qu elle n ait du on observe, en special, au De etrc produite; et c est ccla-meme que
apparemment immediats, que par
valeur de
la
la
1
1
Magistro.
Ce
sur
augustinienne essentielle? 1
11
origine et
de
commence
dialogue
son
le
avec
la
langage
Pour des questions plus
de
du
surtout,
temps,
conventionalisme.
13
Mais
stoicisme
les
plus caracteristiquement
en
quelle
est
12 ,
questions
1
intentionalite
comme
traditionnelles,
nature des mots, Augustin
la
la
question
humain:
quoiqu
cut
il
penche vers
1
approfondissement
qu indique passage
9 10
13
le
travers
Cf.
De Doctrina
Cf.
De Doct.
Cf.
par
homme (c est comme ailleurs,
ce
impose a Saint Augustin. N6anmoins,
la
du
relations
langage
penchant conventionaliste). I
homme
3 (texte de
1,
I,
s
1
avec Ici,
ed. bcncdictine,
BA
I
4,
p.
18);
2, 2.
tibi
Christiana IV, 12, 27 (texte de
Christ. IV, 12,
De Doct.
"Quid
12
a
aussi
Contra Academicos
Cf.
2 et IX, 8
les
vrai
1
des
28
efficere uelle,
Pepin, Saint Augustin
J.
Cf.
De Doct.
1
ed. benedictine,
BA
11, p. 466).
14, 30.
Christ. IV, 16, 33.
uidemur
Cf.
-
Christ.
II,
24,
et la
37
-
le
concernant
traditionnelles,
du langage avec la r6alit6, demeureraient exterieures au on ne passait du probleme, d apres notre auteur, si
relations
nocud
de
celles
usage des vues connues
fait
cum
loquimur?"
De Mag.
1, 1.
Dialectique, Villanova, 1976, pp. 72-98.
25, 38.
Conf.
IV,
le
2,
Trivium
question de
et
Philosophic:
memoria Dei 14
1
,
dialogue
exception de
augustinien
avec
1
la priere,
intention generate de
communication a
1
1
1
evidemment au sens
prise
pas
1
A
usage des mots.
qu
emporte sur Pexterieur.
usage des mots est
du langage des mots: elle
A
De
le
negative,
la
pedagogic,
intention ne
depasse toujours, cause de cela, le fondement de 1
De
interieur, ainsi Trinitate.
Magistro correspond, chez
mais
la
comme
du langage humain devra etre chcrche a
Cependant,
1
le
Saint Augustin, posterieurement, dans le
critique
theme de
qui annonce le
de communication. 15 Alors, ce que le c est Pirreductibilite de cette intention de
etablit,
parce
1
large
Pefficacite
effet
537
du langage chez homme, dans le De Magistro, ordre des buts que Ton poursuit communement par
intentionalite
1
se trouve reduite a 1
Le De Magistro de Saint Augiistin
reflechie,
de
1
1
s identifie 1
interieur
intentionalite
1
le
que
montrera
16
moment de
auteur, au
efficacite
des
mots.
Toutefois,
du langage,
on y discerne des developpements d importance majeure pour Pepistemologie des sciences du langage et pour la philosophic de la connaissance en general. D apres un aussitot
exercice
s
que
decele
y
la
negativite
17 d explanatio grammaticale Augustin change point de vue du dialogue, en remplacant 1 orthodoxie de
elementaire
completement
le
,
18 Des lors, non plus le par 1 heterodoxie de la libre reflexion. point de vue de la grammaire institute, mais celui de la seule raison nous 1
ecole
fera 1
une autre grammaire beaucoup plus representative de C est cela qu il s agira de montrer dans le premier
decouvrir
ordre reel du langage.
De
alinea de notre essai sur le s
Magistro de Saint Augustin. Ensuite, on
appliquera a degager, parmi les conditions de
necessite de communication, dementir 1 autonomie des mots la
Vostensio:
theorie
la
la
et
generate
experience concrete de
1
connaissance.
Ce
sera le
de rendre compte de des
conditions
1
la
moment de analogie
objectives
de
de la
connaissance.
14
15
CL De Mag.
1,2.
CLDeMag. I, 1; 10, 30. Au moyen de idee de uerbum 1
De
Trinitate IX, 6, 9-11,
90-104, 464-498).
17 18
Cf.
De Mag.
2, 3.
Cf.
De Mag.
2, 4.
16;
XV,
mentis et du modele trinitaire de la psychologic: Cf. 17 - 16, 26 (texte de ed. benedictine, BA 16, pp.
10,
1
Lamas De
538
De
la
nous
sorte,
commc
avons
De
philosophic positive du
Oliveira Xavier
s
Magistro, qui
but
surtout
ouvrcnt par
de
virtualites
les
meme
la critique
du
point de vue conventionnel des sciences du langage.
1.
Grammaire conventionnelle
grammaire rationnelle
et
Augustin admet, au De Magistro,
comme choses 1
et
signe,
considere selon
le
exterieures,
qui
en
auteur reconnaissait que
fait
complexite. entre les
liaison
la
double liaison a 19
la
necessaire a la communication des esprits.
20
le
contenu
de
mots montrent
les
les
deux
1
esprit
De
au
Ordine,
choses
les
aux
et
etait
du De Magistro est, double liaison, en examinant
choses
surtout
etant
dialogue
mots dans
des
negativite
les
ce
Deja mots et
Le
pourtant, celui de mcttre en question cette
jusqu a quel point
mot
notion aristotelicienne du
la
la
role
et traduisent
critique
ne
il
cotes,
et
faut
1
Or,
esprit.
aboutissant
a
pretendre
pas
la
y
rencontrer une theorie positive du signe. Celle-ci n est vraiment ebauchee qu au De Doctrina Christiana, ou Ton assigne de 1 importance exegetique a Pensemble des arts liberaux. Mais, en dehors de ce propos, construire
une
theorie
du
generale
n a
signe
pas
soin de
le
concerne
1
esprit
d Augustin. Et cela, peut-etre, pour deux principales raisons: d une part, autonomie du langage plutot qu il en Saint Augustin est critique envers autonomie suffisante d un objet, pas de est le defenscur, et, sans 1
1
conditions pour la constitution d une science separee; d autre part, c est le mot, le signe le plus richc en virtualites, qui joue le role de cas
exemplaire du genre du signe. Tel le
De
est,
en particulier, ce qui se passe dans
Magistro.
En
fait,
dans
ce
dialogue
philosophique,
quelques elements de grammaire.
21
Ncanmoins,
on ne se ils
sert
que de
a
prouver,
suffisent
par la seulc reflexion, que celle-la ne traduit pas convenablement
1
ordre
Cette double liaison retrouve des antecedents aussi bien chez Aristote que chez les cf. J. Pepin, op.cit. pp. 67-68, 79-82, ou Ton fait ressortir des affinites entre trinomes suivants: bvo^a.-Xojo^-npa.Tf^a (Aristote), (rr^jLa.Zvov-^CKroi -rvy^dvov
stoiciens: les
(stoicisme) et dictio-dicibile-res (Principia Dialecticae,
20 21
Cf.
De
Ordine
II,
12, 35 (texte de
1
PL
ed. benedictine,
32, 1411).
BA
4,
pp. 224-226.
G. Bellissima, "Sant Agostino grammatico", Augustinus Congres International Augustinien, Paris, 1954, vol.1, pp. 35^2. Cf.
Magister.
Actes
du
Trivium
et
Philosophic:
Le De Magistro de Saint Augustin
539
du langage des mots. La grammaire de Pecole, plus fondee sur des autorites que sur la raison, ne connaissait pas les regies du langage que le De Magistro permet d enoncer: la regie de la nomination et la regie de reel
la
communication.
La
nomination, en particulier, etablit que tous les mots sont des noms, tandis que la grammaire conventionnelle consent a dire 1.1
de
regie
seulement que
On
la
noms
les
de
de Pexperience ordinaire de le pronom haec a la place
mettre
22
conjonctions
Penonce 23
et,
moyen de
tires
quelques exemples possibilite
sont une espece de mots.
Pevidence de cette regie au
est conduit a
que,
atque
at,
Pemploi du verbe
;
est
erat in Christo est et non, sed est in
"Non
1
1
analyse de
usage des mots: la de Pensemble des
comme
illo
erat"
sujet
dans
(2 Cor.
1,
24 la precede de la traduction en tant que re-nomination construction de pronuntiata complets, selon le mot de Ciceron, comme
19)
le
;
;
"displicet
avec
quia"
le role
et
"placet
qui renferment les conjonctions quia et
si",
si
25
du
sujet.
Parmi ces exemples,
les deux premiers et le dernier montrent que des mots, qui n appartiennent pas a la classe (pars orationis) des noms,
peuvent,
toutefois,
nominative du
dans
recevoir,
sujet. Aussitot,
la
et
observations du point de vue du sens: dans le
Paul,
qu
il
le
mot
joue,
est il
faut
qu
des noms, ainsi que fait
de
la
role
le
joue
il
le
le
la
phrase,
la
fonction
troisieme ajoutent des
exemple emprunte a Saint mais ce n est pas comme verbe quelque chose d autre, a la ressemblance
du
signifie
nom
de
syntaxe
deuxieme
le
uirtus
1
sujet,
mis a
la
meme
place; d autre cote, le
traduction des langues vient signaler que les mots isoles ne
sont traduisibles que
s ils
signifient
comme
des noms, c est a dire, par
rapport a une reference objective exterieure, au
moyen de
laquelle
ils
Done, Pensemble des cas examines nous fait voir des mots qui ne sont pas des noms au sens strict (morphologique), mais qui fonctionnent comme des noms dans Pordre du discours (point de vue puissent se correspondre.
syntaxique) autant qu
comme
noms, en denotant quelque chose d autre qu eux-memes (point de vue semantique). Par Pelargissement 22 23 24 25
Cf.
De Mag.
Cf.
De Mag.
5, 14.
Cf.
De Mag.
5, 15.
Cf.
De Mag.
5, 16.
5, 13.
ils
signifient
les
Lamas De
540
nom
du concept de
suppose le principe de 1 universel de la
a
ces
communes
possibilites
de
intelligible
regie,
Oliveira Xavier
1
a
d autres mots,
induction, necessaire a la construction
on parvient a
noms
ouverture du domaine des
1
a tous les mots, ce qui fait le contenu dc la regie de la nomination. II
et
26
cependant, d evaluer le jeu des autorites au long du de cette regie des mots. On peut 1 etablissement
convient,
chemin qui mene a
poids des autorites evoquees, Saint Paul ct Ciceron, est d importance mineure, puisqu clles sont tout a fait laterales a 1 obtention de la regie: 1 autorite dc Saint Paul vaut a 1 egard des choses, mais elle
verifier
le
que
27 n est pas incontestable au sujet des mots Ciceron, a son tour, est un modele ferme dans le Triuium, mais ce qu Augustin prend de lui, c est un exemple douteux et un nom technique de la dialectique, qui n influent ;
au
point
resultat
qu
il
s agit
de
28
produire.
En
fin
de
les
compte,
ne sont la que pour rcndre manifeste leur superfluite par raisonnement. D ailleurs, au analyse tout empirique des mots, rapport dans le De Magistro, exprime, a notre avis, le desir, chez Augustin, de autorites
1
retrouver un regard naif sur 1.2
La
regie
de
la
la realitc
meme
du langage humain.
communication, de son cote, demontre que
usage des mots est naturcllement disposee pour communication, ce qui repond a une question fondamentalc tionalite
de
1
1
intcn-
le
but de
et
prealable
la
au domaine technique de la grammaire institute. Afin de prouver la necessite de cette regie, un exemple suffit: celui ou Ton decompose les possibilites de sens du mot homo dans Penonce "utrum
interrogatif
interrogation
est
homo
homo
deconcertante,
29 sit".
puisqu
elle
30
Au
premier abord, cette met en doute le jugement Neanmoins, par la mediation
d identite auquel on songe immediatement. de 1 analyse, on doit reconnaitre une ambiguite originaire dans des
mots,
qui
peut
rendre
equivoques
nos jugements:
il
s agit
le
sens
de
la
un signe refiechi, en se double possibilite, pour chaque mot, en signifiant quelque signifiant soi-meme, ou d etre un signe transitif, d etre
26
28 29 30
Cf.
De Mag.
5, 14; 5, 16.
Cf.
De Mag.
5, 15.
Cf.
De Mag.
5, 16.
Cf.
De Mag.
8,
Cf.DcMag.
22
8, 22.
-
24.
Trivium
et
Le De Magistro de Saint Augustin
Philosophic:
541
En particulier, le mot homo peut etre chose d autre que soi-meme. du de signe syllabes ho-mo ou de Pentite signifiable de compose Phomme.
Ton
Si
actualise
homo
occurrences de
a
combinaisons de sens pour interpretations possibles de
de
1
1
meme
le
demandent des jugements d
double
cette
Pinterieur
mot,
interrogation,
identite,
a
dans
possibilite
enonce
cite,
les
deux
on obtient quatre
par consequent, quatre
et,
seulement
desquelles celles
savoir,
homo
ou
deux
est
un
terme univoque dans les deux occurrences, qu il soit un signe reflechi ou un signe transitif; par centre, les deux autres combinaisons, ou le mot
homo
n est
pas
s
univoque,
a
opposent
tout
jugement d
identite.
En
par analogic, nous tenions compte aussitot de la duplicite de sens des autres mots de 1 enonce (utrum, sit), la seule possibilite de les outre,
si,
reflechis nous empecherait meme de d une comprendre qu interrogation. En effet, Pambiguite non mais aussi actuelle, c est a dire, toujours presente simplement potentielle, a 1 esprit, entre les sens reflechi et transitif de chaque mot, rendrait la
comme
prendre
il
des
s agit
signes la
communication impraticable. Des dans
1
des
usage
Pequivoque,
Sans
choses.
On
possible.
langage
et
telle
voit
soit
mots,
surtout
celui
il
lors,
de
disposee
qui
consiste
a
que notre intentionalite, maniere a eviter le plus
faut
confondre
les
mots avec
les
disposition, pas de communication, pas de jugement par la Pimportance du probleme de Pintentionalite du
de ce qui puisse determiner
celle-ci.
Or, ce qui dispose habituellement notre facon de prendre les mots, chez Augustin, c est un reglage de notre attention vers les signifiables des mots (sens transitif) plutot que vers les signifiants par eux-memes
C est
qu Augustin considere une regie du langage nous traduisons par regie de la communication. que comme condition necessaire de la communication verbale,
(sens reflechi).
aussi ce
(loquendi regula)^, et
En
c est
effet,
34 Mais, de que cette regie est premierement enoncee. fois reiteree, en temoignant tres clairement de la
langage avec Pesprit:
double
Cette Dialecticae,
32 33
PL
possibilite 32, 1413-1414.
Cf.
De Mag.
8,
Cf.
De Mag.
8, 24.
"/.../;
comme
liaison
intime
du
condition de possibilite des jugements sur les
partie
du
concept
de
uis
uerbis
dans
Principia
22-24.
adsentior enim e
ea feratur animus,
fait
plus, elle est trois
quorum
tibi
ista
sermonicari nos omnino non posse, sunt
signa".
De Mag.
8, 22.
nisi
auditis uerbis ad
Lamas De
542
choses loi
de
35 ;
la
Olivcira Xavier
en tant qu applicable aux circonstances empiriques d apres unc 36 raison naturelle et, fmalcment, en qualite de constituer une ;
de
inclination
conformement
1
attendu
esprit,
a elle-meme.
Ton ne peut
que
ne
pas
penser
pas
37
Apres tout, on peut, certes, se demander si les deux regies demeurent tout a fait grammaticales, etant donne que Tune dement la autre s en passe completement, ressemblant grammaire officielle et esprit. On peut meme conceder que la grammaire ne plutot a une loi de 1
1
soit
qu un
tendance
"decor
de
n aboutissions
la
et
Magistro^, a
grammaire
ces
qu a
De
au
fond"
reduire
a
y verifie quelque
n aurions
nous
si
Mais,
logique.
nous
observations,
s
que
39
la
conclure
a
que
negativement, au sujet du dialogue philosophique d Augustin, qu il est sur le chemin oppose a la constitution dc la grammaire comme science
autonome,
de
et,
la
sur
sorte,
Toutefois, notre propos est
ici
chemin oppose au progres du savoir. inconformite des celui de montrer que
le
1
existence deux r6gles avec supposer grammaire d une autre grammaire, que nous appelons rationnelle, puisqu elle rend compte de la raison la plus interieure a ordre des mots, aussitot qu elle traditionnelle
la
fait
1
1
ne depend
Que
pas des autorites clues dans la
raison,
exclusivement
de
la tradition
la discipline.
que Ton decouvre au fond du langage, ne
grammaticale,
communication, laquclle que la raison meme de
tient la
c est
ce
manifeste
que
la
soit
regie
de
pas la
a la raison inscrite dans nos esprits. Mais,
regie de la nomination ne soit pas simplement
presupposes philosophiques. En veritc, cette regie serait a peine passible d etre formulee, si elle ne donnait de logique, c est ce
qu en accuscnt
les
id quod significatur adtendere et ex placuit enim ct recte placuit signo dato "/.../; eius consideratione uel dare uel negate quod dicitur." De Mag. 8, 23.
ergo quaerit, utrum homo nomen sit, nihil ei aliud quam esse respondeam; est. Si autem quaerit, significat ex ea parte se uelle audire, qua signum utrum animal sit, multo procliuius adnuam; quoniam, si tacens et nomen et animal tantum quid esset homo requireret, placita ilia loquendi regula ad id quod his duabus "Qui
satis
enim
syllabis
significatur,
animus
etiam tola definitio diceretur,
^
Cf.
J.
ncque
quidquam
animal rationale
non possum non putare ad
"Quia
simul
Collart,
atque
"Saint
ista
id
conclusionem
uerba
Augustin grammairien dans
Augustiniennes 17 (1971), p. 284. 39 Cf. Idem, ibid., pp. 287-289.
De Mag.
referri, scilicet
intentio."
le
nisi
responderetur
mortale."
sonuerint, ea ualet, ut auditis signis ad res significatas feratur
significatur,
plurimum
curreret, id est
De
animal,
uel
8, 24.
quod
his
regula,
De Mag.
Magistro",
duabus
quae
syllabis
naturaliter
8, 24.
Re\ ue des Etudes
Trivium
1
et
Philosophic:
Le De Magistro de
543
Saint Augustin
essor a une conception prealable dcs mots, savoir, que le propre de la
de ceux-ci est le fait de nommer. Telle est la pensee sur les mots en general, qui devient explicite au cours du De Magistro, ainsi que 40 le rend evident le point de vue semantique de la regie de la nomination. signification
Or,
c est
une
la
philosophique,
parties principales 41
Mais
langage. 1
esprit
n
il
enracinee
chez Platon, pour qui
privilege s
trouve
se
qui
du discours
le
d Augustin,
langage avec
idee
nommement
et
tradition
la
noms
etaient les
unites exemplaires de Panalyse
les
des
les
dans
noms ne
etait question,
viendrait
De
au
connaissance, afin d evaluer
pas,
du
peut-etre,
a
Magistro, de la relation du
pedagogique de meme question, converge encore 1 usage de Petymologie 42 populaire de nomen a partir de noscere laquelle annonce ce que Ton vient apres a demontrer: le fait que la connaissance est une condition la
Vers
celui-la.
le vrai
role
la
,
de
implicite
sur
augustinienne
communication:
le
Cependant, des
langage
a
mots,
la
la
preoccupation la
correspond
plus
de
regie
la
le dialecticien ne songeraient a grammairien, mise en question tout a fait philosophique de intentionalite essentielle du langage humain. si
celle-ci, 1
nomination.
la
ni
ce n etait
des
Alors,
degager dans
que
De
le
ni
le
la
deux regies du langage, que 1 ont vient de Magistro de Saint Augustin, ont trait surtout a des les
propos philosophiques, la grammaire, qu elles inaugurent, est, elle-meme, de soi philosophique. Accorde cela, peut-on voir, dans la grammaire rationnelle du dialogue augustinien, une anticipation de la grammaire speculative toutes
les
du moyen age? Le rapprochement est possible du fait que deux ont essaye de depasser la grammaire constituee et
chez Saint Augustin, parce que la grammaire conventionnelle etait trop prise a la surface des mots, pour convenir a 1 etre authentique du langage; chez les modistes du XIII C siecle, parce qu il fallait retablir instituee:
un domaine propre a de Part premier du
la
grammaire, par
Triuium
par
la
de
suite
la
penetration progressive
dialectique.
En
semantique des deux regies augustiniennes annonce deja Toutefois,
significandi.
tandis
"Num adhuc dubitas demonstrauimus, nomina esse? De Mag. 5, 14.
Cf. Cratyle
42
Cf.
388
De Mag.
5,
a;
424 b
U.
-
alias -
Non
425 a (sur
que
quoque dubito,
la
la
grammaire
construction de
1
art
portee
theme des modi
speculative
orationis
partes
quandoquidem
la
outre, le
eodem
de
modo,
fateor ea significare
de nommer).
1
ere
quo
aliquid."
Lamas Do
544
engagee dans un
etait
scolastique
Oliveira Xavier
d autonomie,
effort
dialogue augustinien se voulait surtout rationnelle retrouver
a
tendait logique.
Mais
reduise
a
fondement
le
commun qu
la
grammaire du
par consequent, elle
et,
devait
elle
cela ne signifie pas necessairement que la
la
on
logique:
montrer
de
vient
les
que
avoir
avec
la
se
grammaire deux regies
grammaticales d Augustin dependent d une philosophie du langage plutot que de la logique. Ce qui parait s imposer, dans le dialogue augustinien, c est
grammaire dans epistemologique. DCS
souci de fonder la
le
la
raison,
en sorte qu
elle
lors, la grammaire, comme les son tant ne vaut mots, que par sa nature science, objet, par pas rationnelle, c est a dire, son fondement intelligible, a la fois interieur et
receive de la legitimite
superieur.
De
2.
la
de
psychologic
communication
la
a
la
philosophie
de
la
connaissance
les
Cependant, s
que
regie de
pose
le
vers
la
laquelle,
la
tour, les
experience.
decisif: banal,
II
s agit
de
effct
de produire
parce que
apparents
des
1
la s
ne
est vrai
La methode ce
d un
fait
commun, quoiqu inapercu dans
mots43
;
car
decisif,
tout empirique, que but,
connaissance doit
la
applique aussitot a prouver par
evidence
efficacite
dans
il
communication au moyen des
il
pedagogique du langage question connaissance du role de la communication. 1
suivre
Magistro,
une relation de connaissance, encore non
inclut
choses nominees. Par consequent,
une condition plutot qu un
effets
De
le
rationnelle. S
mots. Neanmoins, c est cela qu Augustin I
dans
langage,
la
son
a
discernce, avec ctre
du
decouverte d une grammaire communication suppose celle de la nomination, celle-ci probleme de la connaissance. En realite, la disposition des mots fin de la communication depend de leur essence nominative,
epuisent pas a la
analyses
est
fortement
1
nous et,
auteur du
aussi la
oblige
des
De
demonstrative
lors,
banal que
soudainete des a
mettre
a separer
en la
Magistro continue de
de
la
preference
autem homines, ut cos, qui non sunt, magistros uocent, quia plerumque tempus locutionis et tempus cognitionis nulla mora interponitur, et quoniam post admonitionem sermonicantis cito intus discunt, foris se ab eo qui admonuit didicisse 1
"Falluntur
inter
arbitrantur."
De Mag.
14, 45.
Trivium
d Augustin pour
que de 1
et
Philosophic:
la vie
Le De Magistro de
psychologique,
comme domaine
concretion de ses analyses sur
la
le
545
Saint Augustin
d experience, ainsi
oppose a
s
langage, laquelle
abstraction de Pobjet des sciences du Triuium.
On
se
cette
sert,
mots dans de differentes
de quelques
fois-ci,
circonstances psychologiques de reception par rapport a la connaissance
des choses et des mots eux-memes:
choses qu 44
L
ni la
memes, du
fait
qu
1
etat
mots ne
les
la
parce que
signes,
de connaissance
1
etat
d ignorance des choses signifiables, 1 etat de connaissance des
montrent pas; a connaissance de leurs les
signifiables
trouve deja
se
incluse dans la connaissance des signes respectifs45
et
acquise
etat ordinaire
originaire
sont des signes: a
ils
parce que
1
d ignorance des signes (exs. caput et verifie experience que les mots ne produisent pas, par euxconnaissance des choses qu ils signifient, ni la connaissance
des signes et a tegtnina).
de non connaissance des
a Petal
signifient (ex. sarabarae), a
ils
;
enfin,
a
etat d ignorance des signes, parce que les mots ne sont, dans ce cas, que des sonorites insignifiantes. De plus, attendu que la connaissance des signes ne se parfait que par la connaissance de leurs signifiables, il faut 1
reconnaitre que celle-ci est une condition plutot qu un effet de celle-la. 46
De
on a rendu manifeste que
cette facon,
soil,
1
efficacite
la
des mots:
connaissance, quelle qu elle la
connaissance n est point
communicable par des mots.
litteralement
De
le
Certes,
connaissance a mais,
a
exterieure
est
par
1
egard du langage, par
anteriorite
1
d Augustin
Magistro
tres
fragile
1
denonce
1
exteriorite
de
la
anteriorite de celle-la a celui-ci,
de
contingentes, c est a dire, qui peuvent etre
circonstances
ou ne pas
etre.
psychologiques
Au
surplus,
on
n a remarque, au sujet des signes donnes, que des connaissances sensibles, lesquelles sont, en elles-memes, aussi exterieures que contingentes. Or, 1
effectif
usage
des
mots,
qui
realise
une
intentionalite
plongee
a
de
nous-memes, ne peut pas dependre de circonstances comme de ses conditions de possibilite. Une connaissance contingentes, circonstancielle n est pas une condition de possibilite; celle-ci doit I
int6rieur
participer d 44
Cf.
De Mag.
"Cum
docere
une necessite indifferente a Pexperience.
me
enim
necessite de
10, 33.
mihi
signum datur, si nescientem me inuenit, cuius uero scientem, quid disco per signum?" De Mag. 10,
nihil potest; si
1
"Ita
D une
magis signum re cognita
quam
signo dato ipsa res
discitur."
De Mag.
rei
signum
33. 10, 33.
sit,
Lamas De
546
Oliveira Xavicr
est, toutefois, le genre de connaissances que Saint Augustin toute connaissance des signes, posterieurement, au De dans presuppose
cette sorte,
des signes,
connaissance
comme
connaisssances
les
Trinitate:
la
valeur de la communication entre les
connaissance tout
court.
47
a
des choses purement
sur
portent
necessaires
et
prealables
Ces donnees
hommes
de
la
anterieures
a
et la valeur
sont
intelligibles
quelque
intelligibles,
toute experience de communication et a toute acquisition de connaissance.
Le De Magistro en
ligibles,
c est
encore avec effet,
est
dans
qu elles etaient mais seulement a
a dire,
compte de connaissances
tenu
deja
tant
communication, sensiblcs,
avait
pour ressemblance
requises la
le
,
pas
primaute intellectuelle que leur donne le De Trinitate. En dialogue pedagogique d Augustin, la connaissance intelligible
pourvue
est
Pillumination
48 intelligibles
la
de
la
personnelle, qui est celle Christ
la
connaissances
des
au sujct des noms de choses
essentiellement une relation personnelle entre
intcrieur,
intel
de
effectivite
1
ici
fondue
49
la
propre
contingcnce
de
Christ et
le
toute
a
sujets intentionnels et libres.
avec
1
idee
de
sensible
metaphore
vcrite
relation
dans
usitee
homme inter-
La personne du
avec
et
l
1
agent
la
de
tradition
platonicicnne pour traduire la connaissance des intelligibles. Cependant, Pillumination, ainsi personnifiee, devient, a son tour, le modele de toute
de connaissance, sensible
relation
extrinseques de
possibilitc.
En
et
veritc,
intelligible, 1
quant a ses conditions
anti-formalisme du
De
Magistro
jusqu a pcrsonnifier toute relation de connaissance, laquelle est vraiment irreductible au rapport abstrait d un sujet avec un objet: un il ne connait sujet peut se rcpresenter un objet dans sa conscience, mais va
point par-la la realite. Pour connaitre la realite,
il
faut
qu
elle
nous
soit,
en quelque sorte, montrce, et c est cela-meme qui n est pas dans le 50 mais, par contre, opacite de ceux-ci pouvoir des mots, a cause de c est cela qui est le propre dc la lumicre. Celle-ci se distingue de tout 1
signe par la qualite de la transparence. 47 48
49 50
Cf.
De
Cf.
De Mag.
Trin.
X,
;
51
1, 2.
5, 14: ex. uirtus.
Cf.DeMag.
11, 38.
Cf.DeMag.
11, 36.
Caractere qui n appartient pas, par exemple, au geste du doigt tendu, lequel est un acte meme de montrer plutot qu un moyen de montrer quoi que ce soit: cf. signe de 1
Trivium
et
Philosophic:
Le De Magistro de
547
Saint Augustin
Toutefois, la lun-iere n est que le moyen, ou mieux, le milieu par
excellence de celle
action de montrer; elle ne suffit pas a la realisation de
une action d un
est
qui
1
ostensio
quelque
la
des qu
intentionnel. Alors,
sujet
faut
il
realite,
voir
y
il
d un
action
1
agent
est
toute realite connaissable soit aussitot ostensible, en d autres mots,
qu
elle soit
en
faisant
realite
ait
y
52 En outre, comme que celui-ci soil Dieu ou 1 homme. une condition necessaire de la connaissance, il faut que
intentionnel,
V ostensio
de
faut
il
53
Or, pourvue d une disponibilite naturelle pour etre montree. echo d une dualite de type platonicien, est sensible toute
ostensible
aux
Des
lors,
Pintelligence.
et
sens,
toute
intelligible,
ostensible
realite
par rapport a cette division de
1
y a deux
il
etre,
a
d ostensio, ce qui fait de celle-ci un precede analogique a 1 egard du sensible et de 1 intelligible. 54 C est ce que nous appelons analogie de Vostensio", c est a dire, la theorie generale des conditions
genres differents
"1
de
objectives
de
compte
toute la
L ensemble
connaissance.
de
complexite
de montrer chez
de
en
Vostensio,
ces
conditions 1
integrant:
rend
intention
agent, moyens de 1 action meme, et chose avec sa disponibilite pour etre montree et connue. Done, dans 1
action
De
auteur
1
Magistro,
les
1
ressortir
surtout,
fait,
de
conditions
les
et la le la
connaissance qui ne dependent pas du sujet connaissant. II
En
verite,
exteriorite
au
apercoit
1
du
activite
que
1
sujet connaissant;
au contraire,
connaissance n est pas une lecture
que
on
ostensible
De Mag. 52
53 54
dialogue
identifie
55 ;
a
augustinien,
litteralement
par centre, au cas de
De Mag.
10, 32.
Cf.
De Mag.
10, 32.
me autem
aliquid
docet,
menti praebet ea quae cognoscere 55 Cf.
la
1
exige.
realite,
1
aide
1
1
deux
de
la 1
exemples de demonstration du
equivoque, toujours
demontree
action
avec
oiseleur demontrant ses
Faction
demarches a
10, 34.
Cf.
Is
Vostensio elle
de
litterale
demonstration des actions ostensibles par 1 homme: fait de marcher conduit, en toute circonstance, a 1
de
effectivite
celle-ci a de la profondeur et ne s epuise jamais dans d elle-meme ou dans son cote ostensible. C est ce que 1 on
que
parce 1
la
remarquer
cependant,
faut,
n aneantit point
De Mag.
3, 6; 10, 29.
qui
uolo."
uel
oculis
De Mag.
uel
11, 36.
ulli
corporis sensui
uel
ipsi
etiam
Lamas De
548
Oliveira Xavier
chasse, Augustin reconnait expressement la necessite de Pintelligence 56 afin d eviter toute equivoque de litteralite. Alors, chez le spectateur
la
,
d une
c est
depend
Pefficacit6
intelligible,
de
celle-ci,
illumination,
1
chez
active,
intelligence
qui
et
destinataire
de
que Vostensio de meme, exemplairement,
deploit
le
Pactivite
judicative
en outre, requiert des conditions de volonte pour
I
ostensio,
du
accueillir
57 sujet
,
et,
une lumiere
personnifiee.
Apres dans
le
nous pouvons conclure que Saint Augustin temoigne, Magistro, aussi d un rationalisme fier, par ses reflexions
tout,
De
grammaticales peu conventionnclles et Pepistemologie rationnelle du Trillium qui en resulte, que d un personnalisme deja chretien, par 1 antiformalisme en matiere de connaissance, nommement, par
1
anti-litteralite
rdel, et, en somme, par le fait meme que le probldme connaissance s exprime toujours, au cours du dialogue, en termes de
de Pintelligence du
de
la
pedagogic.
Lisboa
56
^
Cf.
De Mag.
"Quisquis
10, 32.
autem cernere
uel potius ipsius locutionis;
58
CLDeMag.
11, 38.
potest,
/.../."
intus
De Mag.
est
discipulus Veritatis, foris iudex loquentis
13, 41; cf.
De Mag.
14, 45.
ROBERTO LAMBERTINI
Logic as a Science and
The purpose
of this paper
comparing them
logic
Its
is
Object According to Gentilis de Cingulo*
to present Gentilis de Cingulo s ideas about
to those of
for
1 Radulphus Brito. With the choice of do not want to suggest any direct
this comparison I between the two authors: relationship
Radulphus the
of
function
modistic
theory.
logical
of his
modistic
the
logical
we can
thought,
outstanding
has rather
position
the
in
a well
times,
Parallelling
order to see to what extent
my work Radulphus
his
given
representing,
discussion
epistemological
in
the
developed paradigm of two authors can be useful in
consider Gentilis as an exponent of
while
the
modistic
character
of
his
2 grammatical works has been already ascertained. The modistic theory of intentiones in their relationship to the object of logic stands out as one
of
most
the
interesting
features
of
their
approach
to
"metalogical"
problems; thus, attention has been concentrated on the parts of Gentilis works which make use of these concepts. 3 This work is a shorter version of the paper presented August, 1987. Because of the limits decided by the editors, the
in I
Helsinki on the 24th of had to leave out part of
and
all Latin quotations, reducing also the footnotes to the minimum. I will to this subject in a more extensive study, but now I want to thank Prof. D. Buzzetti, Prof. F. Del Punta, Prof. S. Ebbesen, Costantino Marmo, Andrea Tabarroni for their most valuable advice and S. Kelly for restoring my English.
text
come back
About Cingoli. Wiss.
life and works of this Bolognese magister see Grabmann, M., "Gentile da Bin Aristoteleserklarer aus der Zeit Dantes", in Sitzungsberichte der Bay. Akad.
(1940)
2,
now
recollected in
Paderborn-Munchen-Wien-Ziirich
Grabmann, M., Gesammelte Akademieabhandlungen, pp.1639-1724; but also da Cingoli", Rech. Theol.
1979,
the
recent
II,
contributions
anc. et med. 46 (1979), by Hissette, R., "Note sur Gentile pp.224-228 and "Note complementaire sur Gentile da Cingoli", Rech. Theol. anc. et med. 47 (1980), pp.281-282; for Gentilis cultural context interesting also Siraisi, N., Taddeo Aldcrotto and his pupils, Princeton 1981. About Radulphus Brito reference has to be made, at least, to Radulphus Brito, Quaestiones super Priscianum Minorem, eds. J. Pinborg and H.W. Enders, Stuttgart-Bad Cannstatt 1980 and to J. Pinborg, "Radulphus Brito on Universals", CIMAGL 35 (1980), pp.56-142.
2
See
Pinborg,
J.,
Die Entwicklung der Sprac/uheorie im and passim.
Mittclalter,
Miinster
i.
W.
1967, pp. 103-105, 113, 122 1
Cf.
Pinborg,
J.,
"Die
Logik der Modistae", Studio Mediewistyczne 16 (1975), pp.39-97, devoted much attention to the modistic interpretation of
especially at pp.49-59, who the Gegenstand der Logik.
Lambcrtini
550
Gent His conception of logic necessary that young people exercise themselves in logic in order to learn it ... so that once they have grown up they can abandon these exercises and judge correctly thanks to the education received in their is
"It
in
Adapting
youth."
Aristotle
which
Politics
s
this
a
way
from
quotation refers
actually
to
VIII
the
Gentilis
music,
Book
of his
opens
his conception of Scriptum super artem veteran giving clear expression to as a conceptual tool whose goal is to serve other sciences. More
logic
proper sense and per se, logic is, in fact, together with grammar and rhetoric, an organum for the other sciences. In the same sense he defends logic in another principium arguing polemically than a science
against jurists their
in
its
who do
argumentations
compared their
use of logic in their books, and carry on opinion they should be hystorialiter. In Gentilis not
by nature, because they obey every science, even for grammar,
to servants, or better, to servants
books;
5
is
logic
Gentilis this
be
is
possible
necessary
for
necessary
although grammar comes
would
make
as far as
for
a
order
the
in
first
grammar
scientific
of learning.
According
to
taught fabulative; but logic
is
consideration
of
6
this
discipline.
Notwithstanding his preference granted to the practical aspect of logic, no univocal answer to the question regarding its Gentilis gives nature. In his quaestio devoted to this problem he maintains that logic
primarily exactly,
modus sciendi, but is a modus sciendi in
a
it
science because
it
seems
solution
also
a
science
to
Radulphus is it
a is
position
science,
and
base myself on the transcription from the Manuscript Conv. Soppr. I.X.30, f.lra-va prepared by Shona Kelly, make use of it. I
use
the
ms.
Palermo,
Biblioteca
it
is
a
subiectum. This
the
exactly
same for
the
issue.
same
possible for logic to be a science and
nale,
I
its
on
is
More
quid.
respect to other sciences, but
demonstrates some properties of
similar
Radulphus asserts that logic reason; he also maintains that
5
secundum
Comunale,
2
Firen/e,
who
Qq.D.142,
Biblioteca
kindly allowed
f.Slr
according
Nazio-
me
to
to
A.
made available to me. Concerning the transcription, which has been kindly contents of this ms. several additions will be necessary to what is to read in Lohr, 26 (1970), pp.153-155. Ch., "Medieval I^atin Aristotle Commentaries. Authors G-I", Traditio
Tabarroni
6
s
This statement
is
coherent with what we can read
the Quaestiones super Priscianum Minorcin, Pisa 1985, p.13.
in
R. Martorelli Vice s edition of
Logic as a Science According to Gentilis de Cingulo
modus sciendi at the same time. 7 Still, there is a accent when the two philosophers must order
551
certain difference of
a
logic
the
according
which divides sciences into theoretical and practical ones. In prohemium super artem veterem Radulphus speaks of logic and
classification his
grammar logic
as scientiae speculativae adminiculativae atiis? while for Gentilis
a practical science as far as
is
investigandi in
of
reducing
characteristic:
terminologies,
subiectum.
its
something regarding risk
it
to
logic
their
aim
at
9
Both thinkers
an
modus when it demonstrates seem to have felt the
serves other sciences as
speculativis, but remains speculative
instrument
solutions,
although
preserving
the
lacking
by
scientific
any
scientific
of
different
a
discipline
means dignity
of
whose instrumental function could not be denied.
Wliat
One
is
logic
about?
of the reasons
-
why
according to Gentilis
seniores should
-
abandon
the study of logic and devote themselves to sciences of an higher degree
because logic does not regard real beings existing outside the mind. This statement raises the question about the proper subject matter of is
logic.
Radulphus and Gentilis agree to
in defining syllogism as the object
the possibility of dividing
in
of
different
logic; according parts they both offer a subdivision of logic in the different books of the medieval tradition. But Radulphus solves the problem of the subject matter of logic
with
an
answer
which
is
twofold:
he
it
says
that
syllogism
be
can
considered logic s subject matter per attributionem, while intentiones secundae or entia rationis can be said to be subiectum per predicationem. Gentilis expresses himself in a less precise is
de modis
entis factis
main difference
way
ab anima or de entibus
consists,
of course,
in
the
asserting often that logic factis
ab
intellectu.
10
The
absence of the expression
See Ebbesen, S. and Pinborg, J., "Bartholomew of Bruges and his Sophisma on the Nature of Logic. Introduction and Text", CIMAGL 39 (1980), pp.iii-xxvi & 1-76, where at pp.xii-xv the authors present an edition of Radulphus first question on Porphyry. ft
See Ebbesen, S. and Pinborg, J., "Gennadios and Western Scholasticism. Radulphus s Ars Vetus in Greek Translation", Classica et Medie\
Brito
pp.263-319, especially p.299. Q See the ms. Palermo, Bibl.
Com.
quaestiones on
2 Qq.D.142, containing also Gentilis
Porphyry, f.74rb.
See Gentilis, Scriptum, (according to ms. Firenze, Bibl. Naz., Conv. Soppr.
I
X.30)
f.lrb.
Lambcrtini
552
As
intentiones secundae. -
second
which
intentions,
three
the
among
can be defined in terms of a subdivision of
-
according to Radulphus
these
the whole extension of logic
a matter of fact,
of
operations
on the
depends the
traditional
distinction
uses
Gentilis
intellect.
same
the
11
His Scriptum super subject matter the second Porphyry assigns intentions, to the Categories the real things ut slant sub primis rationibus to the Peri Hermeneias the oratio significans verum vel intelligendi, without mentioning the second intentions.
division
totam artetn veterem
as
to
The general concept under which we can
falsum.
consider the different
factum ab intellectu", while Radulphus tries to unify the whole realm of logic under the concept of second intention, and not without problems, as Pinborg has rightly pointed out especially for the intentions of the second or third operation of
subjects
logic
of the intellect.
12
to
according
is,
As
far
as
Gentilis,
"ens
can understand,
I
many
us to
lead
clues
think that the main disagreement between Radulphus and Gentilis could consist in their conception of second intentions, or at least in the this concept. In
terminology they use to define
on
this subject
in
which
intentions, that
Gentilis
is
it
both
deal
philosophers
is,
order to shed more
necessary to pass to the analysis of the
the
with
intensively
first
light
commentary and
second
commentary on Porphyry.
on first and second intentions
division of logic proposed in its principium, Gentilis on Porphyry passes to the discussion about the subject of commentary the book. His first answer is that the subject matter is universale non quodcumque. The interesting part of his answer is of course the
After
usual
the
"non
expression different
quodcumque",
of
meanings
opposition
Gentilis
proposes
animam and
existens extra
understood
as
a
See Gentilis, Scriptum,
13
Cf. Pinborg,
"Die
is
See Gentilis, Scriptum,
is
implies a distinction 1^
"universale".
or
p. 58.
f.lva.
The
first
drawn between universal
essentia
produced by our
f.lrb.
Logik...",
term
it
universal as intentio.
quiditas
individuancia, which
12
the
because
The
abstracted intellect
"real
only
conceptual as
thing"
from as
the
among
its
for
res is
vera to
be
principia its
esse
Logic as a Science According to Gentilis de Cingulo
for
abstractum;
reason
this
universal, however,
which
predicated of the things
is
res
This
vera.
kind of
obtained by means of abstraction and can be abstracted from
is
it
can be called
it
553
-
Gentilis says
-
is
not the
object of the Isagoge.
The subiectum that
namely short
gnoseological
which
intellect,
of Porphyry
one which
book
s
is
another kind
of universal,
called secunda intentio.
is
explanation,
identifies in
According to Gentilis originates from the activity of our
it
an abstracted quiditas, for example
in
homo,
the property of being predicated of accidentia. is
On
this
called species:
property
this
and has only an esse
is
many objects differing only through based that kind of second intention which
not a real entity existing outside of our mind
is
animal
in
Summarizing the results of this distinction, we could state that aim is to distinguish the subject matter of Porphyry from the
Gentilis
provided
things,
that
here
"thing"
is
understood
as
a
an
of
result
abstraction of a quiditas which exists in the real world. According to
him
Porphyry does not discuss relations between existing things, but inves tigates the main features and the relations existing among psychological entities,
namely these second
modi
the expression
intentions,
which can also be designated by
intelligendi.
While the Scriptum stops
its
analysis here, in other
more complex
position about this problem; 17 short tract on universals which bears the title
takes a
works Gentilis
this is the case "Comentum"
of his
but
is
a
rather systematic discussion about the nature of the universals. This short
work
between universal as a thing and as the beginning of the commentary on Porphyry:
also begins with the distinction
intention which
is
made
at
but in this tract Gentilis tries to explain in a ideas regarding this subject. First of
all,
more thorough way
his
he specifies that the universal
considered as a real thing can be distinguished further in two aspects; in fact, when our intellect abstracts the universal from the objects in which it
15
exists
extra
animam,
See Gentilis, Scriptum,
f.lva.
See Gentilis, Scriptum,
f.lvb.
See Gentilis, Scriptum,
f.lvb.
For a Cingoli
tra
it
can
do
it
in
two
different
ways,
partial transcription of this text, see Marchegiani, L., "Gentile da aristotelismo e averroismo alia fine del XIII secolo", Annali della Facolta first
di Camerino (1968) pp.132-136; I use my own transcription Firenze, Biblioteca Mediceo-Laurenziana, Strozziano 99, ff.43a^45v.
giuridica
namely
from
the
ms.
Lambcrtini
554
the
to
relation
a
preserving
supposita
or
In
not.
this
way
Gentilis
explains the origin of two different kinds of universals which are referred to
by
"homo"
universals precisely,
ratione
and
"humanitas"
intelligcndi,
sub
or
logician.
under a secunda secundus modus
On
pritna
which
expressions 19
intencione
considered
are
sub
or
homo
other hand, our intellect can consider
the
intelligcndi
namely on the fact that
modo
primo
synonymous by the
as
an expression which of secunda intcntio;
ratio intclligcndi,
concentrates on
intellect
should not forget that both kinds of
must be regarded, according to Gentilis, as res verae. More they are res verae considered sccundum quod slant sub primaria
intelligcndi,
Italian
We
.^
or
is
in
synonymous of this
our
case,
peculiar property which is found in homo, can be predicated of more objects which differ
a
it
from one another only accidentally. What we inlelligendi something under that property.
call species
is
exactly the
modus
Concluding his tract, Gentilis reminds us that the word real existing thing, but signifies both the second intention and the the and then second the intention, thing. Therefore the subject primarily
"species"
matter of Porphyry
s
book
be the universal, although not taken
will
absolute sense, but as related to the real existing things.
in
an
20
Radulphus intentions s theory of intentions, which is closely connected to his of universals, has been described several times, so that we do not theory
Radulphus Brito
need,
in
this
Knudsen
thing,
21
As
activity
1
8
21 in
in
full
of thing,
Radulphus
2
intellect.
universals
come
The most
See Gentilis, Comcntum,
f.43r.
Sec Gentilis, Comcntum,
f.43v.
Sec Gentilis, Comcntum,
f.45r.
first
specifies that a real existing
because only intentions
to actual existence through the
interesting
features
of
his
theory,
See Pinborg, "Die Ix)gik...", pp.50-51, and Knudsen, C, "Intentions and Impositions", The Cambridge History of Later Medie\ al Philosophy, ed. by N. Kretzmann et alii,
Cambridge 1982, pp.487-490. ~~
Both Pinborg and intention and second
length.
only potentially a universal,
are universals in actur the
it
triad
a matter of fact,
a res, can be
of
explain
him speak of a
after
intention.
to
context,
Sec Pinborg,
"Radulphus
Brito on
Universals", p.
86.
Logic as a Science According to Gentilis de Cingulo
combined
however,
are
intentions
on one hand, and between
a
the
intention
abstract
first
distinctions
the
in
only
intentions are said to be
expression
and
intelligendi
first
second refers to a
The
and
it
for their ontological status,
concrete
first
entity,
understood in
is
of being and
this
way".
This
the thing
is
Radulphus maintains
be
can
explained,
The
difference
abstract intention.
first
between
second
and
concrete
second
the intentio secunda in concreto If
way. or
"specialitas"
"genus"
"generalitas"
abstract
one: the intentio secunda in abstracto
first
the capacity of being predicated
is,
we
if
therefore,
concrete intention, while the
first
of the thing according to a particular apparens or
being, that
The
apparens
or
cognition
mode
of complex entity which
"humanitas"
distinction
intellection
Gentilis
first
or
psychological
term as signifying a
intention parallels the
that
the
extramental world quantum ad rem.
in the
"homo"
consider the
in
with
concrete intentions are in the intellect quantum ad rationem
first
between
its
thing as
should signify a sort
known qua known. As that
"the
and second on the other. While
24
a
as
intellect
between concrete and abstract
identical
is
intellection of a thing according to exists
first
555
or
is
signify
mode
of
of different things; but
defined as the thing
"species"
will
25
the
is
itself
understood
second concrete intentions,
denote second abstract intentions.
and Radulphus
first
results
of this
corroborate Pinborg
comparison between Radulphus and Gentilis
idea of a link connecting modistic
s
grammar with
a
peculiar attitude towards logical issues. Actually, both philosophers share a conception of logic
possesses
an
prominence
aimed
independent
at
preserving
object.
Gentilis
it
nature as a science which is
more
inclined
to the practical aspect of this discipline, as a
maintaining at the same time that logic as far as
its
proves some properties of
is
its
modus
subject,
which
is
J.,
"Radulphus
Brito
s
See Ebbesen, Pinborg,
"Gennadios...",
Sophism on Second
p.307.
sciendi,
independent
Roos, H., "Zur Begriffsgeschichte des Terminus "apparens" in den des ausgehenden 13. Jahrhunderts" in Virtus politico. Festschrift Gcburtstag von Adolf Hufnagcl, Stuttgart-Bad Cannstatt 1974, pp.323-334. Cf.
See Pinborg,
give
also a speculative science, in
Schriften
(1975), pp.141-142.
to
Intentions",
logischen
zum
75.
Vivarium XIII. 2
Lambertini
556
of that of other sciences. In this
my
opinion
we
are allowed to interpret in
and not semiocinalis
also his repeated assertion of a rationalis,
way
character of logic as a further attempt to defend the autonomy of this 26 On the other hand, it is evident that the search for a discipline. unifying subject matter for the whole field of logic
the
same
On
trend.
theoretical
this
is
an expression of
however,
topic,
we
notice
a
Gentilis. For the former the significant difference between Radulphus and subiectum logicae owes its independence to the fact that intentiones in
concrete are neither psychological entities (which would be the object of 27 for the latter the logician natural philosophy) nor exlramcntal things; studies essentially entia facta ab intcllcctu.
not be
to
impossible
settle
becomes more apparent
As we have are
which would
conflict,
connection with the discussion about Porphyry.
in
seen, the setting of the problem
very similar, and similar
is
concepts the two logicians employ. They both distinguish
the
also
Such a
with regard to the general object of logic,
by means of the existence in the things of two kinds of properties upon which such levels are founded; Radulphus distinction between intcntio in abstracto and intcntio in
between two
concreto
is
levels of intentions, explained
difference between
by the
paralleled
exactly
fact
the ratio intclligendi
that
and the
Gentilis res
at
points
which
is
the
conceived
the by the intellect according to that ratio. Moreover, they are aware of their referred to or as possibility to consider intentions as absolute
evidence of a supposita. Without any doubt these correspondences give find whose basic of tradition common expression in a concepts thought,
between very similar language. Nevertheless, examining the main contrast Radulphus and Gentilis with regard to the issues involved, it seems to
difficult
interpret
diverge about
the
it
as
simply due status
ontological
to
different
of what
they
terminologies. call
intcntio
They
secunda
and about what they consider as the proper subject matter of Porphyry: for the Italian logician a second intention is a ratio, a modus inlclligendi,
structure,
which
exist
only in our mind: for Radulphus it is a complex whose existence is twofold. In order to
a res sub intentione,
appreciate this difference
26
This
is
About
the case also for this topic cf.
we should remember
grammar, which
Pinborg,
"Die
is
Ix)gik...",
that this twofold peculiar
considered a scientia rationalis as well. p.54.
557
Logic as a Science According to Gentilis de Cingulo
status
is
by Gentilis not to intentions but to res 28 it from a second intention.
attributed
exactly when he
and
vera,
tries to differentiate
Conclusion
on the background of a common conceptual tradition, the present comparison between Radulphus and Gentilis corroborates once again Pinborg s idea of the unity of the
By
some
out
pointing
differences
modistic logic as community of problems and of basic concepts, rather
than
At the present
of solutions.
premature
to
or
disagreements
stage
of the
research
would be
it
evaluate the exact significance of agreements and
try to
to
establish
historical
connections
positions. But even the present contribution can show
among -
I
different -
think
importance of a thorough scrutiny of Gentilis works, especially in a like in
the
field,
the history of logic between the thirteenth and fourteenth century,
which,
as
a
in
puzzle,
every
little
piece
we succeed
provides us with a better understanding of the whole.
in
locating
29
University of Bologna
28 for
Also the different
Radulphus
while for Gentilis
29
Cf.
is
it
Pinborg,
it
classification
the
name
denotes the
J.,
"A
of
of the term humanitas could be of first
res vera sine
abstract
habitudine
intention
ad sua
some
interest:
or prima cognitio hominis,
supposita.
Note on Some Theoretical Concepts of Logic and
Grammar",
Revue Internationale de Philosophic 29/113 (1975), pp.286-296, now as N X in Pinborg, ed. Sten Ebbesen, Variorum Reprint, London 1984. This short J., Medie\>al Semantics, essay shows in the best way the usefulness of the study of logical debate of that period as a whole.
MARIA GABRIELLA LO PRESTI
La
come diffiniendi disciplina libro del De Divisione Naturae
dialcttica
nel
1
di
La
interno
all
come pervicne
cosi
dialettica,
Giovanni Scoto Eriugcna
conce/ione
della
del
dalla
latina
tradi/.ione
ad Eriugena,
daH organix/azione
risultante
Sapere,
1
specifica fun/ione complessiva strumenta/.ione logica propcdeutica alia Scien/a. Eriugena nel De Divisione Naturae ha maturate tale tradi/ione dcllc
attraverso
passato
delle
soprattutto
rapporti
dclla
centralita
all
Arti
assolve
liberal!,
del
espericnza
De
motiva/ioni giuntegli il
Confcssore,
con
dialettica
le
Pracdestinatione fonti
dalle
greche
ed
alia
in
particolare
definendone
discipline,
interno della scicn/a e dichiarandola con
essa
e,
luce
dei
rislrutturazione
alia
perviene
altrc
di
la
la
sua
coincidente
vera remrn contcmplatio, in quanto diffiniendi disciplina.
Per
la
proprietas
dialettica e
la
I
Massimo
e
Dionigi
come
sctte
che di
capace
la
riguarda
rifondare
il
come
ruolo che
loro complesso, perche capace di dichiarare stessi della scien/a, nei termini del
diffiniendi disciplina
al
Ao^oc, che
le
discipline
nel
occupano
proprio interno le
infatti,
sono propri.
i
principi
Come
tale
essa assurge a vera scien/a conoscitiva capace, dai principi, di definire
suo stesso ambito ponendo ratiocinatio
i
termini della sua argomenla/ione, ossia dclla
e per qucsto vera rcnun contctnplalio:
Marziano Capclla, Agostino, Cassiodoro, Isidore tale
tradizione,
il
tcsti
di
di
Siviglia,
Alcuino.
A
proposito
di
La
philosophic an moycn 1973; Grabmann, M., Die Geschichte der ungedruckten Qucllen, I: Die Scholastische
rifcrimcnto fondamcntali sono:
age, Paris 1952, I,a Nuova Italia, Firen/.e scholastischen Methode nach gcdrucktcn und Mcthode von ihren erstcn Anfangcn in der
Gilson,
bis
Vatcrlitcratur
zum
Bcginn
des
12.
Jahrhundcrts, Freiburg im Brcisgau 1909; Cappuyns, M., Jean Scot Erigene. Sa vie, son oeu\re, sa pensee, I,ouvain-Paris 1933; Schrimpf, "Johannes Scottus Eriugena und die Rezeption des Martianus Capella in Karolingischen Bildungswesen", in: Eriugena, Studien
zu seinen Quellen, hrg. Beierwaltes, Heidelberg 1980. o
Anche
a
"metodo"
proposito
csprime greco soprattutto a Dionigi i
della
ratiocinatio
eriugeniana
e
delle
questioni
relative
al
deH argomentazione dialettica, reso interno all argomenta/.ione stessa che suoi principi, si deve far riferimento alle principal! auctoritates del mondo 1
Areopagita e Massimo
il
Confessore.
La
come
dialctlica
559
diffiniendi disciplina
nos inter artcs disciplina prohibct poncre, diffiniendi adiungentes dialcctica cuius proprielas est rerum omnium quac intclligi possunt naluras diviaere coniungere discemere propriosque locos iimcuique distribuere atquc idco a sapicntibus vera renim 3 contemplatio solet appellari?
Quid
valore
II
oristico
Qui
1
la dialettica del
ordine platonico
5
innanzitutto la divisio, ossia
Praedestinatione
avcva
nella quadripartizione della dialettica, 4 qui e
posto in rilicvo e fatto interne contraddistingue
De
o definitorio, chc nel
una sua collocazione a parte
complessivo processo dicotomico che Divisione Naturae.
al
De
viene invertito per cui
la
dialettica
un processo discensivo
di
specificazione dal
genere sommo, ed un processo ascensivo
di ritorno al principio
prevede
da cui e
sorta la divisione, la resolutio.
complessivo procedere dialettico e cosi chiarito:
II
pars philosophise quae dicitur dialectica circa horum generum divisiones a generalissimo ad specialissima iterumque collectiones a 6 specialissimis ad generalissima versetur. Ilia
Omnis divisio, quae a Graecis /aeptcr/jpc. dicitur, quasi deorsum descendens ab uno quodam diffinito ad infinilos numeros videtur, hoc est a generalissimo usque ad specialissimum, omnis vero recollectio veluti quidam reditus iterum a specialissimo inchoans et usque ad generalissimum astendens vocatur. Est igitur reditus et resolutio individuorum in fprmas formarum in genera, generum in oyvLCCC,, oixrLOLrum in sapientiam et prudentiam ex quibus omnis divisio oritur in
De
Nel la
easdemque
finitur.
Divisione Naturae e
la
divisio
ad assumere valore fondante
definizione e questa ha identicatamente valore probative:
Nam
tarn late patent dialectic! loci ut undecumque dialecticus animus natura rerum argumentum quod rei dubiae facit fidem repperit locum argument! esse describat (seu argument! sedem). 8 in
Perche abbia valore dimostrativo "luogo"
II
argomentazione deve incentrarsi nel della natura gia individuata, deve esprimere la sua definizione. luogo non e altro infatti che la definizione della natura: lohanni Scotti D.N.) D.N. 48fi,B.
Sheldon-Williams,
(Da ora 4
La
in avanti
dialettica
aTio5c(,KT( II
Fedro e
K7),
La
a
Repubblica.
D.N.486,B.
8
De
D.N. 463,B. D.N. 474,D.
Eriugcnac Periphyseon, Liber ftimus,
Praedestinatione veniva distinta
in:
Dublin
1969
SICU PCTCKT),
ai otXvTiKT) cioe divisoria, dcfinitiva, demonstrativa, resolutiva.
riferimento
6 1
nel
1
Platone
riguarda
la
concezione
della
dialettica
stabilita
nel
Lo
560
Prcsti
Ac per hoc datur intelligi sive locum quis dixerit sive finem sive termmum sive dcffinitiqnem sive circumscriptionc unum idipsum significare,
Essa equivale
all
ambitum ambito
stabilito dai termini fissati dal
locus nisi ambitus
Nil aliud est concluditur.
Termini che per
videlicet finitae naturae.
la
loro
stabilita
Ao^oc,: certis
quo unumquodquc
garantiscono
la
possibilita
terminis
del
stcssa
discorso:
enim nil aliud locus sit nisi terminus atque diffmitio uniusin aliquo sit, cuiusque finitae naturae profecto locus non appetit ut scd omnia quae in eo sunt ipsum merito termmum finemque suum sine quo in semper desidcrant in quo naturaliter continentur et
Si
infinito fluere videntur. Locus itaque in motu quac in eo sunt ad se moveantur; ipsc vero stat.
Ma
per giungere a stabilire
termini
tali
il
est
cum omnia
la ratio
eriugeniana,
non
Ao-yoc,,
dcfmire ed e dunque proprio la complessa opera/ione compie esaminare nelle sue parti proprietas della diffmiendi disciplina che bisogna dialettica eriugeniana. per cogliere la spccifica valen/a speculativa della del
la
Essa consiste
in:
naturas dividere coniungcre discemere e dunque:
propriosque locos unicuique distribucre
della dialettica precisazione del processo diairetico e analitico esaminato, risulta che 1 atto di divisione, attravcrso cui si individuano
Secondo gia le
.
la
"nature",
consiste nella divisione dei generi nelle loro specie fino agli
Solo attraverso tale divisio e possibile il coniungere, cioe porre costruire lo relazione, costruire legami logici tra le nature individuate,
individui. in
stesso
impianto conoscitivo.
mostra responsabile del
proprios
locos
di tali
Ma
cio
tutto
rimanda
operazioni e che decide,
unicuique
distribuere,
cioe
al
discemere che
come
fissare
si
atto conclusivo, i
termini
della
definizione. II
verbo discemere che esprime
Ratio dialettica attraverso atto
che pone
richiesta
di
la
i
quali
definizione,
identificare
il
si
il
possesso
di
principi
interni
alia
riesce a far differenza tra le nature,
rimanda
al
soggetto di
tale
differire,
fa
determinazione. principio del proprio atto di
Al porre atti di determinazione, al pronunciare definizione corrisponde cioe un internarsi di tale processo del Ao^oq nel tentative di fissare chi 9 10
D.N. 483,C. D.N. 474,B.
La dcticne
potenza di
la
come
dialettica
tale determinare.
nell
Ao^roc,
pronunzia
il
mihi
sua
diligentiusque
cogitanti
561
momento
Per questo, nel
della
totalita
esprimere la termine natura:
Saepe
diffmiendi disciplina
esperienza
in cui
il
conoscitiva,
quantum
suppetunt yires percipi vel intentionem eius superant primam summamque divisionem est in ea quae sunt et ea quae non sunt hprum omnium generale11 vocabulum occurrit quod graece (pucrtc,, latine vero natura vocitatur
rerum omnium quae
inquirenti
e
dalla
discretiva
la
principio
responsabile della
non
sunt"
La inizio
chiarire
di
difficolta
vel
suoi
i
e
a
che,
somma
che
termini
stessi
differentia
"prima
animo
questo
divisio in ea
la
ratio si
mostra
et in
ea quae
punto,
quae sunt
pone a
e della articolazione interna alia natura in quattro specie. discretiva
impone come primo, come termine
si
differentia
da cui deve incominciare
di
la ratiocinatio:
Sed prius de summa ac principal! omnium, ut diximus divisione quae sunt et ea quae non sunt breviter dicendum existimo.
in
ea
Non enim
ex alio primordip ratiocinationem inchoari oportere video, nee solum quia pruna omnium differentia sed quia obscurior caeteris videtur esse et
Nella
primordialis
est.
omnium
discretiva
usato in funzione attributiva, dichiara la
quale
dialettica
la
e
il
il
differentia,
verbo
discernere,
soggetto della proprietas secondo
capacita di porre definizioni e ne stabilisce la
primordialita.
La differire
e
differentia primordialis
interne
alia
capace
ratio,
fino alia inconcettualita dei principi:
quae non sunt e
esprimono 1
la
argomentare
la
non
e responsabile dunque del sue division! e determinazioni
discretiva
delle
la divisio
quarta forma della natura datita
dialettico,
dei
"termini"
o
in
ea quae sunt
nee creat nee
"quae
"luoghi"
TO ov ma,
creatur"
massimi cui giunge
sono ancora un tentativo da parte del
porsi contro un oggetto un
ea
et in
relativamente
ai
Aojoq
principi,
di
tale
posizione risulta impossibile, e concetto del principio non riesce ad essere.
La
oggetto
divisio,
principio che,
in
impossibile
qualche modo,
riesce a dirsi all interno del
argomentativo
dialettico
chi
Ao^oc, si
al
12
D.N.441A D.N.
443A
mostra
la
stesso. In tali termini del
pronuncia
che, eriugeniamente e la divinita. 11
Ao^oc,,
natura del
nella indeterminazione che lo riguarda,
e
lo
stesso
procedere
soggetto
del
Lo
562
Presti
esprimc ncl Ao^-oc, la non assimilabilita del principio al il differire del principio che ha piano conoscitivo, il suo differire da esso: mcsso in movimcnto la ratiocinatio c la rcgola al suo interne, nel
La
divisio
momento
vuole dirsi nella sua assolutezza,
cui
in
termini inscindibili nell esscr concepiti, nella relazione divisio:
ea quae sunt
et
in
cui
la
pone
li
ea quae non sunt.
Affidato ad essi due
il
risultato e che concetto della differenza
riesce ad essere; nella divisio di
sono due
risultato
il
chiudere ancora un ambito
secondo termine
il
non
fa saltare la possibilita
concludere cio che tramite
di definizione, di
primo termine stava per essere "concepito", il risultato e una relazione che, per sua stessa struttura, non puo avere un luogo, non puo essere
il
circoscritta.
La
delta
relazione
dalla
divisio
dunque
esprime
divino,
il
rincomprensibile:
Incomprehensibile enim rationi
et intellectui
divinum
est.
Nel rimando continuo del concetto, espresso dalla divisio, atto proprio della dialettica nel suo procedere secondo definizione, in queslo transitarc del
Ao^-oc,
realizza
si
costruisce
una sorta
uno spazio infmito
di "movimento impossible".
Nullum motum
determinazione
di
principio ac fine carere posse.
ncl tentativo di esprimere
"movimento"
accadere nel Ao^oc,
la divinita nella
Deus autem anarchos, hoc praecedit nee
eum
ut
efficit,
si
14
Deinde considera quia omne auod principio caret quoque motu carere neccsse est. Tale
cui
in
13
il
et
omni
fine
differire del principio, fa
sua potenza di determinazione: sine
est sit,
principio,
est
nil
quia
eum
nee finem habet, quoniam infinitus
est.
"Motus
infinite
deo dare non possum, qui solus immutabilis di
determinazione
e
dunque occupato
essere scienza di definizione, e dell indeterminato, di
6catpCTLKT7
logiche rispetto a 13 14 15
D.N. 514,8.
D.N.514,B. D.N.
516A
una sorta
di
come
tale essa e
"medio",
dalla il
est
..."
Lo
dialettica
spazio
nel
suo
continuare a mediarsi
che, nel suo complessivo processo
avaAuTt/co, tramite il risultare negativo delle categoric Dio ricostruisce il nascondimento del suo principio. e
La
dialettica
come
563
diffiniendi disciplina
Sed, ut Sanctus pater Augustinus in libris de Trinitatis theologiam, hoc est ad divinae essentiae investigationem
kategoriarum virtus omnino extinguitur. quae nee dici nee intelligi potest per omnia
La capacita
di scienza e insita
Quoniam videmus aliud aliud ipsam animam quae
Nam
si
m
omnibus
in
dum
ad
pervenit
ea verp natura deficit.
nelPanima:
esse
constitutas
anima
in
liberales
artes,
quasi quoddam subjectum est artium, artes veluti inseparabifia naturaliaque animae accidentia videntur esse verp
e sembra essere garante per
lei di eternita:
Siquidem a philosophis veraciter quesitum repertumque est artes esse aeternas et semper immutabihter animae adherere ita ut non quasi accidentia quedam ipsius esse videantur sed naturales virtutes nullo modo receaentes nee recedere yalentes nee aliunde yenientes sed naturaliter insitas, ut ambiguum sit utrum ipsae aeternitatem ei praestant quoniam aeterne sunt eique semper adhaerent ut aeterna an ratione subiecti quod est anima artibus aeternitas sit, administratur (OVCTLO. enim animae et virtus et actio aeternae sunt) an ita sibi invicem coadhaerent dum omnes aeternae sunt a se
invicem segregari non possint,
essendo
le
o
VcvepyCa.
aristotelicamente accidentia
intese
aril
dell
operatic
anima
capacita
o
virtutes
effettiva
di
costituenti
Scienza,
suo
essere in atto:
Nam cum
in omni rationabili intellectualique natura dico 8vva.iJLiv eyep^aayque, hoc est essentiam virtutem operationem (haec enim
teste sancto Dionisio inseparabiliter sibi quoniam immqrtalia atque immutabilia) num tibi verisimile videtur certaeque rationi conveniens omnes liberales disciplinas in ea parte quae cvcpfCa. id est 19 operatic, animae dicitur aestimari ... ,
La
virtus
principio
dialettica,
condannata
e
completamente.
La
che ha operato ponendo concetti, difronte a
deficere,
a
meno
venir
ad
al
suo
estinguersi
20
diffiniendi disciplina
differire del principio,
termina con un atto
di indefinizione,
che determina e circoscrive
lo stesso
con
il
ambito della
Scienza.
16
17
D.N. 463,B. D.N. 486,C
-
486,D.
18
Migne 19
P.L. vol.
D.N. 486,C
-
CXXII De
divisione
Naturae ed. H.J.
Floss,
IV
iibro, 749.
486,D.
punto e ancora Dionigi la fonte piu prossima ad Eriugena. Nella Teologia Aoyoc; nel suo procedere ascensivo verso Dio, dichiara la propria incapacita esprimerlo. II XOT<; nei termini dionisiani si fa completamente muto fronte al a.y&c XK.y aH inesprimibile. In questo
mistica di di
il
oXo<;
T
&<povo<^
Lo
564
Presti
Cio oltre che dalla prima e somma divisione e ribadito dalla divisione in particolare dalla quarta forma: quae nee quadriiorme della Natura e crcat
nee creatur.
creare
nel
la
tentative
doppia negazione e di
principio 6 identicamente
Palermo
bloccare 1
nel
dell attivo
Ao^oc,
la
e
del
passive
del
differenza assoluta del
atto di determinazione dell
ambito conoscitivo.
CHARLES
H.
MANEKIN
Logic and Science in Gersonides
In recent years there has been a growing interest in the philosophical
and
scientific
works of R. Levi ben Gershom (Gersonides), a fourteenth-
century rabbi and philosopher. Gersonides wrote independent treatises in
astronomy, mathematics, and geometry, as well as commentaries on of
Averroes
commentaries
on
historians of philosophy for his
Wars of the Lord,
Aristotle.
magnum
He
best
is
many known among
opus of religious philosophy, the
1
medieval Jewish philosophers Gersonides was known also as a sharp and somewhat controversial logician. His logical writings achieved a wide audience in the Middle Ages, if we judge from the number of
Among
extant
Hebrew manuscripts and from
the references to these writings in
the works of later Jewish logicians. Parts of his
Commentary on Logic, on Averroes Middle commentary Commentary on the Organon, were translated into Latin and were printed in the Venice edition of which
is
a
Averroes
works.
and
into Latin,
is
is
The Book of the
His original treatise on inference,
Correct Syllogism, and which includes his
extant in
Hebrew and
modal
logic,
was
Latin manuscripts.
also translated
2
Although they were written in the early fourteenth-century in what today Southern France, Gersonides logical writings fall within the
tradition of logic developed
knew
in
familiar
Hebrew with
the
paraphrase. There
by the Arab Aristotelians, whose works he He himself informs us that he was not
translation. text is
of
also
Aristotle
no
but
had
clear evidence
that
to
rely
on
Averroes
he was aware of the
contemporary scholastic tradition of logic, although it is one of those strange coincidences of history that he apparently was in Avignon at the For a recent account of Gersonides life and works, see Charles Touati, La pensee et theologique de Gersonide (Paris 1973), pp. 33-48.
philosophique
See
Charles
Manekin,
Proceedings of the American
"Preliminary
Observations on
Academy for Jewish Research
Gersonides Logical (1985), vol. 52, pp. 86-113.
Writings",
Manekin
566
same time
William of Ockham. Their social and intellectual worlds
as
were, of course, quite separate.
most
Like
medieval
saw
Gersonides
philosophers
theoretical
a
connection between logic and science. On the one hand, he adopted the conception of logic as an art and not a science, which he
Aristotelian felt
implied
that
logic
was
be considered independently of science.
to
This meant not only that the study of logic science, but
we
as
also,
see
shall
is
that
below,
study of
the
to
prior
notions such
logical
as
by considerations of scientific utility. But on the other hand, Gersonides also adopted the Aristotelian
inferential validity are unaffected
view
of
an
as
logic
for
organon
scientific
a
inquiry,
tool
the
for
of knowledge. The art of logic, even in its most theoretical mathematical manifestations, such as the theory of the modal
acquisition
and
is
syllogism,
never pursued entirely for
its
own
sake, but in part for the
sake of science. While considerations of scientific
an argument
s
validity,
utility
do not determine
they can be used to justify setting forth a logical
doctrine which has been
shown
to
be
valid.
And
in fact
we
find that
on
several occasions Gersonides defends a particularly controversial doctrine
by appealing to
scientific
its
My
utility.
paper
will
be devoted to an
analysis of three of these occasions.
The
first
which
I
should like to consider occurs
in
his
commentary
3
Middle Commentary on the Categories. As is well known, the traditional commentators wondered why the Categories was included on Averroes
in
the logical writings, since
it
appears to deal with such an eminently of reality.
metaphysical topic as the classification of
many was
to
them took
suggest
extramental
either of
that
the
doctrine
existents
qua conceived. The second was with
line
Among
the
Arab
lines
of interpretation.
existing,
but
to suggest that it
deal
first
with
qua
should be excluded from logic
Aristotelians, Alfarabi and Averroes chose the
of interpretation, Avicenna the second, with
C. Categories, I^idcn
problem
The
spoken about, or the doctrine does indeed deal
rather
that existents perse are not considered in the Categories.
*
solve this
of the categories does not
extramental existents and hence
altogether. first
two main
To
Hebrew MS. Warncro
all
three agreeing
4
42, 1:1, fol. 21r.
the scope is beyond precise formulation of the views of the Arab peripatetics of this paper. See I. Madkour, L Organon dans le monde Arabe (Paris 1948), pp. 79-84
The
Logic and Science
Gersonides opposed
in
Gersonides
own, somewhat
his
567
interpretation of
startling,
the place of existents in the Categories to these others: the doctrine of the
concerns
Categories
are
they
existents
For us
about.
spoken
and not
themselves
in
understand even
to
a
in
what
with
acquainted
The
such
art of logic
concepts
preliminary
practitioner to possess
its
knowledge about extramental reality. But what sort of knowledge? At this
as
extramental
namely
classify,
must assume
far
we must be
fashion such concepts as quantity, opposition, or substance,
existents.
so
in
some
sort of
dilemma.
Gersonides
faces
a
has argued that logic must begin with an investigation of reality, but he also accepts the Aristotelian view of the
extramental
of logic
study
point
He
as
propaedeutic
and independent
to,
out of the dilemma
science. His
the
study of
to maintain that logic
must not
way make any assumptions about extramental is
reality
of,
that
require scientific
explanation. Logic assumes things not according to the
but only according to the
exist
Here Gersonides
exist.
Averroes, standpoint
namely, of
held
assumed
to
takes
the
a
to
that they are
the
way they really commonly believed to
which appears repeatedly in the Organon are from the
doctrine
discussions
accepted
"generally
relevant
interpretation entities
that
way
in
opinion",
and gives
subject-matter
of
to exist in the Categories are those
namely,
exist,
perceptible
objects.
it
the
an interesting
Categories:
The
which are commonly would exclude
This
imperceptible objects such as the celestial intelligences, whose explanation requires the science of physics and metaphysics. I
6
do not wish to suggest that Gersonides intends via the Categories a logic which only applies to perceptible objects. In his
construct
to
own formal
logic
he never
restricts
his
term-variables
to
range
over
perceptible objects, and one imagines that he would reject any suggestion of that sort. To fathom his intentions one must go back to his inter pretation of the traditional claim that the study of logic should be prior
the study of other sciences. Given the admission of existents within
to
the
and
domain of H.
logic
we saw
that this claim entails a restriction
on the
Middle Commentary on Porphyry s "Isagoge"...and on (Cambridge, Mass. 1969), p. 32. Cf. A. Sabra, "Avicenna on the Subject Matter of Logic", Journal of Philosophy 77:11 (Nov. 1980), pp. 746-64.
Aristotle s
5 6
Davidson,
Averroes
"Categories"
C. Categories, 111:1, fol. 60v. C. Categories,
1:4, fols.
26v, 28v.
Manekin
568
type of existents admitted. But this restriction
is
only temporary.
student advances in his philosophical studies he of
scope
which
to
objects
logic,
via
the
As
the
able to enlarge the
is
doctrine
of
the
Categories,
which were unknown previously. This does fundamental changes because the new things are
applies, thereby allowing things
not
for
call
any
subsumed under previous
move from
categories.
there
Nevertheless,
have
will
to
be some adjustments when we
a pre-scientific classification of reality to a scientific one.
take one example brought by Gersonides: Aristotle lack
contraries
but not of
all
s
claim that substances
of perceptible objects, according to Gersonides,
true
is
To
substances; imperceptible objects such as the four elements
do indeed possess contraries
we draw from more accurate
in their pristine state.
The
conclusions that
pre-scientific logic are sometimes revised in the light of a
description
of reality,
although these
revisions
are
not
fundamentally the understanding of reality provided by
sufficient to alter
Aristotle in the Categories.
Here, then,
we have an example
of a controversial interpretation of
the subject matter of the categories, which the conception
is
defended by appealing to
of logic as organon for science. Since the art of logic
enables one to distinguish between the true and false in things, which is also the intention of science, logic will have to investigate extramentally existents.
We logic
example of the influence of science on Gersonides theory of modal propositions. Consider the following
find another
in
his
sentences: (1)
Every
man
is living.
(2) Every walker
What first
is
moved.
modality of these sentences? According to Averroes, the sentence is necessary, while the second is not. For a sentence to is
the
be necessary, two conditions must be
fulfilled:
the predicate must apply,
or belong, necessarily to the subject, and the subject must always that
is
but (2) is
to say, fails
walking.
be
instantiated.
Both sentences
to satisfy the second, for there
Averroes,
like
other
satisfy the
may be
Aristotelians,
first
times
when no
an
intimate
sees
exist,
condition,
thing link
between time and modality; furthermore he requires the subject of a 7
C. Categories, 11:12,
fol.
28v.
Logic and Science
universal
sentence to exist for the sentence to be true.
affirmative
there are no walkers at time is
(2)
569
Gersonides
in
t,
then (2)
is
not true at time
t,
If
and hence
not necessary.
Gersonides once again disagrees with Averroes. He argues that such are necessary because the relation of subject and predicate
sentences
expresses the necessary relation of species and genus, even though the
He
species and genus are non-substantial.
calls
this
or per accidens because the underlying subject, that to
necessity incidental
animal, happens
is,
9
be described by the attribute of walking. Were the dispute to end here, we would have an
interesting,
if
somewhat outdated, disagreement over the classification of a type of modal proposition. But from Gersonides subsequent objections to Averroes
we
see that the logical issue reflects a fundamental difference of opinion
over an issue in the philosophy of science, namely, what are the types of sentences that
things which
science
is
serve as premises in scientific demonstrations. We Averroes sentences are necessary only if they refer to
may
have seen that for
always
to
exist,
if
you
will,
natural kinds. Since the task of
us with knowledge of the essence of things the
provide
propositions of science will always refer directly to objects of this kind.
Gersonides disagrees,
I
think,
both on the basic conception of science as
well as the logical structure of the sentences of science.
What
science
not merely the essence of things but rather the intelligible
discovers
is
order of
reality,
what he
calls
elsewhere
its
law or nomos.
He
views
that are incidentally necessary as fitting premises for demonstrations because they express the necessary connection of species
sentences
and genus, of definition and definitum. Gersonides does not enunciate writnigs,
logical
but
it
can be
conception of science in his
this
inferred
from some of the arguments
which he brings against Averroes treatment of sentences such as (2). For example, he argues that Averroes theory cannot account for clearly
On Latin
The
fifth
wrote
point see Averroes third and fifth Questions on Logic which appear in the Junctas edition (Venice 1562-1574; rept. Frankfurt am Main 1962), vol 1. translated into Hebrew in Gersonides lifetime, and Gersonides "Question" was
this in
a
commentary thereon. An English
"Question"
appears
in
Nicholas
Rescher,
translation
Studies
in
from the
the
Arabic
History
of the third of Arabic Logic,
(England 1966), pp. 91-105. 9
Correct Syllogism, 1:1, 805), fol. 94v.
Parma Hebrew MS.
Biblioteca Palatina
II
v.67 2723
(De Rossi
Manekin
570
An
necessary sentences that express natural laws such as
moon
when
occurs
moon
the
shadow of the
enters the
of
the
event
eclipse of the
moon
the
for the
earth, is
transitory. designated by phrase eclipse Furthermore, Gersonides argues that Averroes theory must also treat geometrical theorems as contingent, since the geometrical figures which
they describe
may
or
Aristotle
s
scientific
demonstration.
Finally,
superior to
statements
are
most capable of
Gersonides argues that incidentally necessary sentences are necessary sentences for the purpose of scientific
essentially
demonstration, because necessary
mathematical
that
opinion
not exist (be instantiated). Yet this contradicts
may
connection
cognizing them, the intellect apprehends the
in
of
subject
and
of the terms
virtue
by
predicate
themselves. Gersonides remarks: In fact, the demonstrations which are best verified by the intellect are those which are composed of incidentally necessary premises, because the very terms themselves entail that the predicate will be affirmed or denied of the subject. These necessary premises appear to be both necessary and essential because we cannot suppose that the opposite of such a sentence will exist at some time. [Tnis is so] since a definition win not be separated from its definitum, nor a
genus from
What
is
its
species.
of interest here
behalf of the
value
of
demonstration
with
an
considerations
of
is
Gersonides juxtaposition of an argument on
incidentally
argument
scientific
necessary for
are
utility
statements
their
for
necessity.
marshalled
in
the
scientific
Once
again
context
of a
purely logical discussion.
My
final
Gersonides,
concerns
example
the
doctrine
of
the
yet
debatable
another
fourth
figure.
syllogictic
doctrine
of
Unlike most
medieval logicians, Gersonides defends at length the necessity of positing a fourth syllogistic figure, in which the minor term is the predicate in the
minor premise and the major term
is
the
subject
in
the
major
premise. I
of
the
emphasize that Gersonides fourth-figure
moods but
defense also
of
is
not merely of the validity
the
necessity
af
positing
a
separate figure. In fact he argues that their validity follows self-evidently from the validity of the corresponding first-figure moods, for the order of
10
the
premises
does
Correct Syllogism, 11:11,
fol.
not
43r.
affect
the
satisfaction
of
the
first-figure
Logic and Science
conditions.
syllogistic
11
He was
figure,
also
moods be
the fourth-figure
that
Gersonides
in
571
aware that Averroes had suggested
treated as indirect
moods
a position which can be traced to Theophrastus,
of the
first-
and perhaps
to
Aristotle himself.
What was so much
not
pursuing
at stake for
Gersonides
the
of
validity
Hebrew
A C
Is
or
is
to
it
be the aim of a
utility
was in
few words should Arabic and
were constructed so as to answer
The answer
not?
Hebrew
technical term for which in
was considered
this point a
their
syllogistic in those inquiries. In the
tradition of logic, syllogisms
the question,
as
premise-pairs,
To understand
scientific inquiries.
be said about the place of
these
in positing the fourth-figure
is
to
question, the
this
derush or mevukash (quaesitum),
syllogistic
demonstration. Syllogisms as
result were constructed to yield the derush; if they did not, i.e., if they yielded a conclusion whose minor and major terms were reversed, then such syllogisms were considered to be of no value for scientific
a
demonstration.
With
mind we can appreciate
this in
the following argument for the
fourth figure offered by Gersonides: If one
moods
figure
a
in
separate figure, but
to arrange the fourth-
fails
rather
treats
them
as
indirect
moods they
of the first-figure, they do not yield the derush, which means that are without value for scientific demonstration. In three of the
moods (Bramantip, Dimaris, Camenes) one can convert moods where
indirect
conclusion so as to yield the derush, but in the two conclusion 12
possible.
in
particular
Only
we
if
be able to produce
And it is
all
negative
we
Fresison),
them
see
may
arise in
one
the
extra-logical
criterion
of scientific
concept of inferential
validity.
which Gersonides
cites
strictly
1894), p. 291.
utility
logical
and
rejects,
that
syllogisms
that all.
do not Granted,
11:6, fol. 114r.
This point was noted
(London
we
This should be contrasted with Averroes
yield the derush are, strictly speaking, not valid syllogism at
Correct Syllogism,
the
not
scientific investigations,
s
logic, without impinging upon the
11
is
in a separate figure.
informing Gersonides
view,
this
the concludent premise-pairs that yield the derush.
important to arrange then,
and
posit a separate figure, argues Gersonides, will
since these premise-pairs
Here,
(Fesapo
the
by
J.
N. Keynes
in
Studies
and
Exercises in
Formal Logic
Manekin
572
says Gersonides, that such a syllogism as long as the conclusion follows
and not per accidens then there
is
useless for scientific inquiry, but
is
from more than one premise necessarily
a valid syllogism.
13
Moreover, he argues that considerations of scientific utility should outweigh psychologistic scruples about the so-called naturalness of the fourth figure.
To my knowledge Gersonides
as
the
irrelevant
way of
claim
that
the
fourth
is
the
figure
first
logician to dismiss
represents an unnatural
a charge which appears in logic-textbooks through the
thinking,
nineteenth century. His response to this charge sheds a great deal of light
on
own conception
his
of logic,
and
its
relationship to
scientific
inquiry:
Averroes statement that we do not possess this figure - even if we concede this point it is no objection against us. For when we mistakenly consider two inconcludent premises to be concludent, as in the case of two affirmative premises in the second figure, this art corrects our error and provides us with knowledge 01 which we were ignorant at the beginning of our speculation. But if this art investigated only by means of that which we know naturally, then pur exertions in it would be an idle exercise. For it would not inform us of anything which we did not already know. This is completely evident.
As
for
naturally
is
It
possible
to
understand Gersonides
response to Averroes in
two ways. He may be saying simply that the "unnaturalness" of the fourth figure does not diminish its logical importance, for logic takes us beyond what we know by nature, i.e., originally, or in our natural state. But he
may be
making
intuitiveness
of
the
certain
stronger valid
point
patterns
that
of
the
oddness
inference
are
an
or
counter-
insufficient
ground for rejecting them. On the contrary, since logic proceeds from what is known to what is unknown, it is likely that there will be such our reasoning leads us to these patterns, useful to retain them, then we cannot reject them
strange patterns of inference; or
if
we
find
it
if
because they represent an "unnatural" way of thinking about things. I have attempted to show here that to support several key logical doctrines Gersonides appeals to their scientific utility, and in this respect
an important connection between logic and science in his logical writings. Whether the connection exists in Gersonides scientific writings is a separate question that awaits investigation. One can only speculate there
(
14
is
C. Prior Analytics, Leiden
Correct Syllogism,
Hebrew MS. Warnero
11:6, fol. 114r.
42, fol. 129v.
Logic and Science
in
Gersonides
573
importance Gersonides attached to science, and particularly astronomy, might have had some influence on the inclusion of scientific that
the
considerations
in
his
logic.
In
any
naturally from the Aristotelian view of
of knowledge.
University of Maryland
event,
such
an
inclusion
follows
logic as a tool for the acquisition
CHRISTOPHER JOHN MARTIN
Bradwardine and the Use ofPositio as a Test of Possibility
Thomas Bradwardine Causanim
creation based on this
will
I
paper
De Causa
s
published
in
Dei,
1344
is
Contra Pelagium Et De Virtute an account of God s relationship to
Duns Scotus theory
of the will and
examine the
device
logical
which
its
freedom. 1 In
Bradwardine uses
throughout his book as a test for possibility and ask what us about mediaeval theories of modality.
its
use can
tell
At the very beginning of which he takes to be most
his
certain:
book Bradwardine
sets out a principle
2
God is to the highest degree perfect and good, nothing might be more perfect and better.
(1)
The
principle
authorities
but
requires that
we
we
in as
much
as
supported with references to a large number of also offered a proof the first part of which
is
are
consider a definition of what
it is
to
be possible:
For the purpose of abbreviation let A stand for something so and good that nothing is capable of being more perfect or perfect Setter. Possible is understood in the usual way of speaking, or if necessary, to the highest degree absolutely; for that, that is to say, which per se and formally simply does not include a contradiction or repugnance. From which namely, posited and admitted as absolutely possible according to trie variety of obligation known as positio, there never follows in a good and simply formal consequence the absolutely impossible. That is to say, there does not follow something which per se and formally simply includes a contradiction. For every repugnance gives rise to and spawns a contradiction.
Thomae Bradwardini, De Causa Dei, Contra Pelagium Et De Virtute Causarum, London, 1618, Photoreprint, Minerva Verlag, Frankfurt, 1964. The work seems to have been available in some form for up to ten years before its publication. See W.J. Courtenay, Adam Wodeham: An Introduction To His Life And Writings, Leiden, Brill, 1978, p. 117, n. 5. 2
DCD,
I.I, p. 1.
Presumably Bradwardine an ass This would yield of a general topical principle that if one cannot and the claim that being a man and
DCD,
such as
I.I,
a
p.
man
2.
is
.
means by
a repugnance an impossibility contradiction by the application of the pair of opposites inheres then the other a
being an ass are opposed in this way. In century this principle was not universally accepted but it would apparently have been acceptable to Bradwardine. For more details on opposites see my Embarrassing Arguments and Surprising Conclusions in the Development of Theories of the
twelfth
Bradwardine and the Use of Positio as a Test of In the fourteenth century logic
was usual
it
575
Possibility
to require in order for
a consequence to be
propositions
good that is impossible for the logically antecedent be true while the consequent proposition is false. No
to
all
was made between the
distinction
argument and the truth of a
validity of
conditional.
Two
methods of
different
consequences were generally
classifying
introduced. According to the
holds for
first, a consequence is formally good if it uniform substitutions from some class of expressions. For
all
Aristotelian
example,
hold
syllogisms
is
consequence
materially
good
if it
second
true and the consequent false.
now be
case
the
consequent
that
though
false,
A
consequence
may be
this
a
is
consequence
simply
for the antecedent propositions all to
antecedent
all
A
nouns.
good but not formally good.
classification,
no time possible
at
is
common
of
substitutions
if it is
good
the
to
According
uniform
all
and Boethian hypothetical
syllogisms
categorical
for
is
good
propositions
so at
some
nunc
ut
are
time.
if it
cannot
and the
true
A
be
consequence
holding per se and simply formally would thus, presumably, be one which is
good at all time and is so Bradwardine claims
in virtue of its form.
no-one who
that
accepts
what
only
follows
A
exists in an obligation of positio simply formally from the supposition can be led to an absolute impossibility and infers from this that it is
A
possible that
exists.
The second
that a
per se necessary being
which
is
in turn
more
necessary being and step
is
follows
not and,
has been shown that of a positio
from the supposition 5
Finally
existence of
God
is
that
we have
since
course,
upon the claim
perfect than a simply actual being
perfect than a merely possible being.
another application
exist.
of
it
step of the proof rests
more
is
A
the
is
a
A
is
result
to
it
4
Thus
The
possibly exists.
prove
a
that
description
of
A
is
a
third
contradiction
a necessary being but that
desired that
A
exists
it
does
necessarily
God, a proof
the
that
necessary.
the Conditional in the Twelfth Century to appear in the Proceedings of European Symposium on Mediaeval Semantics, Poitiers, June 1985.
the
Seventh
necessary if it never was, is not, nor ever will be able contrasted with the per accidens necessary which is not and never will be able not to be so but which was able not to be so.
Something
is
per
It
is
not to be so.
Bradwardine
se
to be
also
supports
this
claim
by
considering
potential to something which does not exist. Such a potential and so the non-existent would be dependent on that with potential and thus could not satisfy the definition of A.
the
attribution
of
a
would have to be passive the
corresponding active
Martin
576
The in
obligation of positio
general for his account of possibility.
on
the twelfth century
fourteenth century
to explore possibility
in
him
it
particular
and theological discussions. Bradwardine is perfectly provides
proof and In fact positio was used from
thus crucial to Bradwardine
is
with
his
s
and consequence and
in
the
played a central role in philosophical
about the importance of positio.
explicit
Aristotle
of
interpretation
It
of
definition
s
contingency: defines in Prior Analytics, 1, contingent Philosopher tne opposite of necessary, in the following way: apply tne terms to DC contingent and contingent to that which does not exist necessarily, that is to say absolutely, but with which win come about on posited in being, nothing which is impossible With which posited in being", he says, that is in account of
the
...
"I
it."
that species of obligation which is called positio, "nothing will come about , that is fall out in a simply formal consequence "which is that is to say simply and entirely absolutely what impossible", formally implies and includes a contradiction.
what we obligation of positio thus formali/.es for Bradwardine 7 Whatever Aristotle Aristotle s Principle of Actualization.
The
may
call
understood by to
objection
actual would
with
God
s
this
claim
a
it
principle,
that
clear
is
something
is
He
entail a contradiction.
for
that
possible
Bradwardine the only is
to
that
suppose
it
associates possibility in this sense
absolute power:
absolutely is an active power, in so precedes an act and it is not limited or determined by for something. That may be called absolute power, or the power to be possible is said that which in virtue of non-repugnance, which does not formally include a contradiction or repugnance in a good simply formal consequence.
Power considered simply and far
as
In
order
it
then
we need
absolute power positio.
6
to
properly
Bradwardine
understand
s
notion
of
to understand the workings of the obligation of
Rather than considering only one account from the large number
DCD
III,
52,
here
existence
837D.
I
obviously possibility used
of
criterion
p.
but
do not want there in
the
is
at
proof
to
is
Bradwardine
criticize
least in
the fact
appearance a
criterion
of
proof for
s
a
problem
God if
of contingency.
s
the
The
take positio as a test of possibility in general easy, however, since one make and requires for two-sided possibility that both a proposition and its negation each be able to survive aspositum in any positio. solution
For see 8
J.
is
a
DCD
III,
as note 6
God
discussion
Hintikka,
is
I
said to
of
Aristotle
s
account
Time and Modality: Studies
of
terms of actualization in Theory of Modality, Oxford, 1973.
possibility
in Aristotle s
Even more explicit is the continuation of the passage quoted it is from this power, absolute and for non repugnants, that be omnipotent and is truly so.
52, p. 837C. consider that
Bradwardine and the Use of Positio as a Test of
known I give the 9 to them all.
that are
be
Possibility
577
following outline of positio as what seems to
common The
obligation of positio consists of an exchange between an and a respondent. The opponent generally chooses a proposition opponent which is believed to be false but which the respondent grants to be possibly true. as
true
He
then obligates the respondent to answer his questions
the proposition were true.
if
is
The
proposition
supposed to be
initially
and each succeeding proposition a propositum. The opens with one of the most common expressions
called positum
obligation
typically
found in mediaeval philosophical
texts:
let
be supposed to be the case
it
... esse ... and the use of this expression is thus <ponatur in formalized in the obligation. For the remainder of the exchange, that is
that
>
the
until
call is
respondent
let
time
the
obligation
>
cease
aim of the
the
,
to reply consistently to the questions put to him.
The aim
concede an impossibility. What accounts as conceding an impossibility will thus determine what is possible and, for Bradwardine at least, what is within God s of the opponent
is
to force his respondent to
absolute power. Thus truth about the past this
Principle,
if
is
someone were
to hold that the negation of any
impossible in the sense forbidden by Aristotle
would be
revealed
in
an
obligation
which
in
such
s
a
conceded by the respondent. The obligation should then be called to a halt and the respondent accused of an incorrect response. The proposition
that
is
point
is
everyone
agrees
that
the
concession
of
contradictory
propositions brings the obligation to an end in failure for the respondent
but depending on one
s
view of
possibility there
might be other ways of
failing.
The rules for proceeding in positio may be (RO) The positum is to be conceded. (Rl)
given as follows:
10
A
propositum which follows from any conjunction of propositions already conceded with the negations of propositions already denied is
For
be conceded.
to
more
details
see
Section
16
of
The
Cambridge History
of Later Medie\-al
Philosophy, Cambridge, 1982.
speaking Bradwardine is using positio possibilis in which a positum is and only if it is possibly true. There is another variety of positio, positio impossibilis, in which one is allowed to consider what follows from an impossibility and which employs a stricter account of truth for consequences. All the remarks which follow concern positio possibilis. Strictly
defensible
if
Martin
578
A
(R2)
propositum the negation of which follows from any conjunction
of propositions already conceded with the negations of propositions
already denied
be denied.
to
is
Any propositum which
(R3)
which
is
is
to
irrelevant
the positum, that
to say
is
not to be conceded according to (RO) or (Rl) or denied
according to (R2)
be conceded
to
is
if
in fact true
is
it
and denied
in fact false.
if it is
For Bradwardine
follows
be understood as
to
is
formal consequence but usually the requirement
follows
simply
only for following in a
is
simple consequence.
These
rules recall in a rudimentary
form those used
in
modern
logic
maximally consistent with rules of inference. That is to of axioms and to a given system respect no contradiction from which sets of may be derived say propositions of
of sets
construction
the
in
propositions
within the system but which are such that
member
if
any proposition which
is
not
Any
set of propositions
consistent with respect to a given logical system has a
maximal consistent
a
is
added, a contradiction
derivable.
is
extension.
Interpreting
modal
for is
the
world
logic,
name w,
we may if
only
members
of
is
N
accessible
say,
is
is
possible
,
where p
of the description of a possible
part
consistent
p
with
the
N
set
consisting
of
every
necessarily true of w. If the set consisting of p and is
consistent then
is
it
may be extended
to a
maximal
the description of a possible world which
from w.
11
The
accessibility
is,
as
or relative possibility of
modal
to another varies according to the different system of
one world logic
say that the proposition
is
p
consistent set which
we
terms of the modern possible world semantics
of a proposition,
proposition which the
in
this,
under consideration.
We may possibilities
however,
think in the
same way about
which we suppose to be open to
the
accessibility
relation
is
the it.
If
something
actual world
and the
we
think in this way,
to
be
read
off
the
which we suppose to be available. Thus if we wished to hold every non-contradictory world is an alternative to the actual world
alternatives that
See 1968, p.
G.E. 155,
Hughes and M. lemma 4. Especially
which Hughes and Cresswell logics in Ch. 3 of their book.
Cresswell,
An
Introduction
to
Modal
Logic,
London,
striking is the parallel between positio and the use to introduce the notion of validity for various
games modal
Bradwardine and the Use of Positio as a Test of
579
Possibility
we are committed to understanding terms of what modal logicians call the system S5. This account of possibility seems to me to be just the one which is
and
every other possible world,
to
possibility in
used
The
in positio.
world
and only
if
proposition
same time
true at the
is
p
possible
,
true
is
of the
no repugnance follows from the assumption
if
as
actual
that p
is
those propositions which are necessarily true
all
of the actual world. This will be so just in case this set of propositions
can be extended to a complete description of a possible world. Positio was in fact a rather less general procedure but
no
difference
proposita
to
means
much from
its
proper
the actual world and
positio clear
accounts
of
expose is William of
example
divine
on
makes
this
of
irrelevant
in
foreknowledge
it
will
only be very partially described
for ever.
repugnance
and
Ockham his
treatments
different
understandings of what
different
will
treatment
that that the possible world constructed will not differ
since the obligation cannot go
Different
The
construal.
of
A
is
possible. very treatment of future contingency and
s
Tractatus
De
Et
De
view
may
Praedestinatione
Praescientia Dei Respectu Futuronun Contingentium. 12
Ockham
s
best be presented in a diagram:
W(t)
is
W(t) the
FUTURE
PAST
timey
the bundle of possible histories open to the world at time instant.
@
is
the
actual
of
the
t,
world.
Every proposition is assigned a truth-value at every time with respect to each possible history. For every time up to and including t any proposition which entails nothing about times later than t, is assigned the same present
truth-value
true
at
time in
that
and only if t, proposition which
true at
if
necessarily true at
In
505-539.
Guillelmi
de
t.
On
it
is
all
histories.
true at
entails
t
history
A
in all
nothing
proposition p
members
about
is
necessarily
Thus any
of W(t).
times
later
than
t
is
the other hand a proposition q simply about the
Ockham, Opera Philosophica,
vol.
II,
St.
Bonaventure,
1978,
pp.
Martin
580
future
Socrates will
<e.g.
world
at
and only
if
t
sit
there
if
at
t*
contingently true of the actual
is
>
corresponding proposition about the present
w
true of
at t*
and there
some member
is
Furthermore any proposition which
t*.
true at
itself
is
t
the
past,
t*
which
at
sit
w
5
of W(t) such that the
Socrates
of which
it
is
sitting
is
not true at
entails a proposition contingently
for
t.
entails
Socrates will
God knows that @ is the He knows what is contingently true about
sit
at
t*
.
Ockham
also holds that
actual history of the world
so
future.
The
class
available to
makes
of histories W(t)
Ockham
provides
all
undertaken
a positio
for
the
alternatives
at
work
in the world,
we would
Thus Robert Holcot
in positio.
Furthermore as he Praedestinatione the
powers and
in
his
discussion
of future
will
fact
A
will
occur, the respondent accepts the positum (Po)
is
it
possible that
first
since
to the
is
repugnant
However,
infallibility.
limitation
possibilities
will not occur.
that
contingents
an event
13
Granting
God knows
A
will
A
that in that
not be
.
A
He
propositum (Prl) God knew that A will occur positum on account of God s omniscience and
must now deny the it
it
occur and that he yesterday conceded that
will
a
expect these differences to be reflected
form of a positio to the claim
in the
is
cannot change the past.
different sorts of
an objection occur but yet
raises
are
that
t.
repugnance associated with alternatives outside of W(t)
He
and
De
at
clear in a positio at the very beginning of
upon God s absolute power. Even If someone holds there are
is
>
Thus there are contingently true example it was true yesterday that
contingently true at
about
propositions
Socrates will
w
some member
is
next propositum
the
(Pr2),
opposite of (Prl) yesterday under no obligation
,
is,
You conceded
the
he claims, irrelevant
positum and so must be conceded. Next (Pr3) is proposed: You responded wrongly yesterday This must be conceded since God knows
to the
.
that
A
will
occur
was
false yesterday in the positio but the
respondent
conceded yesterday, in fact and in the positio that God knows that A will occur. Rather than taking this as a refutation of the claim that A is possible, however, Holcot cites, as it were, a derived rule for positio: Given a possible positum impossible
13
.
Something
is
it
is
at
not improper to concede the per accidens
some time per accidens impossible
if
it
Robert Holcot, In Quattuor Libras Sententiarum Questiones, Lyon, 1518; reprinted by Minerva Verlag, Frankfurt, 1967.
Bradwardine and the Use of Positio as a Test of cannot then
have been
at
any
time be so but
later
some
at
581
Possibility
earlier time
could
it
14
so.
s approach thus seems to be different to Ockham s. The Venerable Inceptor would presumably have argued that the proposition You responded wrongly yesterday is in fact contingent and so it is
Holcot
power of God the one He has
make
within the absolute
to
future different to
in fact chosen. Holcot,
it
true today by choosing a
on the other
be a truth about the past and his account of it will on what he thinks about God s relation to the per accidens depend necessary and the possibility of His choosing a past different to the one hand, takes
it
He
fact
has
Holcot
now
hi
chosen.
This point
raises
Ockham which
relationship to
s
will
I
in
freely
Sentences
not pursue here since
discussion of the proper definition of what
is
it
He
I
want
it.
for a will to
is
commentaries on Distinction 39 of Book
his
well known.
about
questions
interesting
and a modern account of
to turn to Scotus treatment of positio
Scotus act
to
I
of the
claims that freedom must be understood in
terms of the logical possibility that a being willing to X at an instant t wills to X at t and D is a might will not to X at t. That is to say if
A
complete description of the world at set of all propositions true of the t
if
to
and only
X
at
t
.
D
if
A
-
{
wills to
t,
world
X
at
at
t
}
t,
is
is
the maximally consistent
then
A
willing to
t
to will not to
t,
to
X
at
t
wills to
consistent with
Cast constructively in terms of a positio
X at freely wills X at that is to with th&positum A wills not to X at will
that
if
we may
and only
if
it
X A
freely at wills not
say that a is
possible
and only if a positio beginning say t leads to no repugnance. if
In his discussion of this possibility Scotus states as an objection to this
account of freedom of the will a second derived rule (or positio: a contingent falsehood is to be posited true> of the present instant then the present instant must be denied to so that if "If
be"
and it is posited that you are in Rome, then the present instant must be denied to exist. Because if that you are in Rome is false of an instant A, it cannot be verified of A; either it is verified by motion or by change: not by motion since there is no motion in an instant, not oy change because when there is change then there is a limit to the change", and then it would be both true and false in A; therefore if it is "it
is
false that
you are
in
Rome",
va.
Reading
"for
text
Holcot, op. cit., has impossible .
ff.
h
iii
ra
-
possible
<positum>
where the printed
Martin
582
posited that you are in Rome is true, since this may not be true A, as has been proved, A must be denied to be.
Scotus
is
apparently quoting from William of Sherwood
s
16
in
work
(?)
on obligationes and he goes on to reject the rule by saying simply that positio can be conducted perfectly well without it. It should be noted, however, that Scotus there
is
argument only applies to the
above but does not claim that
defined
possibility
exists with respect
is
claims that
supposed
same
this
be
to
based
entirely
potential
Thus so
to non-voluntary, irrational, causation.
far as
a black thing be white,
creatures are concerned the possibility that this
He
will.
a real potential for opposites in the will corresponding to the
if
upon non-voluntary causation,
corresponds not to logical consistency but rather to change over time. Scotus goes on, however, to associate the same power for opposites with
The
the divine will acting in the eternal present.
power and what
it
entails for
human freedom
is
exact construal of this
a difficult question which
cannot go into here. There is a problem, however, if Scotus wishes to hold that truths about the past are necessary to the extent that God is
I
bound by them. 17
No
such
difficulties
he bases possibility on
arise
God
s
for
Bradwardine when, following Scotus,
absolute power in the eternal present.
rule governing the present instant does not apply to
God
since
it
is
The
based
merely on the per accidens necessity. All possible histories are available God and to claim that it is possible for not-p to be true at t when p is in fact true at t is simply to claim that He might choose a different to
history for the world.
Bradwardine goes on
to
complete the story begun
by Scotus:
A
With
in London, if it
<man>
A
loannis
Omnia
Duns
Studio
et
Scoti,
A
Lectura
Cura Commissionis
in
Primum Librum Sententiarum
,
d.
39,
n.
56,
Opera
Scotisticae, vol. 17, p. 498.
Edited by R. Green in The Logical Treatise De Obligationibus: An Introduction and of William Sherwood (?) and Walter Burley, Ph. D. thesis, Louvain, 1963, to be published by The Franciscan Institute, St. Bonaventure, NY. 1 7 See Calvin Normore s account of Scotus view on future contingents in the Cambridge History of Later Medie\ al Philosophy, section 18, pp. 367-9. Critical Texts
Bradwardine and the Use of Positio as a Test of that this
is in London in A is London inhere per se and
<man>
does being A. Indeed
in in
583
Possibility
not absolutely necessary, nor essentially to this
<man>
in
so far as the nature of the thing and the absolute power of things is concerned it is not repugnant that this not inhere in him in A. He might indeed have taken a journey some time or before have finally arrived in Rome. ago and in
A
A
Simo Knuuttila has marks a
possibility
before
that
He
claims
what has been called a
held
logicians
19
A
(S)
innovation in mediaeval thought.
mediaeval
of
theory according to which possibility was in effect defined as
statistical
follows:
radical
Scotus
Duns Scotus treatment
recently argued that
proposition p
at
possibly true at a time
is
some time
or will be true at
t
t
later
than
and only
if
t
if it
is
true
t.
According to the theory a dated event is bound necessarily to the time at which it occurs and so the future is determined necessarily to be the
that
way
distinguishing
Apparent counterexamples are dealt with by supernatural power of God from natural possibility. be.
will
it
the
Aside from the direct evidence to the contrary, the difficulties posed by a definition of possibility like (S) would seem to require that any mediaeval using it offer an argument in its favour. As far as I know,
we
however, none has so far been found. Rather
mediaeval
between
distinction
and
composite
are referred to the
divided
readings
of
propositions such as the black thing is possibly white This is false read in the composite sense as truth of the following is possible: that .
"the
thing which
sense
as
is
black
that
white
is
thing
which
"
but
may be
it
now
is
black
true read in the divided is
mediaevals, however, read the divided sense as black
possibly white at
is
some
time
later
since for a white thing to be black there it
potential
It
is
Somewhat
the need
account
acceptance of the statistical reference to the future.
18
The
later
.
which
time
is
Many now
is
required
must be an actualization of the
has for being black and change, which
potential, requires time.
statistical
.
white
possibly that thing
the actualization of
is
for change,
I
rather than
think,
of possibility which
requires
the
paradoxically the best example of a philosopher holding a
account of modality
may
well be Bradwardine.
God
has chosen
DCD III, 52, p. 838.
but it serves to make in Modality in Scholasticism Reforging the Great Chain of Being, Dordrecht, Holland, 1981, pp. 163-257.
This
positio.
is
See
only
S.
a
crude
Knuuttila,
characterization
Time
in
,
point about Knuuttila ed.,
my S.
Martin
584
the actual world-history and every possibility
of His absolute freedom of choice. All possibility for natural beings there
is
no
present
find
positio
If
modality.
with
in
terms
thus supernatural and
is
alternative to the actual world.
Knuuttila has identified Scotus in
be analyzed
to
is
rejection of the rule concerning the
move away from
a
we examine one
theory
of
of the earliest texts on positio, however,
we
the
statistical
there at least the rule seems not to presuppose a statistical
that
definition of possibility. 20
The
Obligationes Parisiensis,
which apparently dates from the
last
of the twelfth century, presents a sophism concerning the use of
third
We
the rule about the present instant.
matter of fact Socrates present
The positum (Po)
instant.
propositiim (Prl)
argues that
it
A
exists
are asked to suppose that as a
white and that
is
.
If
A
is
Socrates
is
the propositum
follows that Socrates
is
white
in
name
a proper is
for the
and the
black
first
is
conceded, the opponent
A
which
is
impossible and
so the respondent must have responded wrongly since he started from
something possible.
On
the other hand,
with the rule, denies (Prl), (Pr2)
the respondent, in accordance
proposed:
A
was going
to
exist
.
be denied the opponent claims that the respondent has denied true, and presumably irrelevant, so he has responded incorrectly. he concedes (Pr2), the opponent proposes (Pr3): A has existed Should
Should
what If
is
if
this
is
.
be conceded the opponent accuses the respondent of conceding a falsehood which does not follow from the positum. If (Pr3) is denied, the
this
opponent finally proposes (Pr4): A will exist This we are told should not be conceded since it is impossible but on the other hand should not .
be denied since
The
it
follows from what has gone before.
solution to this sophism according to the
unknown author
is
to
concede (Pr2): A was going to exist to deny deny (Prl): A has existed and to concede (Pr4): A will exist Thus the (Pr3): proposition Socrates is black must be supposed true at some time earlier
A
exists
;
to
;
.
than
A
require.
rather than later as the statistical definition of possibility would
The author goes on
to note that
A
will
per accidens being conceded in the exist
is
impossible but that this does not conflict with its of possibility positio. Thus even at this early date positio as the criterion
seems
to
be
understood
in
terms
of
the
construction
of
alternative
20
Some Thirteenth Century Tracts on the Game of Obligation In L.M. de Rijk, Vivarium, XII, 1974, pp. 94-123. On the basis of references to the Parisian Schools of the later twelfth century I think that these texts should be dated before 1200. ,
Bradwardine and the Use of Positio as a Test of possible histories. Scotus certainly does suggest a
new way
of looking at
these alternatives in terms of his account of the freedom of
but this was not obviously a
move from
585
Possibility
God
s
will
a statistical to a non-statistical
theory. I
the
hope
obligation
what
have said has shown that an understanding of of positio is important for those studying mediaeval
that
I
philosophy and theology and that any account of mediaeval theories of possibility should pay attention to the use of this device.
University of Auckland
MUNOZ DELGADO
VICENTE
Los cnunciados
1
.
"insolublcs"
en
sumulas (1518) dc Juan dc Oria
las
Breve introduction
Juan
ha
Oria
dc
Universidad
nominalium y ad Buridan.
sido
modum
dc
profcsor
Salamanca
dc
los
por
logica
anos
y
natural
filosoffa
1509-1523.
Ensenaba
parisicnsem, ulili/ando cspccialmcnte a
en in
la
via
Ockham
y
1
En aparecc,
las bibliotecas
desdc
el
dc
siglo
la
Universidad dc Salamanca y dc sus Colcgios
XV, una
notable
prcsencia dc
manuscritos de
autorcs inglcscs, especialmentc dc Oxford. G. Bcaujouan ha cstudiado e identificado en Salamanca, cntre otros manuscritos, un resumcn dc los
Sophismata dc Hcytesbury,
los
Insolubilia
dc Wiclef,
Burlcigh, R. Allington, Bradwardinc, Swineshead,
las
obras de
W.
etc.
perfodo de profcsorado dc Oria es singularmente intcrcsante, porque coincide con la apcrtura oficial al nominalismo y al Paris del Monteagudo dc Juan Mair, con la trai da dc nuevos profesores de la El
capital franccsa.
2
Dcntro de esc contcxto dc relation con Oxford y prcscntar del
el
los
Tractatus insolubilium,
Tractatus
consequentiaruni,
quc ocupa formando parte
fols.
dc
quicro dcntro 22v-24v, Paris,
Summulae
sus
(Salamanca 1518), de las que estamos publicando una recdicion moderna y actuali/ada. Juan de Oria estudia los insolublcs en el horitonte dc la infcrcncia, colocando esc
tcma
a continuation del Tractatus exponibilium y
antes dc las Obligationes.
Introduccion V. Munoz Delgado, espanola de Teologia 43(1983) 75-116.
al
pcnsamiento
de
Juan
dc
Oria
,
Rc\ ista
~
G. Bcaujouan, Manuscrits scientifiques medifcaux dc rUniversite de Salamanque (Burdcos 1962) 3,21-31,59; Id., La science en Espagne aux XIVc et XVe siecles (Paris 1967) 26-8,33-6. Munoz Delgado, La logica nominalista en la Universidad de Salamanca (1510-1530) (Madrid 1964) 65-90. Johannis de Oria, Summulanun volumcn introduccion general sobre la obra de Oria.
primutn
(Madrid,
CSIC,
1987),
con
Los enunciados
"insolubles"
Oria ha sistematizado
manera ordenada. Sigo que
en las sumulas de Juan de Oria
587
doctrina de los insolubles y la expone de
la
de temas del
la disposition
de
original,
tal
forma
un resumen de su exposition y un estudio
este trabajo es, a la vez,
de sus doctrinas.
2.
Los enunciados
reflexivos y los insolubles
mas extenso que insoluble y abarca algunos enunciados que no pueden llamarse propiamente insolubles. El enunciado reflexivo siempre
Reflexivo es
se significa a
sobre
mismo, es decir hay la reflexion de la segunda intention primera. For eso Oria, en el Tractatus de conceptu (f.52r), habia
la
escrito
si
intentio
"Secunda
velut
est
conceptus
reflexus
respectu
prime
intentionis".
La
reflexion de la segunda intention
puede
ser
de manera inmediata
como
sucede, respectivamente, en estos dos ejemplos, hec est y mediata, falsa, refiriendose a si misma, y hec non est vera, que de manera mediata se refiere a la contradictoria
Ademas,
Con
verdad o falsedad.
misma sub
de
la anterior.
ha de referirse a
la
palabras de Oria, la reflexiva se significa a
si
es importante observar
que
la reflexion
ratione veri vel falsi, para distinguirla de la autorreferencia en
con
enunciados
nociones
que
propiedades
trascendentales,
de
derivan
se
la
verdad
o o
tambien
en
relation
como hec
falsedad,
a est
necessaria, hec est impossibilis.
Estas dos ultimas son tambien reflexivas y Oria destaca que, aunque la
verification y suposicion son en realidad propiedades de los terminos
dentro de
la
como un
todo;
(suppositio t
proposition, verdad y falsedad son atributos del enunciado sin
las
embargo,
propiedades logicas de los terminos al todo enunciativo o proceden de
ordenan
ampliatio, etc.) se
el.
La verdad y falsedad son logicas.
For tanto
termino,
al
For reflexiva
reflexion
la
fundamento de todas
puede
referirse
las
propiedades
a la suposicion de algun
todo o propiedades derivadas de cualquiera de esos aspectos. eso, hoc est hoc, indicando ambos pronombres el predicado, es
en orden a
la
hoc se relaciona con ratione
el
veritatis
en
verdad de la
estas
consequentia est vera.
En
tal
enunciado, porque
la
suposicion de
verdad. Igualmente tambien hay reflexion sub frases el
hoc consequens
antecedente,
el
est
falsum,
ergo
hec
primer pronombre produce
Munoz Delgado
588
una reflexion mediata; en el consiguiente, el segundo pronombre origina 4 una reflexion inmediata dependiente de la primera. Queda, pues, establecido que la reflexion sub ratione veri vel falsi propiedades de los terminos, que se relacionan o verdad-falsedad del enunciado como un todo. Asi tambien
ha de extenderse a derivan de
la
entendemos
las
doctrina de Oria de que hay enunciados insolubles, en cuya
la
formulacion no entra reflexividad,
la
como en
segunda intencion
ni
ninguno de esos tipos de
estos famosos enunciados ego nihil dico, ego iuro
me
insolubles en sentido estricto y periurare y similares. Estos no serfan Oria los trata al final de todo, proponicndo una definicion de insoluble
algo diferente.
Con estamos
tenemos explicada
esto
para
preparados
entender
reflexiva est propositio significans se veri vel falsi vel aliarum
Enunciado
enunciado reflexive y definicion de Oria: "Propositio
passionum has
de
nocion
la la
mediate vel immediate, sub ratione consequentium" (f.22v).
abarcando muchos mas enunciados
reflexivo aparece asi
Lo
esencial, en el insoluble, es la auto propiamente falsificacion, ya de manera directa e inmediata, ya como consecuencia. Insoluble, para Oria, es el enunciado que afirma su propia falsedad. For
que
insolubles.
los
propone esta falsificans mediate
definicion:
ello
significationis",
abajo, apartado
8,
insolubilis
"hec
est falsa,
proponemos
seipsam
est
propositio
se
affirmationis vel intrinsece
inmediate, sub ratione
vel
como
"propositio
demonstrando"
(f.22v).
Mas
la otra definicion.
Hay que notar que la autofalsificacion se ha de hacer de manera afirmativa, sub ratione affirmationis. En virtud de tal restriction, que ser est falsa, la importante en nuestro logico, un enunciado como hec non contradictoria de hec est falsa, no es insoluble en rigor.
De
este
modo
la
autorreferencia, en el enunciado reflexivo, se hace
propiedades derivadas de la verdad-falsedad y se expresa de manera afirmativa o negativa. En cambio, el insoluble es siempre autofalsificacion, es decir sub ratione falsi, y
sub
ratione
veri
vel falsi
o
en
orden
a
expresada de manera afirmativa, mediata o inmediata. Ademas, se deriva de que la falsedad se sigue de su falsificacion significado y de ser segun 4
ella
misma
auto
propio
expresa. For eso este enunciado y
Summulae (Salamanca 1518), De insolubilibus f.22v. Oria, a esa edicion. contraria, las citas de Oria se refieren siempre a ese tratado y 5
la
Salvo
indicaci6n
Oria, Ibid., f.24v. Cf. Bricot, Thomas, Tractatus insolubilium (Nimega, Ingenium Publishers 1966) 18,69,70,73,74. V. esa nueva definicion de insoluble en el apartado 8.
Los enunciados
"insolubles"
en las sumulas de Juan de Oria
589
que no diga ninguna otra cosa, no es Oria tampoco ticne propiamente insoluble, hay dificultad en aplicar a ese enunciado la doctrina de las obligaciones, que similares ego dico falsum, supucsto
no
la codificacion
expresa
de
las
autofalsificacion.
condiciones de
la
disputa escolastica. Podria
que ego dico falsum se autofalsifica ex casu y por convenci6n o acuerdo entre los que llevan la discusion. Pero, en ningun admitirse, segun Oria,
caso,
es autentico insoluble, tanto
modo de Heytesbury, o que Con Oria podemos
que se
le
ponga como
se adopte otra posicion.
obligatoria,
al
6
1Q
La
2Q
La
contradictoria de cualquier enunciado insoluble nunca es insoluble. 3
La
de
contradictoria
cualquier
estos
enunciado
corolarios
de
reflexive
es
significa
sub
ratione
veri
lo
vel falsi,
en
dicho:
reflexivo.
es reflexiva. 4Q
un enunciado insoluble
contradictoria de reflexiva
inferir
cuanto
La proposicion que verdad y
falsedad son el fundamento de todas las propiedades logicas y la reflexion referirse a las propiedades de los terminos, al todo o algo derivado
puede
de cualquiera de
modo
3.
ellos.
5- El insoluble
se formula sub ratione falsi, de
aflrmativo.
Verdad y falsedad en
enunciados insolubles y
los
suposicion de los terminos
El segundo tema y la segunda dificultad se refiere a las causas de verdad falsedad en los insolubles. La razon de llamarse insolubles esos
y
enunciados se deriva de que aplicando la doctrina de la causa adecuada de la verdad y falsedad de las proposiciones ordinarias a las reflexivas resulta
que son
concluir
que con
resolver
la la
al mismo tiempo verdaderas y falsas. Por eso, hay que causa de verdad o falsedad del insoluble no se puede
doctrina
ordinaria
aplicable
reflexivos.
Se
les aplica
razonablemente
utilizando
la
definition
comun de
afirmacion de
la
el
a
los
no-insolubles
nombre de
insolubles,
y no
porque
proposicion verdadera conduce a
la
verdad o falsedad simultanea en dos contradictorias. Lo
que en un enunciado ordinario es causa de su verdad (ita esse sicut per propositionem significatur) o de su falsedad (ita non esse sicut per 6
Oria, f.22v-23r; Bricot, 74; Alberto de Sajonia, Perutilis Logica (Hildesheim, G. Olms 1974) 43v; Francesco Bottin, Le antinomic semantiche nella logica medievale
Verlag,
(Padua,
Antenore
Kretzmann,
A.
1976)
121,128-130;
Kenny, J. Pinborg, Philosophy (Cambridge 1982) 252.
eds.,
Paul
The
Vincent
Spade,
Cambridge
History
Insolubilia
of Later
,
en N. Medieval
Munoz Delgado
590
propositionem
puede
sigtiificatur)
resultar aquf al reves,
significa ser lo
es falsa
es.
como en hec
est
7
que porque que For esas razones, en los insolubles, hay que cambiar la definition de enunciado verdadero y enunciado falso. La proposition verdadera se
falsa,
define:
vera est que significat
"propositio
non sequitur ipsam esse
La de
comun en tiempos de
De
la
(f.
non
22v-23r).
Oria, que asf acepta la position
ita
debe formularse
falsa,
esse sicut
ita
que significat non sequitur ipsam esse veram"
"propositio
esse
falsam".
falsa est
esse sicut est et ad
ita
est
ad
vel
Es un
ita
reajuste
esse asf:
non
muy
m&s comun. 8
esa doctrina ampliada sobre los enunciados verdaderos y falsos se
Q siguen algunos corolarios: 1 Cualquier proposition es falsa si significa su propia falsedad tanto de mancra mediata como inmediata. 2 Cualquier C proposition, que significa que su contradictoria es verdadera, es falsa. 3 Cualquier proposici6n, que significa que su contradictoria no es falsa, es
significa a
no
falsa,
afirmativa es falsa. 4 Q
En general, toda proposition que se o como falsa, como no verdadera o verdadera como misma, ha de ser juzgada tal como ella se autocalifica; pero la con
verdadera y
la
si
tradictoria tiene valor opuesto. 5 Q
contradictorias
falsas.
Hes
est
No
vcra
hay inconveniente en admitir dos y hec non est falsa, son ambas
verdaderas, pero sus contradictorias son falsas
scgunda no es propiamente
pronombre
se refiere a la
Oria propone
la
al
mismo tiempo, aunque ambos casos, que
insoluble. Se entiende, en
misma proposition
(f.
la
22v-23r).
regla de que, para juzgar de la verdad y falsedad
de esos enunciados, hay que atender especialmente a se autosignifican de manera inmediata.
Como
la
una extension del tema y como una
los
enunciados que
dificultad
pendiente,
examina nuestro logico la famosa rcgla para determinar la verdad de los enunciados: una afirmativa es verdadera^ cuando sus extremes suponen
por
mismo
lo
y,
en
caso contrario,
es falsa.
Oria examina todos los
reajustes y condiciones que se han anadido a esas reglas, que se aplican
solamente a
"Causa
enunciados puramente categoricos y no reflexivos.
los
adequate
non esse
veritatis
vel
falsitatis
in
aliis
propositionibus,
ita
sicut
est
que
per propositionem significatur, reperitur in istis in proprietate, quinimmo causa veritatis in aliis est causa falsitatis Vid. las notas 15 y 16.
vel
cum
illis",
E.J.
Ashworth,
esse
opposita
Oria,
f.22v.
Language and Logic in the Post-Medieval Period (Dordrecht, D. Le traite des Propositions insolubles de Jean de Celaya litteraire du moyen age 37(1962) 263-64; Bricot, 20-21;
Reidel, 1974) 112; M.L. Roure, Archives d histoire doctrinale et
Angel D Ors, La doctrina de las proposiciones insolubles en de Soto Cuadernos salmantinos de filosofia 13(1986) 193-95. ,
ita
En
,
las
"Summulae"
de Domingo
Los enunciados
"insolubles"
en las sumulas de Juan de Oria
591
extremes de una proposicion pueden suponer por lo mismo y ser falsa, como hec est falsa y puede haber enunciados con extremes que no suponen por lo mismo y ser
en
efccto,
enunciados reflexives
los
como sucede en hec
verdaderos,
est
los
referida
vera,
a su contradictoria,
que es verdadera.
De manera
homologa, se ha de hablar de
la regla
para
la
verdad de
enunciados negatives:
la proposicion negativa, cuyos extremes suponen es mismo, por falsa y es verdadera cuando sus extremes no suponen lo mismo. Esta por regla de la verdad-falsedad en las negativas tampoco se cumple en los reflexives, donde un enunciado como hec non est falsa,
los
lo
referida a su contradictoria, es verdadera y los extremes lo
mismo. Igualmente hec non est vera expresada de no suponen por lo mismo.
si
no suponen por
misma, es
falsa y
sus extremes
La razon
esta en
que
los
insolubles y reflexives tienen causas de
verdad y falsedad distintas de las categoricas ordinarias. Por eso no cumplen las famosas reglas de verdad y falsedad en las afirmativas y 9
negativas.
4.
Principals opiniones acerca de
la naturaleza
de los
enunciados insolubles
Ahora nuestro Oria posiciones
como
diferentes
estudia el insoluble en
con
la
si
correspondiente
mismo, enumerando seis Nos sirve tambien
critica.
testimonia de los conocimientos que, acerca del tema, circulan en
Salamanca por 1518.
No
cita
a ningun
autor y solamente
expone
las
doctrinas.
Primera opinion. Los insolubles no son proposiciones, porque no tienen verdad y falsedad determinada, lo que es algo esencial en la nocion de enunciado. Para encontrar la verdad o falsedad de un insoluble, habria 10 que superar una circularidad infinita y sin termino. Oria refuta esa position, diciendo que el insoluble representa al entendimiento una signification determinada y una verdad-falsedad tambien
9 Oria,
Summulae,
G. Olms Verlag 1980)
L.M.
de
Rijk,
ed. 1987, 1,187-88;
Domingo de
Soto,
Summulae
(1554) (Hildesheim,
f.36v.
Some Notes on
5(1966) 109; Bottin, 47^49.
the
Medieval
Tract
De
insolubilibus
,
Vivarium
Munoz Delgado
592
determinadas.
Aun un
determinado y
lo
entcndimiento no este scguro de cual es su verdad. enunciados, como hec est falsa, tienen valor determinado. el
aunque
paria, fortiori
enunciado como buf est buf tiene valor vcritativo mismo sucede con proposiciones dudosas como astra sunt
Segimda
opinion.
Ensena
determinados, pero uno significado, es
que
simpliciter y
verdadero
insoluble
el
otro
el
por
simpliciter,
ej.
modo de significarse y autofalsificarse, quid. De su contradictorio habria que al
manera opuesta. Aqui no habria y
est
enunciado es falso secundum
para admitir en los contra-
secundum
parece una posicion contradictoria, porque al admitir dos esse et se esse falsum) y dos valores, hay que (ita
quid.
le
si
preguntarse
lo realiza
de
modo
manera inconiunctim,
se significa de tal
habria de ser tratada.
Nunca una
Tercera opinion.
proposicion.
Cuando
referencia
o
se trataria de
el
falsa. Si la duplicidad
una propositio plures y
11
parte de
la
proposicion supone por toda
se afirma ego nihil dico, en el uso
esa
a
manera separada. En
copulative o de
primer caso, la copulativa es simpliciter verdadera
la
pero de
otro
significados
como
esos valores,
Oria
el
A
hec
quid. For parte del falsa; pero, en cuanto
predicar
dificultad
veritativos
secundum
simultaneamente verdad y falsedad, poniendo un valor simpli
dictorios citer
tal
valores
ticne
A
se
la
comun, se excluye
entiende nihil dico aliud ab hac
proposicion y vez de hablar de insolubles y reflexion, de primera y segunda intention, seria mejor atender al sentido comun y ordinario de los hombres. Generalmente no se entiende la misma proposicion y suele
propositione.
referirse a
En
un tiempo
anterior.
Segun esta opinion,
causas de verdad y
las
falsedad en los reflexivos e insolubles serfan las generales.
Oria refuta esta opinion diciendo que no da razon de 12 falsedad de enunciados como hec est falsa, en autorreferencia.
la
verdad-
Opinion cuarta. Se supone la distincion de los tres lenguajes, mental, hablado y escrito con la subordination de estos dos ultimos al mental. La problcmatique des propositions insolubles du du debut du XlVe, suivie de edition des traites de William Shyreswood, Walter Burleigh et Thomas Bradwardine Archives d histoire doctrinale et litteraire du Cf.
XHIe
P.V. Spade, 247; M.L. Roure,
siecle et
I
,
moyen age 45(1970) 12
Spade,
248;
216-43.
Roure,
Language and Logic,
104-105.
1970,
270;
Bricot,
50;
Soto,
f.
152r.
col.2;
Ashworth,
Los enunciados
en las sumulas de Juan de Oria
"insolubles"
593
Gregorio de Rimini y Pedro de Ailly parten probablemente de la doctrina de Heytesbury de que en el lenguaje mental no hay insolubles ni autorreferencia.
Pedro de Ailly resuelve
problema de
el
los insolubles diciendo
que
son propositiones plures, es decir, por ej., hec est falsa se subordina al mismo tiempo a dos proposiciones mentales separadas, una de las cuales es verdadera y la otra falsa. Oria senala
inconiunctim, una de
que se refiere a dos mentales en virtud de la signification primaria de
las cuales
terminos es falsa y la otra una reflexion sobre esta primaria. Los enunciados mentales a que se subordina el insoluble no son insolubles. Oria resume esa opinion y la critica diciendo que la proposition los
mental y escrita
tampoco
deben
la vocal-escrita
no
significa
lo significa la mental.
mismo. Ahora bien, falsa. Por
significar lo
que una de
las
mentales sea
la vocal-
lo
tanto,
13
Los insolubles son enunciados copulatives hipoteticos, compuestos de dos partes, significando la parte primera lo fundamental y Opinion
la
quinta.
porque
la
parte anterior. Serfan enunciados simpliciter falsos,
falsifica la
segunda
parte segunda es falsificante
parte es falsa, lo es el todo.
Ashworth y
de
Jorge
explica
Bruselas,
formal, expresado por significado secundario,
por toda la insolubles son todos
supone
La
en una copulativa, cuando una
y,
contradictoria seria simpliciter vera.
que destacan singularmente esta opinion Trutvetter distinguiendo
el
directo
primario,
significado
y
en su sentido normal, y el material, cuando un tdrmino
los terminos tornados indirecto,
reflexivo,
proposition
y
la
falsifica.
en virtud de
falsos,
En
leyes de
las
esta la
version,
los
conjuncion. El
insoluble seria propiamente la signification secundaria, que tambien es falsa.
porque con cuando una proposition es copulativa y cuando no Oria
Opinion
critica
sexta.
a esta doctrina,
La
doctrina
propia
establecida por Oria al explicar,
que hacer para definir
que 13
se
pueda
Ashworth,
la
aplicar
Ibid.,
a
108-110;
Ashworth,
como hemos
los
Spade,
Ibid., 110-11; Oria, f.23v.
insolubles
253;
Pedro
y
de
lo es.
Se
Oria.
14
trata
de
la
doctrina
cambios que hay enunciados de forma
visto, los
verdad y falsedad de
(Dordrecht, D. Reidel, 1980) 3-8. 14
de
no apareceria claro
ella
los
reflexives.
Ailly,
Son
Concepts
las
and
nuevas
Insolubles
Munoz Dclgado
594
condiciones de verdad y falsedad, que ya
de
Oria, los insolubles
verdaderas o
falsas,
significado total.
hemos
En
visto.
esta opinion, la
son proposiciones puramente categoricas, simpliciter atendiendo a los valores veritativos por parte del
15
Esta doctrina procede en lo esencial de Swineshead, que modifica algo de teorfa de la verdad como correspondencia, exigiendo ulteriormente que, ademas de la correspondencia con la realidad, no haya autofalsifi-
como
cacion,
transcritas,
formula
se
segun
el texto
en
La doctrina de Swineshead (f.
de verdad que dejamos
definiciones
las
de Oria. la
describe largamente la Logica
194- 195) de Pablo de Venecia y fue adoptada por Juan Mair,
Magna Domingo
de Soto, Lax, Celaya y tambien Oria con algun pequcno reajuste. Sequn ellos, hec est falsa es falsa, porque se autofalsifica y hec non est falsa es tambien falsa, referida a la anterior, porque niega que las cosas sean
como
modo, que tambien expone Oria y acepta famosas consecuencias opuestas a las leyes logicas parcialmente con las generales: dos contradictorias pueden ser falsas; una consecuencia correcta son. Este es el primer
puede tener antecedente verdadero y consiguiente sinonimos pueden tener difcrente valor
falso;
dos enunciados
veritativo, etc.
Bricot, Tateret, Trutvetter y otros quieren evitar esos inconvenientes
y para ello distinguen la proposition afirmativa y la negativa, en cuanto a las
normas de verdad. Una afirmativa
condiciones
senaladas,
como no son o esas
decir,
En cambio, una
autofalsifica.
de
es
dos
si
tiene
es verdadera,
significa
cosas
las
negativa es verdadera,
una contradictoria que se
condiciones
basta
para
que
el
si
cumple
como son si
las
dos
y no se
significa las cosas
autofalsifica.
enunciado
Cualquiera
negative
sea
verdadero.
Segun est falsa
es
este
segundo
falsa,
modo
porque
se
de explicar
autofalsifica,
verdadera, porque su contradictoria es
enunciados resulta que hec pero hoc non est falsa es
los
falsa.
Transcribe la nueva version, que ahora introduce Oria, de la verdad-falsedad enunciados: significare ita esse sicut est et ad sic esse non sequitur ipsam esse falsam vel suam contradictoriam se intrinsece falsificare. Et hoc quoad veritatem. Vel significare non ita esse sicut est vel ad non sic esse non sequatur ipsam esse veram aut suam contradictoriam esse falsam. Et hoc quoad falsitatem" (f.24r). V. la nota 7. Pone estos dos ejemplos hec est falsa y hec non est vera, quo son ambas falsas. Pero, respecto de la negativa, anade que hay otra manera de entender su valor, haciendola verdadera, porque su contradictoria hec est vera es falsa. Cf. el texto que transcribimos en la nota siguiente.
en
los
"est
Los enundados
"insolubles"
Oria recuerda aqui
las
en las sumulas de Juan de Oria
595
dos modalidades que hay, dentro de esta
sexta posicion, sin pronunciarse por ninguna ni citar a ningun autor.
De
problema de
el
los insolubles,
que estaban de moda en su tiempo,
pronunciarse tampoco por ninguna.
5.
En
enunciatione (f.24r) recuerda tambien estas dos maneras de solucionar
Los
sin
16
insolubles y las reglas de la consecuencia
Examina ahora con alguna detention la Se regla: ex vero non sequitur falsum.
validez universal de la celebre aplica a los razonamientos con
insolubles?.
Pone, falsum,
como
ejemplos,
refiriendose
el
estos
casos:
pronombre
al
hoc
est
falsum,
consiguiente
en
ergo
hoc
ambos
est
casos.
Igualmente, suponiendo que solo existe este razonamiento en Darii: Omnia conclusio est falsa, Conclusio de Darii est conclusio, ergo conclusio de Darii
Y
est falsa.
otro
este
paralelo:
nulla
conclusio
est
omnis
vera,
conclusio de Celarem est conclusio, ergo nulla conclusio de Celarem est
Finalmente, pone este ejemplo: hec non est vera et hec propositio ergo hec est falsa, referido el pronombre al consiguiente.
vera. est,
Los ejemplos son bastante comunes en solucion al problema tiene dos salidas,
dos
los
modos de
recordados en
la
explicar
la
los logicos del tiempo.
como recuerda
verdad
y
falsedad
La
Oria, aludiendo a
de
los
insolubles
ultima opinion.
Para muchos logicos,
la regla
de lo verdadero no se sigue lo falso no
vale en los enunciados reflexives y autofalsificantes.
La segunda
solucion admite la validez universal de las reglas de
razonar. Pero los insolubles tienen distinta forma y en ellos la verdad o
falsedad
se
explica
de
diferente
manera.
Se
trata,
por
tanto,
de
He
aqui las dos reglas de verdad-falsedad en los dos modos que distingue nuestro secundum istum modum ponitur ista regular quecumque propositio, que suam contradictoriam formaliter verificat, seipsam falsificat et est falsa et sua contradictoria Oria:
vera...
"a)
b) Sed,
secundum priorem modum, dicitur oppositum; quecumque propositio, que falsificat vel se non verificat, est falsa et sua contradictoria vera",
seipsam intrinsece
Celaya, en Roure, 1962, 263-64; Spade, 250-51; Ashworth, Thomas Bricot (d.1516) and the Liar Paradox Journal of the History of Philosophy 15(1977) 267-80. Oria, f.24r.
Cf.
Bricot, 21-22;
Language and Logic,
112-13;
Id.,
,
Munoz Delgado
596
enunciados
distintos
y
pucstos no hay propiamente argumentation.
6.
En
formas logicas diferentes.
de
Los enunciados sinonimos y sus
los
ejemplos
17
valores veritativos
El problema consiste en si, dentro de la esfera de los insolubles, pueden darse dos enunciados sinonimos con diferente valor veritativo, es decir
que uno sea verdadero y falsa,
ambas
refiriendose
el
otro falso. For
hec
ej.,
est falsa
y hec est
a la enunciada primeramente. Pareceria que la
primera formulation es falsa y falsedad de la primera.
la
segunda verdadera, porque afirma
la
problema. Oria distingue tres maneras de resolverlo y de dar una respuesta adecuada. Naturalmente, las tres soluciones dependen Este es
de
la
el
de
definition
verdadera.
proposition
pronunciarse en favor de ninguna. El primer modo de solution sostiene que
Explica
las
tres
sin
dos proposiciones del
las
ejemplo son sinonimas y ambas falsas, porque hec est falsa se autofalsifica a si misma y a su sinonima y lo mismo sucede con la segunda formulation. Porque toda proposition autofalsificante tambien falsifica a su sinonima.
Lo mismo
sucederia con
hace verdadera a su sinonima.
mismo
tienen siempre el
De
la
este
que se autoverifica que tambien
modos dos enunciados sinonimos
valor veritativo.
modo
de responder a nuestro problema defiende que las dos proposiciones del ejemplo no son sinonimas, porque son dos modos de significar diferentes: uno mediante el cual un enunciado se autofalsifica El segundo
y otro mediante
pues
el cual se significa
sinonimia,
general,
ninguna
insoluble,
como
El tercer
la
porque son
dos
insoluble,
como
que otra proposition es
modos de la
significar
primera,
es
falsa.
No
diferentes
sinonima
de
y,
hay en
la
no
segunda. Se trata de enunciados codiferente estructura. admite que dichas proposiciones son sinonimas, pero
modo
primera es falsa y la segunda verdadera. Razonar a sinonimis sigue siendo formalmente correcto, aunque tengamos antecedente verdadero y la
17
Oria, f.24r; Soto, Summulae, Salamanca, 145-155, 349-153.
f.!54r;
Munoz
Delgado,
La
logica
nominalista
en
Los enunciados
consiguiente
"insolubles"
como
falso, 18
ya
en las sumulas de Juan de Oria
queda
indicado
al
hablar
de
597
las
reglas
consecuenciales.
Verdad yfalsedad en
7.
El
tercer
los
modo de
enunciados contradictorios
resolver
el
problema
de
los
sinonimos
parece
aunque no se pronuncia por ninguno. En efecto, estudia ahora una nueva dificultad y es si ese tercer modo evita que haya simpatizarle
a Oria,
conceder
que
verdaderas o
en
los
insolubles
dos
simultaneamente
contradictorias
falsas.
que admiten que, de ese modo de explicar los sinonimos, se siga la existencia de dos contradictorias verdaderas y aun de dos falsas al mismo tiempo, refutando argumento por Oria refuta a
los
enunciados
argumento. El problema era muy famoso y los logicos espanoles del tiempo suelen tratarlo en referencia a Bricot, dentro del contexto de su position anteriormente expuesta. 19
8.
Los
insolubles sin terminos de segunda intencion
Termina Oria con una breve consideration acerca de
los insolubles
en
cuya formulation no entran terminos de segunda intencion ni se autosignifican sub ratione falsi, como los ha defmido al principio del tratado.
Propone ahora Oria una nocion de insoluble algo
ms
amplia, en
contraposition a la nocion inicial que unfa insoluble y reflexive
y, por siempre entra la segunda intencion. Esta nocion mas amplia de insoluble seria formulada asi: "insolubile est propositio ad quam sequitur
tanto,
oppositum eius quod
significatur per
algo ampliada permitiria tratar
me
18 19
periurare
y a otros,
como
ipsum
immediate".
Esta definition
insolubles a ego nihil dico, ego iuro
que no estarian comprendidos en
la
primera
Oria, f.24r, Ashworth, 1977, 269-79.
Oria, Ibid.; Soto, Summulae, f.153; Pedro de Espinosa, Liber insolubilium (Salamanca c.1533) sin paginar. Espinosa cita varias veces a Bricot y a Heytesbury; Domingo de Soto a Ockham, Bricot y Martin de Magistri. Me refiero solamente a los tratados de insolubles.
Munoz Delgado
598
con
definition
comunmente
9.
que
comenzamos
este
Tales
trabajo.
tratados en los logicos del tiempo.
son
insolubles
20
Conclusion
He
seguido, en la exposition,
el
texto de Oria de tal
manera que
estas
paginas son tambien un resumen. Me parece que queda claro que el centro de la version de Oria esta en la notion de verdad y sus causas. Puede
permite atender a varias de distintas alternativas. El tratado
advertirse
algo de incoherencia que
opiniones
sin
pronunciarse
entre
breve, pero suficiente para ver la
linea
le
que conoce
de Bricot, Juan Mair, Celaya,
lo principal del
etc.
sin
tema y
las
es
esta en
que se decida por
los
diferentes malices de esos autores.
Probablemente toda su information
le
viene a traves del Paris de
Monteagudo, ya que de ese ambiente vienen varios a Salamanca a ensenar en los anos de Oria, como Alonso de Cordoba, Martinez Silfceo, Domingo de San Juan, etc. Todos ellos eran aficionados a la logica. Bricot y Heytesbury parecen haber sido espccialmente populares en insolubles en Salamanca.
el
tema de
los
21
Universidad Pontificia de Salamanca
20
Bottin, Bricot, 18,44,50,69-70; definition de insoluble, segun Oria. 21
V^ase
la
nota
2.
64-65.
En
el
apartado
2
hemos
transcrito
otra
PAOLA MULLER
The Descensus ad Inferiora in
13th
William of Shyrcswood and Peter of Spain
four of terms: acknowledged properties supposition, appellation and copulation. Supposition was the
century
signification,
logicians
most studied property in
playing,
a
fact,
and
syntactical
in
central
semantical
fundamental divisions
in
common
some groups
the role
development of proprieties terminonim, in medieval logic, taking on numerous
functions.
Recent
research
supposition theory, where to different authors and
it
is
the
shown the
has
possible to find
use
of
similar
techniques to characterize the different suppositions. In these techniques it is interesting to focus on the descensus ad inferiora, that can be
considered a logical procedure through which or
the
we can
proposition. This technique,
falsity of a
as
establish the truth
supposition theory,
undergoes a gradual evolution up to the 14th century theory. During the 12th century we can simply note some references to descensus without a definite theory
while the
in
the
and sometimes even without an adequate exemplification,
13th century the descensus theory begins to develop with of
exemplifications
including
a
or
conjunction
such
common
evolution
the it
logical
term
to
disjunction is
inferences
from
unique
singular
a
of correspondent
interesting
to
study
the
a
singulars.
positions
supposition,
To
analyze
treatment
exactly as is stated in the treatises of
or In
to
the
following
of William
Shyreswood and Peter of Spain, as two examples of attempts technique to the division of supposition. inferiora it must be included within the
proposition
single
sentence
of
to apply this
the descensus
of the
theory
ad of
Shyreswood and Peter
of Spain.
William of Shyreswood
The Oxford a
logical
logician William of Shyreswood, in approximately 1250, wrote
treatise,
Introductiones
in
Logicam.
In
line
with
medieval
600
Miiller
he devotes an important section to the properties of terms, 1 especially signification (praesentatio alicuius fortnae ad intellectuni) and supposition (ordinatio alicuius intcllectus sub alio\ specifying that such tradition
definitions instead,
a
are
referred
to
the supposition
secundum quod sunt
in
actu.
In
habitu,
the significatio alicuius ut subsistcntis, that
is
more
of signification or,
sort
as
precisely,
is
the signification of subsistent
things, or those that are put to sub-iacere.
Shyreswood proceeds to subdivide supposition
further.
characterized
the
differentiation
actual
between
is
context,
of
supposition,
material
supposition,
which
by
cannot
3
The
first
syntactical
meaningfully
express the supposed term, and formal supposition, including the various the
suppositions:
significative
when
simple,
the
term supposes for the
and the personal, when it supposes for the things itself, meaning acting as subject. Formal supposition can be further divided into common in
and
discrete.
Both simple and personal supposition branch out further: the simple in accordance with the different significant ways of the dictio, the 4 is instead distinguished in determinated, when the term personal supposes for some things individual, and in confused, when it supposes for many. This confused supposition is further subdivided into merely confused and into confused and distributive, when the term stands for
many,
so
For
the
Introductiones
as
autem
every
in
The
represented.
terms
confused
William
of of
Logicam,
Logicam",
individual
C.Lohn-P.Kunze-B.Mussler, "William Traditio 39 (1983), pp. 219-299, p. 265 5.01.
of
definitions
Introductiones in "Ex
for
the
properties
of
see:
ed.
and
Shyreswood, Shyreswood,
patct, quod significatio est in omni parte seu dictione orationis, suppositio nomine substantive tantum vel pronomine vel dictione substantiva. Haec enim rem ut subsistentem et ordinabilem sub alio. Copulatio autem in omnibus
hiis in
significat adiectivis et participiis et
verbis."
(Ibid.,
p.265 5.03)
For the distinctions between suppositions
see: Ibid., p. 266 5.1.2-4.
1
sic. Quaedam est determinata et quaedam confusa. Confusa confusa tantum, quaedam confusa et distributiva (...). Et est determinata, quando poterit exponi locutio per aliquod unum. Et hoc est, quando dictio supponit pro aliquo uno, ut cum dico: homo currit. Ita potest esse vera quolibet currente. Confusa autem, quanto dictio supponit pro multis (...). Confusa suppositio est, quando dictio supponit pro multis vel pro uno multotiens sumpto cum potentia ibidem tenendi pro multis, ut si quilibet videat Sortem tantum, tune omnis homo videt hominem. Hie homo "Item
sic.
personalis dividitur
Quaedam
non supponit pro multis, sed pro uno multotiens sumpto cum potentia etc. Sed si dicatur: omnis homo videt Sortem, hie Sortes, licet supponit multotiens, non tamen potest cerni ibi pro multis et ideo non stat confuse." (Ibid., p.265 5.1.6., p.269 5.1.13)
Dcscensus
TJie
William of Shyreswood and Peter of Spain
supposition can be mobilis
distributive possibility
in
or immobilis,
of operating the descending from
5
according to the
common
the
601
term of the
analyzed proposition to the few individuals included in the term.
So we
have come to the application of descensus to the singulars. Shyreswood, in fact, thinks that an expression meaning a multiplicity in a proposition, even though showing the different corresponding individuals, creates the
any singular and supposes
possibility of applying a logical inference to
in
a confused and distributive way. Shyreswood, however, does not specify
what type of inference can be applied,
to
if
conjunction; but by referring to the assertion:
quod pro
quolibet",
we can presume
that
it
is
the disjunction or to the "supponit
For Shyreswood, then,
original proposition to the corresponding singulars. it
possible to
is
when
descend to individuals
in
ita
pro multis,
correct to pass from the
every distributive proposition,
they are considered in themselves; such descent however can be
prevented by the addition of some syncategorematic words. For example, while from the proposition: Sortes
"ergo
currit",
homo
"omnis
currit"
from the expression:
is
it
omnis homo
"tantum
similar to the precedent, but for the addition of tantum to infer:
that
"tantum
Sortes
currit",
because other
men
Shyreswood gives such great importance he specifies some rules, by which it
correct to argue:
-
it
currit"-
not proper
is
can run too. confused supposition
to is
find
the
of affirmative
and
possible
to
application of the logical inference to singulars.
Specifying 6
negative signs is
correct
to
the
est
iste
(e.g.,
asinus"),
of distribution
are added to terms, William says that while
from
descend
corresponding singular
homo
means
different
when they
it
a
negative
from is
"nullus
not
universal
homo
correct
affirmative universal proposition (e.g., from
cannot infer
"omnis
homo
est iste
animal").
to
est
proposition
asinus"
do the
"omnis
homo
to
"ergo
to
it
the
nullus
same from an est
animal"
we
This difference depends on
"Confusa et distributiva quaedam mobilis, quaedam immobilis (...). Mobilis autem, quando potest fieri descensus, ut in praedicto exemplo in hoc termino homo. Immobilis est, quando non potest fieri descensus. Dictio enim supponit distributive, quae supponit pro multis ita quod pro quolibet. Ergo potest fieri descensus ad quodlibet. Et dicendum, quod in omni distributiva suppositione potest fieri descensus quantum est de se, potest enim impediri per aliquod adiunctum." (Ibid., p.266 5.11.6-7) 1
signum distributivum confundit terminum sibi immediate adiunctum confuse et Sed signum affirmativum confundit terminum remotum confuse et distributive. Unde sequitur: nullus homo est asinus. Ergo nullus homo est iste asinus. Sed non sequitur: omnis homo est animal. Ergo omnis homo est hoc animal." (Ibid., "Omne
distributive.
p.2695.1.14)
Mullcr
602
term.
analy/ed
-
affirmative or negative
-
the property
this
Moreover,
of universal signs following the
does
descent
logical
A
and
concern
not
but
the
the two propositions E, predicates. to dcsccnsus the of the denies technique applying possibility Shyreswood A propositions predicate, because he has not had the intuition of logical
of
subjects
their
inference to a proposition including a predicate as being the disjunction terms. This descent, in fact, can be correct because it leads to of single
a
the
of
composed
categorical
and
subject
the
it
animal",
esl iste
correct to say:
is
animal vel
With
ille
respect
Shyreswood affirms singular. In the
homo
est animal,
the
while
said:
homo
it
est iste
ergo omnis homo
...".
the
that
it
of
predicate is
correct
universal
negative
to
to
others
by
proposition,
descend to the corresponding
example given by William the singular
connected
not
is
vel
to
"omnis
of
disjunction
what is predicate of the original proposition. Exemplifying is not correct to infer "omnis homo est animal, ergo omnis
or
disjunction
will
punctuation marks. Successive authors, instead, the predicate of the E proposition it is possible
is
in that
unique
or
conjunction
it
by
point out that from to
descend to the
of corresponding conjunction or to the disjunction or to the conjunction from a inference a valid dcsccnsus predicates. So Shyreswood intends by to a unique singular proposition, the subject of which is a common term, proposition, the subject of which
common In
speaks giving
when
term
is
discrete term
a
included under the
in the line of predication.
the exposition of the rules of confused supposition Shyreswood 1 about asccnsus in subiccto, without specifying the meaning or
an adequate exemplification. The ascent from singular, possible one can infer a proposition including a general term from a
singular century,
one
arbitrarily
corresponding,
the technique following the
will
logical
be,
especially
in
the
descent to singulars
in
14th the
in explanation of the differentiations of supposition. Shyreswood asserts, distributive and a confused from is it that fact, possible to pass
the merely confused, because supposition to a determinate one and not to in some cases distribution could remain immobile. To explain this affirmation,
^
Shyreswood
asserts
that:
"non
dicitur
immobilis,
quia
non
in subiecto, scd quod non dicitur immobilis, quia non possumus asccndere non possumus descendcre. Distributio est enim ipsorum suppositorum. Ergo cum hoc non possumus dcscendere ad supposita, quia suppositio est pro supposito." (Ibid., "Sciendum
quia
p.271 5.1.18)
Dcsccnsus
Tlic
in
William of Shyreswood and Peter of Spain
603
possumus asccnderc in subiccto, sed quia non possumus dcscendere. Distributio cnim est ipsorum suppositorum." So William reaffirms once again that what characterizes supposition s mobility or immobility is the descending to singulars. Shyreswood formulates the descensus ad inferiora theory in a very simple way while speaking about supposition, without profiting from or
about
theorizing posterior
the
logicians
different
articulations
that
be
will
conjunctive or disjunctive predicate); without applying
to
of
types
personal
Shyreswood regard
to
but
supposition,
introduces
by
only
to
it
to different
or
mobility
immobility.
speech about logical descending even with
the that
copulation,
studied
conjunction or to disjunction,
to
descending
(logical
ordinatio
is
alicuius
in a
Shyreswood distinguishes copulation
intellectus
way very
supra alium.
similar to supposition.
Concerning the subdivision of confused copulation, William asserts that 8
as qualislibet or quantuslibet, distribute as regards their
copulative signs, substantives.
possible
to
E.g.,
from the proposition:
"qualislibet
descend to the so called copulata
determinate singulars
copulation:
However Shyreswood
"ergo
that
specifies
albus
the
homo
specialia,
homo
expression
is
in
is
the
to
currit et niger
homo
it
currit"
that
etc.".
the
said
a merely confused way, because it is correct to example supposes descend to correspondent singulars. That is from qualislibet homo does in
depends on the sign indicating a certain accident and distributing as to substantive. In William of Shyreswood we find therefore an application of the theory of the logical descent to not
follow ergo
to
singular
the
immobility; this if
Socrates;
is
it
of
distinction
confused
supposition
s
mobility
an as yet simple and not well defined application, even
at the level of exemplification there are already intuitions, that will
developed and included
"Huiusmodi signa copulatio distributiva
cum
dico:
qualislibet
ad copulata specialia (...). (/W
Dictio
significat
p.271 5.1.27)
or
copulativa est.
distribuunt
Suppositio autem
homo sic:
suorum substantivorum, unde sua suorum substantivorum confusa tantum, ut
respectu
copulatio distribuunt. Unde possumus descendere currit, ergo albus homo currit et niger etc. aliquod et istud distribuunt respectu sui substantivi."
currit
,
ilia
qualislibet
accidens
be
theory of personal supposition.
in the
homo
Miiller
604
Peter of Spain
Peter of Spain
of the properties of terms, Logicalcs, dedicated to the analysis
Summulae
out
points
immediately 9
there
signification:
an
to
attributes
the Vlth Treatise of his Tractatus, called afterwards
in
is
sound
vox
or
supposition
someone
because
signification
articulate
between
distinction
the
impositor of
function
the
and
designating
who identifies the something, standing out from William of Shyreswood, with its referring to actually subsistent a term of character significative things. Supposition, instead, it
is
secondary as regards signification, because tails
the use of a term, having qua
is
10
already a meaning, to designate
Peter of Spain analy/es the supposing term whether different types of supposition, depending on common or discrete. The most important subdivision of common is
Given
something.
is
supposition
into
this
introductory distinction,
natural
and accidental supposition.
defines the natural supposition as the use of a individuals
term.
participating
Accidental
in
supposition
that (cxigit adiimctum),
is
it
is
term
for all the
use
the
individuals to the specification of which
more
common
Peter of Spain
nature designated by the analy/.ed of a common term for those
universal is
11
it
is
necessary to add something
included
in
a syntactical context.
So
there will be different suppositions, depending on what is added to the name is included in a proposition, syntactical starting term. But, once the is supposed other context has, among powers, the capacity to modify what in fact, is
by the term. Accidental supposition,
subdivided into simple and
9
For the different acccptions of significant) and suppositio Tractatus called aftcnvards Summulae Logicales, ed. L.M. de Rijk, 80 8-16. B.V., Assen 1972, pp. CXXIX-303, Tract. VI p.79 1 1-14, p. 10 It
Frcge and Saussurc, asserting But while for Peter of Spain
recalls
Bedeutung. suppose,
in
a
that just
the
points
supposition.
These affirmations show up
a
certain
Peter
of
Spain,
&
Comp.
Sinn is the condition of the terms - substantives - can Ever refer. can every term substantivated terms can have
certain
or Saussurian perspective Fregcian out that just the substantives or
Shyreswood
sec:
Van Gorcum
distance
between
the
mentality of
medieval and modern logicians. What characterizes substantives with medieval grammars, and verbs their possibility of presenting objects, substantial property that adjectives is do not have. From this come out as signification and supposition bind the word to of the first case as universe of forms, in the second one as universe in reality,
existents. 11
For the
p.81 1-6.
distinction
between
common and
discrete supposition, see: Ibid., p.80 19-22,
Dcsccnsus
Tfie
in
William of Shyreswood and Peter of Spain
605
12
that is the Simple supposition does not concern individuals natural supposites -, but the name s meaning, the form common to
personal.
name
s
natural
its
supposites.
expression
and
supposition
Peter
homo
"omnis
is
it
put
of
est
for
asserts
Spain
the
animal"
own meaning,
its
Considering instead the proposition
est
"homo
animal
that
is
has
simple animal nature.
the term
species",
the
in
that
simply
term
homo
has
simple supposition and stands for an exlramental reality of which species can be predicated. In examining the above mentioned exemplifications 13
do a process carrying from the general proposition to a particular one, that is passing from simple supposition to a personal one. There is in fact personal supposition when Peter of Spain asserts that
a
common term
used
is
Peter
inferioribus).
of
correct to
is
it
for
all
Spain
the
affirms,
individuals
without
expression descensus, but using processus, that a
to
particular,
includes
it
adopting is
it
suis
(pro
the
technical
correct to descend to
one particular from the general and not to the
only
conjunction or the disjunction of corresponding singulars.
For Peter of Spain, like for Shyreswood, personal supposition is 14 differentiated by determinated and confused. It is determinated when
common
the
term, assumed indefinitely or with a particular sign, supposes
under
for all the individuals included relative
to
homo
in
all
-
predication.
proposition,
it
either running or
makes
adopts
position,
the
-
if
currente").
example:
following
"homo
refers to,
currit",
the
word
and so supposes
for,
not running; but, included in the said
the sentence true
locutionem veram pro
however truth conditions are
the expression
in
an extrapropositional context
individuals,
("reddit
E.g.,
itself;
it
refers to
whom
is
running
Peter of Spain, to clarify this "animal
est
Sortes,
animal
"Accidcntalium suppositionum alia simplex, alia personalis. Simplex suppositio acceptio termini communis pro re universal! significata per ipsum." (Ibid., p.l 11-13) 13 Cfr. ibid., pp.Sls 19-30. 1-9.
est
est
suppositionum alia determinata, alia confusa. Determinata suppositio habet terminus communis indefinite sumptus vel cum signo particular!, ut homo currit vel aliquis homo currit Et dicitur utraque istarum determinata quia licet in utraque illarum iste terminus homo supponat pro omni homine tarn currente, quam "Personalium
dicitur
quam
.
non currente, tamen uno solo homine currente vere sunt. Aliud enim est supponere et est reddere locutionem veram pro aliquo. In praedictis enim, ut dictum est, iste terminus homo supponit pro omni homine tarn currente quam non currente, sed reddit locutionem veram pro currente. Quod autem utraque illarum sit determinata patet, quia
aliud
cum
dicitur
animal
est
(72>iV/.,p.82
animal
est
Sortes, animal est Plato, animal est Cicero, et sic de aliis; ergo hie est figura dictionis a plurihus determinatis ad unam."
omnis homo 13-26)
,
Miillcr
606
de aliis; ergo animal est omnis homo". In it is possible to ascend from the complete how out he points way series (ct sic de aliis) of singular propositions to a unique proposition Plato, animal est Cicero, et sic this
common
including a
term and an affirmative universal
does not use yet the term ascensus -
not of logical descending
more
but
figura
notice
that
sign.
Peter of Spain
spoke of process and
neither does he theorize about this technique,
est having explained the example, asserts; It is ad unam". determinatis interesting to pluribus
after
simply, a
dictionis
as before he
-
Peter
propositions with
"hie
of
the
does
Spain
conjunction
not
ct,
the
join
rather
different
singular
connects them with
he
a
in the punctuation mark: the comma, indicating a very short pause used enumerations. The et instead joins like terms in a proposition. The choice
comma
of a
instead of the conjunction brings the discussion to a level
more grammatical than
logical.
strictly
Peter of Spain does not theori/e
about the doctrine of logical ascending from particular to general. Concerning confused supposition and its eventual division, Peter of
and then explains some doubts about
asserts a position
first
Spain
to
it,
15
Peter of Spain in fact initially affirms that in the end. it confused supposition can be distinguished as confusa necessitate signi vel
confute
modi, when the term necessitate
rei,
But later he
at
when
issue points out any supposition,
term supposes for
the
assserts:
"destruimis
quandam
indicated
essences.
divisionem antecedentem, hanc
confusarum suppositionum alia est confusa necessitate signi necessitate rei. Dicimus enim quod omnis confusio alia
scilicet:
modi,
necessitate modi." So what produces confusion term in question and not the object: so we are in a
Peter of Spain after the
term can suppose possibility in
the
all
and as confusa
-
initial
In
this
immobile way, according to the
case Peter of Spain uses the technical
expression desccnsus and applies this technique
"Suppositionum
confusa
necessitate
confusarum rei."
(Ibid.,
alia
p.83
linguistic context.
of descending to any singular included
-
or the impossibility
the considered term.
est
the sign following the
division, later refuted, asserts that a
a mobile or in an
in
is
vel
est
4-5)
confusa
in
necessitate
the exemplification.
signi
vel
modi,
For the exposition of the doubts
alia cfr.
16
est
ibid.,
pp.83ss 24-27, 1-29, 1-23, 1-8. 16 "Sed
quia
confuse
licet
et
distributive supponit quia tenetur pro omni homine; mobiliter vero, Sortes vel fieri pro quolibet supposito, ut omnis homo; ergo
descensum
omnis homo; ergo Plato Sed iste terminus animal dicitur confundi immobiliter, quia non licet fieri descensum sub eo, ut omnis homo est animal; ergo omnis homo est hoc .
animal
;
sed
ibi est
processus a simplici ad
personalem." (Ibid.,
p.83 13-19)
Ttie
Descensus
William of Shyreswood and Peter of Spain
in
omnis
In fact from the expression Sortes"
or
remarks. is
The
Plato".
"ergo
homo"
it
analysis of this
is
607
correct to descend
"ergo
rise to
some
example gives
the descensus does not occur in a syntactical context, but
First,
applied to substantives taken
for
from a term with an
themselves:
affirmative universal sign to a singular, individual one. Second, there
form of
logical descending to disjunction, but
common
including a
rather
propositions, descents: from
but rather this
Peter
way
does not follow
homo"
"ergo
Sortes or Plato or ...".
two
descents
logical
well
between
distinguished
to
from the expression "omnis homo est animal" omnis homo est iste animal", because this "ergo
descend to singulars. In the
In
if
we cannot descend represents
...",
the
originating from the same common term. Confused supposition can be immobile when it is not correct
themselves, even
a
term to the disjunction of correspondent singular is to the disjunction of two singular logical
homo, ergo Sortes or omnis homo ergo Plato, of Spain does not unite two predicates with
but
disjunction,
is
not from a proposition
is
it
"omnis
"omnis
it
fact
to
passage from simple supposition to a personal one. It that Peter of Spain meanwhile to explain confused
must be pointed out s
supposition to
the
mobility
-
had
particular
the possibility to infer from the general
is
to
uses
immobility
exemplify
that
adopt the
an
extrapropositional
analyzed
previously
example,
to
again
syntactical,
joining the study of the relation between simple and personal supposition.
Peter of Spain goes on to analyze mobility and immobility of confused it
considering
supposition
impossible
that
a
common
term used as a
predicate could have a confused supposition mobile or immobile
proposition
s
subject
is
an
with
affirmative
universal
sign,
when
as
in
the the
aforementioned example.
The theory analysis
of the
of logical descending distributive
comes out even
sign nullus^ and,
in
regards to the
in
consequence,
in
the
exemplification of negative universal propositions. Peter of Spain in fact asserts that
from the sentence
"nullus
homo
est
asinus"
it
is
possible to
descend both to the conjunction of corresponding subjects - "ergo Sortes - and to the conjunction of non est asinus, neque Plato, et sic de aliis"
datur regular quotiescumque hoc signum nullus communi, confundit ipsum distributive et mobiliter; et Unde potest fieri similiter terminum cui adiungitur mediate. Ut nullus homo est asinus descensus sub subiecto sic: ergo Sortes non est asinus neque Plato et sic de aliis, et "De
immediate
hoc
signo
adiungitur
nullus
tails
termino
.
nullus homo est asinus; praedicato sic: Fanellus et sic de aliis." (Ibid., p.219 10-18)
sub
ergo
nullus
homo
est
Brunellus
neque
Miiller
608
predicates aliis"
-,
"ergo
of Spain
reveals
singulars
was
theorized in
the
present
its
mechanism
own to
13th-century technique
in
supposition, but
articulations. facilitate
progress will proceed at its
the
to
treatises
logical
immobility of the supposition
find
Brunellus neque Fanellus et
sic
de
of the positions of William of Shyreswood and Peter
that
immobility of confused
a
est
going on more than Shyreswood.
The examination
as
homo
nullus
The
it
of logical establish
was not
logical descent
descent to mobility
or
yet
developed and
is
adopted simply
the understanding of the mobility and the in the exemplifications. It is a
same
rate
as
theme whose
supposition theory and will
fortune in the logical doctrines of the masters of logic of the
14th century.
Catholic University of Milan
CALVIN
NORMORE
G.
Ockham on Time and the Nature
To
understand
fully
Ockham
s
of Logic
we must understand how Ockham
logic
distinguishes logica from other sciences. This paper considers the question with special attention to the status of temporal inferences which seem to
be
concludes
It
philosophy.
either
classified
plausibly
For Ockham a science
more than an
has no
its
philosophy asking
who
subject
or
no
has
as
of
part
principled
natural
of
way
sciences. is
He
a collection of habitus.
that
insists
it
accidental unity and that to ask of (say) natural as
if
king of the
is
of logic
part
Ockham
that
from other
distinguishing logic
as
it
had only one 1
world".
The
a
"is
question similar to
habits of which a science
is
a
collection are either mental sentences or dispositions to
sentences.
Ockham seems
to think that
it
is
produce mental normally the latter but would
deny the label to the former. I shall argue later that the collection of habits which make up a science is closed under entailment. not,
If
I
this
think,
is
Ockham
correct then a science in
what contemporary logicians would A fundamental distinction concerned to draw
is
that
s
sense
is
very
much
like
call a true theory.
among
between
Ockham
which
sciences
scientia realis
and
is
scientia rationalis.
kinds are collections of mental sentences but the subjects and predicates of these sentences differ in kind. scientia realis is a
Sciences of
all
A
collection
of mental sentences
whose
subjects are of
scientia rationalis a collection of sentences
are of second intention. intention
is
Ockham
s
distinction
not easy to draw correctly and
one way of getting a
strict
intention
Guillelmus Libri
I-III,
ed.
N.Y. 1985) Prol.
if
it
A
may
subjects and predicates between first and second
indeed be incoherent, but
construction of the term
is
out the universe of objects (call these zero intentions). first
intention.
first
whose
by
A
only signifies things of zero intention.
first
picking is
of
concept
is
concept
A
de Ockham, Expositio in Libras Physicorum Aristotelis. Prologus et V. Richter and G. Leibold in Opera Philosophica IV (St. Bonaventure, s.3,
p.10, line 103.
Normore
610
of second
This has the odd consequence that
otherwise.
intention
transcendental terms, including strict
of what they signify
is
s
Ockham seems happy
very"?
in
sciences.
several
different sciences can share the
To
to
A
less
some
intention just in case ...
first
and second intention
another curious question:
raises
taxonomy do sciences have to be to be
can appear
of second intention.
first
of zero intention and so on
Ockham
drawn,
different "not
are
,
exactly the distinction between
However gets
being
construction might assign concepts
all
distinct?
The answer seems
how to
be
admit that the same subject [term]
Indeed he goes further, admitting that
same sentence. He
writes:
evident from the first question that it is not inappropriate for the same thing to be the subject in some truth on account of the different sciences different pertaining to is derived. Similarly it same conclusion which the through principles is already evident that it is not inappropriate for the same thing to be the subject of different sciences because of its different characteristics (passiones}. So it is in the case proposed because this truth God is the first cause pertains to metaphysics and to different theology, because the one science infers it from principles from [the principles of] the other."
Not
Ockham are of
the
only
is
it
can
different
sciences
intention and others
admits
this
the
in
whose
the same sentences but, some sentences whose subjects
share
admits, a single science can have
first
Ockham
third
subjects are of second intention.
same passage which
I
think establishes the
earlier claim that sciences are closed under entailment.
should be said that the Philosopher not only here but in many other places in natural philosophy and other scicntiae reales is not speaking of terms and for terms so that terms stand for terms for things. This is because such propositions in which terms stand for terms not for things frequently follow from propositions in which terms stand for things. And so it is evident that this in which the terms proposition "Substance is the subject of quality" stand for terms not for things follows from propositions in which terms stand for things. Hence this proposition is not inappropriately is evident placed among the others in natural pnilosophy. Thus it that some part of natural philosophy which was treated by Aristotle is not a scientia realis unless it is just as logic is a scientia realis; It
Nor
2
is
Guillelmus
this
de
3
anything disturbing.
Ockham, Scriptum in Librum Sententiarum Brown in Opera Theologica I
Distinctio Prima, ed. G. Gal et S. Prol. q.IX, p.275, 18ff. 3
Ockham, Exp.
in Lib. Phy.
I,
c.4 in
O.P.IV
p.58, 128-129.
Ordinatio. (St.
Prologus
Bonaventure
est
s 1967)
Ockham on Time and the The
would be bootless
part of this quote
first
closed under entailment because the
from others this
(and
Ockham intention
is
given as the reason
why
is
that
says
explicitly
(supponunt pro
fact
why
want
not
did
I
Nature of Logic
to
scientiae
same
introduce
text
whose
terms
follow
may
this
were not
sentences follow
certain
that
they are in the
sentences
terminis)
if
611
But
prematurely),
are
from
science.
of
terms
second of
first
intention (supponunt pro rebus). This result guarantees that the boundary
between
(say)
and
logic
cannot
physics
be
a
matter
simple
of
the
intention of terms in each.
how much
Exactly
interpenetration between the levels of terms will
be forced to allow? So
far
as
can see the answer
I
is
-
an enormous
amount. For example:
Animal
is
the genus of human.
A genus can be predicated of the instances of its species. Every human
we
Here
have
distinguishing the
is
a
an animal. prototype
sciences
a
for
on the
whole
basis
class
of
inferences,
so
of intention seems a hopeless
task.
There may be other distinguishing
characteristics
one could
use.
For example Ockham suggests that it doesn t pertain to logic to know particular consequences but only the nature of consequence in general,
and
in discussing physics
he suggest that
should be noted that according to the Commentator in comment 16 that it pertains to logic to consider in general how one science differs from another but it pertains to this science to consider how It
it
These
differs texts
from
that.
suggest that logic
is
from the other sciences
distinguished
what might such generality consist? The texts quoted suggest that logic is concerned with the general conditions which govern arguing or distinguishing. This would explain why
by
its
first
generality. In
and second intentions might be thought to
the needed distinction.
The general
yield
an approximation to
conditions for arguing and discussing,
because they concern relations among ways of relating and classifying 4 5
Ockham,
Sent. Prol. q.VII in O.T.I, p.201, 10.
Ockham, Exp.
in Lib. Phy. Bk.II Scc.4 in
O.P.IV, p.258,
18ff.
will
Normore
612
be given in second-intentional terms. Because this is so sentences of will have terms of second intention in subject position - at -
principaliter
between
but
and the other
logic
One might
s
the
generates
least
distinction
sciences.
mark
from (say) natural seems
logic off
especially formal. Something like this
is
logic
Ockham
suggested by
what
be
not
think that what does
that
is
philosophy
would
that
logic
claim that logic helps us diagnose the formal but
not the material defects of arguments. But what does the metaphor of
form and matter come to here?
Ockham is
arguments of Saxony
and
s
predicate
terms
its
If
and
this
matter of a sentence with
of the
identification
syncategoremata.
from
and matter of sentences and
never says what the form
but what he does say suggests that he would accept Albert
form
the
its
copula
concern with relations among syncategoremata. is some evidence that this is Ockham s view but
There
considerations militate, decisively the
I
those
who
claim that an argument
same form which has
the
claims
that
premisses to
an argument be true and
is
that there are valid
logic considers
The second
forms.
mata
such cases
differ greatly.
is
valid
is
its
it
not
and
1
(St.
in
case
it
is
Unlike
argument of
false,
Ockham for
impossible
and he
is
two
its
very clear that
not a formal matter.
considers matters other than relations
among
consideration begins with the fact that syncategore In Quodlibet
prepositions,
the category
in futuro,
at least
that validity,
One consequence arguments which are not formally valid. If is
II
q.
19
at
least
Quando.
1
Ockham
in
example.
by
et,
vel,
Ockham
The category
which are terms whose
includes adverbs and
Quodlibet 6
formal in some clear sense, but
terms
is
a formal concept.
itself
in
just
conclusion
implausible to think of conjunctions like as
One
it.
valid just in case every
conjunctions among syncategoremata and include
subject
associated
true premisses has a true conclusion,
the impossibility involved here
of this
think, against is
paradigmatic logical relation,
its
and
then the generality of logic derives
correct
is
with
It
V is
q.
9 he seems to
not
particularly
non and even
si
counts as adverbs
or ergo all
the
includes words like nunc
signification
is
determined by the
Guillelmus de Ockham, Quodlibeta Septem, ed. Joseph C. Wey in Opera Theologica IX Bonaventure, N.Y. 1980). cf. Quod.II q.19, p. 193, 19 and Quod.V q.9, p.516, 65ff. Guillelmus de Ockham, Summa Logicae, ed. P. Boehner, G. Gal, and I (St. Bonaventure, N.Y. 1974). cf. S.L. I, c.59. 1.1. p.lSOff.
Opera Philosophica
S.
Brown
in
Ockham on Time and the Nature of Logic
613
natural philosopher and not the logician because they require for their
understanding an understanding of time.
among them reflects a
would be
parasitic
deep feature of
Ockham
it
If logic
explored the relations physics. This
upon the conclusions of s
which Marilyn Adams the ways in which things
philosophy to
has recently drawn attention, that for Ockham are are as much experienced as the things themselves. 8 But
we
the
terms
ways
are
things
of
complexes
using
categorematic
express
and
syncategoremata express how we experience to be it seems things they may well be acquired in experience. If this is so their treatment may well belong to Natural Philosophy.
We more
the
If
syncategoremata.
can give some flesh to these general considerations by looking
Ockham
at
closely
discussion
s
are those in which
inferences
an inference
crucial in
if
of temporal inferences.
temporal words are
crucial.
Temporal word is
A
the validity of the inference depends on
the sense that the uniform replacement of
it
in
by another grammatically
it
acceptable word can yield an invalid inference.
Ockham
Striking about logical
works
Ockham
is
its
treatment of temporal logic in his explicitly
s
superficiality.
considers
in
his
The
discussion
inferential
only of
relations
truth-conditions
for
which tensed
sentences or in his discussion of immediate inferences involving them are ones involving the scope of the tense indicator - cases like whether we
can infer can
"Deus
The
t.)
fuit
only inferences
which
ones
are
desinit
semper
from
creans"
Ockham merely
"Creans
semper
fuit
Deus".
treats in his discussions of incipit reflect
the
fact
that
on
(We and
Ockham
s
exposition, sentences involving these terms have one negative and one
Even Ockham
affirmative exponent.
s temporal syllogistic is, in a sense, can be modelled entirely superficial. completely merely by supposing that the tense of the copula makes the subject and predicate terms of It
tensed sentences stand for objects which may or may not be those these terms stand for in present-tensed contexts, and by then applying standard to
syllogistic
cf.
the
new terms
Marilyn M. Adams, William
thus generated.
Ockham (Notre Dame,
9
Only one of Ockham
Indiana, 1987) ch.
s
9.
o
Ockham S.L.II,
c.7,
discusses
s
discussion
his
incipit fullest discussion
discussion
and
of of
desinit
conditions for tensed sentences can be found in immediate inferences involving them in S.L.II, c.22. He in S.L.I, c.75, S.L.II, c.19 and 23 and S.L.III-I, c.5. His
truth
of temporal syllogisms
is in S.L.III-I,
c.17-19.
Normore
614
of
discussions
temporal
assumptions; the context It
well
is
is
known
seems
logic
to
Ockham
that
substantive
two theories of future
develops
one of which he ascribes
contingents,
more
require
future contingents.
Aristotle
to
and the other of
which he adopts himself. These two theories differ significantly but they share some crucial theses. Both recognize a difference in the modal status of the past and future which
seems
at
least to require that
time
is
not
Both accept the necessity of the genuine (as opposed to the future-infected) past and so seem to accept a close interweaving of time and modality. To explore the physical consequences of these views we circular.
Ockham s account of time. Ockham provides the nominal definition of time work. One such is in the Summula Philosophiae
must look
his
at
at several places in
Naturalis.
The
text
reads:
Since therefore all agree that time is a measure of temporal things and of change (motus} and rest, that thing will be time which we can certify about the duration of temporal tnings and of change and rest. Thus, this can be a description picking out what the term means (quid nominis ipsius): time is a measure of all things whose 10 duration the intellect can certify through something better known.
Here Ockham makes
clear
that
duration of things, of change and of
time
rest.
only the starting point for the physicist
s
But
means this
a
standard of the
conceptual analysis
analysis of time.
The
is
physicist
aims to discover what time really is. This is done by discovering what can serve as a standard of the kind required. The physicist notes that a we consider a changed thing which change could be such a standard "if
we know
to
11 quickly".
us that
its
be uniform, that
Ockham motion
is
is
we
is
the discovery that
Venus
Moreover time
the
1
Guillelmus Philosophica VI 11
12
Ockham,
de (St.
the
first
is
is
moved
thing
equally
the outermost sphere of
the morning star, but
primum motus but
ibid. 1.98-100. c.7, in
O.P.VI, p.358.
is
c.3,
more than
is
a physical discovery.
as measurable
Ockham, Summula Philosophiae
Lib.IV,
-
not a conceptual point any
Bonaventure, N.Y. 1984) Lib.IV,
Ockham, Summula
is
primus motus. Physics tells and most uniform and so it is uniquely
need. 12
the Aristotelian universe. This
is
always changed uniformly, that
the fastest
suited to be the standard
So what time
is
finds such a thing in the
Naturalis, ed. p.352, 184-89.
by the mind and S.Brown
in
Opera
Ockham on Time and the Nature of Logic
615
usable by the mind as a standard of measurement. Time is the primiim motus but time does not mean primum motus The relevant measurement .
is
measurement of duration. What
the
Ockham (dum) time
of duration
says
13
Ockham
exists".
duration?
is
that
"to
endure
is
only to exist while
uses this account to explain
why
perpetual
and sudden changes are not in time. They are, respectively, too and too short to be measured by the parts of time. Time, then, is long that which measures the existence of temporal things, motion and rest. It things
is
a certain motion
-
namely
that of the
primum
mobile. What, then,
is
a
motion? In several places in
what
Ockham
changed. For example should be understood
speaks of change as involving a difference
Physicorum he writes It that the Philosopher s reason consists in this, that nothing is said to be changed with respect to something more now than before, unless it has something different now than is
in his Expositio
before.
Elsewhere he explains that to have something different now from before exist a thing or quality which did not exist
need not mean for there to
and
before,
before
is
this
is
And
because
a
thing
having a place
s
it
did
have
not
For example, he writes
sufficient.
impossible to pass from contradictory to change (mutatio) but through every change something is acquired and when someone first sits and afterwards does not sit, there is a passage from contradictory to contradictory therefore something is acquired, it should be said that all such [sentences] are verified through local motion and therefore it is frequently possible that a place is acquired. if it
is
said that
contradictory
Since the
without
it
is
any
change of the primum motus
conclude that time consists in the differences
is
motion we may
local
in the places
occupied by
primum motus. But not the differences in places occupied by the primum motus as a whole because, since it merely rotates, the primum motus as a whole does not change places. The relevant differences are the
the differences in places occupied by parts of the primum motus.
But not
measure 13 14
of
just
the
Ockham, Summula Ockham, Exp. Guillelmus
A.Gambatese
et
To
serve
as
place
must
obey
any differences of place would do. kind
required,
the
differences
in
a
Lib.IV, c.13, in O.P.VI, p.382, 78.
in Lib. Phy. L.III, c.3, s.2, in
O.P.IV, p.456, 18-20.
de Ockham, Expositio in Librum Perihermenias S.Brown in Opera Philosophica II, p.300, 72ff.
Aristotelis
c.16,
ed.
Normore
616
constraints.
uniform (or
For example, they must be continuous and they must be at least uniformly diform) in direction. But to speak of a
change of place as uniform different
of the
states
say that a
than (say)
body at
first
is
and then
a
and then
c
and c be
b,
a,
from the
different
distinct
^
at
first
occupies. Let
it
able to order the
method
a
moving body by
spatial dimension of the places places on some line:
To
we must be
direction
in
at
b and
at
b and then
a
at
c rather
finally at
we need
a
way of
assigning priority. Since places can be traversed in either direction they
do not have an In
may be
at in
intrinsic
least
ordering which will do the job.
one place Ockham suggests
some sense
a logical ordering.
that
the ordering of time
He writes:
Besides, whenever there are some things ordered of which one is in one signa or instant and another in another, although it would be repugnant for the posterior to be in the first instant with the prior, however it would not be repugnant for the prior to be together with (sirnul) the posterior in the second instant. For although the prior and posterior are not together in the first instant of duration, yet they can be together in the second instant of duration.
Thus we can
tell
the prior from the posterior in time because the prior
can endure to be together with the posterior but what is posterior cannot predure to be together with the prior. This accords nicely with the Aristotelian intuition that change
has
a
natural
dovetails
nicely with
the
claim,
future contingents, that the past
there were in something at identical
with
or
t
than
later
is
a passage
from potency to
more important
and,
direction,
a t.
common
present
Ockham
s
power is
to
be
at
t
,
then
the
precisely
t
act
and so
purposes,
it
two theories of
necessary while the future
is
It
to
for
is
not. If
would be either
ordering of powers
which provides the temporal ordering. Here the claims about inference which Ockham makes (for example) in De Praedestinatione, are interwoven with his claims about the physics of time. physicist
determines
asserting that true
it
is
way avoid 1
if
to
it
assigning
de
is
because time
is
as the
be that we can accept principles like that is about the past secundum rem then if
a proposition
necessarily true.
Guillelmus
It
it
I
do not see how Ockham could
in a principled
to both sciences.
Ockham,
Distinctiones IV-XVIII, ed. G.
I.
Scriptum in Librum primum Sententiarum Ordinatio. Etzkorn in Opera Theologica III, d.9 q.3, p.296, 15-22.
Ockham on Time and the Nature of Logic What
is
the upshot?
Ockham seems
not to have a principled
distinguishing logic from other sciences. But I
is
617
why should
this
way of
bother him?
conclude by suggesting that it would not. Ockham s heart not in the distinction of sciences because he has nothing invested in
would
like to
the
programme which
that
is
sees the sciences as fundamentally different. But
another subject.
Erindale College, University of Toronto
The Ohio
State University
CLAUDE PANACCIO
La logjquc commc
A
la
toutc fin dc son
introduction
aristotclicienne,
logiquc "pratique
et
speculative"
.
cette affirmation, puis soutenir
dans
1
de
interprctation
certaines
la
de
particularites
sa
a
Occam
dc commcntaircs sur
serie
Occam pose quo 1
non
science pratique selon
la
cst
logiquc
unc
Je voudrais d abord elucider
qu
il
nous d
logique
son
approchc
sens de
le
prendre tres au serieux
faut la
Occam
la
science
pour
bien
comprendre semblent
autrement,
qui,
dcroutantes.
1
.
La
notion dc science pratique
Rappelons d abord que pour notre auteur une la logique ou la theologie n est pas une
discipline
comme
entite
intcllectuelle
numeriquement
de multiples habitus"", dont chacun est une qualite psychologique recllc d un esprit individuel. Chacun de ses habitus est un savoir distinct -une connaissance distincte - dans la mesurc ou il une,
mais
concerne
collection
"une
telle
proposition plutot que n importe quelle autre. La science
theologique, par exemple, comportc (entre beaucoup d autres choses)
la
connaissance de
et
elle
cree
comprend le
la
proposition
est
"Dieu
a
fois
la
triple
et
unique",
aussi la connaissance de cette autre proposition:
monde".
Ces deux connaissances sont
distinctes
1
une de
"Dieu
1
a
autre;
3 Occam, ne pas etre acquises en meme temps Et chaque connaisance de ce genre est une entite singulicre reellc; c est un accident
elles peuvent, dit
-
ou une
qualite,
.
si
Ton veut
-
de
Occam, en bon nominaliste, refuse de
1
individuel
esprit
trailer
une
qui
la
possede.
discipline scientifique
ou
et non speculativa" (I-lxpositionis in libros artis scicntia est practica prooemium, OPh II, p. 7). Toutes les references au texte d Occam renvoient aux deux Universite Saint-Bonaventure Institut Franciscain de series de volumes editees par "...ista
l
1
les Opera philosophica (OPh} et les (N.Y.) abreviations habituelles pour les litres de traites. :
"...una
3
collectio
Ordinatio
I,
multorum
Prol., q. 12
habituum" (id. p. 4).
(OTh
I,
p. 337^40).
Opera
theologica
(OTh).
J utilise
les
La un
comme science pratique selon Occam
logique
comme
savoir
unc
connaissants individuels:
independanle dcs sujcts de theologie en soi, ecrit-il par
abstraitc
realite
n y a pas
"il
619
4 exemple, qui nc soit pas en quelque intellect" Cela explique pourquoi on peut distinguer, comme de son Commentaire des Sentences, deux sens du mot .
une science
premier sens,
ou
theologie
connaissances
la
resoud
elles.
au debut 5
En un comme la
"scientia"
une
en
ordonnees entre
mais
le fait
intellectuelle,
discipline
se
qui
logique,
distinctes
une
est
il
.
de
multiplicite
En un deuxieme
sens, designe chacune de ces connaissances distinctes, c est-adire chaque habitus psychologique reel de connaissance, chaque connaissance par un sujet donne d une proposition donnee. "scientia"
Quand on
la
done, que
dit,
logique est une science pratique, on
prend le terme de "science" dans son premier sens, celui de d habitus intellectuels".
Quant a
ce qu
savoir
il
veut
dire
"collection
en parlant de science pratique
que speculative, Occam s explique brievement la-dessus au debut de 6 certains de ses commentaires du corpus aristotelicien et surtout il y plutot
,
un
consacre
Commentaire des Sentences epistemologique de
statut
dans
developpement
important
la
a
1
d une
occasion
theologie
comme
le
Prologue
discussion
de
son
detaillee
science: est-ce
du
une science
ou une science pratique? Les trois dernieres questions du Prologue portent la-dessus, pres d une centaine de pages au total dans edition Saint-Bonaventure La question 10, d abord, examine la notion speculative
1
.
de
"praxis",
notre
qui designe, pour Pessentiel, toutes les operations qui sont en et
pouvoir
rationnel.
qui
La question
peuvent
faire
Pobjet
d un
choix
volontaire
et
11 porte sur la distinction generate entre science
j y reviendrai dans un instant. La question directement au probleme de savoir si la theologie est 12, enfin, attaque speculative ou pratique. La conclusion d Occam, soit dit en passant, est
speculative et science pratique; s
que
la
theologie
est
une
collection
certaines sont d ordre speculatif est a la fois triple et
aime de tout notre
doit etre
"...nulla
5
Ord.
I,
et
un")
est theologia in se ita
Prol., q.
1
(OTh
I,
de
(comme
connaissances
"Dieu
a cree le
d autres sont d ordre pratique
coeur",
quod non
"le
sabbat doit etre
sit in
aliquo
intellectu".
diverses
dont
monde",
"Dieu
(comme
"Dieu
respecte").
(id., p.
342).
p. 8-15).
Voir les prologues de YExp. in libr. Praedicamentorum (OPh II, p. 137), de super libr. Elenchorum (OPh III, p. 4) et de YExp. in libr. Physicorum (OPh IV, p. 14). 7 Ord. I, Prol., q. 10-12 (OTh I, p. 276-370).
YExp.
Panaccio
620
ressort de ces divers passages que, pour
II
d une
science
caracterisent
se
pratique
les
conclusions
traits
distinctifs.
Occam, deux
par
Premierement, ce sont des propositions qui portent sur nos oeuvres, sur cela qui peut etre accompli par nous
-
tandis
a
la
que
Occam
s
exprime
necessaire
suffisante
et
speculatives
propres cette
si
Mais
.
Occam
dit
peut
il
ccrit-il,
donne pour exemple
y
certains
le
sciences
les
Commentaire
necessaire
-
(c est-a-dire
la
savoir
le
des
Sentences,
n est pas suffisante:
une science speculative
avoir
endroits,
pratiques
des
"de
Et
.
tire
qu les
remplir: directives
il
nos en
il
du De
psychologic d Aristote), qui peut etre classce comme speculative bien qu concerne en grande partie les oeuvres humaines.
Anima
C est
elle
y a une deuxicme condition qu une science pratique doit conclusions qu elle tire doivent etre des propositions
il
Ellcs
(directivae).
directement guider
doivent
bien
admis en toutes
est
1
action.
Je dis
Occam
lettres
"directement", par parce qu qu en un sens n importc quel principe peut servir a orienter action on lui adjoint d autres premisses. Par exemple, la connaissance de il
1
dans
arts
les
triangle a trois
"tout
proposition
proposition directive science
cotes"
si
la
peut etre utile de diverses facons
s agit pas pour autant d un savoir en question n est pas elle-meme une proposition
mecaniques, mais la
pratique parce que
Une
-,
trait
a la fois
etait
premiere particularity
dans -
En
operations.
differcncier
pour
reconnatt que cette condition oeuvres,
nos actes de raisonnemcnt ou
des oeuvres interieures,
la
nos
qu a
comme 9
sciences
sont
logique, par exemple, porte sur
physique, qui est surtout speculative, a principalement
choses
d autres
ce
La
.
comme
certains de nos actes intellectuels,
nos actes judicatifs
8
il
ne
11 .
pratique,
done,
est
une science dont
les
conclusions
sont des propositions qui (1) portent sur nos propres operations, ct (2) sont directement directives. partir de la, Occam distingue deux sortes
A
de connaissances pratiques
"In
nobis
ilia
(...)
11
notitia practica
Id.,
Id., p.
\
Exp. in
operibus nostris
p. 314-315.
12
:
autem conclusione quae
cum
Voir par exemple "...de
12
316-317.
sit
libr. artis
(...)
scitur
de opcribus
notitia nostris..."
practica
proocmium (OPh
potest esse scientia
ponitur aliquid
(Id., q. 11, p. 315). II,
p. 7).
speculative"
(OTh
I,
p. 315).
operabile
a
La -
logique
comme science pratique selon Occam
621
connaissancc pratique dictativc (dictativa), qui dicte ce qui
la
doit etre fait et ce qui ne doit pas
1
etre; elle fixe les fins et
les devoirs; -
connaissance pratique ostensive (ostensiva), qui se contente
la
comment
d indiquer
accomplie, sans dire
La
logique,
comme
si
une
a
appartient
precise-t-il,
certaine
elle doit
etre
1
cette
etre
peut
entreprise
ou non. deuxieme
tout
categorie,
grammaire, la rhetorique et 1 art mecanique. Ce dernier, par ne nous dit pas si une maison doit etre construite ou non exemple, (cette decision, dit Occam, releve de la "prudentia"), mais si on veut la
construire une maison, elle tienne
qu non
I
art
mecanique nous apprend comment faire pour la logique ne nous dit pas s il faut ou
De meme,
un syllogisme dans
faire
quand
debout.
se taire (cela doit,
j
telles
circonstances, ni
discourir et
quand
imagine, relever aussi de la
"prudentia")]
mais
nous montre comment reussir un raisonnement ou un discours qui tienne debout si on a decide d en faire un. elle
Occam, dire que la logique est une science est une collection ordonnee de connaissances
Bref, chez c est dire et 1
qu
elle
ostensives,
portant
sur
de
certaines
nos
occurrence nos actes intellectuels de discours
2.
Quelques consequences dans
la
Cette conception du statut de sur la fa^on dont
dont
Summa la
Occam aborde
traite cette discipline.
et
operations
pratique, directives
mentales,
en
de raisonnement.
logicae
logique a d importantes repercussions effectivement les questions particulieres
Ses traites de logique doivent etre vus
des ouvrages pedagogiques, par lesquels
comme
developper chez ses lecteurs et chez les etudiants en general des aptitudes determinees a accomplir correctement et de facon consciente et reflechie certaines operations,
dont
il
nous
fournit
1
auteur
lui-meme
la
visait a
lisle:
(1)
1
aptitude
a
discerner le vrai du faux; (2) la promptitude a repondre aux arguments et
aux objections; (3) la facilite a distinguer chez les auteurs ce qui doit etre pris au sens litteral et ce qui n est que facon de parler 13 Dans cette perspective, un traite de logique doit etre aborde comme une espece .
de guide de
Exp. in
la
praxis intellectuelle, et
libr. artis
prooemium (OPh
II,
p. 6).
non
pas, par exemple,
comme une
Panaccio
622
meme
entreprise theorique fondationnellc au
de Russell. Cela
me
jette,
semble-t-il,
litre quc ccllcs de Frege ou un eclairage revelateur sur divers
passages de la Summa logicac en particulier, qui ont parfois intrigue et deroute les commentateurs. En void quelques exemples. endroit des paradoxes Premier exemple: 1 attitude d Occam a les huit cent cinquante pages menteur. Sur celui du comme semantiques l
seulement
Summa
la
que compte
aux
consacrees
sont
dans
logicae
1
edition
14
ou
paradoxes
trois
Saint-Bonaventure, "insolubilia"
Occam
.
y
au paradoxe du menteur des memes a il conclut lapidairement qu et principes le chercheur partir studicux pourrait resoudre tous les autres "insolubilia", que, dit-il, je esquisse une solution,
fort intercssante
du
reste,
"ce
aux ingenicux, car je n
laisse
15
traite
present
Le contraste
.
complet"
parle de cela
ai
est
ici
que pour rendre rapport
par
frappant
le
aux
logiciens d aujourd hui, qui voient dans les paradoxes logico-semantiques
une menace grave aux fondemcnts de la rationalite. Et il Test tout autant par rapport a d autres medievaux a peine plus tardifs: Jean Buridan, par exemple, discute longucment et en detail un grand nombre de paradoxes apparents. Cela peut s expliquer d une part par le fait que pour Occam, les fondements de la rationalite nc sont nullement en cause dans la
comme discipline pratique, et par ceci, comme cclui du menteur n intervicnnent
logique elle-meme
d autre part, que
les
en
paradoxes
pr6s
jamais
dans
intcllectuel
travail
le
et
paradoxes chez un Buridan
commence
logique
proprement
courant:
scientifique
semble etre
peu leur
L importance accordee aux
resolution ne presente guere d interet pratique.
me
realite a
1
indice
de ce que deja
la
dcveloppce che/ cet auteur a un niveau pour ellc-meme en quelque sorte, plutot que pour
a
etre
spcculatif ct
sa valcur instrumentale.
Deuxieme exemple:
les
que
14
la
Summa
logicae, III-3,
"Quod
relinquo ingeniosis, quia
46 (OPh
complementum..." (id., p. 746).
S.L.
I,
33 (OPh
I,
p. 95).
.
"suppositio"
propriete semantique de
^ 16
16
I,
la
il
Or
("significare"),
il
admet -
"suppositio"
la
et
signification
premiere partie de
la
"signifier"
definition la notion de
de
definitions
supposition. Lorsqu au chapitre 33 de Occam veut definir le verbe
de
la
la
Summa,
utilise
dans sa
tres clairement ailleurs
reference,
si
Ton veut-
p. 744-6). ista
(...)
non
inscrvi
nisi
proptcr
istius
Summulae
La
comme science pratique selon Occam
logique
623
n advient aux termes que lorsqu ils sont utilises dans des propositions 17 Certains commentateurs ont vu la la preuve d une priorite, pour Occam, .
du complexe propositionnel sur le terme isole, une sorte de holisme a la Davidson. Michael Loux va mcme tres loin dans cette direction en reconnaissant dans ce passage de
avec
rupture
1
atomisme
philosophie occidentale
semantique
18
1
occurrence
a
de
notion
la
1
marque d une jusque
prevalait
en
ici
et
signification
ses
:
la
pour Occam
ses diverses subdivisions, 20
dans
detail ailleurs
vient
que lorsque
veritable
la
,
le
recourt
il
en
sont
definitions
19
ne permettent done pas d attribuer une une ou 1 autre des deux notions. elles
circulates;
priorite conceptuelle a
qui
la
J ai discute cette question
.
mais je veux seulement rappeler moment de definir la "suppositio" inversement
Summa
la
Une telle circularite ne fait probleme que si on aborde la comme un systeme constructionnel au sens de Carnap, c est-acomme une serie ordonnee de definitions qui, partant de certains
logique dire
concepts
non
primitifs
definis,
introduirait
progressivement,
sur
cette
un arsenal de notions de plus en plus complexes. Mais ce base, n est pas ce que fait Occam et ce n est pas non plus son ideal. Si Ton accepte sa caracterisation de la logique comme science pratique, on tout
comprend
qu
cherche
il
lecteurs des outils
qu
les etudiants
que
de
celle
II
a
definitions,
fournir
a
ses
se permet, pour ce faire, de miser dans les
Summa
la
ont acquise a
"suppositio".
ses
par
soient capables de manipuler dans leurs propres
ils
operations intellectuelles.
premiers chapitres de
plutot,
L ordre
sur une certaine familiarite pretheorique la
petite ecole avec des notions
conceptuel
n
est
ici
pas
celui
comme de
la
construction theorique, mais celui d un apprentissage progressif et de plus
en plus
raffine.
Je
tirerai
mon
exposee dans
verite
la
troisieme exemple de
deuxieme partie de
formule, en termes de comparaison entre la
du predicat, 17
S.L.
I,
I,
M.,
"Signiftcatio
New Scholasticism, 19
C.
53 (1979),
Panaccio, C.,
du signe (sous
la
Summa
logicae.
"suppositio"
du
Occam
y
sujet et celle
p. 193).
18
Loux,
la
theorie des conditions de
conditions de verite de diverses sortes de propositions.
les
63 (OPh
la
and
Suppositio:
Reflections
on
Ockham
s
Semantics",
The
p. 407-27.
d Occam: signification et supposition", dans Archeologie Brind Amour et E. Vance), Toronto, Inst. Ponti. d Et.
"Guillaume
dir.
de
L.
Mediev., 1983, p. 265-86; et "Propositionalism Franciscan Studies, 44(1984), p. 61-70. 20 S.L. I, 63-64 (OPh I, p. 193-196).
and Atomism
in
Ockham
s
Semantics",
Panaccio
624
J ai
ailleurs
suggcre
de
(et
fac.on
dans un
detaillee
plus
en
ouvragc
en que ramenant certaines formes propositionnelles qui, chez Occam, font objet d un traitement separe, a une ou 1 autre des quatre formes canoniques du theorie
cette
preparation)
etre
peut
grandement
simplifiee 1
1
carre
interesse pour
cette
ou
affirmative
particuliere
m
runiverselle
aristotelicien:
c est
instant,
1
Pourquoi?
simplification.
runiverselle
affirmative,
21
la
negative
particuliere
me
Parce que,
logiciens d aujourd hui (et a juste
les
ce
qui
ne precede pas a semble-t-il, ce genre de
que notre auteur,
simplification thdorique, qui est tellement prise
la
negative,
Mais
.
lui,
mathematiciens
les
par
et
sans nul doute), nc presente
litre,
pas d avantage pratique ou pcdagogique. II est bien connu, par exemple, que la reduction des connecteurs verifonctionnels a un seul qui a etc
accomplie par Sheffer en 1913 ne ni
propositionnel
Son
interet
est
en rien
facilite
1
apprentissage du calcul
controle pratique des inferences, bien au contraire!
le
purement
de
s agit
il
theorique:
restreindre
le
plus
nombre de concepts
primitifs requis dans un certain systeme possible maximiser de facon a en formel, clcgance et la cohesion d ensemble et a le
1
meme
focaliser,
du
enseigner
comment
coup,
C est
scientifique courante.
impose ne sont
s
le
travail
fondationnel.
discerner efflcacement
de
pas
pourquoi
meme
Occam,
veut
lui,
du faux dans
le vrai
1
enquete
exigences de simplification qu
les
nature
que
dont
celles
les
il
locigiens
contemporains sont coutumiers.
Un 1
attitude
d
les
en
ici
1
facon
la
permettera de conclure, celui de taxonomie aristotelicienne des
comme
sert,
cadre general de son expose sur
la
est
la
de
endroit
bien sur,
troisieme partie de
qu
particulier, celui
sophismes
telle
a
la
Summa, mais
sans,
de toute
comme
considerer
la
interessant
un cas et
s
sophismes dans
evidence,
L
Occam
II
sophismes.
me
dernier exemple, enfin,
il
s
de
par division: distinction
un instrument scientifique tres fecond. en explique lui-meme au passage en discutant la distinction "Quant
entre
entre sophismes par composition
a savoir, ecrit-il, s
ces
il
sophismes, je ne
beaucoup, car je ne crois pas que ce savoir
soil
Cf. Panaccio, C, "Pour une theorie occamiste des Materiaux pour une histoire des theories linguistiques (sous Lille, Univ. de Lille III, 1984, p. 211-6.
la
faut entendre
m en
tres
conditions dir.
de
utile
de S.
de
soucie pas
pour
verite",
Auroux
et
les
dans al.),
La sciences
logique
comme science pratique selon Occam
22 .
particulieres"
de distinguer
les divers
Ce qui importe, ajoute-t-il, c est d etre capable sens d un discours ambigu et non pas de savoir
un sophisme dans
classer
625
telle categoric plutot
que
telle autre.
Le point
de vue pragmatique est nettement affirme dans ces lignes et, ce qui est encore plus revelateur, il est mis en relation directe avec la pratique des sciences
devolu a court
speciales: la
Occam prend au
logique,
passage
celui
recapitule
serieux
le
role
traditionnellement
d etre Vinstrument des autres disciplines. Ce exactement ce que j ai voulu ici mettre en
evidence.
Universite du
"Utrum
Quebec a
tamen
euro, quia hoc scire p. 787).
isto
Trois-Rivieres
modo
sit
accipienda distinctio istarum
non reputo multum
utile scientiis
fallaciarum
specialibus".
(S.L.
non multum
III-4,
8,
OPh
I,
VLADIMIR RICHTER
Historische "Dc
Ockham und
in
1.
DC
dcr
von
DC
Logic"
DC gcltcn
Logiktcil
De
arils
fiir
rcpriisentativ
Lcistung
spc/ifischc
Rahmcn
Darstcllungcn im und in logicac 1
und
longior
(Tractatus
logicac
Burlcys Tractatus
Ara. 3 Historisch durftc dcr
dicsc
Kommcntierung dcr Topik cntstandcn
conscqucntiis aus dcr
Die Siimma a)
als
Ockhams Siimma
in
puritate
2
brcvior)
cine
1st
Hiilfte dcs 14. Jh. Ihrc
1.
conscqucntiis
Traktatcn
scin.
dcr
Burlcy
conscqucntiunun
gcncralibus
refills
"British
Bcmcrkungcn
rcgulis gcncralibus corLScqucntiarum"
/.B. hat hicr folgcndcn Inhalt:
Zusammcnfassung dcr Topik dcr Bocthianischcn
Tradition, Kap.
1-9;
daruntcr b) Thcoric dcr Conscqucntiac dcr Modallogik (Kap. 10-16), 3 Kapitcl c)
DC
acquipollcntiis niodalium (Kap. 14-16);
Summc
dcr
daruntcr 6 Kapitcl
Topik
dcr
aristotclischcn
Tradition
(Kap.
17-37),
Inductionc (Kap. 31-36) und cin Kapitcl ubcr die
DC
Aquivokation (Kap. 37);
DC rcgidis gcneralibus conscqucntianun (Kap. De obligalionibus (Kap. 39-45); e) DC insolubilibus (Kap. 46). f)
d)
1
Wilhclm
v.
Siimma
Ockham,
logicae,
cd.
Ph.
38);
Bochncr,
St.
Bonaventure,
N.Y.,
1975, Tcil III-3.
2
Walter
Burley
(Burleigh),
Raised Edition of the Tractatus 3
De
with Tractatus longior, artis logicae Ph. Bochncr, St. Bonaventurc, N.Y., 1955.
puritate
bre\-ior, cd.
the
II Stump, Topics: Their Development and Absorption into Boh, "Consequences", in: N. Krctzman, A. Kenny, J. Pinborg Later Medical Philosophy (Cambridge 1982), 273-299 (cds.), The Cambridge History of und 300-314. - N.J. Grecn-Pederscn, "Fxirly British Treatises on Consequences", in: O. Lcwry (cd.), The Rise of British Logic (Toronto 1983), 287-307.
Sichc die Beitrage von
Consequences",
4
und von
I.
O. Bird, Topic and Consequence of Formal Logic 2(1961) 65-78.
in
Ockham
s
in: Ix>gic",
Notre
Dame
Journal
"
regulis generalibus
"De
in
consequentianim
Ockham und Barley
627
De obligationibus und De insolubilibus fehlen in AuBerdem sind dicse Teile in der Hss.-Familie dem letzten Teil De fallaciis (Teil III-4). Auch das
Die letzten zwei Tcile
eincr Reihe von Hss. 5 Intacta
die Aquivokation hat keinen einheitlichen Ort. Z.B. steht in
iiber
Kap.
hinter
erst
(CA O.67) und in der Easier Hs. (Bibl. univ. F.II.25) dem Kapitel 30. De aequipollentiis fehlt auch in
einer Erfurter Hs. dieses
hinter
Kapitel
einigen
Hss.
Summa
ist
Diese
der handschriftlichen Uberlieferung der
Instabilitat
daB diese keine
ein Zeichen dafiir,
einheitliche Entstehungs-
geschichte hat.
Fur
2.
die
relative
folgende Hypothese aufgestellt:
wieder
diese
dem
vor
Summa
Relation,
dieser
Chronologic
vor
6
Werke
longior.
Tractatus
Fur
longior,
den
Boehner
Ph.
hat
Tractatus brevior vor
Tractatus
dem
drei
der
Summa
zweiten
besitzen
wir
Teil
und der
wohl
ein
Zeugnis von Frater Johannes Nicolai, zusammen mit dem Terminus ad quern fur den Tractatus longior: 1329. DaB der Tractatus
verla Bliches
brevior vor der
Summa
Dazu zwei
Boehners Vermutung. Bemcrkungen. Die erste betrifft den
entstanden
kritische
ist, ist
zuletzt
Nach meiner Meinung handelt es sich um genannten eine Kompilatio aus dem Tractatus longior. Daher kann seine Abfassungszeit auch bis nach dem Datum 1329 als moglich angesetzt werden. Der Tractatus brevior.
Prolog seiner Absichtserklarung, die nur fragmentarisch eingelost wird, paBt wenig in Burleys Lebensabschnitt nach 1327, da er sich mehrere
Jahre
Hof
Abgesandter des englischen Konigs Edward III. am papstlichen 7 Avignon aufhielt. Daher betrachte ich auch Burleys Autorenschaft
als
in
fur diesen Tractatus als fraglich.
Die zweite Bemerkung
zum vor
das Verhaltnis der
1324,
Summa,
1
Summa
logicae
an, diese sei
noch
Ockhams Kommentierung der Physik entstanden, 8 "Ferienarbeit". Diese Annahme habe ich unlangst einer
als
ss.
De puritate, Zur
Summa nehmen
wahrend
moglicherweise
}
betrifft
Tractatus longior. Die Editoren der
pag. VIII.
Biographic
von
Burley
siehe:
C.
Martin,
Studies presented to Daniel Callus (Oxford 1964) 194-230. 8 Summa, 36*.
"Walter
Burley",
in:
Oxforder
Richter
628
Kritik unterzogcn.
9
Auch
Ockhams
die Autorcnschaft
fur die
Summa
habc
der
Abfassungszeit Frage gestellt. Als Terminus ante quern Ob diese werden. 1328 der Summa kann etwa das Jahr angenommen Annahme der Abfassungszeit fiir die Summa mil Burleys Autorenich dabei in
spateren
schaft des Tractatus longior vertraglich
ist,
halte ich ebenso
fiir
fraglich.
Auf jeden Fall sind diese Fragen der Authenti/itat sowie der Abfassungsdefinitiv zeit und des Abfassungsortes beider Werke heute noch nicht beantwortet. Dies ware aber sehr wichtig
des 14.
Jh.,
3.
die Geschichte der Logik
Re/cption von der /weiten Halfte der zwan/.iger Jahre des
auch besonders im Zusammenhang der
Ockhams Denken 14. Jh.
fiir
in Paris in
friihen
10
11 haben auf die Bedcutung des Salamucha 1938 und Ph. Boehner 1952
Kapitels
De
regulis generalibus
conscquentianim
in
der Logik des 14. Jh.
eine Rcihe von Regeln, die als cine hingewiesen. Dieses Kapitel enthalt miUelalterliche Form (Theorie) der Aussagcnlogik betrachtet werden kann.
Summa
In der
(Kap. 39).
am Ende
steht dieses Kapitel
Denn De
obligationibus
und De
des Teils
De consequents
insolubilibus sind wahrscheinlich
erst spater hinzugekommen und sind im Grunde eigenc Traktate (Tcile) der Logik. Es war daher ein Fortschritt ein systematischer Absicht, als die Traktate De puritatc ariis logicae dieses Kapitel bereits am Beginn ihrer Abhandlungen De consequentiis behandelt haben. Sowohl der Autor des Elementarium logicae als auch der des Tractatus minor (zwei unter
dem
EinfluB der
kleine
Summen
Gedanken des
Summa
in
den vicrziger Jahren des
der Logik, die
Ockham
Tractatus longior gefolgt
12
zugeschrieben werden),
und haben dem Kapitel
den ihm gebiihrenden Platz generalibus consequentiarum Lehre De consequentiis (De locis) zugewiesen.
9
V. Richter, Authenticity of 10
W.J.
Paris",
in:
"In
dem
regulis
am Beginn
der
Writings",
in:
Franc. Studies 45(1985), 93-105.
the University of at Reception of Ockham s Thought a I Unh ersite de Paris. Vignaux (eds.), Preuve et raisons 43-64. tneologie au XIV* siecle (Paris 1984),
Courtenay, Z. Kaluza,
"The
P.
Logique, ontologie
et
11
Medical Logic, Manchester
12
sind
De
Search to the Historical Ockham: Historical Literary Remarks on the
Ockhams
Ph. Boehner,
entstandene
14. Jh.
1952, 52ff.
E.M. Die Edition dieser 66-173. 24(1964) 34-100; 25(1965) 151-276; 26(1966)
Werke
wurde
von
Buytaert
besorgt.
Franc.
Studies
regulis generalibus consequentiarum" in
"De
wurde
Inhaltlich
4.
Es
analysiert.
daC
zeigt sich,
puritate
durch
629
Boh 1962 13
I.
hier cine logische Theorie der Implikation,
und der Negation vorliegt. Hier noch zwei interpreta zu diesem Kapitel und zur Analyse von Boh. Bemerkungen Die erste Hauptregel lautet: omni consequentia bona simplici (...)
der Verbindung tive
De
dieses Kapitel von
Ockham und Burley
et
"In
non potest esse verum
antecedens
pretiert diese "P
-->
Q
=>
Regel
u.a.
auch
als eine
Zu
dieser
-iO(P.-iQ)".
Denn
14
sine
Boh
I.
consequente".
inter-
Regel der Modaltheorie, wie folgt: habe ich einen Interpretation
doch kein Satz und keine Regel irgendeiner modallogischen Theorie. Das non potest ist hier nur eine faqon de parler, deren man sich ofters bedient, wenn man z.B. sagt, daB aus dem Vorbehalt.
Definiendum
dies
ist
"notwendig"
Die zweite
wie
antecedens.
folgt:
"Quidquid
und
consequens".
ad
Hauptregel.
Diese
ist
lautet in zwei aquivalenten
ad
sequitur
antecedit
consequens,
Quidquid Diesen Hauptregeln sind zwei Regeln
...
15
zweite
die
betrifft
nichts anderes als die Transitivitatsregel
Varianten
und umgekehrt.
die Definitio folgt
Bemerkung
ad
sequitur
ad
antecedit
antecedens,
beigefiigt,
welche der
Widerlegung einer sophistischen Argumentation dienen: "Quidquid sequitur ad antecedens, sequitur ad consequens. ... Quidquid antecedit ad consequens, antecedit ad
antecedens."
In
allgemeiner
Form
findet
man
diese Transitivitatsregel in Tractatus longior an einer anderen Stelle,
im
aber gleich im AnschluB an diese Hauptregel. 16 Im AnschluB an diese Hauptregel erwahnen die beiden Traktaten De puritate Tractatus
noch
brevior
zwei
"Quidquid
weitere
denen
die
erste
lautet:
sequitur ex consequente et antecedente, sequitur ex antecedente
1
per
von
Regeln,
abgeleitete
Regel ist im Grunde eine von Gentzen 1934 18 genannt): (so
Diese
se."
"Schnittregel"
P
->
Q, Q.P
->
R
=
P
->
spezielle
Form
der
R
1-5 I. Boh, Study in Burley: Tractatus De regulis Notre Dame Journal of Formal Logic 3(1962) 83-101. "A
in:
De puritate,
pag. 61,
15 Ibid., pag. 62,
16
17
lin. 30ss.;
lin. lOss.;
pag. 199,
pag. 200,
lin.
lin.
generalibus
consequentiarum",
26s.
11-14.
Ibid., pag. 69, lin. 16ss.; pag. 200, lin. 20ss. Ibid., pag. 62, lin. 12s.; pag. 203, lin. 7s.
18
G. Gentzen, "Untersuchungen iiber das logische 39(1934) 176-210, 405-431 (Reprint, Darmstadt 1969).
SchlieBen",
in:
Math.
Zeitschr.
Richter
630
Dieser hat die Bcdcutung dieser Rcgcl in dcr Mctamathcmatik unscres Jh. cntdcckt. Im Mittclaltcr wird dicsc Rcgcl zwar auch weitcrs z.B. im im Tractatus minor) erwahnt, bleibt aber praktisch Elementarium (nicht
"ohne
Anwendung"
"Aussagenlogik"
und gcrat dahcr
in
Vcrgesscnheit, samt dcr gesamten moderncn Logik wieder-
dcs Mittclaltcrs, bis dicsc in der
cntdcckt wurde.
Universitat Innsbruck
ANDREA TABARRONI
Predicazionc esscnziale cd intenliones
sccondo Gentile da Cingoli
1
La
logica a
Bologna nel XIII secolo
Le nostre conoscenzc
sull
insegnamento della logica
Benche collocate
secolo sono tuttora assai scarse. nel
curriculum scolastico medievale
insegnamento sia
numerose
tracce
lasciato
del Duecento. -
contesto
-
cattedrali
,
nella
Fa eccezione
-
lo
in posizione strategica
e pertanto certamente materia di
-
studio
della
logica
mendicant!
non sembra aver
produzione letteraria dei magistri
e quindi
assume particolare spicco
Gentile da Cingoli, maestro
la figura di
XIII
nel
Italia
sia nelle univcrsita sia negli studia degli ordini
scuole
nelle
in
italiani
in
questo
di logica e di filosofia
naturale a Bologna negli ultimi anni del secolo.
Dobbiamo poi
1941),
alle
Grabmann (Grabmann
innanzitutto alle ricerche di Martin precisazioni
fornite
da
altri
raccolte intorno alia sua vita (Hissette 1979).
studiosi,
Dopo
poche notizie
le
aver studiato a Parigi
probabilmcnte negli anni ottanta del secolo, Gentile dovette iniziare
insegnamento bolognese intorno
il
suo
1295. In quella che era allora la piu
al
importante universita della Penisola, egli entro a far parte della cerchia dotti che si riuniva attorno alia figura di Taddeo Alderotti, medico
di
e
insigne Italia.
tra
Proprio
i
primi rappresentanti della rinascita delParistotelismo in
connubio
Poriginale
medica e promozione
della
culturale della Facolta di
nuova
tra
filosofia
rinnovamento
di
andava allora formando anche dal punto di 1981). Tra i discepoli dell Alderotti, Gentile e
si
promettente carriera logica fino
e
della
alle
risultati allievi
di
filosofia.
XIV
secolo
degni del massimo rispetto, se
si
quali Guglielmo da Varignana, che di
vista 1
istituzionale
(Siraisi
unico che rinuncia
alia
medico per rimanere fedele alPinsegnamento della La sua attivita come magister dovette protrarsi
prime decadi del
d Arezzo, successore
tradizione
periodo il clima del resto Bologna, che
segnava
Medicina ed Arti
della
in quel
e
fu
senz altro
esercitata
con
deve giudicare dalla qualita fu
di
medico apprezzato, Angelo
Gentile sulla cattedra di logica, e
il
misterioso
632
Tabarroni
Urbano
cui
Avcrroista,
si
dcvc un amplissima Expositio del commento
avcrroistico alia Fisica di Aristotele.
Anche per
dovettero escrcitare,
dottrine
come
1
2
XIV
L
per
Gentile
iniziatore di quella tradizione
che caratterizzo
-
naturale del
chc
oltre
questo,
1
che
influenza
effettiva
sue
le
puo essere senz altro considerate autonoma - in logica e in filosofia
ambiente universitario bologncse nel corso
1
secolo (Maier 1955).
insegnamento logico di Gentile da Cingoli
come maestro
Dell attivita di Gentile
Scriptum super artcm
possono aggiungcre un
rimane soprattutto uno
di logica ci
conservato
veterem,
in
Ad
4 manoscritti.
esso
si
de universalibus, delle Questions, giunteci purtroppo incomplete, suU Isagoge di Porfirio ed infine un Commento agli Analitici primi, la cui autcnticita non 6 stata tuttavia ancora assicurata. Si
un corpus
di
tratta
Tractatiis
tutto
di
al
grazie
rispetto,
si
qualc
potrebbe
delinearc un profilo sufficientemente articolato delle dottrine logiche di
questo maestro. Puo suscitarc quindi un certo stupore che, a diffcrenza
quanto e
awenuto per ancora
stata
sia
oggetto
spicgazione, almeno tuttora
stato
sue teorie grammaticali,
le
parziale,
incoativo
attenzione
di
delle
di
da
parte
studiosi.
degli
di
Gentile non
la logica di
La
questa lacuna puo essere trovata nello
conoscneze
nostre
intorno
dottrine
alle
logiche che vcnivano insegnate nelle universita alia fine del XIII secolo.
Sono
trascorsi
infatti
solo
12
anni
scomparso Jan magistrale, il nuovo
da quando
lo
un saggio Pinborg e riuscito a sintetizzare, paradigma teorico giunto a maturazione con Radulphus Brito e che egli ha intcso caratterizzare come "logica dei modisti" (Pinborg 1975). Durante in
questi
la
anni,
delle
pubblicazione
di
opere
commento
Sofistici dovuti alia scuola di Pietro di Alvernia e a
Simone
agli
Elenchi
Faversham
di
ha fornito nuovi importanti contributi di conoscenza. Ma cio che manca tuttora e un panorama sufficientemente ampio e dettagliato del periodo che vide sul
la
gestazione e
concetto di intentio
dal 1275 al 1300.
riferimento
La
1
-
affermazione delle teorie semantiche imperniate vale a dire, grosso modo, del periodo che va
difficolta di ricostruire
senza
teorico
con precisione un quadro
dubbio
scoraggiare puo quindi intraprendere lo studio delle opere di Gentile. Tanto piu se
che anche
in
questo,
come
in
altri
periodi
creativi
della
chi si
di
voglia
considera
storia
della
Predicazione ed intentiones secondo Gentile da Cingoli
metalinguaggio della teoria, pur se
il
logica,
costituzione
una
di
in decisa
evoluzione verso
formalmente
tecnica
terminologia
633
la
e
prccisa
relativamente autonoma, risente tuttavia degli schemi epistcmologici allora normativi,
metafisica
della
quelli
Nonostante questo
-
possa risultare utile
e
teoria
della
conoscenza.
della
e anzi, proprio in ragione di queste difficolta
abbozzo
1
di analisi
che mi propongo in questa sede
di tentare in relazione alia dottrina degli universali di Gentile
e detto, di una presentazione ancora prowisoria, in cui
si
per quanto
vogliono fissare
XIII e
La
3
E
XIV
i
una ricerca
risultati di
primi
sulla logica
si
bolognese del
secolo.
teoria delle intentiones
rivolgersi
caso di un logico medievale
nel
naturale, al
commento
sll
trarre
per
Isagoge
come Gentile da indicazioni
dottrina degli universali. In maniera conforme ad
quel
da Cingoli
sua teoria della predicazione essenziale. Si trattera,
in particolare, alia
e,
credo
-
anche
periodo,
porfiriano
Gentile
Puniversale
come
identifica
come
inteso
secunda
altri
circa
Cingoli, la
commentatori
oggetto intentio.
del
sua di
trattatello
Con
questa
assunzione, la teoria dei predicabili viene a trovarsi fondata su di una precisa concezione del processo di formazione dei concetti e di invenzione
nomi: si tratta qui infatti del luogo teorico in cui si incontrano semantica e gnoseologia (Ebbesen 1981). La formazione dei concetti e spiegata da Gentile facendo ricorso al modello classico della teoria dei
L intelletto umano
opera
punto
nella sua continua
giunge ad un certo
ad
isolare
una
classe
comuni,
precisamente,
Pintelletto
comune
i
di
in
sostiene
individui
cosiddetti
e
egli
modi
grado
di
che
mostrano
essendi attribuire
di possedere o proprietates Piu .
una
caratteristica
a questi individui, poiche nota che ciascuno di essi e in grado di
operazione affatto peculiare, come ad esempio eseguire ragionamenti nel caso degli uomini. Questo tipo di operazione
compiere
un
tipo
distintiva veniva dell
e
,
caratteristiche
1
-
di classificazione e identificazione degli oggetti,
dell astrazione.
di
delta apparens nella terminologia dell epoca. Sulla base
uniformita dell apparens rispetto ad un insieme di individui, Pintelletto
dunque
in
grado
di
inferire
attribuita a questi individui,
sua volta,
e
il
prodotto
di
che una proprietas comune puo essere
ad esempio la razionalita. Tale proprietas, a un essenza comune (o quidditas) che ora
Tabarroni
634
1
e
intelletto
in
di
grado
dalle carattcristichc accidental! di
A
questo
gli
in
come
impositio
un
gioco
altra
astrazione,
capacita
una rclazione convenzionale
oggetti della propria attivita.
designate
di
ciascun individuo.
entra
punto,
dell intelletto, quclla di stabilire
un processo
attraverso
isolare,
Si
tratta
nominum ad
peculiare
tra
nomi e
i
del processo che veniva allora
significandum. Secondo
la teorie dei
un procedimento intellettuale complesso logici modisti, imposizione attraverso cui e possibile assegnare un oggetto o una classe di oggetti e
1
come
ad un nome, a partire dalle modalita cognitive secondo sono dati all intelletto. In forza dc\V impositio,
significato
cui quello o quegli oggetti
nome
dunque, il concezione
un
al
come
termine
condividono cui
quella
intcllecta
est.
e
quidditas
chiamata
ciascuno
significhcra
"homo"
la stessa quidditas, sulla
e
cognitiva
ut
res
la
significa
Applicando
questa
caso della formazione dei predicati universal!, ne dcriva che
stata
dai
daH
modisti
ratio
modalita
Questa
intellctto.
modus
o
intclligendi
o anche intentio. Gentile afferma dunque che, secondo
intelligendi
termine
la
res
la
intellecta
significa prima accezione, prima intentione L universale assunto in questa accezione, cioe come non costituisce ancora tuttavia oggctto formale della scientia Porphyrii. il
che
base della modalita cognitiva secondo
isolata
logici
individui
degli
"universale"
.
sua
sub res,
1
La quidditas
tipo,
dai
la
il
processo di astrazione
essere intesa anche secondo una modalita cognitiva di diverse
infatti
pu6
isolata dalPintellctto attraverso
quale, poiche presuppone logicamente la prccedcnte, viene delta del
logici
periodo sccunda
sub secunda intentione e
intentio.
In questo caso,
la
res
intellecta
quidditas considerata secondo la sua proprieta
la
di essere predicabilc di molti, cioe
appunto
di essere universale.
Lo
studio
delle intcnzioni seconde, vale a dire di quelle modalita cognitive su cui
fondano 1
le
relazioni
formali
tra
i
predicati,
e
si
secondo Gentile
allora
oggetto proprio della teoria logica degli universali, cosi
come
essa viene
formulata ncll Isagoge di Porfirio.
4 Predicazione essenziale ed intcntiones
La
teoria
semantica messa
Porfirio considera dunque un elemento estensionale,
in
all
la
opera da Gentile nel suo
interno del significato di ogni res,
e
Commento a nome comune
un elemento intensionale,
Sulla base di questa distinzione fondamentale
vengono
Vintentio.
affrontati
anche
i
Predicazione ed intcntiones secondo Gentile da Cingoli
due
nuclei
problematici
ordinamento
dell
dei
del
principal!
trattato
secondo
predicati
di
Porfirio,
modello
noto
il
635
quello
dell arbor
Porphyriana e quello della predicazione essenziale.
L ordinamento
dei
predicati
secondo
essenziali
genere,
e
specie
infatti, secondo Gentile, alle relazioni sussistenti tra le prime intenzioni, le quali, a loro volta, sono fondate direttamente sulle relazioni estensionali che sussistono tra le proprieties o modi essendi da
differenza e dovuto
e genere rispetto ad prime intenzioni. Cos! da cui e tratto perche proprieta (essere sussistente, corporeo, e di da cui e tratto animate, sensibile) piu generale quella (essere
sono
cui
tratte
le
"animal"
la
"homo"
"homo"
sussistente,
animate,
corporeo,
sensibile,
e
razionale)
individui
gli
cui
quest ultima proprieta sono una parte di quelli cui inerisce
inerisce
la
se cioe si considerano prima. Dal punto di vista intensionale, tuttavia non le res ut slant sub primis intentionibus, bensi le prime intenzioni in
se
,
1
generis.
ordine
ed e Vintentio speciei che contiene Yintentio della specie infatti sono contenute tutte le
inverte
si
Nell intenzione
Da
intenzioni dei generi superior!, piu una.
una posizione, per cosi dire, e dovuta, secondo Gentile,
al
che
fatto
parte sua, la differenza occupa
rispetto a genere e specie.
"collaterale"
differenza
la
Essa
e tratta da
una
non contiene
proprieta semplice e non-indipendente. Vintentio differentiae
un soggetto, qualis, mentre
in se le intenzioni di altre differenze e tuttavia essa implica
un ente
sussistente.
generi e specie
si
Per questo essa
si
predicano per modum
modum
predica per
quid.
questo modo, con la sua trattazione dei predicabili essenziali, Gentile disegna un ordine intensionale di contenuti semplici e composti In
(rationes
intelligendi
o
possibilita della predicazione essenziale.
cui
un predicate
di livello superiore
Gentile sottolinea
secondo: intentio
"oportet
infatti quella
si
relazioni
Elencando
le
puo predicare
fonda
si
la
condizioni secondo di
un suo
inferiore,
delFinclusione intensionale del primo nel
ratio superioris includatur in
quod
secondo
cui
sulle
intentiones},
ad
nome
cui, esempio, mediante Vimpositio costituisce un segmento Poiche dunque istituito il nome il
inferior!".
"animal"
di quella
e
La
stato
secondo
ratio
o
istituito
cui e stato
propositionibus dicendo hoc est hoc significatur esse predicatum quodammodo in subiecto", con la "homo".
proposizione res,
"homo
est
mentre viene reso
"in
animal"
esplicito
intentiones. In questo caso,
viene asserita un identita a livello delle
un rapporto
infatti,
giacche
si
di inclusione
tratta di
a livello delle
una predicazione
Tabarroni
636
essenziale, soggetto e predicate
un unica quidditas, intesa
rifcriscono ad
si
tuttavia sub diversis rationibus intelligent.
un nodo ccntrale
Si tocca qui
vicnc
un opzione
luce
alia
L
intentiones. tutta
conseguenza
soluzione
dalla
medievale,
del
e
di
dipendente, per un logico
e
problema
un
metafisico,
essenziale,
predicazione
teoria dci predicabili,
in cui
fondamentali della teoria
le scelte
della
interpretazione
la
carattere
di
preliminare
metaphysical commitment, che governa delle
semantica modista,
dcll intcra
metafisico
la
riguardante
composizione delPessenza delle sostanze composte. Tale problema, nel periodo in cui oper6 Gentile, veniva affrontato secondo due possibili e
schemi
altcrnativi
di
dell unicita
teoria
seconda che
a
soluzione,
Punicita o per la pluralita delle
forme
ci
si
pronunciasse per
(Roos 1974). Secondo
sostanziali
la
che era stata quella di Tommaso, ma radicali come Sigieri di Brabante e Boezio di Dacia
della
forma
-
anche degli aristotelici ad ogni predicato essenziale - da quello di genere sommo a quello di corrisponde in re una sola forma sostanziale, quella specifica. specie ,
Della diversita dei predicati viene percio dato conto facendo riferimento ai diversi
che
modi
sono
in
diversi
grado
punti
sostenitori
della
corrisponde
in re
direttamente dell unicita
biunivoco contrario
le
diverse
delle
principio
e
Pintelletto
sotto
essendi che concorrono a costituire la forma sostanziale e
di
di
trarre
vista,
pluralita
le
la
delle
o
opcrationes intentiones
medesima forme,
ad
quidditas.
ogni
da
apparentia
mediante
cui
Viceversa,
predicato
cui
significare,
per
i
essenziale
una diversa forma o quidditas e da esse Pintelletto trae sue intenzioni. Ne consegue che, mentre per gli oppositori
forma il rapporto tra res c intentio e un rapporto al ad ogni diversa intenzione corrisponde una diversa res essere res teoria una stessa i della sostenitori puo per della
-
,
considerata secondo diverse intenzioni. Di qui discendono owiamente due diverse possibili teorie del significato, che infatti
per un
si
contesero
il
campo
lungo periodo della storia della logica medievale.
Gentile da Cingoli fu deciso e coerente sostenitore di una di queste teorie, quella tipica dei logici modisti, secondo cui non c e corrispondenza
biunivoca tra
le
cose e
i
concetti.
consiste nel fatto che essa costitui
L importanza
storica della sua scelta
un paradigm a teorico autorevole per
rappresentanti della scuola bolognese di logica per tutto
Universita di Bologna
il
XIV
secolo.
i
Predicazione ed intcntioncs secondo Gentile da Cingoli
637
Riferimenti bibliografici
da Cingoli mi sono servito della trascrizione da me compiuta dello Scriptum super Porphyirium contenuto nel ms. Firenze, Biblioteca Nazionale Centrale, Conventi Soppressi J. X. 30 e di quella, Per
il
tcsto di Gentile
gentilmente messa a mia disposizione dall amico Roberto Lambertini, del Tractatiis de universalibus, contenuto nel ms. Firenze, Biblioteca Mediceo
Laurenziana, Strozziano 99.
Ebbesen S. 1981 Commentators and Commentaries on Aristotle s Sophistici Elenchi, vol. I, Corpus Latinum Commentariorum in Aristotelem Graecorum VII.l, Leiden.
Grabmann M. 1941 da Cingoli em
Gentile
Hissette R. 1979 "Note sur Gentile da medievale 46, 224-228.
aus der Zeit Wissenschaften,
italienischer Aristoteleserkldrer
Dantes, Sitzungsberichte Miinchen.
der
Cingoli",
bayer.
Akad.
der
Recherches de TJieologie ancienne
et
Maier A. 1955 "Die
per
Bolqgneser Philosophen des 14. Jahrhunderts", Studi e memorie Bologna, n.s. vol. I, 297-310.
la storia dell Universita di
Roos H. 1974 "Zur Begriffsgeschichte des Schriften des ausgehenden
Festschrift
mm
75.
Terminus 13.
Geburtstag
apparens
Jahrhunderts",
von Adolf Hufnagel,
Cannstatt, 323-334. Siraisi
N. 1981
Taddeo Alderotti and his
in in
Pupils, Princeton N.
J.
den logischen Virtus
politico.
Stuttgart-Bad
ANTONINO TINE
Simonc
In
comunicazione
qucsta
Simonc
Favcrsham
di
Limitcrcmo Porphyrii \ Tractatus
la
ci
Quaestioncs
(Summulae
per
scoria
dclla
c
di
logica.
,
Commcnto
ai
c Quaestiones super Elenchorum*. Quaestiones super libro Porphyrii, chc c una sorta libro
introdu/ionc gcncralc a tutta
disciplina
scien/a
Quaestioncs super libra
scgucnti:
logicales)
allc
tra
Praedicamentorunr
libro
super
csaminarc alcunc opcrc
rapporto
il
tcsti
ai
Ic scicn/c
di
proponiamo
conccrncnti
nostra indaginc
Ncl procmio di
Favcrsham c
di
chiunquc
tradi/.ionc
la
dcdichi
si
parlando dclla
logica,
aristotclica,
alia la
vicne
riccrca,
dclla
priorita
utilita di
affcrmata, su
logica
qucsta sulla
tuttc
Ic
altrc singolc scicn/c.
modum secundum quern in singularibus scientiis ex aliquo noto oporteat dcvcnire in cognitioncm alicuius ijgnoti, sic ut non quaeratur aequalis ccrtitudo in omnibus, nisi secundum exigentiam naturae subiectae. Et ideo logica, licet sit quaedam scicntia in sc, est tamen modus scicndi aliarum. Insa cnim tradit
L Autorc
ribadisce
rationis
investigationcm 6
c chc
incogniti"
a cio che
non
il
che
concetto
il
ex
cognito
modo secondo
lo e ancora,
cui la
"modus
scicntia
"omnis
devenit
scicndi
communis omnibus
Magistri Simonis Anglici sivc dc Favcrisham, Opera omnia, vol. prior, cura et studio Paschalis Ma/y.arclla,
~
Carmclo Ottaviano, Le
Faversham,
Memoria
CCCXXVII,
Serie VI, vol.
di
C.
Cedam, Padova
"Quaestiones
Ottaviano,
Ill, fasc.
IV)
per
I,
Opera
scientiis",
logica, T.us
1957.
super libro Praedicamentorum" Realc Accadcmia Na/.ionale dei
Roma
quandam
cognitionem alicuius ragione passa da cio che c noto in
di
Simone
Lincei
di
(Anno
1930.
the genuine text of Peter of Spain s Summulae Lambert Marie de Rijk, logicales, II, Simon of Faversham (d. 1306) as a Commentator of the Tracts I-V of the Summulae", Vivarium VI (1968), 69 e segg. Cf.
Simon
"On
Faversham, Quaestiones super libro Elenchorum, ed. by Sten Ebbcsen, John I,ongcway, Francesco del Punta, Eileen Serene, Eleonore Stump, Pontifical Institute of Mediaeval Studies, Toronto 1984.
Thomas
of
Izbicki,
Quacst. sup. Porph.
6
cit.
13.
Ibid.
Ibid. Cf. Alberti Magni, Logica, Liber I, De Praedicabilibus, Trac. 1,1 De natura quamvis scientiae sint Logicae, cap. I (Ed. A. Borgnet, Paris, Vives 1890), pp. 1-2: multae, et quaelibet specialem habet modum, qui differt a modo alterius, sicut et "...
Simone va
prima
apprcso
di
si
rischio di sowertire
dedicano
corpo che all
altra
ogni
639
scienze
Non
disciplina.
monstrano
alle arti lucrative,
anima. Uomini
di quelli dell
modorum,
le
si
possono imparare
non
vuolc correre
si
ordine del sapere. Coloro che trascurata
1
impresa scientifica. Poiche "omnes artes
istorum
Faversham e
la logica e le altre scicnzc, se
contemporaneamente il
di
di preoccuparsi piu dei beni del
sono del tutto inadatti
di tal fatta
secundum aliquem
inventae sunt
scientiae
et
videlicet
la logica
dividendo
diffiniendo,
8
vel
syllogizando"
e
poiche queste tecniche vengono insegnate dalla logica, e chiaro perche questa non puo essere trascurata e non puo stare se non Nella prima delle Questioni su Porfirio, sia
logica
scienza
o
pratica
razionale.
scienza puramente speculativa
1
primo posto. Autore si chiede se
aver
Dopo
"considerat
al
precisato
naturas et quidditates
propriamente parlando, non considera le risolve la questione, affermando che la logica e intentiones, che speculativa:
mentre
la
che
logica,
la
una
rerum",
res,
sia
ma
le
pratica
quia docet syllogismo operari: docet enim syllogizare, diffmire et dividere et talia. Speculativa autem est. quia omnia ista non docet propter opus; sed propter scientiam; aocet enim logica syllogizare, ut per doctnnam illam possimus nos rectificare in aliis practica,
scientiis.
Nella seconda questione discutendo se dell universale possa esservi scienza,
1
Autore afferma che
la
"scienza
e una conoscenza
intellettuale"
che di tutto cio che e per se intellegibile puo esservi scienza
unaquaeque
scientia
rationis
ab
differt
quoddam commune quod
est
altera: in
ex cognito devenitur ad
quocumque modo
omni
est
tamen unus communis modus
scientia.
cognitionem
Et
hoc
incogniti:
sia
scientiae
e
per
per
est
quod per investigationem hoc enim fit in omni scientia
demonstrativa, sive non demonstrativa. Et gratia illius communis, est in omni scientia modus communis omnis scientiae. Et hie modus est per dicta,
sive
sit
actum
rationis, qui ratiocinatio sive argumentatio est, de cognitione cogniti procedens scientiam ejus quod erat incognitum, secundum quod Isaac in libro de Diffinitionibus (ed. J.T. Muckle, Isaac Israeli, Liber de Definicionibus, XII/XIII (1937/1938) p. in
AHDLMA
321.)
rationem
diffiniens,
dicit
quod
ratio
est
animae
intellectuals
virtus,
faciens
generaliter vocans et large, omne quod secundum intellectum simpliciter, vel quoad nos antecedit ut cognitum, per cujus cognitionem ductu rationis devenitur in notitiam incogniti." La teoria secondo la quale non si
currere causam in causatum.
possono
apprendere
Causam
contemporaneamente
la
scienza
e
il
modo
di
absurdum est simul quaerere scientiam et Aristotele, Metaf. II, 3: Arist. Lat. 2 (Leiden 1976) 39-40. "...
XXV
8
Quaest. sup. Porph. 9
Ibi, 17-18.
cit.
13-14.
essa
si
modum
trova
in
scientiae",
Tine
640
La sua conclusione
dcfinizione sia per dimostrazione.
puo
La prima
Questioni sulle categorie
delle
Simone trova modo
ancora
vicne
causa";
diffinitionem
vel
sostiene che
puo
scientia est per
causam,
12
Poco
avanti
piu
illius
habetur
scientia
"omnis
1
...
per
Autore
esservi scienza di tutto cio intorno a cui accade che
rettamente,
quelle cose circa le quali
che
detto
poi
essa se
causas cognoscimus, et quod
che
ricordato
demonstrationem".
per
possa errare o agire
Viene
"omnis
unumquodque cum
quia scire opinamur 11
affermare che
di
domanda anch
si
Nel corso della sua argomentazione
delle categorie possa esservi scienza.
est
e che dell universale
10
esservi scienza.
perche
puo accadere
affinche
di
scienza
la
o
di errare
qualcosa
e
direttiva
di agirc
si
tutte
rettamente. scienza
esservi
possa
in
si
richicdono tre condizioni: cioe che quel qualcosa sia un ente, che esso sia
che abbia parti che
intcllegibile c
intorno
a
cui
essere
possano
nccessario che cio di cui
abbia proprieta e affezioni che
come
definizione di scienza
ricorda
celebre
la
E
aggiungendo che anche
conosciuto
e
parti.
"habitus
di esso, dal
momento della
propositio
demonstratio quia
se
per
"...
della
acquisitus per demonstrationem", egli
della
dc omni eo quod est 19: Ibi, per diffinitionem, vel per demonstrationem
mezzo
per
e propter
scienza e duplice: quella che
la
la
Occorre infine che
A
dimostrazione.
per
distinzione
E
probativi.
momento che
necessario poi che abbia parti che lo
tutto
possano dimostrare
si
awiene
conoscenza
la
15
un discorso che ha
definizione c la dcfmizione e
che
procedimenti
eseguiti
momento che
dal
proprieta e affezioni
e scienza sia intcllegibile dal
vi
scienza e un abito intellettuale. costituiscano
lo costituiscano e
intellegihile
potest
quid,
acquista dcr
si
esse
scientia
vel
...".
Quest, 12
s.
libro Praed.
cit.
261.
Ibid. Ibid.:
scientia
"De
enim
omni eo de quo est
directiva
in
recte; ideo ^
rccte
et
agere
quae contingit errare
et
esse
potest recte
agere;
scientia;
sed circa
et
est nisi coordinatio
coordinare autem
supra;
circa
recte agere; idco etc. Minor probatur, quia praedicapraedicahilium [probabilium Ottaviano] secundum sub et praedicamenta secundum sub et supra contingit recte et non
praedicamenta contingit errare
mentum non
errare
contingit
hiis
etc."
hoc enim quod de aliquo possit esse scientia tria requiruntur, ens et quod ipsum sit intelligibile et quod habeat partes constituentes ipsum, proprietates et passiones quae possunt probari de hoc". Per il concetto secondo cui si puo avere scienza solo di cio che e, cf. Aristotele, Anal. Secondi, 263-264:
Ibi,
scilicet
71b25-26:
OUK
"Scientia
ideo
"Ad
quod ipsum
scibile
intellegibile",
ccrrc
sit
TO
quidam
esse
oportet Quaest.
^T)
s.
ov
crtt crrcartfat; Categ. 7b23-8al2.
habitus
intellectualis
intellegibile;
libro Praed.
cit.
et
est;
ideo
263-264.
est
illud
enim
de quo
perfectio est
intellectus;
scientia
oportet
et
esse
Simone
Faversham
di
641
e le scienze
dimostrazione propter quid e quella che si acquista per dimostrazione Per mezzo di quest ultima constatiamo che la cosa e cosi, non l(>
quia.
risaliamo
causa 17
sua
alia
dimostrazione
e
ma
scienza
la
accontentiamo
ci
propter
ci
quid
di
sapere
danno invece
\"oti
le
.
La
cause,
di risalire al dioti\
permettendoci Nel commento
Simone da una errata etimologia
Tractatus
ai
termine scienza, quando a proposito della parola logica
del
scrive:
uno modp loyca
dicitur a logos, quod est sermo, et ycos scientia quasi rationatis scientia; et per istam interpretationem est una de sermocinalibus scientiis et extendit se ad trivialem scientiam. Alio modo dicitur a logos grece, quod est ratio latine, et ycos scientia, quasi rationalis scientia, aue est directiva rationis alicuius, que est propria operatic hominis.
Simone
riporta
opinione di Alberto secondo
1
cui:
comparantur ad loycam sicut idiota ad sapientem. Idiota enim nescit se errare nee errorem aliorum corrigere. Et ideo dicit alie scientie
quod
aliquis
nescit
sciens
tamen
se
alias scientias preter loycam, ipse scire sicut comburit, nescit ignis
est
sciens,
se
tamen
comburere. Piu oltre spiegando
1
incipit dell
opera
artium et scientia scientiarum ad habens", <
in
di Pietro Ispano,
"Dialectica
omnium methodorum
est ars
viam
principia
Simone afferma:
Scientia nichil aliud nominal
anima
scientiae,
quam quemdam habitum intellectualem Et hoc possumus trahere ex diffinitione ponit Philosophus Sexto Ethicorum quod scientia est
quiescentem.>
quam
5
Ibi, 266: "Scientia est habitus acquisitus per demonstrationem; demonstratio autem duplex est, scilicet demonstratio quia et demonstratio propter quid; et ideo scientia duplex est, quaedam acquisita per demonstrationem propter quid et quaedam acquisita per demonstrationem quia, prima habetur per causam, secunda non."
Cf.
Aristotele,
nesciunt;
(XXV,
hii
Metaph.
(artifices)
I.
1
"Expertes
autem propter quid
2) Metaphysica, transl.
Anonyma
sive
enim ipsum sciunt quia, sed propter quid et causam cognoscunt." Aristoteles Latinus Media ed. Gudrun Vuillemin-Diem, Brill, ,
Leiden 1976, 8 15-16. Idem, Analitici Secondi, 78al3; 78bl2-13; 78b34; 79a2-3, 12, 14-16. La distinzione tra conoscenza quia e propter quid si trova in molti autori medievali e meriterebbe da sola una specifica trattazione. Si veda, per es. Pietro Rossi, classificazione delle scienze in Roberto Grossetesta", in L Homme et son univers au Moyen Age. Actes du septieme congres international de Philosophic medie\>ale, ed. Christian Wenin, Louvain-La-Neuve 1986, II, 648-651; Idem, Roberto Grossetesta, Metafisica della luce, Rusconi, Milano 1986, Introduzione pp. 37^2; vedi anche Graziella Federici Vescovini, che se ne occupa a proposito di Grossatesta e precisa che la scienza subalternante o superiore e quella che fa conoscere secondo la causa sostanziale o il propter quid del fenomeno, mentre la scienza subalternata o inferiore fa conoscere solo il quia, presentandoci la cosa secondo le particolarita accidentali, Vivarium VI (1968) p. 40. "La
18
1
de Rijk,
"On
the genuine
...",
cit.
78.
19
Ibid. Cf. Aristotele, Metaph.: ut cum ignis exurit..." Arist. Lot. cit. vedi Aristotelis Opera omnia, graece et latine, Firmin-Didot, Parisiis 1983, vol. 19 (Metaph. 1,1). "...
8, II,
20;
469,
Tine
642
habitus intellectualis in anima existens verus et semper firmus. Per artem nichil aliud intelligimus nisi quemdam habitum intellectualem ad per applicationem ad opus. Dicitur ars per applicationem mtellectum, dicitur scientia secundum quod quiescit in anima.
E poco
dci
parlando
avanti,
piu
tra
rapporti
la
e
dialettica
le
altre
discipline aggiunge:
Notandum quod quod excelfat omnes
dicitur ars artium scientia scicntiarum ex
<non>
eo
Sexto scientias, Philosophus>
secundum quod Philosophus dicit III De anima, quod organum organorum non quod in dignitate excellat alia organa, quia cor est dignius organum quam manus et similiter caput, sed intelligendum quod maius est organum pro tanto, quia omnibus aliis orgams necessaria ministrat, ut capiti capucium, calceos pedibus, et sic de aliis. Sic dico in proposito quod dialectica non dicitur ars artium pro tanto quod in dignitate excellat alias scientias sed dicitur ars artium ex eo quod aliis scientiis necessaria porrigit et ministrat.
intelligendum,
manus
est
Aliae enim scientiae per dialecticam praeparantur. Quod enim aliae scientiae habcnt modum diffiniendi, dividendi et argumentandi, hoc totum habent per loycam, quia loyca omnia ista docet. Sic ergo
quod
<patet>
Simone
modo
ut
dictum
poi che una scien/a
rileva
in
dialectica
sive
logica
sed hoc
scientias,
dignitate
excellit
alias
est.
dice piu degna di un altra in tre
si
modi: o per la dignita dell oggetto di cui si occupa, come la metafisica che si occupa di Dio; o per la sua tecnica di dimostra/ione; o, infine, procedimenti delle altre scien/e. La logica o perche regola e dirige i
dialettica
6
prima rispetto
altre
alle
scicn/,e,
in
quest ultimo senso, cioe
procedimenti delle altre scienze. E perche regola e dirige 22 la si dice che che logica apre la via ai principi di tutti metodi. i
per questo
i
dc Rijk, cit. 81. Cf. Aristotele, Fisica, VII, 3: T$ -yap Tjpc^ifjcrat K.a.1 CTTTJIXXL TTJV Sul rapportc arte-scienza si veda il 8LO.VOLO.V cnt crracnDat K.a.1 tppovccv Xcjo^cv. in Bulletin de Philosophic medievale 28 (1986) rccente articolo di Helene Merle, 95-133; in particolare le pp. 115-130 dedicate al concetto di arte nel XIII secolo e la "Ars",
bibliografia pp. 130-133.
2*
de
Rijk,
cit.
Ho
modificato
que
ms. della Bibl. Antoniana di Padova Scaff.
e
la
il
testo
dell ed.
de
Rijk,
basandomi
sul
XX 429.
22
Su questa nozione aristotelica della dialettica che leggiamo in Top. 101b3-4: c^cTcurTtKTj 656i e^ct in cui (StaAc^Tttcii) yap oucra Ttpoc; rac, arrourwi t&v ^c&oSuv ap^dc; methodos significa scienza, ecco quanto scrive Simone. "Ad evidentiam istius est notandum quod via nichil aliud est quam medium deveniendi ab ignorantia ad ipsam scientiam. via,
Illud
declare
requiritur etiam
in
naturalibus, quia in via naturali requiruntur
quod non
sit
impedimentum
in
tria,
scilicet
ipsa via, requiritur etiam
quod
ipsa ille
ad potestatem et facilitatem (facultatem?) et valetudinem corporis adveniendi ilium terminum. Si enim via fit opposita et habet pedes (pedem Padova) ineptos, faciliter non potest venire ad talem terminum. Logica enim omnia ista facit, quia per habeat
Simone
Anche
"dialettica
24 metodi".
logica e
la
la
643
e le scienze
Elenchorum troviamo
nelle Quaestiones super libra
sccondo cui speculative
Faversham
di
che conduce a tutte
via
le
altre
la
teoria
scienze,
e pratiche, e che per questo motivo Aristotele dice che essendo arte della ricerca apre la via ai principi di tutti
Anche
concetti che
troviamo,
qui
ma
leggono nella introduzione
si
forma piu
in
alle
sintetica,
gli
23 la i
stessi
Question! su Porfirio. Viene
che chiunque voglia perfezionarsi nelle scienze altissime, quali sono quelle speculative, bisogna che si perfezioni prima nella logica, che e ribadito
il
modo
funzione
conoscere.
"organica"
In
non
ci
maniera ancora piu efficace nel Elenchorum viene affermata la
libro
della logica, in quanto tutto
che essa e ordinata
scienze
25
Quaestiones novae super
alle
proemio fatto
del
stesso
alle altre scienze
a nulla servirebbe
fossero,
il
come la
suo frutto consiste nel
a suo fine.
logica;
di
E
se le altre
conseguenza e
per medium homo devenit ab ignorantia ad ipsam scientiam, ut in
docet arguere (de Rijk; agnoscere Padova). Ex dictis viam habens ad alias scientias, et ideo dicit Auctor quod ipsa logica docet medium deveniendi de cognito ad incognitum, et ipse Auctor optime dicit quod est habens viam ad principia omnium methodorum id est scientiarum. Notandum circa hoc quod dicit principia, quia logica determinat de principiis aliarum scientiarum, ideo nota quod principia duobus modis considerantur: uno modo quantum ad id realitatis quod est in ipsis, et hoc modo metaphysica determinat de principiis aliarum scientiarum. Alio modo considerantur quantum ad id rationis quod est in ipsis et hoc modo logicus determinat de principiis aliarum scientiarum; et declaratur sic: accipias tribus lineis illud habens tres contenta, figura plana, principium: triangulus est
Topicorum Aristotelis, quia omnibus sequitur quod ipsa
ibi
est
<et
hoc>
Quaestiones veteres super libro Elenchorum ed. 24
cit.
27.
Ibi, 27.
ricordi
Si
che Alberto
Magno
ha
insegnato
nel
Trattato
I
intorno
ai
Predicabili
privilegio di essere scienza in se e nel contempo uno strumento per la costruzione di tutte le altre scienze. Essa puo essere paragonata al martello che il fabbro con un arte speciale costruisce nella sua fucina e che, una volta costruito,
che
logica ha
la
serve
a
costruire
scientiarum,
sicut
il
tutti
in
gli
altri
fabrili
in
strumenti:
qua
"Patet
specialis
est
quod logica una est specialium fabricandi malleum: cuius tamen
igitur
ars
usus omnibus adhibetur quae arte fabrili fabricantur", D. Alberti Magni, Logica, Liber I, De Praedicabilibus, Tractatus I, De natura Logicae, cap. I, p. 2 (Ed. A. Borgnet, Paris, Vives, 1890).
Tine
644
organo dclle scienze e sen/a 26 Anche qui di nessuna cosa. conoscenza cssa non si avrcbbc pcrfctta scienza e dcfinita come conoscenza intellettuale.
giustissimo affcrmarc chc la logica e
Pensiamo che darci
c
la
sulla dottrina di
sua prossimita
si
Simone intorno
alle
doltrine
tra
Simone e
maggiore conoscenza dei rapporti potra avere quando
di la
brani che abbiamo sopra riportato siano sufficienti a
una prima informazione mostrarci
a
i
1
di i
Alberto Magno.
Una
suoi contemporanei
si
Simone
la
delle opere di
disporra delle edizioni
alia scienza
-^o
maggior
sono ancora manoscntte.
parte delle quali
Universita di Catania
26
Quaestiones super libra Elenchorum, cit. p. 102: lihrum Praedicamcntorum dicit qucxl philosophia
"lit
in
ista
trcs
advcrtcns Simplicius super partcs
dividitur,
scilicet
in
speculativam, practicam et organicam; partem philosophiae organicam appcllans ipsam non est sui ipsius gratia, scd gratia logicam. lit valdc rationahiliter: organum enim cuiusdam alterius institutum est. Undc ct servus, quia non est sui ipsius gratia sed I Politicoalterius, ideo convenicntcr organum dici potest, ut apparct per Philosophum
rum qui dicit quod "servus est organum animatum homo alterius existcns". Totum autem fructus logicae consistit in hex: qucxl ordinatur ad alias scicntias sicut ad finem. Unde si non essent aliae scientiae ad nihil utilis essct logica, et ideo convenientissimc logica
organum scientiarum
Ibi.
scientia scientiae, sc
et
rei. lit
p. 107: in
se
cum
est, et sine ilia nullius rei
"Dicendum
est
hahetur pcrfecta
notitia."
accipiendo nomcn scientiae, quaelibct quod nulla est communis. Proprie enim accipiendo nomen sunt per cognitio intellcctualis, ipsa erit de iis quae propric
specialis est, et scientia sit quacdam
obiectum principale obiectum intcllectus. Per se autcm ideo proprie accipiendo nomen scientiae, scientia est de rebus et quiditatibus intcllectus
28
est
quidditas rcrum."
Le informa/.ioni piu aggiornate su Simone di Faversham si possono leggere nel vol. Introduction di Simon of Faversham, Quaestiones etc. Si veda in particolare articolo del compianto P. Osmund I^ewry, The Rbbcscn, pp. 1-22. Si veda anche de in Bulletin commentary of Simon of Faversham and Ms. Merton College "Simon of Faversham and Philosophic medifrale 21 (1979) 73-80. Andrea Tabarroni, Durandus de Alvernia on the Science of Logic", Knowledge and the Sciences in Medic\ al Philosophy. Abstracts, Reports from the Department of Systematic ITieology, un codice miscellaneo (Ms di rifcrisce 178, University of Helsinki, VI, 1987, p. Palermo, Biblioteca Comunale 2. Oq. D. 142) contenente un ccrto numero di opere consciuti fra il 1250 e il 1350 circa. In logiche scritte da autori anonimi o scarsamente un commento, finora non noto, all /lrs vetus attribuito nel codice a Durando di Alvernia si trovano dottrine affini a quelle di Simone di Faversham e frequenti richiami a Alberto Magno e Pietro di Alvernia. Questi ultimi due Autori, come e noto sono come hanno fatto rilevare Grabmann e, presenti negli scritti del Maestro inglese, recentemente, Ebbesen (op. cit. in particolare p. 13): "There are also remarkable similarities between other of Simon s and Peter s works; Simon s Quaestiones on Por 1
cit.
1
288",
phyry, for example, share
much
with Peter
s."
MIKKO YRJONSUURI
Obtigationes, Sophismata
Some modern commentators have suggested that
and Oxford Calculators
of the logica
moderna genre of
obligationes
the disputational rules discussed in these treatises
were
followed in disputations de sophismatibus belonging to the curriculum of late medieval universities. 1 This would naturally imply a close connection between treatises on obligations and collections of
sophisms. This connection has nevertheless not been studied carefully. In this paper I will discuss the concepts of casus and positum, which
seem
to
be connected to each other, and which seem to illuminate the
between obligations and sophismata. I will begin from Walter s and William Ockham s treatises on obligations, and then go on to Hurley Richard Kilvington s Sophismata and William Heytesbury s Regulae solvendi relation
sophismata.
1.
Obligations
Treatises de obligationibus disputations.
denied
if
They
ask
the respondent
The answer
discuss
rules
of correct
response in special which sentences should be granted and which is
given a positum which he must hold as true.
to this question
is
given in the form of rules,
whose basic
which follow from the positum must be granted, must be denied and others, called irrelevant, must repugnant propositions be treated in accordance to their truth value. In any case, contradiction idea
is
that propositions
must not
arise.
The
logic of the rules
is
propositional. Often the rules of
2 obligations are discussed by examples and sophisms.
See e.g. Alan R. Perreiah, "Logic examinations in Padua circa 1400", History of Education, 13 (1984), pp. 85-103; C. L. Hamblin, Fallacies, Methuen, London, 1970, pp. 125-134.
For introduction to obligations, see e.g. Ignacio Angelelli, "The Techniques of Disputation in the History of Logic", Journal of Philosophy, 67 (1970), pp. 800-815; Simo Knuuttila and Mikko Yrjonsuuri, "Norms and Action in Obligational Disputations", Die Philosophie im 14. und 15. Jahrhundert. In Mcmoriam Konstanty Michalski (1879-
646
Yrjonsuuri 3
s Obligational disputations in Walter Burlcy structure double with often treatises begin is
respondent
of
4
s
The
suppositions.
by the
both casus and positum
given
and William Ockham
In the
opponent.
the casus are granted only following disputation sentences entailed by the to when they are irrelevant positum. Often the rules force the
with the casus. respondent to grant sentences inconsistent casus certifies the state of statement s to explicit Hurley According
matters behind the false positum.
mean
that casus
a disputation
must be
would be a
in
way
5
Burley
Rather
true.
it
examples show that he did not
s
sets a falsehood as the basis of
from the positum.
different
seems
It
that casus
understood semantically, as describing possible configuration of the truth-values of put forward in the
propositions a certain status for a proposition while positum just gives disputation, indifferent to its truth-value. Ockham follows Burley in this issue.
determining
things
Ockham
to
According
some
concerns
casus
particular
thing
(de
re
6
concerns propositions. particulari) whi\c positio Let me clarify the relation of positum and casus by discussing one a Burley s treatise De obligationibus. Burley gives which it may be granted that "positum is false",
in
sophism presented rule
according
to
although we may
not
that
grant
According to Burley the rule
is
is "p
useful,
false",
p
if
is
the positum.
but not essential to the art of
7
obligations.
Olaf
1947),
Pluta
Amsterdam, Fourteenth
1988,
Studicn
(/.), (Bochumer 191-202; Paul
Spade,
pp.
Century",
Kretzmann
et
al.
(eds.),
Cambridge University Philosophy (CHLMP), A. From the beginning to the "Obligations:
zur
Philosophic
"Obligations:
10),
B.
R.
B.
Developments
Griiner, in the
The Cambridge History of Later Medieval Eleonore Stump, 335-341; Press, pp. Early
Fourteenth
Romuald
Green
Century",
CHLMP,
pp.
315-334.
3
Burley
has
treatise to
Introduction
the
been
Logical
edited
Treatise
by
"De
obligationibus",
part
in II,
his
in The Cambridge Translations of Medical Philosophical Kretzmann and E. Stump, Cambridge University Press 1988.
translation
4
Ockham
logicae (P.
N. Y.,
s
discussion of obligations
Boehner, G. Gal,
The Franciscan
S.
is
Brown
in
An
dissertation
Louvain,
1963.
Texts,
vol.
Partial I,
N.
of his Summa chapters 39-45 of part III-3 (Opera Philosophica 1), St. Bonaventure,
(eds.\
Institute, 1974, pp. 731-744.)
unius casus non obligat sed certificat, et quia possum esse certus de veritate admitti positio que ponit Socratem sustinere vero, et potest pro reliquum oppositorum Burley, op. cit., p. 46. esse album, prius dicto in rei veritate: Socrates est niger
5
"Sed
.",
autem potest esse casus semper re, particulari, positio "Item, unius propositionis indefinitae vel particularis", Ockham, op. cit., p. 735. 7 est falsum, concedi potest haec propositio: de eo "Alia regula est: quando positum est concedendum ipsum esse falsum." Burley, op. cit., p. tamen, quod ponitur, numquam
6
debet esse de
et
de re
Obligationes, Sophism ata
As an apparent where the positum nothing else
which
false",
-
irrelevant
"only
Rome".
positum. In this situation
is
granted in
"
are in
to defend
it
Rome
in
is
fact
in certain way.
Then
You
positum? The
and according are in
Rome
Rome
1.
You
nothing else
3.
are in
positum
is
is
You
proposed
are in
Rome
.
to Burley s general rules
is
false"
if
You
it
should be
should not be
it
are in
Rome
is
the
accepted as possible
assumed
positum
are in
as casus
granted, irrelevant and true
false
granted, true according to casus
only this is positum
5.
the
disputation can be summarized as follows:
2.
4.
if
granted because of the casus. After this it is are in Rome is false". It follows from the two
You
You
"
is
it
is
true and
is
even
false
granted as sequent, but according to the rule discussed
granted that
"positum
is
it
earlier propositions,
a casus Burley assumes that is
it
referring to the positum
positum",
to Burley
proposed that
As
proposed that accordance to the rule because it
You
committed
this is
According
are in
is
is
647
Calculators
objection to the rule Burley imagines a situation "You
the positum
respondent that
is
and Oxford
Rome
is
granted, follows
false
Burley s solution of the sophism is that "only this is positum" must be denied, because it is repugnant. 9 It makes no difference that it is true
The
according to casus. is "
false"
You
and
are in
"
You
Rome
set of propositions
are in is
Rome
false"
and
is
the
"You
"You
are in
positum"
are in
is
Rome",
"positum
inconsistent, since
Rome"
are inconsistent.
we must deny the last member of an According Burley inconsistent set of propositions, when other members are already either accepted as positum or granted when proposed. The sophism is interesting since it shows that Burley thought that to
s
obligational disputation
rules
may
very well be conducted with
full
acceptance
62. o illud arguitur: ponatur te esse Romae; et volo quod nihil aliud sit positum. positum est falsum. Debet concedi per se. Deinde: tantum hoc est positum (demonstrato posito). Hoc debet concedi, quia verum per casum. Deinde: te esse Romae est falsum. Si concedas, concedis de eo, quod est positum, ipsum esse falsum. Si neges, cedat tempus, tu negas sequens. Sequitur enim: positum est falsum, et tantum te esse "Contra
Deinde:
Romae
ponitur, igitur te esse
Romae
est
falsum."
Burley, op.
cit.,
pp. 62-63.
o "Dicendum
Burley, op.
cit.,
est:
negando istam
p. 63.
"tantum
te esse
Romae
ponitur",
quia repugnans
est."
648
Yrjonsuuri
of the fact that the positum defended as true
cannot be connected to modern clear
sequent asserts that antecedent
would
here
be
the
true,
11
The
where p
is
is
only
disputation where
positum. Burley
is
it
to
be
in
his
is
true
procedure
Subjunctive
positum is not assumed answers committed to the
true:
of Burley
many
examples he does grant
s
irrelevant propositions, which are true just because positum
of
falsity
p
not grant anything which logically entails the denial of
the positum, but he may, and in
semantic
s
counterfactuals.
subjunctive
some way assumed
respondent
He may
positum.
from
different
suppositions are in to
procedure since
,
often the respondent must not respond
the positum were true.
if
often differs from the disputation also
10
is false.
As Burley elsewhere remarks,
is
s
Hurley
no one would accept a subjunctive conditional whose con
that
as he
false.
is
subjunctive counterfactuals
the positum
is
but
accepted,
not
is
false.
The
in
the
granted
disputation.
2.
Richard Kilvington s Sophismata
The 47th sophism sophism, as the sophism
Kilvington
s
looks
Sophismata
not formed like Burley
is
contains
sophism
of
like
obligational
contains discussions of the correct rules of obligations, but
it
only
s
obligational sophisms. Kilvington
The sentences
casus.
a
s
proof and the
the
in
disproof are granted as regulated by the rules of obligations supposing that the casus
is
read as a positum}
2
The sophisma sentence seated" (= KJJ). The casus
of this sophism
you know that the king
is
seated,
know
seated"
that the king
Paul
has
Spade
counterfactual
is
not
is
given by Kilvington
and
(=
if
(p -^Kjy)
deberes respondere ac
This sophism
has been
si
Counterfactual
positum esset
discussed
&
Reasoning",
in re
"If
the king
argued that obligations amount to See esp. his "Three Theories
on
know
"You
reasoning.
Kilvington and Swyneshed Logic, 3 (1982), pp. 1-32. "Nee
is
verum",
that the king
the king is
of
account
Obligationes:
Burley, op.
seated,
~p)). Because
theoretical
History
is
not seated, you
(~p->Ka
a
is
of
Burley,
and Philosophy of
cit., p.
53.
by some modern authors considering theory of
Strode on Inconsistency in Obligational E. J. Ashworth, "Ralph forthcoming in Proceedings of Eight European Symposium for Medie\ al Logic and Semantics (Freiburg 24-27 May 1988), (Analytica), Philosophia Verlag; Spade, "Three theories pp. 19-28; E. Stump, "Roger Swyneshed s Theory of obligations", Medioe\ o, 1 (1981), pp. 143-153; E. Stump, "Obligations: pp. 329-332. obligations.
Cf.
Disputations",
...",
A.",
Obligationes, Sophismata
the
king either
know
"You
the
(= Kgp V
seated"
not
king
is
Ka ~p),
formulates
Kilvington sentence.
is
or
is
that
seated,
Calculators
the casus
implies
know
seated or you
and
proof
the
the
With of
disproof
disjunction
the king
that
as Kilvington recognizes.
the
649
this
not
is
disjunction
the
sophisma
13
Let us look
at
first
must be granted that (= ~Ka ~p), because
the proof. According to rules of obligations
"You
it
is
do not know
imply the
(~Ka ~p)
the king
that
not
is
it
seated"
no way inconsistent with the casus. and the negation of its second
true and in
Ka ~p)
However, a disjunction (Kj) v disjunct
and Oxford
first
part (Kj)).
The sophisma sentence
thus
is
proved.
The disproof negation of the
(=
seated"
formulated in similar way. Kilvington connects the
is
first
~Kap)
disjunct,
or
do not know
"You
with the whole disjunction (Kj) v
second disjunct (Ka ~p) is proved. As sentence, we have the disproof.
it
is
the
that
Ka ~p),
king
is
and thus the
inconsistent with the sophisma
Both the proof and the disproof depend on a premise which is granted as true and irrelevant. Kilvington s solution of the sophisma is based on the idea that these reasons are not sufficient. 14 According to Kilvington there are propositions that are true and irrelevant, but must
be denied because they would not be true
According
of
solution
s
the positum
if
the
were
the
sophisma, proof and the disproof must be doubted. sentence should not be granted nor denied, it Kilvington
sophisma 15
However,
dubitanduni)
is
not
remarks
Kilvington
to
equivalent
that
doubtful"
"is
be
"must
true.
irrelevant
Also the
of the
premises doubted.
to
must
doubted"
be (est
dubium).^ Thus doubt whether one
(est
Kilvington is not maintaining that one may be in knows. Instead Kilvington simply points out that often the respondent must respond with doubt to propositions he knows. Kilvington says that 1-3
See Spade, Obligations",
Stump different
"Three
Theories
...",
pp. 144-145 and Stump,
discusses (in
solutions,
but
pp.
19-20;
"Obligations,
Stump,
A.",
p.
"Roger
Swyneshed
s
Theory of
329-330.
"Roger Swyneshed s Theory of Obligations", pp. 146-149) three shows that two of them are rather weak. I omit here these
two. 1
See Spade,
Obligations",
"Three
Theories
...",
p.
22 and Stump,
"Roger
Swyneshed
s
Theory of
pp. 151-152.
1
licet ista propositio sit dubitanda a te, non tamen est concedendum propositio Rex sedct est tibi dubia. Unde iste terminus dubitandum a me Text cited in Stump, "Roger Swyneshed s est superius ad istum terminum dubium mihi "Et
quod
tamen,
ista
."
Theory of
Obligations", p.
151, footnote 27.
650
Yrjonsuuri
the respondent must doubt whether the king to the casus is
It
he knows whether the king important to notice that
followed as Kilvington supposes,
it
is
is
is
seated.
if
Burley
seated, although according
s
of obligations are
rules
not possible to form both the proof
and the disproof of this sophism in the same disputation. The opponent must choose either one of them. Therefore the sophism needs a solution if it
only
must be consistent
a sense defined by Paul Spade as follows:
in
two disputations constructed from the same positum and differing only with respect to the order in which sentences are proposed are such that the respondent is required to concede a sentence in one disputation "No
and
to
deny the same sentence
in
another
disputation."
sense of consistency
is pertinent only to disputations However, where the respondent judges propositions with respect to a fixed model where they are true or false. It seems that Burley did not think that
this
would
positum
fix
of model.
kind
this
In
disputations
obligational
of
Burley propositions are answered one by one with differing criteria for granting them. As Kilvington thinks that the sophisma needs a solution,
he seems to have a different conception of the status of positum
in
an
obligational disputation.
may
It
be
that
Kilvington
s
terminology
is
related
to
this
already noticed, Burley and Ockham made interpretative viewpoint. As between scmantically understood casus and purely the distinction I
inferentially followed positum. easily
follow casus,
According
he knows
if
how
Ockham
to
to
and positum.
Kilvington
positum interchangeably and, Ockham and Burley. If
casus
is
it
seems seems,
to in
some
use
the
it
fixes a
does not
differences between
concepts casus
and
the sense reserved for casus in
a counterfactual supposition about things,
natural to think that
He
follow positum.^
discuss the rules of casus, he just points out
casus
the respondent can
semantic model
or, in
it
seems quite
other words,
some
imagined alternative of the actual world as the basis of the disputation. If
the casus
of Kilvington
s
sophisma
disputation, Kilvington s views
Spade, 1
8
Three Theories
...",
p. 9.
seem
See also
fixes
a
semantic model for the
quite natural. According to the
model
p. 11.
"Sed iste modus opponendi et respondendi non servatur quando ponitur casus, propter quod differt casus a positione. Scito tamen quomodo respondendum est facta et aliqua positione, potest leviter sciri quomodo respondendum est posito aliquo casu, ideo sufficiat pro nunc de positione tractarc." Ockham, op. cit., p. 736.
Obligationes, Sophismata
we
are informed about king
the
king according determine whether
s
we know
Calculators
651
we cannot determine whether seated; consequently we cannot
but
sitting,
model
the
to
and Oxford
is
according to the model that the king
is
seated.
may be
It
that
sophisma discusses rules
this
suggested but not discussed by Ockham. gives rules of obligations different
If so,
it
is
from the rules
Burley and Ockham, because their positum
is
for
semantic casus
quite natural that
it
for
positum given by understood to be followed
only inferentially.
3.
William Heytesbury s Regulae solvendi sophismata
John E. Murdoch has argued in
the
Regulae^ Heytesbury
and he aims
at
is
correct
giving
different kinds of
problems
Heytesbury has metalinguistic strategy concerned with disputational situations,
that
and easy-to-use rules
in disputation.
20
for answering to According to Murdoch these
rules are usually metalinguistic.
Most of the text of Regulae consists of disputational situations in which the rules apparently give wrong response. Heytesbury solves these sophisms one by one in order to show that his rules are valid in any situation.
purpose
Heytesbury also gives some clear examples of his rules, but the the discussed sophisms seems to be providing apparent
of
of
counter-examples
his
rules.
Most of
the
considered
sophisms
are
formed by imagining a casus involving some limit-decision problem. It has often been pointed out by modern commentators that casus may according to Heytesbury be impossible in nature, if it only is free from 19
See
e.g.
John.
E.
Murdoch,
"Prepositional
A
Analysis
in
Fourteenth-Century Natural
Case Study", Synthese, 40 (1979), pp. 117-146; "Scientia Mediantibus Philosophy: Vocibus: Metalinguistic Analysis in Late Medieval Natural Philosophy", Sprache und Erkenntnis im Mittelalter, Akten des VI. internationalen Kongresses fur Mittelalterliche Philosophic
der
Societe
Internationale
August-S.September 1977 in
Bonn,
pour
L Etude
(Miscellanea
de
la
Mediae\
Medievale 29. Walter de Gruyter,
Philosophic 13/1),
Berlin, 1980, pp. 73-106.
20
I have used the 1494 edition by Bonetus Locatellus, Venice, of many of Heytesbury s works. The prologue and first chapter of Regulae solvendi sophismata has been translated by Paul Spade (William Heytesbury, On "insoluble" sentences, (Mediae\ al Sources in Translation 21), Pontifical Institute of Mediaeval Studies, Toronto, 1979). Heytesbury states the aim of his work quite explicitly in the prologue (f. 4va in the
1494 edition, pp. 15-17 in Spade s translation).
652
Yrjonsuuri
contradictions.
21
As an imagined
casus
allowance
the
gives
basis
for
putative
natural logically possible counter-examples, impossibilities shows that Heytesbury s rules must hold in any logically possible casus. This brings the rules nearer logical than physical truths. the
of
In connection to obligations the metalinguistic character of the rules
suggests that Heytesbury would be leaning towards Burley rejecting Kilvington
22
revisions.
s
seems
In fact, this
to
s
theory and
be the case. The
chapter on epistemic logic in Regulae argues against Kilvington s views. When commenting on obligations Heytesbury almost explicitly restates s
Burley
and Ockham
now
Let us
s
23
theory.
turn to one of the epistemic sophisms of Heytesbury as
an example. This sophism est Socrates", which
tries to
You both doubt and know
prove that with
repugnant Heytesbury s general rule what doubts. one Heytesbury gives his stating that no one cannot know
"hoc
casus as follows:
is
24
[A] Ponatur quod [1] tu scias quod hoc nescias tu quod hoc sit Sor, |3] scias
sit
hoc, demonstrato Sor,
[2]
tamen quod hacc propositio hoc est hoc significat precise quod hoc est hoc, J4J et etiam quod ista propositio Tioc est Sor significat precise quod hoc est Sor. [B] Sit enim Sor coram te, quem scias esse homincm, et nescias ipsum et
esse Sortcm. It
is
very interesting to notice that this casus
A
(above marked by
and B).
A
seems
divided into two parts
is
to give a
of propositions (1-4),
list
which are posited (ponatur), while B describes a situation. However, part B is not referred to in the discussion, it seems to serve only the purpose of making
more
The problem
understood.
by
the
how
clear
four
propositions
the
four propositions in part
A
are to be
sophism is to determine what is implied part A. Heytesbury uses quite often the
in the in
phrase sequitur ex casu. and the Enterprise of Science in the I,ater Middle "Philosophy Y. Elkana (ed.), The Interaction between Science and Philosophy, Humanities Press, 1974, p. 69; Edith D. Sylla, "The Oxford Calculators", CIILMP, pp. 557-558 and Curtis Wilson, William Heytesbury. Mcdie\ al Logic and the Rise of Mathematical Physics, (University of Wisconsin Publications in Medieval Science, 3), Madison, 1956,
John
Murdoch,
in
Ages",
p. 24-25.
However,
must
it
be
noticed
that
uses
Heytesbury
the
word casus
in
a
way
terminologically nearer Kilvington than Burley.
Heytesbury, chapter
De
Ashworth,
De
scire
"Ralph
sensu et
et
composite
dubitare,
Strode on
..."
ff.
diviso,
13vb-14ra
and Stump,
f.
and
"Roger
4ra-rb; f.
Swyneshed
pp. 153-163, esp. p. 162, footnote 36. f.
12va-vb. Solution of the sophism
is
found
in
f.
Regulae solvendi sophismata, See also discussions in
16va.
15ra-rb.
s
Theory of
Obligations",
Obligationes, Sophismata
s
Heytesbury suppositions
Ockham
made
used with positum, the
In
treatises.
s
to
obligation
resembles
casus
two-part
often
in
and Oxford Calculators
obligational
Burley
s
treatise
very
much in
disputations
the
653
the
two-part
Burley
word ponatuf
is
and
s
typically
with those propositions which the respondent has
i.e.
grant.
Heytesbury
s
words
enim"
"sit
belong also to
s terminology connection to casus. Heytesbury s discussions in his sophism concern to problem of determining what follows from part A of the casus. Heytesbury s procedure is analogous to obligational reasoning in Burley s and Ockham s
in
Burley
treatises.
Heytesbury in
propositions
part
everything
grants
A
which
propositions do not imply that something
is
from
follows
show
of the casus, and tries to
the
four
that these four
both known and doubted.
one important difference between Heytesbury s However, sophism and obligational disputations of Burley and Ockham. In there
double
the
proposition
the positum
disputations
obligational
casus:
is
given
structure
as positum
of
is
inconsistent
typically
suppositions
must be deemed
is
built
false
so,
with
the
that
the
according to the
s sophism we can see the double structure, but the two parts of casus are consistent. Actually what is posited (ponatur) must be evaluated to be true according to the de re -part of the casus. Heytesbury s sophism does not proceed in the
semantically understood casus. In Heytesbury
standard obligational way.
sophisms irrelevant propositions, which are from the positum, play an important role. Most logically independent obligational sophisms of Burley are based on problems arising from In typical
obligational
different order of putting forward propositions. The order is important because a proposition answered according to the reality (or casus) early in the disputation might have got different answer, if it had been put
forward only
later,
when
it
has
become
relevant due to earlier answers.
the above discussed sophism by Heytesbury such problems of order do not occur, since the whole disussion is based on propositions, In
which must be similar
way.
If
classified this
relevant.
feature
can
Most of be
his
sophisms are
generalized,
it
built
suggests
in
that
obligational sophisms could be distinguished from the standard sophisms
simply by the role of irrelevant propositions. While standard sophisms of sophismata-colleciions as well as obligational sophisms used the idea of
basing the disputation on assumptions, obligational theory specialized on
654
Yrjonsuuri
situations
where the
ly irrelevant to
of the assumption clashes with truths logical
falsity
the assumption.
Conclusion
From
the discussed examples
between
and
realistic
it
linguistic
seems
safe to conclude that distinction
suppositions
understand details of the logic used both
The
distinction
is
very clear
in
in
is
necessary
sophisms and
in
order
to
in obligations.
obligations treatises, but can be found
also in sophismata-lilCTature.
some theoretical disagreements between different medieval more intelligible through making this distinction. become authors Kilvington s much discussed revisions to the obligational rules seem to be Also
based on such difference
interpretation of positum. Also Kilvington
in
different views
on some
issues of epistemic logic can
and Heytesbury reduced to differing interpretations of casus. The above considerations give some s
obligations
could
serve
ideas are present in the
Nevertheless
it
seems
as
a
methodology
way casus
is
support for
handled
to
the
idea
s
be
that
sophismata. Obligational
in the
clear that obligational theory
is
discussed examples.
not limited to the
purposes of sophismata. Obligations were an independent logical genre with
its
own problems.
University of Helsinki
INDICES
Index of Manuscripts
AVRANCIIES
Biblioteca Na/ionale Centrale
Bibliotheque municipale 226
II. II
BAMBERG Staatsbibliothek Class. 40
276
190
KARLSRUHE
BASEL Universitatsbibliothek
281
Conv. Soppr. D.IV.95 91-96 Conv. Soppr. I.X.30 550, 551, 637 Biblioteca Riccardiana 916 98
B.V.77
327-329 183
F.II.25
627
B.II.21
Badische I^andesbibliothek 106
43
KRAKOW Biblioteka Jagielloriska 2602
408
BERN Burgerbibliothek 61
Bibliotheek der Rijksuniversiteit I lebr. Warnero 42
CAMBRIDGE Gonville and Caius College Library 281 (674) 385
98
1253 1356
lat.
lat.
279 419, 421, 422
25, 33-42
LONDON
56 British Library
CHARTRES
Add. 22,719
27 43
Harley 3095
Bibliotheque municipale 90
43
CUYK EN ST. AGATI IA C
Universitatsbibliothek
26 98
II. IV.13
Kruisherenklooster
566, 572
LEIPZIG
181
Peterhouse College Library 158 Trinity College Library B.I. 29 R.15.16
University Library
LEIDEN
149
12
Biblioteca
12, 13, 16-18,
MILANO G 108
Ambrosiana
100
inf.
22
MONTECASSINO DIJON
Archivio dcll Abbazia 332
Bibliotheque municipale (Bibliotheca Publica Collegii Divio-Godranii) 441
152
MUNCHEN Bayerische Staatsbibliothek
EDINBURGH National Library of Scotland
Adv. 18-6-11
98
Clm 183 57 Clm4603 279 Clm 14557 276
27
NAPOLI
ERFURT
Biblioteca Nazionale
Wissenschaftliche Allgemcinbibliothck der Stadt Amplon. 335
Amplon. F.133 Amplon. F.239 Amplon. 0.67
lat.
VII.B.25
328
lat.
VII.G.98
326, 328
103
374 64, 65
627
OXFORD Bodleian Library Auct. D.2.1 2312 Canon.Class.lat.278
Canon.Misc.219
FIRENZE Biblioteca Medicea Laurenziana Strozz. 99 S.
Croce, Plut. XII
553, 637 sin.3.
419, 420, 422, 423
Digby 76 Digby 108 Digby 221 Lat.misc.e 79
101
408 410 56 102
97 410
Index of Manuscripts
658
Laud. lat. 67 Seldcn sup. 24 Balliol College Library 36 Mcrton College Library 288 Oriel College Library 15
387
184, 185, 386,
104
TROVES
101
Bibliotheque municipale 269 1101
327 279
644
1381
279
104
VATICANO
PADOVA XX 429
Biblioteca Antoniana Scaff.
642
(CITI
A DLL)
Biblioteca Apostolica Vaticana Barb. lat. 10
Borgh.
lat.
36
98 190, 193
PALERMO Biblioteca
Comunale 2.
Oq.D
142 550,551.644
PARIS Bibliothequc Nationalelat. 6626 lat. 11860
26
lat.
14570
68 325
lat.
14700 15819
486
lat.
lat.
15859 15887
lat.
16170
lat.
16617
lat.
104
327 373 419 445
PARMA
WIEN Osterrcichischc Nationalbibliothck
VPL4998 20,22 VPL5437 13,22 393 VPL5454
Biblioteca Palatina hebr. IIv.67 2723
(Dc Rossi 805)
569
WOLFENBUTTEL Hcr/.og August Bibliothck 83.27 (Aug. 2) 57
SALAMANCA Biblioteca dc
la
Univcrsidad 1735
410
Index of Names
Achinstcin, P. 172, 178
Adam Anglicus 479 Adam Balsamiensis Parvipontanus 98, 104 Adam Wodeham 180, 181, 185-188, 201, 257,
258,
263,
373-381,
325,
264,
383-
388, 391, 479, 574
Adams, M. McCord
172,
178,
201,
262,
42,
104,
264, 351, 355, 362, 409, 613
Adclardus dc Bath 334, 337
26,
27,
30,
Romanus 55, 103, 250, 325, 366, 342, 344-350, 483, 485-490 Aertsen, J.A. 224 Acgidius
Anthcmius 151 Antonius Andreae 325 Antonius de Parma 192 Apollo 42 Apollonius (grammaticus) 39 Apollonius Pergaeus 41 Apulcius Madaurensis (Lucius) 41 Archytas 41, 141 Arico, G. 44 Ariew, R. 322 Aristaeus 41 Aristarchus 39 Aristoteles
4,
12,
5,
15-20,
13,
22,
23,
56,
58,
Aetius 27 Agncllus de Ravenna 99 c al- Alawf, G. 309-310
27,
28,
32,
39-41,
60,
65,
72,
77,
100,
103-105,
106,
110,
119,
121,
125,
Alamannus, C. 210,211,217
127,
130-136,
140,
141,
143,
144,
148,
Alancn, L. 222, 226-228 Albcricus de Remis 113, 115 Albertus Coloniensis (Magnus)
151,
152,
56, 119, 325, 344, 347, 638, 641, 643, 644
Albertus
de
427-430,
Saxonia 432-435,
408,
410-413,
512-517,
519,
273,
286,
300,
415,
322,
323,
589,
349, 352, 355, 373, 377, 378, 387, 390, 391,
325-328,
392-394,
424, 437, 440,
307-311, 313,
342-346,
330,
398-402, 448,
271,
304,
416,
417,
421,
507, 538, 565, 566, 568, 570, 571, 576, 577, 609, 610, 614, 615, 620, 637, 638,
640-643 Aristoteles (Pseudo-) 153
Arnaldus de Villanova 69 Artus,
W.
3
Asclepiades 48 E.J. 407-409, 412, 592, 593, 595, 597, 648, 652
Augustinus
Alonso, M. 56,58,62,311 Alphonsus Vargas Toletanus 325 Amici, B. 144 Amm, U. 309
437,
50,
119,
248,
249,
257, 260-263, 277, 281, 283, 459, 479, 480, 535-548, 558
294,
366,
(Aurelius)
127-132,
134,
45,
136,
49,
Augustinus Triumphus de Ancona 327 Auroux, S. 624
46, 421
Austin, J.L. 501
Anawati, G. 273
Baccin, N.A. 416
Andronicus 41 Anfredus Gonteri 325
Badawi, A. 268 Back, A. 217
500, 645
Baeumker, C.
Angelus dc Arctic 631 281,
248,
590,
168,
120,
119,
348,
450, 479-481, 506,
Ashworth,
Cantuariensis
170,
251,
266-269,
Allen, J.P. 103 Almagno, R.S. 23
256, 282
169,
231,
299,
c
Anselmus
163-167,
227-229,
94-96,
256,
105
Ammonius Hermiae Amphion 42
90,
294,
A1I ibn al- Abbas 30 A1I ibn Ridwan 99
I.
88,
255,
(sh>e
Angelelli,
87,
54,
288,
Alexander Aphrodisiensis 41, 53, 134, 347 Alexander de Hales 160 Alexander Neckham 97-99 Alexander Sermoneta 438, 443 Alfanus Salcrnitanus 99 Alfredus Anglicus de Sareshcl) 104, C
161,
223,
53,
252,
58,
612 Alcuinus 455,461,558 Alexander de Alexandria 325, 327
C
160,
222,
190-195,
81,
46,
56, 146, 148-151,
Baldwin, J.W. 98 Bannach, K. 298 Barach, C.S. 291
286
325,
Index of Names
660
Bonifatius VIII papa (Benedictus
C.G. 302
Bardili,
Caietanus) 298 Bonner, A. 3,4,8 Bono, J.J. 286 Boole, G. 493, 494, 496, 500 Borgnet, A. 344,638,643 Bos, E.P. 12. 13,15,16.23,418
119
Bartel, T.
Bartholomaeus dc Brugis 551 Bartholomacus Salernitanus 98,
104, 105
Baswell, C. 26 Baur, Ii. 55-59
Baur, L. 25 Bazan, B.C. 127, 135, 137
Bottin,
Bcckmann,
ihn Mar/.ban 266
Bcierwaltcs, W. 462, 558 Bekkcr, I. 153
Brchicr.lv 109, 110 Brennan, R.E. 251 Brewer, J.S. 107
Bcllissima, G. 538
Bel us 40
Bridges, J.H.
107,263 Brind Amour, L. 623 Broadie, A. 496,500
Bcnekc, F.H. 492, 500 Iknjamin, A.S. 249 Benson, R.L.
504
27, 97, 98,
Brown,
Beonio-Brocchicri, M. 324 Bernardus Carnotensis 504 Bcrnardus Claraevallcnsis 331
Bernardus 329 Bcrnardus
323,
Ix>mbardi
J.
328,
1..
333
Silvestris 97,
Billow,
Blumenhcrg,
II.
290
533 228,
449, 481,
231,
328,
482, 501, 514,
Boethius (A.M.T. Severinus)
410, 516,
25,
27,
29,
31-33, 41, 43, 44, 47, 52, 60, 71-74, 77, 84,
85,
87,
248,
249,
95,
252,
100,
155,
181,
Cassircr,
275,
366,
Cassola,
325
Boncompagni, B. 27 Bonetus Locatellus 651
302
598 Celaya, Juan de 590, 594, 595, Chalcidius 66, 104, 147 Charlesworth, M.J. 248 Chatelain, A. 301
Chenu, M.-D.
Boler, J.F. 351, 354, 355, 509 111,
II.
M. 49
Charma, A. 331
Bogdan, R.J. 202 Boh, I. 436, 626, 629 45,
Carreras y Artau, J. 5 Carreras y Artau, T. 5 Cassiodorus (Havius Magnus Aurelius) 43-52, 558
103,
367, 416, 418, 440, 455, 457, 462, 465, 467, 481, 612, 626 Boethius de Dacia 140, 192, 426, 636
Bonaventura
Ifiienis 438 Canguilhcm, G. 106 Cappuyns, M. 463, 558 Carnap, R. 451,452,623 Caroti, S. 225
Caietanus dc
Parma 286
517, 521, 522, 532, 626, 627, 628, 646
225,
306
J.
294
Buytaert, I-.M. 263,521,628 148,
Bochenski, I.M. 437 198, Boehncr, Ph. 442,
(i.
Bussc, A. 46,270 Butimer, C.I I. 6
Blackwell, R.J. 163 Blasius Pclacani de
222,
273
I.
Burchardt, J. 146-149, 151, 289, 290 Burge, K.R. 460 Burgundius Pisanus 99 Burnett, C.S.F. 25, 26, 32
138, 139, 140, 142, 145
Birkenmajer. A.
80-82,
228, 263, 328, 352,
Bultot, R. 281
457
427,429 Bielcr, L. 462 Bird, O. 626
)
Bruns,
Bucheggcr,
J.
437
181,
Bruselas, Jorge dc 593
Bcrtrandus de Alemania 323 Belt, H. 463 Bianchi,
89,
646 326,
325,
Bernstein, R.J. 510
Biard,
S.F.
355, 410, 482, 501, 610, 612, 614, 615,
Bernard, C. 161 Bcrnier,
319, 408, 409, 412, 589,
Bouyges, M. 309, 312 Braakhuis. II.A.G. 418 Brands, H. 445
Bcdoret, H. 58
Bchmanayar
144,
Bourke, V. 163
264,521,522
J.P.
F.
591, 598 Bourgne, R. 68
Bcaujouan, G. 62, 66, 586 Bcccaria, A. 62
130,
155,
159,
255,
110, 170, 333, 338
Chisaka, Y. 155 Chrysippus 41
Church, A. 213
Index of Names
Cicero
(Marcus Tullius) 108-110,
103,
267,
39-41,
27,
305,
504,
535,
60,
536,
539, 540
Diels,
110
Cirlot, J.E.
Colish, M.L. 455, 456, 463
542
Conrad us de Ebrach 325 Conradus de Soltau 325 Constable, G. 27, 97, 98, 504 Constantinus Africanus 27, 98, 99,
Contreni,
Conway,
30,
32,
62,
286 J.J.
97
Donat,
271
Cordier, B. 458
Cordoba, Alonso de 598 Corvino, F. 260,262,264 Costa ben Luca vide Qusta
110
I^aertius
62,
63,
68,
100,
101,
100,
101,
b.
Luqa
Courcelle, P. 46
Courtenay, W.J. 574, 628
139,
143,
184,
J.
270
S.
d Ors, A. 468,590 Dronke, P. 32, 275, 278, 333, 504 Dubislav, W. 270 Duclow, D.F. 463 Duffy, J. 100
Couloubaritsis, L. 163-166
228, 328,
Duhem, P. 138, 322, Dunchad 97,461 Dunya,
Cranz, F.E. 461 Cresswell,
265
483,490 Donatus (Aelius) 39 d Ooge, M.L. 457 Donati,
Corax 40 II.
307,343
113
Copernicus, Nicolaus 138, 176-178 Copleston, F. 4 Corbin,
1
39, 248, Dionysius Areopagita (Pseudo-) 458, 459, 462, 463, 558 Diophantus Alexandrinus 27 Dioscurides 98 Dobsevage, A. 479 Dod, B.G. 27, 28, 95 Dodds, E.R. 458 Dolbeau, F. 43 Dominicus Gundissalinus 25, 26, 32, 53,
55-59,
4
P.
II.
Diogenes
Cleomedes 141 J.
51
Diodorus Cronus 223
Clarke, S. 141 Clavius 106
Collart,
J.
Dieterici, F.
M. 319
Clagctt,
Dewcy,
Diehl, E. 458
S.
325, 327, 331, 342
271
Durandus de Sancto Porciano
M. 578
vide
Guilelmus Durandus de Alvernia 644 Durling, R. 99
Dahan.G. 25 d Alverny, M.-Th. 27,58
Damascius 343 Dancy, R.M. 215 Daniel Morleius 56 Davidson, D. 623 Davidson, H. 566 Davis, L.D. 187 Day, S.J. 532 de Andres, T. 262,264
DeBoni, L.A.
S. 74, 417, 418, 423, 437, 551, 555, 557, 633, 637, 638, 644
Ebbesen,
Eckermann, W. 187 Eco, U. 261,264
Eduardus Upton 202 Elkana, Y. 651 Enders, H. 446, 549 Endres, J.A. 463
Ill
Engelhardt, P. 294, 297 Englert, L. 62
Decarie, V. 72 Delhaye, P. 141
D Elia,
F.
43,
Eratosthenes 41
46
Erdmann,
de Libera, A. 82, 418 Del Punta, F. 342, 409, 410, 417, 549, 638 Demetrius 286 Demosthenes 40 Denifle, H. 301 Denomy, J. 314 de Rijk, L.M. 13, 24, 94, 202, 212, 215, 407, 418,
437, 446,
584, 591, 604,
641, 642, 643
Descartes, R. 106, 107, 110, 479
638,
B. 492,500
Espinosa, Pedro de 597 Esser, C. 155
Etzkorn, G. 263, 324, 616 Euclides 27,36,41,285,286
Evans, G. 353-356,360 Evans, G.R. 25 Fakhry,
M. 309
al-Farabl,
Abu Nasr
62, 68-70, 265, 309,
al-Farghani 32
25,
312
32,
53,
55-58,
Index of Names
662
Favonius Hulogius 459 Fcderici Vescovini, G.
258. 264, 285, 286,
Glorieux, P. 324, 364, 366
641
Goddu, A. 171,234-237,351,358-360
Flatten, H. 277, 331, 340 Floss, H.J. 563
Fodor,
Gilson, E. 106, 108, 129, 351, 558 Ginters, R. 306
Godefridus de
Fournier, P. 323 Frachantianus de Vicenza 438 Franciscus Assisiensis 155-162 Franciscus de Marchia 195, 325
Franciscus de Mayronis 323, 325 Franciscus de Trivisio 257
Grabmann, M.
Frcdhorg, K.M. 74, 263 Frcddoso, A.J. 481,482 Frcdegisus Turonensis 456 Frcge, G. 451, 453, 492-501, 622
Grant,
323,
338,
445,
139,
138,
141,
142,
144,
175,
349
180, 185, 257, 264
Gratarolus, G. 334, 337, 339 Gratiadeus lusculanus 55
31,44,457
Green, R. 248, 468, 582, 646 Green, W.M. 100 Green-Pcdcrscn, N.J. 408, 440, 626
185-187, 228, 263, 328, 352,
180,
479,
410,
38,
133, 286,
E.
Grassi, O.
Gabriel, G. 501
646 Galenus
148,
176, 178, 315, 317, 322, 327, 342,
Funkenstein, A. 145, 175, 178
354,
94,
Gracser, A. 267
Friedberg, A. 89
Gal, G.
325,
Gracia, J.E. 394
S.
Friedlein, G.
226,
520,549,558,631,637
305 Fridh,A.J. 44 Freud,
197,
489 Goichon, A.M. 65, 133 Goldstein, H.T. 309 Gomez Caffarena, J. 368 Gonzalez Palencia, A. 69 Gorgias 40
M. 27
Folkerts,
Fontibus
364, 368, 370, 375, 388, 483, 484, 486,
354
J.
62,
482,
501, 515,
67-70,
98,
99.
610,
612,
104,
130.
290
G. 145, 177, Gambatese, A. 615 Galilei,
178, 215, 230,
483
Garber, D. 171, 178 Garcia Ballestcr, L. 69 Gaskin, J.CA. 306
187,
Grignaschi, M. 53 Groblicki, J. 365 Griiner, B.R. 645
Gualterus dc Brugis 325 Gualterus Burlacus 195, 229,
Gasquet, F.A. 108, 109 Gassendi, P. 140, 143 Gaunilo 248 Gauthier, R.A. 135, 263 Geach, P.T. 213, 215 Gentile, G. 302-304 Gcntilis de Cingulo 549-557, 631-637 Gentilis de Fulgineo 69 Gentzen, G. 629
Gerardus Cremonensis
X
papa 148, 149 Arimincnsis 184, 180, 188, 257-264, 325, 593 Gregorius Nazian/.cnus 463 Gregory, T. 45, 275, 277, 281, 283
Gregorius Grcgorius
28, 53, 55, 56, 58,
67-69
344, 374, 386, 388, 407, 410, 438, 442, 449, 468-
478,
582,
586,
645-648,
626-629,
592,
650-653
Gualterus de Chatton 323,
373-379,
325,
180,
183, 201, 258,
381-390,
479,
525,
526 Gueroult, M.
106
Guilclmus 27, 42 Guilelmus de Alvcrnia 119,294 Guilelmus Buser 408,410,414-415 Guilclmus de Conchis 25, 66,
97,
102,
Gerardus Odonis 325, 328 Gerardus de Senis 325
104,113, 115,275-284,331-341 Guilelmus Crathorn 183-186
Gersh, S. 455,458,459,461,463 Gersonides vide I^vi b. Gerson
Guilelmus Durandus de Sancto Porciano
al-Ghazali,
Abu Hamid
55, 104, 312, 313
Ghisalberti, A. 324
27
427,
428,
430,
651-654
Guilelmus
de
Mara
(si\
e
de
Lamara)
325, 364, 366-368 (sive Pictavicnsis)
25,71,88,101,113,347 Gillispie, C.C.
Hentisberius
434, 480, 586, 589, 593, 597, 598, 645,
Giacone, R. 44, 504 Gianotti, D. 44
Gibson, M. 465 Gilbertus Porretanus
323, 325
Guilelmus
Guilelmus de Moerbeka 314
148,
149,
285,
Index of Names
Ockham
Guilelmus de 94,
141,
183,
185-188,
229,
231-239,
178,
179,
180-
196-205,
209,
227-
A. 30 R.M.T. 89 Hilpinen, R. 438
323-
Hintikka,
14-16,
171-174,
161,
195,
257-264,
325,
327,
328,
386-389,
330,
351-363,
378,
379,
433,
479-482,
516,
519,
521-525,
527,
529,
565,
566,
579-581,
586,
597,
410,
21-23,
298-301,
431,
417,
491-501,
374,
89,
375,
418,
430,
512,
514,
532-534,
609-617, 618-625, 626-628, 645, 646, 650-653
Guilelmus Petri de Godino 325 Guilelmus de Rubione 325 Guilelmus de Sancto Theodorico 280, 331, 334-337, 340 Guilelmus Shirovodus (sive de Shyreswood) 94,
430,
445^154,
518,
520,
582,
J.
Hacking,
I.
L.
491,
492,
494,
495,
Hill,
J. 201, 202, 204, 208, 215, 222, 231, 236, 238, 416, 576
Hippocrates 99,100
41,
57,
58,
62,
67,
98,
Hocedez, E. 250
Hoffmann,
184
F.
Holder, A. 43 Holtz, L. 44
Honnefelder, L. 521,529,532,534
497,
Hubien, H. 438,443 Hudson, A. 360,361 Hughes, G.E. 578 Hugo Benzi 67 Hugo de Novocastro 325, 327 Hugo de Sancto Victore 4,
6,
25,
57,
58, 61, 62, 100, 113
171,178
Hugolinus de Orvieto 264
Hackstaff, L.I I. 249 Haring, N. 71,275,504
Hugonnard-Roche, II. 25 Humbertus de Prulliaco 325
Hagendahl, H. 44
Hume, D. 293,306
Ilalleux, R. 64
Hunain ibn Ishaq
Hamblin, C.L. 645 Hannibaldus de Hannibaldis 325
Hunt, R.W. 25,
Harming, R.W. 65 Hanson, N.R. 172, 178 Harkins, C.L. 23
Hartshorne, C. 509
Harvey, E.R. 26 Haskins, C.H. 34,98 Hay, W.H. 302 Hayduck, M. 273 Hedwig, K. 286 Hegel, G.W.F. 128
Heiberg, J.L. 28,152 Hcndley, B. .502,505,507 Henle, R.J. 249
Henri d Andeli 97,98 Henricus de Gandavo 19, 90, 226, 323, 364, 366-372 Henry, C. 26 Henry, D.P. 215 Hermagoras 40 Hermannus de Carinthia 28,32 Hermes 32 Hermes, H. 501 Herodianus 39 IIerren,
66,
212,
Hirschfeld, T. 148 Hissette, R. 138, 318, 329, 549, 631, 637 Ilobbes, T. 534
Hrabanus Maurus 104
129
Ilaaparanta, 501
Ililka,
592,
599-605, 608 Guilelmus de Ware 325 Guilelmus Varignana 631
Guitton,
663
M. 461,462
Hervaeus Natalis 323,325 Heyer, G. 446 Heynck, V. 366
63, 67, 68,
285
26, 97, 100, 101, 103-105
Hutchins, R.M. 505, 506, 508, 511
lacobus de Losanna 325 lacobus Metensis 325 lacobus Venetus 437 Ibn Adjurrum 272, 273 Ibn Badjdja, Abu Bakr (sive Avempace) 309, 310, 345 Ibn Da ud, Ibrahim 32 Ibn Gabirol, Salomon (sive Avicebron)
248
Abu
Ibn al-Haitham,
c
Al!
(sh>e
Alhacen)
152, 285-288, 292
Ibn Masawaih, Yuhanna 63, 64, 66, 68, 99 Ibn Masawaih (Pseudo-) 70 Ibn Rushd, 64,
70,
297,
Abu
al-Walld (sive Averroes)
133,
135,
191-195,
266,
294,
309-313,
344-348,
434,
479,
300,
565-572 Ibn Sab
c
m
Ibn Sina, 59,
53
Abu
61,
65,
265, 266, 480, 521
AH
(sive
Avicenna)
69,
119,
133,
135,
136,
272-274,
285,
294,
268-270,
Ijsewijn, J. 103 Inciarte, F. 524
loannes 27,42
C
58,
Index of Names
664
loannes loannes loannes loannes 142,
Alexandrinus 100, 102, 103 Baconthorpe 325 de Bassolis 325, 327 Buridanus 12, 18-20, 22-24, 175,
144,
195,
179,
225,
Johnson, R. 460 Jolivet, J. 25,71,82 Jung, C.G. 110 141,
432^35, 438, 442, 427-430, 392-403, 443,534 loannes de Dacia 113, 115 loannes Damascenus 57 loannes Dorp 442, 443 loannes Dumhleton 374 161, 140, loannes Duns Scotus 14, 23, 197,
208,
247,
257,
353,
354,
481,
521,
264,
357-359, 523,
Maior
498
501
388,
390,
534,
574,
Kelly, S. 549,550 27, 215, 324, 407, 468, 589, Kenny, A. 626
382,
F.
Kessler, E. 103 Kcyncs, J.N. 571
Kibre, P. 99 59-61,
144,
190, 192, 193
loannes loannes loannes loannes loannes loannes loannes loannes
167, 170, 293, 452, 479,
I.
Karger, E. 234 Karpinski, L.C. 457 Kelley, F.E. 263, 324, 364
530, 532,
581-585 loannes Fusoris 152 loannes Gerson 480 loannes Guallensis 56, 57 loannes dc landuno 53-56,
Kant,
Kaulbach,
323,
375,
529,
Kann, C. 512
325,
298,
297,
Kaeppeli, T. 323 Kahiza, Z. 628 Kambartel, F. 501
240-
239,
231-234,
227-229, 262,
Jung-Palc/.ewska, E. 190
228-230,
299, 586, 594, 598
dc Mirecuria 325 de Ncapoli 323 Nicholai 627 Ocrcatus 27 de Oria 586-598 Peckham 286
Abu Yusuf
al-Kind[,
63, 69, 285
King, P. 394,443,519 Kirjavainen, H. 196
Klibansky, R. 290, 504 Klima, G. 210,217,218
Kkx-ker, H.R. 298
Kluxen, W. 232,521,522,529 Knealc, M. 446, 448^50, 453 Kncalc, W. 446, 448-450, 453
267, 268, 308-310, Philoponus 343,344 loannes Quidort Parisicnsis 325, 489 loannes de Reading 89-96 loannes Rodington 259 loannes Sarisbcricnsis 27, 71-73, 97, 98,
Kneepkcns, C.H. 408,410 Knudsen, C. 180,525,554
333,502-511 loannes Scotus Eriugcna 249, 455, 456, 459-467, 558-564 loannes de Scvilla 27 loannes de Stcrngasscn Coloniensis 325
Koyre, A. 322 Kraus, J. 183 Kraus, P. 266
Knuuttila, 231,
S.
212,
215,
222,
225-229,
238, 243, 416, 438, 501, 583, 584,
645
Koch,
J.
298,323
Krcimcndahl, L. 306 27, Kretzmann, N.
324, 376, 403, 437, 440, 468, 554, 589, 626, 645
loannes Versor 441,442 loannes Wiclcfus 586
Krieger, G. 521
loannitius 98, 99, 102, 104
Kristeller, P.O.
lodocus Trutvcttcr 593, 594 Isaac Israeli 58, 119,638 Isidorus 64-66
Krop, H.A. 14,23 Kuksewicz, Z. 190 Kunitzsch, P. 28
Isidorus Hispalensis 39, 55, 61, 66, 558 lustinianus 40
Kunze, P. 445, 512, 600 Kusch, M. 231
97, 302,
461
Izbicki.T. 638 ,
W.R. 95 M.L.V. 461
Jacobi, K. 224,446,447
Laistner,
Jacquart, D. 62, 63, 68
Lamas de
Jadaane, F. 267 James, M.R. 25
Lambertini, R. 264, 549, 637 Landgraf, A. 26 Landulphus Caraccioli 325
James, T.E. 408 Jcauneau, E. 66, 276, 333, 456, 461 Jesus Hali 285,287,288
Oliveira Xavier, M.L. 535
Langston, D. 240,247 Laubenthal, R. 311
407,
Index of Names
Lax, Gasparus 594
Leanza, Lear,
Manekin, C. 565 Manfredus 103
44 217
S.
J.
Manitius,
LeGoff,J. 112 Leibniz, G.W. 141, 143 Leibold, G. 180, 298, 522, 609
Lejeune, A. 286 Lemay, H.R. 276 Leonardi, C. 97,461,462 Levi b. Gerson 565-573 Lewis, D. 231,236,243 Lewry, P.O. 407, 626, 644 Ligurius 40
D.C.
108,
258,
264,
286,
287,
322, 323
Linus 42
Lipps.T. 492,501 Livesey, S.J. 89, 90 Lloyd, A.C. 458 Locke,
J.
141
Lohn, C. 600 Lohne,JA. 290 Lohr, C. 445^50, 454, 522, 550
Long, A.A. 267 Longeway, J. 638 Longpre, E. 89 Lo Presti, M.G. 558
Maurus Salernitanus 98, 102, 105 Maximus Confessor 463, 558 Mazzarella, P. 638
Menut, A.D. 314 Mercurius 40, 42 Merlan, P. 129, 458
Mabillon,J. 43 S.
144
Mesnard, P. 106 Meyer, M. 165 Michael Bononiensis 325 Michael Scotus 57, 59
McGarry, D.D. 502-505,507,508,511 Macken, R. 370 Mackie, J.L. 306 McMullin, E. 178, 179 Macrobius 46,275,459 McVaugh, M.R. 69 Madec, G. 465
Michalski, K. 429, 645
Miethke,
Maggiolo, P.M. 311,344 Magistri, Martin de 597 Mahdi, M. 309 Maier, A. 143, 175, 179, 230,
298,
319,
174, 179
342,
Moises 40 Moises b. Maimon
(sive
Maimonides)
248,309 Mojsisch, B. 302 190-192, 375,
195,
376, 483,
489, 632, 637 Maieru, A. 185, 342, 357, 408, 437, 483 Mair, J.R.S. 46
Maloney,T.S. 261,264 Mandonnet, P. 138, 485
J.
Migne,J.-P. 44,484 Millas-Vallicrosa, J.M. 29, 30 Minio-Paluello, L. 95, 105
Madkour, I. 266,566 Maecenas 39
225,
Markowski, M. 13,23 Marmo, C. 257,264,549 Maroth, M. 265 Marrone, S. 368,369 Marrou, H.-I. 49, 535 Marsilius de Inghen 12-23, 325, 408, 410 Martianus Capella 31, 32, 97, 98, 104, 455, 459-463, 465, 467, 558 Martin, C. 627 Martin, C.J. 574 Martin, J. 503 Martinus Alaunovicanus (sive de Alnewyk) 202 Martinus Anglicus 407 Martinus Laudunensis 97, 461 Martorelli Vico, R. 550 Mast, M. 457 Massa, E. 108 Matthaeus de Aquasparta 325 Matthen, M. 215 Maurach, G. 277, 278, 280, 332, 336 Maurer, A. 15, 23, 324, 327, 330, 528
Losoncy, T. 248 Loux, M. 234,236,501,623 Lucilius 39 Lucretius (Titus L. Cams) 141, 293 Luther, Martin 304, 305 Lutz, C.E. 97, 98, 461, 462, 465
MacClintock,
M. 331
Manser, G.M. 313 Mansion, A. 163 Marchegiani, L. 553 Marcolino, V. 180, 258, 263 Marenbon, J. 446, 455 Marius Victorinus 455
Le Blond, J.M. 271 Leff, G. 298
Lindberg,
665
Molland, A.G. 176, 179 Moody, E.A. 228-230, 437, 443, 482, 495, 501 Moos, M.F. 485
Morin,
J.P.
144, 145
Morpurgo, P. 97, 98 Morra, G. 302-304
Index of Names
666
al-Muhashshir ihn Fatik 28 Muller,
119, 196, 206, 207,
J.T.
Muckle,
Paulus,
Muller, P. 600 Mullcr, J.-P. 489
Pesenti.T. 99 Petrus Abaclardus
294 V. 437, 586, 596 Murdoch, J.R. 62, 143, 227, 323, 651 Musslcr, B. 445, 600 Mutahhari, M. 266 Mynors, R.A.B. 45, 46 J.
Munoz Delgado,
Petrus
143,
Aureoli
90,
195,
258,
259,
263,
323, 325, 357
167, 177, 179 176,
179,314-321 Nicolaus de Ultricuria
179, 229,
178,
Petrus de Candia 408,411,413-415 Petrus I Icliae 101 Petrus
174,
175,
Ilispanus 440,
418,
441,
94, 212, Portugalcnsis 446, 599, 604-608, 638,
641
301
Nicomachus de Cicrasa
34, 41, 457,
467
Normore, C. 403, 582, 609 Norpoth, L. 291 Nuchclmans, G. F.
143,
97, 185, 212
101,
120,
123,
128,
413,
PctrusTartaretus 521-534,594 Petrus Thomae 325 Philaretus 99
O O
Connor, W. 294 Donncll, J.R. 94,301,504 Odo Rigaldi 326 Ocstcrle, J.T. 223 O flier, U.S. 328
Phoroncus 40 Piccolomini, A.
144
Picmontc, G.A. 455, 463 Pike, J.F. 509
Oliva, C. 304
Oliver Sutton 89 J.J.
Iximbardus
Petrus dc Tarantasia 325-325
328
Obrador y Iknnassar, M. 6
Meara,
Petrus
484-487 Pctrus Mantuanus 408, 410, 411, 438 Petrus de Paludc 323, 325, 327-329 Petrus Pomponatius 144, 302-304 Petrus de Sancto Amore 55
Nielsen, L.O. 74, 263 Nict/schc, F. 156
O
101,
Petrus de Aquila 325 Petrus de Atarrabia 325
Niccolo da Rcggio 57 Nicolaus Orcsmc 141, 142, 175.
Oakley,
82,
80,
Petrus Alfonsi 29, 30 Petrus dc Alliaco 175, 480, 593 Petrus de Alvernia 419, 420, 422, 423, 632, 644
Newell, J.H. 275 I.
25.
215,331,338,339,440 Petrus de Abano 53, 68, 291
Nardi, B. 45, 304 C al-Nashshar, A.S. 265, 266 106 A. Ncgri,
Newton,
368
250,351,504 509,510 Pepin, J. 536,538 Perreiah.A. 408,409,412,413,645
M. 337
Mundhcnk,
J.
Pcgis, A.C. Peirce, C.S.
639
Pinborg,
J.
27,
261,
263,
264,
324, 407,
418, 419, 422, 426, 437, 441, 468, 549,
462
551, 552, 554-557, 589, 626, 632
Ori genes 46
M.L. 303, 304 46
Orpheus 42,48 Osier, M. 143
Pine,
Ottaviano, C. 638,640 Owen, G.E.L. 216 Owens, J. 521
Plantinga, A. 236, 241, 243 Plato 138, 40, 90, 127,
Piz/ani, U.
169, 249-252, 275, 277, 278, 393, 457, 481, 543, 559
Plinius 39
Plotinus 129, 130 Pluta, O. 229, 293, 429, 438, 645
Panaccio, C. 618, 623, 624
Panofsky, E. 285,290 Pantin, W.A. 89 Paravicini Bagliani, A.
149, 290, 342,
483
Plutarchus (Pseudo-) 27 Polos, L. 213
Parent, J.M. 275,277
Poole, R.L. 71, 275, 503
Parmenides 40
Poppi, A. 409 Porebski, S.A. 323
Paschctto, E. 147, 285
Passmore, J. 363 Paulus apostolus 249, 539, 540 Paulus Pergulensis 438, 439 Paulus Venetus 144, 407-415, 438
Porphyrius
41,
46,
100,
217,
238,
480,
481, 551, 566, 632, 634, 635, 637, 638, 639, 643, 644 Poser, H. 231
Index of Names Potthast, A.
148, 149
Robb, J.H. 399
Preaux, J. 97 Priscianus 26, 39, 102, 104, 504, 550 Proclus 458
Ptolemaeus (Claudius) Puig, J. 307
28, 32, 38, 285
M. 291 Pythagoras 41, 42, 47, 49 Quillet, J. 314,316,319 Quine, W.V.O. 450,453 Quintilianus 40 Qusta b. Liiqa 27, 41, 291 II.
202, 204-209, 259, 325, 580, 581
Robertus Kilwardby 56, 113-115 Rogerus Baco 107-110, 141, 264, 286, 325, 418
308
Radulphus Brito
419,
421, 423-426,
549-
552, 554-557, 632
Radulphus de Longo Campo 113 Radulphus Strodus 407, 408, 410, 411, 413, 415, 437, 438, 440, 443, 648, 652
Rahman, F. 65 Raimundus Lullus
Reina,
ME.
649, 652
Ronca, I. 331,334 Roos, H. 555, 636, 637
Russell, B.
Ruzsa,
Rhazes)
99,
180, 183, 185, 395,
430
(sive
W.D. 4,5,307,342
Roure, M.L. 590, 592, 595 Rufinus 46 Ruinart, Th. 43
285
Reale, G. 267
I.
498,501,622 213
Sabatier, P. 155
Sabra, A. 152,566
Remes, U. 222, 231 Remigius Altissiodorensis 97, 98, 462, 465, 466 N. Rescher, 231, 569 Rhabanus Maurus vide Hrabanus Maurus Ribeiro do Nascimento, C.A. 106 Ricardus Billingham 202, 407, 410-412 Ricardus de Bury 89 Ricardus de Campsall 374, 377, 378, 380, 384-386, 390, 391 Ricardus Conington 90 Ricardus Kilvington 229, 645, 648-650, 652, 654 Ricardus de Lavenham 407 Ricardus de Mediavilla 141, 325, 327 Ricardus Radulphi (sive FitzRalph, Arma-
Saffey,
H.D. 458
Salamucha, J. 628 Saliba, G. 68 Salter, H.E. 89 Salzinger,
I.
8
Sanchez Salor, E. 69 San Juan, Domingo de 592 Saxl, F. 290 Scarpa, L. 459 Schenkl,H. 307,344 Schepers, H. 183-185 Schmaus, M. 364, 365 Schmidt, R.W. 210-212, 214, 216-218 Schmitt, F. 365
Schneider,! 364,371 Schneider, J.H.J. 534 Scholz, H. 437 Schrimpf, G. 455, 461, 558 Schwegler, A. 72
chanus) 325, 374, 381, 382, 386, 387 Ricardus Rufus Cornubiensis 325 Ricardus Swyneshed 374, 480, 586 Richardson, H. 89 Richter, V. 180, 521, 609, 626, 628
Scott, T.K.
Riedl, J.O. 250
Servius 39, 100, 103
Riondato, E. 99
Sheffer,
Risner, F. 146, 150, 286 Ritter,
G.
Ritter, J.
12, 21,
294
23
261-
229, 374, 381, 382, 386, 387, 407, 410, 476, 586, 594, 648,
Rossi, P. 91, 127, 641
Randall, J.H. 302 Randi, E. 139,322,328 Rashed, R. 25
Ratramnus 456 Abu Bakr
161,
Rogerus Swyneshed
Ross, 3-11
Rajna, P. 44 Rand, E.K. 32,366
al-RazF,
250, 252, 253, 255, 256, 296,
Robbins, F.E. 457 Robertus Alyngton 586 Robertus Cowton 325 Robertus Fland 407 Robertus Grossatesta 55, 56, 90-92, 9496, 160, 161, 286, 288, 314, 440, 641 Robertus Grossatesta (Pseudo-) 56-59 Robertus Halifax 325 Robertus Holcot 140, 183-185, 196, 197,
Putscher,
Raabe,
667
424,428 Seneca (Lucius Annaeus) 59 Serene, E. 437, 638
H.M. 624
Sheldon-Williams, I.P. 463, 559, 463 Sheynin, O.B. 171, 179
Shoemaker,
S.
355
Index of Names
668
Siegel, R.E.
286 140,
141,
191,
192,
Thiel, C. 501
Thijssen, J.M.M.H.
636 Sigerus de Cortraco 421 Sigwart, C. 492, 501
Thirlkel,
140,
60,
163-170, 230,
307-309,
343,344 Sinner, J.R.
192,
249-256,
131,
195,
261,
90,
109-
133-137,
142,
14,
4,
130,
19,
210-218, 263,
222-228, 294-2%, 302-
304, 311, 313, 323, 325, 328, 344, 346, 273,
142,
119-126,
111,
J.
Simplicius
24
19,
W.R. 163
Thomas de Aquino
328 Siliceo, Martinez 598 Simmons, E.D. 4 Simon de Faverisham 419, 632 Sikes,
41, 571
Theophrastus
Sigerus de Brabantia
348,
349,
364-368,
383,
398,
400,
371,
374,
379,
381-
485-187, 489, 490, 521,
636
149
N. 549, 631, 637 Skutella, M. 535
Thomas de Argentina 325, 327 Thomas Bradwardinus 142, 575-578,
582,
Smith, A.M. 150, 151
583, 586, 592 Thomas Bricot
595,
Siraisi,
Smith, J.E. 510 Socrates 40
Soderhjelm, Solon 40
W.
30
Sorahji, R. 392
Soto,
590-592, 594, 596, 697
Domingo de
Southern, R.W. 504 229, 407, 450, 451, 478, 589, Spade, P.V. 592, 593, 595, 645, 648-651 Spath, R.J. 163 Spoerri,
M.Th. 106
W.H. 460 Steinschneider, M. 309 Stahl,
Stephanus
de
Aurelianis
(sive
Tempier)
138, 141
Thomas Thomas Thomas Thomas Thomas Thomas
594,
de Buckingham 325 liccleston 89 de Erfordia 419, 421, 422 de Sutton 364-372 de Wilton 190, 192-195 de Vio (si\ e Caietanus)
Trapp,
180, 187, 188, 263
li.
342
Trifogli, C.
Stiefel,T. 339
Troncarelli, F. 43
I-. 229, 324, 407, 410, 440, 477, 626, 638, 645, 648, 649, 652 Sudhoff, K. 56, 58
Stump,
al-Suhrawardi 271 62, 227, Sylla, E.D.
468-
Troupeau, G. Tusqucts,
Una 323,
374-376,
63,
68
3
Juarez, A. 468 S.
286
Unguru,
Urbanus VIII papa 144 Urbanus Averroista 632 Urso Salcrnitanus 98, 105
A.
261,
262,
264,
549,
550,
631,644 Tachau, K.M.
185,
258,
259,
264,
357,
Usener,
360, 362, 363, 374 Tarski, A. 518
Tatianus 40 Teisias 40 Tertullianus 44
Teske, R. 129 Tester, S.J. 32,366 Thaddaeus Alderottus 66, 99, 631, 637 Thaddaeus de Parma 192 Themistius 41, 307, 344, 347 Theodoricus Carnotensis 25, 97, 98, 100, 101
J.
381,
386,388,483,484,489,651
210,
213,214,217,223 Thorndike, L. 103 Thrasymachus 40 Tine, A. 638 Tobin, R.B. 503 Touati, C. 565
Stewart, H.F. 32,366
Tabarroni,
592,
588-590,
597, 598
II.
43
van Brakel, J. 171, 179 Vance, E. 623 Van den Bergh, S. 266, 312 Vanni Rovighi, S. 49 Van Riet, S. 65, 133, 521
Van Steenberghen,
F.
141
Varro (Marcus Terentius)
40, 49, 102
Veraart, A. 501
Verbeke, G. 294, 521 Vergilius (Publius V. Naso) Verhaak, C. 421 Vignaux, P. 628
39, 100, 103
Theodorus 40 Theodosius 27, 40
Vincentius Bellovacensis 56-59
Theophilus 99
Von Moos,
Vitelli,
H. 308,343 P. 503,
508
Index of Names von Wright, G.H. 231-233 Vuillemin-Diem, G. 641
Wiener, Wilks, Willis,
669
509
P.
M. 360, 361, JA. 459
374, 502, 508, 509
Wadding, L. 353,354 Waddings, L.W. 57
Wilson, B. 331 Wilson, C. 651
Wallace, W.A. 230
Wippel, J. 226,364,368 Witelo 146-154,258,262,285-292
Ward, J.O. 504 Webb, C.C.J. 333,503 Webering, D. 173, 179 Webert, J. 167 Wegerich, E. 522 Weidemann, H. 212, 216 Weijers, O. 13, 24, 113 Weisheipl, J. 4, Weiss, P. 509 Wenin, C. 641
8, 25,
Westerink, L.G. 458 Wetherbee, W. 276
Wey,J.C. 328,612 White, A. 465
Wiedemann,
E. 152
Wieland, W. 308 Wielockx, R. 366, 486
Wittgenstein, L. 355,358 Wolfson, H.A. 133, 265, 266 Wolter, A. 240,297,353,354
Wood,
R.
263,
342,
354,
361,
362,
374
Wundt, W.
492, 501
374, 483
Yates, F. 127 Yrjonsuuri, Zabell, S.
M.
229, 438, 645
171, 178
Zayid, S. 273
Zeno 42 Zimmermann, A. Zupko,
J.
392
14, 24, 184, 294,
524
373,
ISBN 95 1-9047-26-3 ISSN 0357-3095 Helsinki 1990
Yliopistopaino
