Concepts of Scientific Method from Aristotle to Newton

JAAKKO HINTIKKA

Concepts of Scientific Method from Aristotle to Newton

In

this

not

shall

I

paper,

to

try

any results concerning the

present

history of philosophers ideas concerning in middle the about the scientific method ages. Instead, I shall comment

history

of philosophy

the

or

on the conceptual frameworks which have been used, or can be used, in such historical studies. It seems to me that our understanding of what the

in

middle

actually

happened

suitable

conceptual framework

the

history

of

the

scientific

historical

problems

shall also suggest that in the study of

I

as

method,

philosophical scholarship, the best

be greatly enhanced by a

which the specific

in

can find their appropriate niche.

can

ages

so

in

walks

other

many

of

of finding the right framework (in

way

the sense of the historically relevant and useful framework)

is

go back

to

the main Greek philosophers, especially to Aristotle, and to try to reach a deeper understand of their ideas. Their philosophy was the most important backdrop of medieval thought, which often can be looked upon

to

as a gradual transition will

an appropriate

actual

historical

from Greek ideas to ours. In other respects, too,

map

of the conceptual situation help to

developments

as

together

pieces

of

a

different

fit

larger

overall

picture.

am

How

do we twentieth-century thinkers view the scientific process, and how do our ideas differ from Aristotle s ideas in this respect? This question might seem to be too In

this

spirit,

I

led

to

ask:

general and ambiguous to admit of a clear response, but in reality there and yet informative answer to it. A twentieth-century is a clear

philosopher

is

likely to think of scientific inquiry as consisting of

making

observations (and gathering other kinds of empirical evidence) and then of using step

them

as a stepping-stone to general explanatory theories.

form data to theories

is

sometimes called a (species that

this

inference.

It

deductive.

The main watershed between

science

the question whether there

is

is

generally agreed

is

so-called

of)

The

scientific

inference cannot be

different overall conceptions of

a nondeductive kind of inference,

usually called inductive inference, to mediate the step from observations

Concepts of Scientific Method

to

theories

general

whether

or

According to the

hypothesis.

this

step

in

is

73

a

principle

matter

of

we cannot infer theories or we can test them by comparing observations. Thus we obtain two of the

latter

idea,

other general truths from phenomena, but their deductive conclusions with

main types of modern models of

scientific inquiry:

the inductivist

model

and the hypothetico-deductive model. Although these two models do not quite enjoy any longer the monopoly they used to have among philo sophers of science, they are being widely used

tacitly

or

explicitly

by

1

historians of philosophy as a part of their conceptual framework.

The basic idea of the Aristotelian conception of scientific inquiry can also be indicated very simply. Aristotle conceives of scientific inquiry literally as inquiry, that is, a questioning procedure. This is shown amply by the Topics, among other things. One precedent for such a procedure were the Socratic questioning games practiced in the Academy. 2 Originally, even deductive inferences were simply special kinds of

moves

these

in

questioning

person would have to

given

give,

answers

viz.

games,

that

every

rational

admissions. Aristotle soon

earlier

his

realized the special role of such preordained answers or admissions tried to systematize

them

He

in his syllogistic logic.

and

even tried to make

syllogisms the only vehicle of putting the first principles of a science to use for the purpose of explaining various phenomena. But even then the road to these first principles remained a dialectical one.

The

interrogative

evidence

in

Aristotle.

called the dialectic

the long

way

or erotetic concept of inquiry In

a

method.

I

more

am

traditional

is

thus amply in

terminology,

it

would be

avoiding this label, however, because on

to twentieth-century philosophy

it

has acquired

all

sorts of

misleading associations. It

is

fairly

clear

that

something

like

the

interrogative

model of

science remained influential in the middle ages. For instance, the various

Their

restrictive

character

is

shown

by

the

difficulty

of

fitting

major

historical

figures into either pidgeonhole. Was Newton an inductivist or a hypothetico-deductivist? Neither shoe fits very well. And the same question can be raised about the medievals.

What

a wider and more realistic conceptual framework for understanding of philosophical, scientific, and theological thought. That is what I shall try to provide here for the history of the scientific method, just as I have (with several others) tried to provide a new framework for studying the history of the the

is

actual

needed

is

history

of being. That earlier attempt is documented in Simo Knuuttila and Jaakko Hintikka, editors, The Logic of Being: Historical Studies, Synthese Historical Library, D. Reidel, Dordrecht, 1986. 2 See here my paper, "The Fallacy of Fallacies", Argumentation vol. 1 (1987), pp. 211238, and the literature referred to there.

concept

74

Hintikka

commentaries on Aristotle terminology of

new

light.

If

Aristotle s

loaded

interrogatively

by the learner", etc. one facet of medieval thought into a enough put there indeed was a relevant element of interrogative

"admissions",

This fact

use

freely

"acceptances

to

is

in

knowledge-seeking

medieval epistemology and philosophy of science,

it

be expected that the logic of such interrogative procedures should have been studied in so many words. This expectation is fulfilled by the 3 important but incompletely understood obligationes tradition. Whatever is

to

problems there is about the interpretation of these questionanswer dialogues, in their standard form (antiqua responsio) they were not, and could not have been, a form of counterfactual deductive detailed

them one was not examining what

reasoning, as has been claimed. For in follows logically from the

but

rather

positiim

plus

follows

from,

logically

the rcsponder

of interrogative or

teristic

in

what

positum or what

initial

inconsistent with

inconsistent

is

admissions. This

earlier

s

or

is

is

by some

logicians.

But

this

it,

the

charac

fact

knowledge-seeking. Admittedly, later

"erotctic"

the fourteenth century obligation-games were given a

twist

in

with,

merely

my

illustrates

more deductive

recommendation of

viewing medieval thought as a transition from the Greek to the modern viewpoint.

might not seem to have a great deal to do with conceptions of scientific method. However, their Admittedly,

at

sight the obligationes

first

close link with the sophismata provides a bridge, for problems concerning

knowledge-seeking and science were frequently dealt with sophismata in logic, theology, and natural philosophy, and the obligations terminology In

general,

rogative

was

We

seeking by means of what 4

inquiry.

This

codification

form of

in this context

largely employed.

obligation-games

knowledge-seeking.

in the

I

illustrate

can

have

of the

study called

dialectical

several this

the

features

kind

of

interrogative

conception

of

inter

knowledge-

model of

of knowledge-

Here the work of Simo Knuuttila and his associates promises to be decisive. I here relying on their results. See, e.g., Simo Knuuttila and Mikko Yrjonsuuri, "Norm and Action in Obligational Disputations" in O. Pluta, ed., Die Philosophic im 14. und 15.

am

Jahrhundert, B.R. Griiner,

The work on

this

Amsterdam

model

is

1988, pp. 191-202.

largely

still

in

progress. For interim expositions,

cf.,

e.g.,

Representation and the Interrogative Model of Inquiry", forthcoming in a volume of new papers on epistemology, edited by Keith Lehrer and Marjorie Clay, Jaakko Hintikka and Merrill B. Hintikka, "Sherlock Holmes Confronts Modern Logic", in

my

"Knowledge

E.M.

Barth and J.L. Martens, eds., Argumentation: Approaches to Theory Formation, Benjamins, Amsterdam, 1982, pp. 55-76; and "The Logic of Science as a Model-Oriented

Concepts of Scientific Method

main conceptual framework

the

is

seeking

historians of scientific

The In

model seems

interrogative

may

inquirer

am recommending

I

the

to

method.

an idealized inquirer

it,

75

at

first

to

sight

from a given

starts

be simplicity

initial

itself.

The

premise T.

on the put questions to a source of information. Depending oracle" we may call this source of information

intended application,

"the

or nature. The inquirer may draw deductive conclusions from T together with the answers. The aim of the game (or the inquirer s aim) is to

prove a given conclusion or answer a question

C

or

(in

the

Normally,

not-B?"

"B

to

another variant of the model) of

presupposition

a

be asked. question must have been established before the question may from the differ How does this model, applied to scientific inquiry,

models of science?

received

turns out

It

be more

to

flexible

than

its

rivals in several respects.

For one

some

most

the

of

the Oracle

thing,

s

answers need not be observations. In variants

interesting

of

the

model,

controlled

But the experiments are conceived of as a scientist s questions to nature. oracle s answers may instead be intuitions of innate ideas or, as in Aristotle, well-established general opinions, endoxa.

be

all true, just

then

is

as endoxa

They need not even

sometimes are deceptive. But

all

that

happens

the inquirer has to ask further questions to establish the

that

veracity of the oracle

One

5

s

particular answers.

of especially important corollary of this wider conception

nature can

tell

the following:

we can

us or what

what

otherwise establish interrogatively

An

in the interrogative

model

is

is

the

important parameter the oracle can provide to the logical complexity of the answers that models of In the received science, both in the inductivist and in inquirer. the hypothetico-deductive model,

game (i.e.,

In

is

assumed

that

nature (who in the

of science plays the role of the oracle) can only provide particular s questions. quantifier free) propositions as answers to the inquirer

the

wider

"Atomistic

is

it

model,

Postulate",

there as

I

is

no longer

have called

it.

any

And

if

reason

to

accept

this

the Atomistic Postulate

not assumed, the rationale of both of these models collapses. For then

in P. Asquith and P. Kitcher, eds., PSA 19S4, vol. 1, Philosophy of Science Logic", Association, East Lansing, 1984, pp. 177-185. See also the work referred to in other notes.

5

For the concept of endoxa and for their role in Aristotle s argumentation, see. G.E.L. Owen, Tithenai ta Phainomena", in S. Mansion, ed., Aristote et les problemes de methode, Louvain, 1961, and. cf. my "The Fallacy of Fallacies", op. cit.

76

Hintikka

there

is

no reason

to conclude that general theories could not

be arrived

deductively from

at

Newton

nature s answers to the inquirer s questions or, as could not be deduced from the phenomena. 6 there are at least two historically important ways in which a

puts

Now

it,

can be thought of as being able to obtain general truths as to his or her questions.

scientist

immediate (non-inferential) answers

The

way

first

is

For

experimentation.

the

outcome

typical

of

has

It

proposition.

quantifier-free

The other way

Aristotle

is

It

s.

form of X. This

external one.

And

X

be

also

will

between

forms

if

is

so,

X

be

the

in

Y

one

for

way.

in

his

s

quantifier 8

s

psychology

soul to take

on

form as any

of the

which necessarily accompanies

Thus any necessary connection

soul.

ascertained

is

no longer a

is

existential

realization

genuine any other form

present

can

"answer"

deeply rooted

a

as

controlled

Newton

essentially is

of thinking according to which to think of the

successful

variables, the controlled

one

least

at

controlled

way

a

experiment and the observed one. The codification of such an

dependent on a universal one. This was

of

the

is

dependence between two

to find a

is

It

post-medieval.

simply

by

about

thinking

them,

9 according to this Aristotelian psychology (and metaphysics) of thinking. This means that for Aristotle general truths can be seen immediately

in

one

s

own

interrogative

soul,

model,

of course after suitable preparation. In terms of the this

means

the

that

oracle

assumed

is

to

give an

Aristotelian scientist general answers, and not only particular ones. In the

of what was said earlier,

light

it

is

therefore small

wonder

that neither

the inductivist nor the hypothetico-deductive model of science played any

appreciable role

in

medieval philosophy.

This does not mean, however, that the Aristotelian idea of direct access to general truths was universally accepted in the middle ages.

soon as

1

As

inference was conceptualized as involving a step from

scientific

Cf. note 4 above.

See

here my paper, 74 (1988), pp. 173-190.

Is

"What

the

Logic

of

Experimental

Inquiry?",

Synthese

vol.

t>

See

here

Interrogative

Jaakko Logic

Hintikka of

symposium on Newton

in

and

Inquiry",

James

Garrison,

forthcoming

in

the

"Newton s

Methodology and

proceedings

of

the

April

the

1987

Jerusalem,

o

This pecularity Aristotelian psychology of thought is so striking that it is barely been acknowledge in its full strangeness (strangeness from our twentieth-century viewpoint, that is to say). For indications of Philosophical Re\ iew vol. 75 (1966), pp. 197-219.

it,

cf.

my paper

"Aristotelian

Infinity",

Concepts of Scientific Method

particulars to a general truth,

it

became

77

was not

clear that such a step

unproblematic, and could not be thought of as nature

direct

s

answer to a

middle ages, the rise of nominalism seems to mark an important watershed in this respect. This is only to be expected in view of Aristotle s idea of the realization of universal concepts in the scientist s question. In the

form of

"forms"

source

a

as

soul

background helps us

Aristotelian

this

Indeed,

human

the

in

of scientific

truths.

understand why the

to

rejection of universals was as crucial a development in medieval thought

as in

understand the impact of nominalism general. For instance, nominalism cannot be construed as a skeptical in fact was. This helps us to

it

philosophy, as several speakers at this very congress will emphasize. Its

seen by comparison with Aristotle

s

methodology which

impact

is

means

giving up, at least partly, the idea that

in effect

nature can give us general

answers to suitable questions by means of a realization of the relevant

forms

in

one

Did

s

mind.

this

mean

The

process?

idea of the scientific

a radical change in philosophers

interrogative

no. For the interrogative

model suggests an

model shows

that

interesting answer,

on the oracle

the effects of an additional restriction

which

is

you can often compensate for s

(nature

s)

answers

10

In fact, logicians by strengthening the initial theoretical assumption T. know that even if answers to questions are restricted to (negated or

unnegated) atomic propositions, there can be theories T which jointly with nature s answers to questions enable the inquirer to establish any true proposition. (These are the theories that are known as modelcomplete ones.) These observations throw highly interesting light on developments in the medieval period. The very same philosophers who began to think of inference as a passage from particular observations to general

scientific

were also among the first ones to evoke prior general propositions back them up. Duns Scotus is an especially interesting case in point.

truths to

He writes

as follows:

11

As

for what is known by experience, I have this to say. Even though a person does not experience every single individual, but

is

Cf. here my The Logic of Science as Model-Oriented Logic", op. cit. In general, the possibility of partial trade off between strong assumptions as to what answerable and strong a priori premises is an extremely interesting fact which can

throw

light

Duns

on

several other historical

Scotus,

Opus

phenomena.

Oxoniense,

Philosophical Writings, p. 109.

i,

d.3,

q.4,

translated

in

Wolter,

Duns

Scotus:

Hintikka

78

only a great many, nor does he experience them at all times, but on frequently, still he knows infallibly that it is always this way and holds ror all instances. He knows this in virtue of this proposition reposing in his soul: "Whatever occurs in a great many instances by a cause that is not free, is the natural effect of that cause." This proposition is known to the intellect even if the terms are derived from erring senses, because a cause that does not act freely cannot in most instances produce an effect that is the very opposite of what it is ordained by its form to produce.

This quotation

interesting in that

is

Duns Scotus was

the

alternative

regularity

knows

intellect

with

of nature

a

idea

for a thinker like

nature

that

t

certainty

that

not

is

character

the

do so apud the

like

from sense-

derived of

answer

can

completely general truths

certain

They are therefore of

experience.

the

Even though nature doesn

questions concerning universals.

Scotum, the

what

illustrates

it

to

premises of

initial

the scientific enterprise rather than answers (new facts) contributed by nature.

What

important here

is

that

is

this

novelty docs

not

Scotus away from the interrogative conception of inquiry. is

to shift the focus

One symptom quoted

from nature

of this

passage,

viz.,

s

answers to

initial

turn

What

Duns does

it

theoretical premises.

what Duns Scotus says in so many words in the that the results based on the principle of the

is

regularity of nature are infallible, even though they are based only on a

sample of the individuals covered by the generalization. In can say, they are just like the results of an interrogative

Duns Scotus does the

Hume

not anticipate

twentieth-century conception

author

refers

in

this

context

s

inquiry.

I

Thus

doubts about induction nor even

even though one recent

of induction,

to

this respect,

Duns Scotus

s

12 "inductive

evidence".

Admittedly, soon afterwards Duns Scotus says that in this way we can But this very lowest degree of scientific knowledge". only reach inferior degree does not mean a lower level of certainty, for the principle "the

of

the

of

regularity

"uncertainty

Thus

and it

Duns Scotus

is

nature

is

said

to

remove

in

such

cases

all

infallibility".

in

principle misguided to see

anticipation of

Hume s

in

medieval thinkers

like

problems or even anticipations of the

hypothetico-deductive or the inductivist models of science. These models came about only when the skeptical ideas found two different inroads into 12

See N. Kretzmann, A. Kenny and J. Pinborg, eds., The Cambridge Later Medie\ al Philosophy, Cambridge University Press, Cambridge, 1982, p. 511. 13

Op.

cit.,

i,

d.3, q.5;

Wolter,

p. 119.

History

of

Concepts of Scientific Method

79

the interrogative conception of scientific inquiry. restrict

nature

like

why

was

is

all

nontrivial initial premises.

modern

crucially important for

Hume

Locke and

One

answers to negated or unnegated atomic ones.

s

has to eliminate in principle

reason

was not enough

It

It

is

to

also

for this

empiricist philosophers

to attack the doctrine of innate ideas.

The same observation

why Newton

explains

s

overall conception of

the structure of science bears striking resemblances to Aristotle in spite

of

mathematical character.

its

answers

general

a

to

14

For according to Newton nature can yield questions, of course not answers

scientist s

as in Aristotle but concerning necessary connections between answers taking the form of functional dependence between variables, "forms"

through a controlled experiment. No wonder Newton, too, believed that general truths can be deduced from phenomena. typically obtained

It

the

of interest to see a

is

abandonment of the

truths.

One

forms

Aristotelian

the

to

corollary

realization of

more

bit

little

of direct

idea

Aristotelian

in the soul is that

the nature of things in question, that

between

logical

and natural

involved in

is

access of

theory

to

general

thinking

as

a

whatever follows as a matter of is,

as a matter of their essential

forms, can be established in thought. There Aristotle

what

closely

therefore no distinction in

is

("formal")

necessity. This conclusion,

which has of course been misunderstood time and again, is shown to be a genuine Aristotelian doctrine in my monograph on Aristotle s theory of 15

Another corollary

modality. clearly

and

conclusion. rational

in

distinctly

Full-fledged

action

in

(i.e.,

a

her

or

akrasia

whoever does

that

is

his

mind,

as

is

syllogism).

avoid

drawing the

in

logic

as

All

these

Aristotelian

impossible 16

practical

realize the premises

cannot

it

is

in

views have their echoes in medieval thought. Of course, in order to be able to see what necessarily accompanies a

form one must

to

general

but

truths,

Accordingly, the

I.

realize

first

fully

an Aristotelian

crucial task for

the

the

form

in

one

s

mind. Hence the

scientist is not inference

formation

of

general

from particulars

concepts

("forms").

premises of an Aristotelian science are definitions,

first

See Hintikka and Garrison, op. cit. The view we reject is represented, e.g., by Bernard Cohen, The Newtonian Revolution, Cambridge University Press, Cambridge, 1980. Jaakko

Hintikka

and Determinism

(with

(Acta

Unto

Remes and Simo

Philosophica

Fennica,

vol.

Knuuttila), no. 1),

29,

Aristotle

on

Societas

Philosophica

Fennica, Helsinki, 1977.

See here

my

"Aristotle

s

Incontinent

Logician",

Ajatus

vol.

37 (1978), pp. 48-65.

Modality

80

Hintikka

and the way

them

to reach

definition of a concept

All

this

Aristotle

is

To

give

essential

its

and parcel of what

part

questions

answerable.

(i.e.,

the dialectial process which leads up to the

is

a full grasp of

concerning

up

this

general

17 "form").

meant by saying propositions were I

that

for

(directly)

answerability assumption can therefore take

the form of giving up the identification of logical (metaphysical) necessity

and natural

nomic

necessity. In so far as this natural necessity

necessity, the step

away from

is

construed as

Aristotle took the form of denying

the identification of unrestricted generality and metaphysical (conceptual)

As

necessity.

Knuuttila and others have spelled out, this step was taken

most resolutely by Duns Scotus. 18

Now we

can

see

scholastic philosophers

that

this

step

was not an

isolated

ideas about necessity and other

in

change

modal concepts.

It

affected their outlook on the entire structure of the scientific search of

knowledge.

These general observations can be illustrated by applying them to the history of one particular concept, that of induction. There exists a useful

study

of

the

of

history

this

assumes

he

concept

by Julius Weinberg,

but

his

unfortunately throughout essay something essentially tantamount to the twentieth-century notion of induction as an inference from particulars to general truths. 19

At

first

sight,

the

story

of

induction

within

an

interrogative

framework might look rather like the "curious incident of the dog in the in Sherlock Holmes: the dog didn do anything. Likewise, night-time" there does not seem to be any niche for the notion of induction in the t

interrogative conception of scientific investigation.

model and allow

Even

if

we

relax our

answers by nature that are true only with a certain probability (and hence can be false), the result is not the inductivist model of science but its mirror image. 20 In inductive logic, we study for

uncertain (nondeductive) inferences from data that are typically assumed to

17

be unproblematic. In the loosened interrogative model we are studying

Cf.

"The

Fallacy of

Fallacies",

op.

cit.

10 Cf.

Knuuttila

s

own

contribution

to

Simo

Knuuttila, ed., Reforging the Great Chain

of Being, Synthese Historical Library, D. Reidel, Dordrecht, 1981. 19

Julius

Weinberg,

History of Thought,

See

here

Inference",

The

and Induction: Three Essays Relation, Abstraction, University of Wisconsin Press, Madison and Milwaukee, 1965.

my paper, "The Interrogative Erkenntnis vol. 26 (1987), pp. 429-442.

Approach

to

Inquiry

and

in

the

Probabilistic

Con cepts of Scien tific Meth od deductive

hence

(and

inferences

certain)

from

81

answers

uncertain

by

nature.

This negative finding

nevertheless

is

itself

quite remarkable, just as

counterpart was in Conan Doyle. It is indeed remarkable how little the medievals had to say about induction in anything like the twentiethits

century acceptance of the term.

There

is

more

be said of

to

this

twentieth-century notion of induction of interrogative inquiry, there that arises naturally

This general

can

they

as

can

scientific inquiry.

Even

follows:

be

Even

concept, however.

an uninvited guest

if

if

21

nature

For instance,

partial.

answers

s

in

can

B

13),

number of

directly find out only

cf.

An.

what characterizes each of a

Likewise, an experimental

scientist

can

what functional dependence obtains between the variables he or she

find is

we can

subclasses of pride.

be

an Aristotelian

search for a definition of pride or magnanimity (megalopsychia, Post.

the

house

in the

a historically important namesake notion

from the idea of

be seen

truths,

is

is

interested in over a

variable.

number of

The experimentally

intervals of values

of the controlled

established dependence can even be different

over the different intervals. Such general but restricted answers lead to the problem of reconciling these partial answers with each other.

Thus

Aristotle writes:

mean, e.g., if we were to seek what pride is we should inquire, in the case of some proud men we know, what one thing they all have as such. E.g. if Alcibiades is proud, and Achilles and Ajax, what one thing do they all [have]? Intolerance of insults; for one made war one waxed wroth, and the other killed himself. Again in the case of others, e.g. Lysander and Socrates. Well, if Tiere it is being indifferent to good and bad fortune, I take these two things and inquire what both indifference to fortune and not brooking dishonour have that is the same. And if there is nothing, then there will be two sorts of pride. I

This reconciliation procedure,

what Aristotle elsewhere

calls

know when

earlier

I

wrote

pretation of Aristotle

my s

subsequent Aristotelians.

See here

Model of

my

paper,

Inquiry",

I

have shown elsewhere,

epagoge

or induction.

paper was

that

concept of induction was

Thus Aquinas

"The

forthcoming

22

is

What

essentially fairly

I

precisely

did not

this

inter

common among

assimilates to each other induction

Concept of Induction in

in the Light of the Interrogative the proceedings of the Pittsburgh Colloquium in the

Philosophy of Science. In

422^39.

"Aristotelian

Induction",

Revue Internationale de Philosophic,

vol.

34 (1980), pp.

Hintikka

82

and the method of looking division. in

the

same

the

"...

method of the

obtaining

quod

in the

thing happens

induction."

23

quid of a

by means of the method of

definition

for

Here

the

thing".

method of

division as

method of

The

context

division

makes

is

happens "used

clear

it

in

that

Aquinas is thinking of an interrogative search for definitions. This is shown by statements like the following: 24 For one who induces through singulars to the universal does not demosntrate or syllogize from necessity. For when something is proved syllogistically. it is not necessary to make further inquiry concerning the conclusion or ask that the conclusion be conceded; is necessary is that the conclusion is true, if the premises

what laid

down

Aquinas mistakenly thinks that the search for definitions An. Post. B 13 (by means of magnanimity example) is by Aristotle to be a method different from division and

However, described

in

intended alternative

famous

are true. [Emphasis added.]

to

it.

nevertheless

is

It

in

that,

significant

the

discussing

chapter of An. Post. B, Aquinas assimilates induction and the

last

search for definitions along the lines of

B

13 to each other, and even

one of the examples employed there. There identity of the two apparently

refers to

definition-seeking (seeking for the

different

quod quid of

of

processes

a thing) and induction

throws some

light on the history of the notion of induction. For instance, we can see in what sense Aristotelian induction must be complete: the different kinds of megalopsychia whose definitions have to be reconciled

with each other must collectively exhaust the entire field of of

magnanimity.

different

subclasses

magnanimity. Of the

reconciliation

exhaustion of

means

This

at

one

and

of magnanimity

course, of the

and

in Aristotle

definitions

all

the the

all

same time particular

instances

exhaust

to

of the

subspecies,

of

instances

the real action in induction

lies

in

not just in the

instances.

all

This shows

how

thin the line

modern conception. This

line

is

from Aristotelian induction to the

was repeatedly transgressed

as early as in

the middle ages.

What question the

is

is

facilitated

extension

An

the inductive reconciliation process like?

and

loc. cit.

this

by a comparison with the quantitative version of

reconciliation

Thomas Aquinas, Commentary Books, Albany, N.Y., 1970, p. 177. Thomas Aquinas,

answer to

on

problem.

the

In

Posterior

this

problem,

Analytics

of

different

Aristotle,

Magi

Concepts of Scientific Method

83

of definition are to partial functions with exclusive ranges

be subsumed

under one single comprehensive functional dependence. I have shown elsewhere that this kind of reconciliation problem occurs often in the of

history science.

and

science

crucial

at

the

in

junctions

development

of

25

It

cannot be subject to simple

easily seen that the reconciliation

is

experimentation with the mathematical expressions of the different functions to be reconciled with each other, and hence has a rules.

involves

It

definite

It it. represents a type of use of mathematics in science, that

element of conceptual analysis to

scientific

including

reasoning,

the

much by philosophers. between the reconciliation problem

has not been discussed very

Here the science

and

megalopsychia to

definitions

similarity

induction

Aristotelian

is

close.

particularly

endoxa.

Here

One

is

One

is

reconciliation

qualitative forms.

some of

tempted to say that Aristotelian induction

modern

to

try

open both

Another problem

is

to systematic

understand what goes

to

both

process,

the is

reconciliation process.

a couple of challenging tasks

research.

inductive

the

example shows Aristotle understood inductive search of contain a heavy dose of conceptual analysis and even

merely a qualitative version of the

historical

as

For,

conceptual reorganization, including the partial rejection of relevant

modern

in

in

its

the

and

its

quantitative

to understand the

and to

into

development of

Aristotelian sense into an integral (though

the concept of induction in

its

not

methodology of modern the functional extrapolation and reconciliation

always

explicitly

recognized)

part

of the

I have argued that what Newton meant by induction. But where he got his ideas from and, more generally, what happened to the notion between Aristotle and Newton largely remains to be investigated.

science.

task

is

Certain things can nevertheless be said.

modern conception

of

induction

began

fourteenth century. Such writers as

to

It

is

rear

unmistakable that the its

ugly

Ockham, pseudo-Scotus

head etc.

in

the

discuss

induction unmistakably as a step from particular cases to a general law that

falls

short

pseudo-Scotus

See op.

cit.,

of

who

necessity.

says

note 21 above.

This

that

is

for

incomplete

instance

stated

induction

explicitly

cannot

by

provide

Hintikka

84

necessity, only evidence.

26

This

is

a far cry

from the Aristotelian idea of

induction sketched earlier. In a wider perspective, an especially interesting point

connection between the

this

of nominalism.

rise

change This

seeking.

A in

to

be a

philosophers concept of induction and connection is shown by the Aristotelian

background mentioned above, and nominalism meant such a break with

a form

seems

in

it

helps

us

to

earlier ideas of

understand

why human knowledge-

nominalist could not conceptualize thinking as a realization of

one

mind and therefore could not assume

s

that

necessary connections between forms could be seen simply by realizing them in

one

s

mind.

A

nominalist, in brief, could not

general questions,

at

least

assume

that nature

answered

not directly, only particular ones. This helps

us to appreciate the impact of nominalism in general.

This

proposed

is

an

here

instructive

can

throw

philosophical thought.

Florida State University

26

Super

Pr.

Anal.

II, 9, 8.

example of how observations of the kind on major issues in the history of light