On Insoluble Sentences: Chapter One of His Rules for Solving Sophisms (Mediaeval Sources in Translation, Vol. 21)

M E D I A E V A L SOURCES IN TRANSLATION 21

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WILLIAM HEYTESBURY ON "INSOLUBLE" SENTENCES CHAPTER ONE OF HIS R ULES FOR SOL VING SOPHISMS Translated with an Introduction and Study by

PAUL VINCENT SPADE

PONTIFICAL INSTITUTE OF MEDIAEVAL STUDIES TORONTO, 1979

CANADIAN CATALOGUING IN PUBLICATION DATA Heytesbury, William, 11. 1340. On "insoluble" sentences (Mediaeval sources in translation; 21 ISSN 0316-0874) Translation of chapter one of Regulae solvendi sophismata. Bibliography: p. Includes index. ISBN 0-88844-270-X

1. Insolubilia (Logic) I. Spade, Paul Vincent, 1944- II. Pontifical Institute of Mediaeval Studies. III. Title. IV. Series. BC21.I64H3813 1979

165

C79-094376-X

© 1979 by

PONTIFICAL INSTITUTE OF MEDIAEVAL STUDIES 59 Queen's Park Crescent East Toronto, Ontario, Canada M5S 2C4 PRINTED BY UNIVERSA PRESS, WETTEREN, BELGIUM

Contents

Introduction

1

William Heytesbury, On "Insoluble" Sentences Prologue Some Previous Opinions Assumptions and Rules

15 18 46 Study

1. Preliminary Notions and the Definition of an Insoluble 2. Previous Opinions 3. Heytesbury's Own View

59 71 79

Bibliography

97

Index of Names

103

Index of Topics

105

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Acknowledgments

I would like to thank Norman Kretzmann for his very helpful criticisms and suggestions. I wish also to thank the Biblioteca Antoniana in Padua and the Biblioteca Apostolica Vaticana for providing me with microfilm copies of manuscripts in their collections, and the libraries of the University of Chicago, the Pontifical Institute of Mediaeval Studies and Indiana University for cooperation without which this volume would have been impossible. This volume is dedicated to the memory of L. H. Hackstaff.

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Introduction

William Heytesbury was born sometime before 1313, probably in Wiltshire in Salisbury diocese. He was a fellow of Merton College, Oxford, in 1330, and was first bursar (i.e., recipient of a scholarship) there in 1338-1339. By 1340 he had completed his regency in arts at Merton and, together with John Dumbleton,1 had been named a foundation fellow at Queen's College, although he soon returned to Merton. Heytesbury was a doctor of theology by July, 1348, chancellor of the university in November, 1371, and may have been chancellor earlier, perhaps 1353-1354. He died at the end of 1372 or the beginning of 1373. 2 Heytesbury's works all seem to have been written during his regency in arts at Merton, and may therefore be dated between roughly 1331 and 1339.3 His most important and influential work is no doubt his famous "Rules for Solving Sophisms" (Regulae solvendi sophismata). 1 On Dumbleton, see Emden [13], vol. 1, p. 603; Weisheipl [47], pp. 199207; and Weisheipl [48], pp. 210-211. (Arabic numerals in square brackets refer to items in the Bibliography.) 2 For biographical information on Heytesbury, see Emden [13], vol. 2, pp. 927-928; Weisheipl [47], pp. 195-199; Weisheipl [48], pp. 212-217; and Wilson [51], p. 7. 3 See Weisheipl [47], p. 196. Heytesbury's works are described in Weisheipl [48], pp. 212-217. On the first work attributed there to Heytesbury (an Insolubilia in two versions), see below, n. 16 of the Introduction.

2

INTRODUCTION

According to the colophon on fol. 17rb of the copy in Erfurt, MS Amplon. 2°, 135, the "Rules" were written in 1335.4 Sophisms of the kind discussed in Heytesbury's "Rules" are problematic sentences about which one can give plausible arguments both that they are true and also that they are false. The discussion of such sophisms provided occasions for medieval authors to focus on important philosophical issues and distinctions. In recent philosophy, sentences like 'The number of planets is necessarily greater than seven" have played a similar role. Although one can argue that, like all purely empirical matters, it is merely a contingent fact that there happen to be more than seven planets, one can also argue for the opposite conclusion as follows: "The number of planets is in fact nine. But nine is necessarily greater than seven. Therefore, the number of planets is necessarily greater than seven." The conclusion is plainly false, but it is not so obvious just exactly what is wrong with the argument. Discussion of the argument has focused recent philosophical attention on the issues of so-called "opaque" contexts and modal logic.5 Such sentences are the modern equivalents of the medieval sophisms. Sophisms, therefore, and the arguments and discussion accompanying them, were not mere "sophistry" in the modern, pejorative sense of that term.6 It was not just a matter of trying to make "the worse appear the better cause"; rather it 4 "Datus Oxonie a mag. Wilhelmo de Hyttisbyri a.o. M°CCC°XXXV°." Quoted in Weisheipl [47], p. 196. 5 See, for instance, the papers collected in Linsky [21]. 6 Nevertheless, the word "sophistical" and its variants were sometimes used in that pejorative sense in the Middle Ages. See, e.g., par. 58 of the translation below.

INTRODUCTION

3

was a matter of trying to determine in a philosophically revealing way exactly why the worse cause was indeed the worse cause. Sophisms are useful pedagogical tools; they provide vivid illustrations of the importance of careful analysis, and show how abstract general principles apply, sometimes with unexpected consequences, to particular cases. It is not surprising, therefore, that a "sophismata-litersiture' developed within the medieval university system. Collections of sophisms circulated, sometimes compiled from several sources, sometimes written by a single author. Although in principle sophisms could be constructed on any topic, in fact most of the major extant collections seem to be confined to issues in logic and the philosophy of nature.7Heytesbury himself, in addition to his "Rules for Solving Sophisms," compiled an influential Sophismata on topics in natural philosophy.8 Heytesbury spent most of his academic career at Merton College, Oxford, a center of great scientific and logical activity during his regency in arts there. Thomas Bradwardine and the so-called "Calculators," including Heytesbury, were at that time exploring the applications of mathematics to physics. The 7 There is a fairly extensive modern literature on the medieval sophismata tradition. A good place to start is Grabmann [14]. John Buridan's very interesting logical Sophismata has been translated in Scott [26]. Norman Kretzmann and Barbara Ensign Kretzmann are preparing an edition and translation, with commentary, of the Sophismata of Richard Kilvington, one of the so-called "Oxford Calculators." 8 See Weisheipl [48], pp. 214-215 for the manuscripts. The Sophismata has been printed in the incunabula edition (Venice, 1494) containing the text of the "Rules" used for the translation below. Wilson lists the thirty-two sophisms in Heytesbury's Sophismata, together with references to later commentaries, Wilson [51], pp. 154-163.

4

INTRODUCTION

influence of their work in physical theory was immense, and spread throughout Europe in a very short time, anticipating in some respects the later work of Galileo.9 Although it has not been so widely studied, their work in logic was also insightful and influential.10 It was in this intellectual context that Heytesbury wrote his "Rules for Solving Sophisms" in 1335. The "Rules" are divided into six chapters.11 The first chapter, translated below, provides some general rules for handling socalled "insoluble" sentences in disputations. We shall return to these "insolubles" shortly. The second chapter concerns sophisms involving the words "know" and "doubt." It is in effect a small tract on epistemic logic. The third chapter deals with logical problems arising from the use of "relative" pronouns, including demonstratives. These three chapters are predominately logical in character. The remaining chapters, however, are concerned with scientific questions, treated in the logico-mathematical style characteristic of the Merton school. Chapter four treats of problems arising from the terms "begins" and "stops." Chapter five is on maxima and minima. The sixth and last chapter ("On the three categories") considers the notion of velocity and acceleration in the Aristotelian categories of place, quantity, and quality.12 These last three 9 On the Merton School, see Clagett [7]; Dales [8], pp. 105-109; and Wallace [45], pp. 53-62. 10 Many of the works listed in Weisheipl [48] are logical works. Ralph Strode, writing in the third quarter of the fourteenth century, claimed with some justification that Thomas Bradwardine was the first to come up with something of real value on the topic of logical "insolubles." (See Spade [30], p. 88.) The influence of Heytesbury's own work on "insolubles," translated below, will be discussed later in this introduction. 11 See paragraph 3 of the translation. 12 The sixth chapter is translated by E. A. Moody in Clagett [7], pp. 235237, 270-277. The translation is reprinted in Grant [15], pp. 237-243.

INTRODUCTION

5

chapters, and especially chapter six, are responsible for the position Heytesbury's "Rules" occupy in the history of science.13 But the first chapter too was important and influential in its own right, not in the history of science so much as in the history of logic and semantic theory. The chapter concerns socalled "insoluble" sentences. An "insoluble" sentence is a paradox or antinomy of the sort typified by the "Liar Paradox," in which someone says "What I am now saying is false" and that alone. What he says must presumably, like all statements, be either true or false. But on either hypothesis one can derive a contradiction by apparently uncontrovertible rules of inference. For convenience, let his sentence be called "a." Then if a is true, what it says must be so. But what it says is that a is false. Hence if a is true, a is false, which would be a contradiction. Similarly, if a is false, what it says must not be so. But what it says is that a is false. Hence, if a is false, then it must not be the case that a is false (and so a has to be true), which would likewise be a contradiction. Hence, there seems to be no way to avoid a contradiction no matter which way we turn. This paradox is no parlor trick; it strikes at the heart of logic (construed to include the theory of truth). For the logical rules by which the contradiction was derived are supposed to be valid in the sense that they cannot lead from truth to falsehood. Yet here such rules lead from what might very well be a truth (that someone utters such a sentence) to a contradiction, and so to a falsehood. The whole enterprise of logic is at stake in this paradox. 13

See Wilson [51], pp. 25-28.

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INTRODUCTION

The modern literature on the Liar Paradox is immense.14 The medieval literature too was quite extensive.15 Heytesbury's text is of crucial importance in this medieval literature. It was widely read, commented on, argued against, and generally used as a standard text on the problem. Among those who made use of Heytesbury's tract in their own discussions, we can cite Angelo of Fossambrone, Cajetan of Thiene, John of Constance, John Dumbleton, John of Holland (whose own tract became something of a standard textbook in some universities), John Hunter, John of Wesel, John Wycliff, Paul of Pergula, Paul of Venice, Ralph Strode, Robert Fland, and several anonymous authors.16 The tract is probably the single most influential specimen of the medieval mso/wM/a-literature. Moreover, although it is rather convoluted in parts, Heytesbury's reasoning is for the most part straightforward and easier to read than many of the other authors'. For the modern 14

See, e.g., the bibliography in Martin [23], pp. 135-149. See Bottin [4] and Spade [30]. 16 See the discussions in Spade [30]. Weisheipl in [48], pp. 212-213, refers to two other fnsolubilia attributed to Heytesbury. I have argued, however, in Spade [30], items xn and xxxix, that these two works are not by Heytesbury. One of them (item xn), preserved in Padua, Bibl. univ. 1123, fols. 22vb-24rb, is said to be "secundum Heytesbury," but disagrees with Heytesbury's "Rules" on the very important principle enunciated in par. 51 of the translation below. Later authors took this principle to be a characterizing feature of Heytesbury's position. The other of these works (item xxxix) Weisheipl cites in Erfurt, Amplon., 4° 270, fols. 37-42v (the correct folios are rather 37rl-39r30), and Vatican, Vat. lat. 3065, fols. 28r-30v. Neither manuscript attributes the text explicitly to Heytesbury. On the other hand, there is a third copy of the work, in Oxford, Bodl., Canon. Misc. 219, fols. 7ra-9rb, where it is explicitly attributed to John Hunter (Venator). Hunter's work seems to be a rearrangement and abridgment of the anonymous item 15

XII.

INTRODUCTION

7

reader, therefore, Heytesbury's tract serves as perhaps the best introduction to this medieval literature. In addition, Heytesbury's text in one respect reaches a level of understanding rarely attained in the medieval discussions of the paradox; in at least some passages, Heytesbury recognizes that there can be no completely satisfactory "solution" to the paradox. Many medieval authors thought there could be. Indeed, although they called such paradoxes "insolubles," many authors hastened to add that this does not mean that there is no way at all to solve them. One anonymous author, for instance, about the middle of the thirteenth century, explains the matter this way: Concerning the tract on insolubles, one has to know first that the noun "insoluble" is used in three senses. In one sense it means that which can in no way be solved. In another sense it means that which can very well be solved as far as it itself is concerned, and yet because of some obstacle is never solved in fact. In a third sense it means that which because of its difficulty is hard to solve. After an analogy to the first sense, the voice is called invisible. After an analogy to the second sense, a stone hidden in the ground is called invisible. After an analogy to the third sense, the sun is called invisible. It is in this last sense that we intend to speak about insolubles now. 17

This view was the standard one, and many authors took pains to make it explicit. William of Ockham, writing in the 17 See Roure [25], p. 248. On this anonymous author's text, see Spade [30], item vi. The text has been attributed to William of Sherwood (Shyreswood) by Grabmann, but De Rijk argues correctly that the attribution is not well founded. (See De Rijk [9], p. 93.) In [10], in, p. 30, n. 28. De Rijk rightly observes that in Spade [30], p. 26, I overstated his argument.

0

INTRODUCTION

first part of the fourteenth century, says: "About insolubles, one has to know that it is not because they can in no way be solved that some sophisms are called 'insolubles', but rather because they are solved with difficulty."18 Again, Albert of Saxony, writing somewhat later,19 says that insolubles are so called "not because they can in no way be solved, but because it is hard to solve them."20 Richard Lavenham, a somewhat derivative writer at the very end of the fourteenth century,21 has a vivid way of making the point: Just as the bond of love is sometimes called insoluble, not because it is in no way dissolvable (insolubilis), but because it is dissolvable with difficulty, so a sentence is sometimes called insoluble, not because it is not solvable, but because it is solvable with difficulty. 22

The guiding idea here is that the reasoning that gives rise to the paradoxes is based on an out and out mistake - a subtle mistake, to be sure, but a mistake nonetheless. The solution to the paradoxes lies in locating the mistake, and in providing some way of avoiding it. Ockham says: Hence one must know that sophisms are insolubles when, by apparent inferences that seem to be governed by necessary rules. 18

William of Ockham [50], m-3, 46, lines 2-4. On the date, see the editors' discussion in their introduction, William of Ockham [50], pp. 47*56*. For Ockham's position on the "insolubles," see Spade [30], items i.xx and LXXI, and Spade [31]. 19 Between 1351 and 1365, according to Heidingsfelder [18], p. 44. 20 Albert of Saxony [1], vi, 1, fol. 43rb. For Albert's position on the insolubles, see Spade [30], item xxiv. 21 On Lavenham, see Spade [41]. 22 London, British Library, Sloane MS 3899, fol. 73r. Lavenham's view is essentially that of Albert of Saxony's. See Spade [30], item LVI. I am preparing an edition of Lavenham's Insolubilia.

INTRODUCTION

9

from some contingent sentence its opposite is inferred. Because it is difficult to block such inferences, these sophisms are called "insolubles."23

In the early stages of the modern discussion of the paradoxes, we find a somewhat analogous state of affairs. Bertrand Russell, for instance, after sketching his famous "theory of types" in the introduction to Principia Mathematica, and after showing how that theory disarms the paradoxes, says: Thus the appearance of contradiction is always due to the presence of words embodying a concealed typical ambiguity [a technical term here], and the solution of the apparent contradiction lies in bringing the concealed ambiguity to light. 24

This stage of the problem, common to both the medieval and the modern discussions, I shall call the stage of "looking for the mistake." In both the medieval and the modern periods, this stage came very early in the development of the discussion. In both developments too, it was very soon realized that the early attempts to solve the paradoxes were either too weak or too strong. Either they did not avoid all forms of the paradoxes, or else they not only avoided the paradoxes, but also prevented certain perfectly innocuous inferences that should not have to be avoided.25 Attempts were made to rectify this situation, to tinker with the theories, or to provide new theories that were more satisfactory. Eventually we arrive at 23

William of Ockham [50], m-3, 46, lines 5-8. Whitehead [49]. vol. 1, p. 65. (Emphasis added.) 25 For the early views in the medieval period, see Spade [30]; and Spade [33], p. 307 and n. 64. For objections to these early views, see Bradwardine's text in Roure [25], pp. 286-296; and the discussion in [30], item i.xiv. 24

10

INTRODUCTION

another stage in the development, a stage I shall call the "comparative stage." On the modern side, this stage may be illustrated by the following comment: "History indicates that the Liar may never wholly be laid to rest, and so progressive criteria marking levels of success may be appropriate."26 The guiding idea here is that the Liar Paradox and its relatives are simply not going to admit of a totally satisfactory solution. The very presence of the paradox, the fact that we feel it to be paradoxical, indicates that some of the commonsense principles we should like to keep have to be given up. Something has to give somewhere. And, depending on what we are willing to sacrifice, various approaches to the paradox are possible. Some of the approaches will be more satisfactory than others. This depends to a large extent on what we are willing to give up. Although this is a common modern view, it was a stage reached in the medieval literature only rarely. In fact, to the best of my knowledge, only Heytesbury reached that level of sophistication, and he himself is not altogether consistent about the matter. The first chapter of his "Rules" reflects both the early stage of "looking for the mistake" and the more sophisticated, "comparative" stage. He opens his chapter with a rather unfortunate simile: The Philosopher says in the fourth chapter of the Categories, "The squaring of the circle, even if it is knowable, is nevertheless not yet known." I think it has to be said likewise that, although the "insolubles" can be solved, nevertheless they have not yet been solved. (Par. 4)

26

Herzberger [20], p. 26.

INTRODUCTION

11

This reflects the earlier, confident stage. There is indeed a solution; we simply have not found it yet. But later in the same chapter, Heytesbury sets out his own position and recognizes that various objections can be raised against it. He finally admits, "Many objections of this sort can be raised against this view, which it would be difficult or impossible to answer to complete satisfaction." (Par. 43) Earlier, Heytesbury sets out three previous opinions, which he wants to argue against, and sketches his own position as a fourth. Then he says: I shall argue first of all in a single way against the first three opinions taken together, then against the individual ones individually, and afterwards against the fourth , which I think ought to be maintained among the others. But I do not claim that it or any < opinion > is altogether satisfactory, because I do not see that that is possible. Nevertheless I rate this one among all of them to be nearer the truth. (Par. 9)

Again, at the very end of the chapter (par. 64), Heytesbury says that "insolubles, as their name implies, cannot be solved without evident objection." In all these places we see the new, "comparative" stage, the view that we must pick among alternative solutions to the paradox, with the tacit understanding that none of them is going to be all that we could want. This relatively high level of understanding is an additional reason for choosing Heytesbury's text as the means of introducing the reader to this medieval literature. The translation below is based on the Venice edition of 1494 (Hain 8437), fols. 4va-7rb. The volume also contains the commentary by Cajetan of Thiene and several other works.

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INTRODUCTION

The text is generally reliable; in only a few places is it necessary to depart from the edition, and then in only minor ways. In several cases I have inserted the Latin original of a phrase in parentheses after my translation. For the most part, I have done this only on the first occurrences of such phrases. Subsequent occurrences are to be understood as translating the same Latin words. Although this makes for occasional awkwardness of English style, I think it is important, in translating a highly technical work of this kind, to be as consistent as possible. In some cases I have inserted words in pointed brackets. These are added in order to make the meaning clearer, and do not involve an emendation of the text. In two cases, I have found it necessary to delete a word from the edition. I have left such words in the translation, but put them in square brackets to signal the fact that they are to be deleted. In a few instances, it has been necessary to change a word - for example, to read "sit" for "scit." In all such cases I have consulted two fourteenth-century Vatican MSS, Vat. lat. 2136, fols. lra-5rb, and Vat. lat. 2138, fols. 89ra-91va, and the fifteenth-century MS, Padua, Biblioteca Antoniana, Cod. N. 407, fols. 26ra-30va. All departures from the Venice edition have been recorded in the notes. The section headings and division into paragraphs are mine. At the beginning of each paragraph of the translation, I have inserted the folio, column and line references to the Venice edition. A detailed study of Heytesbury's text follows the translation.

William Heytesbury On "Insoluble" Sentences

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< Prologue >

1 (4va4) You young men in your first year of logical studies,1 I would deliver into your care, to the extent that the barrenness of my ability would manage, a brief compendium (summa] of the rules for solving sophisms. Not, of course, those sophisms which the subtlety of their discoverers has completely surrounded by apparent contradiction, or those which regularly lie hidden from any logician,2 but rather those which stand out as the common ones, to the extent that the common and daily drill (exercitatio)3 teaches them, and which any respondent (responsalem) ought to know how to unravel. if the wordy bombast of the old sophisters and the disdain of the advanced who are looking for more exalted things did not stand in the way of the enterprise. For, among so many and such great discoveries and new opinions as different as now day after day sprout and put forth leaves, I neither know nor see how they would stop their murmurings while I investigated further things < already > certain to everyone. Yet, because the task is easy and I hope it 1

On the study of logic at Oxford in the fourteenth century, see Weisheipl [46]. 2 It is not clear what sophisms Heytesbury means to exclude here. As examples of the latter kind, we might perhaps consider sophisms concerning the Trinity, which would perhaps remain "hidden from any logician," and pertain properly only to the theologian. 3 The "period of discussion and debate accompanying the lecture." (Wilson [51]. p. 4.)

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PROLOGUE

can have a certain usefulness, I shall not pretend that this pretext is my motive.4 Rather, considering that I proposed to offer it to the above-mentioned students, I shall try to approach this small work, with moderate brevity, as a kind of introduction.5 2 (4va22) I divide our little compendium into six chapters, lest the reader avert his eyes on account of the prolixity of a spread-out and ill-arranged narrative. When it has first been seen what is treated below in the individual chapters, so that everyone may find more quickly what he wants, I shall immediately close this prologue. 3 (4va26) The first chapter, therefore, will set out a known, but not a new,6 compendium of insolubles. The second chapter will solve the sophisms that arise concerning "to 4

The Latin of this puzzling sentence reads "Verum quoniam est iste labor facilis, ipsumque utilitatem quamdam spero posse amplecti, praetensam hanc causam non causabor ut causam." The "pretext" (praetensam causam) is presumably the vain hope that the old sophisters and the others will indeed stop their murmurings while he investigates further things that are already certain to everyone. Heytesbury's real motive is given at the beginning of the sentence. 5 The pompous tone of the paragraph is present in the Latin. The point is that Heytesbury would present his rules briefly, if only others would not complain that he was belaboring the obvious. But since it is easy and useful, he is going to do it anyway for the students' sake. There is some irony toward the end of the paragraph; in at least the first chapter of the "Rules," it is clear that Heytesbury thinks many people have completely misunderstood some of the "things that are already certain to everyone." See pars. 4-7. 6 Despite the disclaimer of originality, no previous author is known to have maintained exactly Heytesbury's position. On this question, see Spade [42].

PAR. 2-3

17

know" and "to doubt," so that they no longer tie up one who is < trying to> solve them. The third chapter considers the difficulty of relative terms, and makes the respondent more certain about them. The fourth chapter explains the replies to sophisms built on the basis of the words "begins" and "stops." The fifth chapter treats the common ways of classifying "the maximum" and "the minimum," lays down true principles, and teaches them by examples. The sixth and last chapter gives instructions about the velocity of motions, and investigates the basis in terms of which it can be considered.

<Some Previous Opinions >

4 (4va37) Returning, therefore, to our topic, I shall say what I think has to be affirmed. The Philosopher says in the fourth chapter of the Categories,1 "The squaring of the circle, even if it is knowable, is nevertheless not yet known." I think it has to be said likewise that, although the "insolubles" can be solved, nevertheless they have not yet been solved. For there are many opinions flying about concerning insolubles. But let someone shout more loudly or be more capable, and, overcome by the applause of his spirits, his mouth will block and close off what he despises with sideward glances in the matter of insolubles as unworthy of solution, so that, growing hoarse, he will not know what clearly accords with reason.8 5 (4va51) In this group, for example, one opinion writes that in the case of insolubles it is quite possible that two contradictories are false at the same time. For one signifies entirely as is not the case (omnino sicut non est), and so it follows that it is false. And the other, although it signifies precisely as is the case

7

Aristotle, Categories 7, 7b31-33: "Thus, in the case of the squaring of the circle, if indeed that process is an object of knowledge, though it itself exists as an object of knowledge, yet the knowledge of it has not yet come into existence." (Oxford translation.) 8 Once again, the rather heavy-handed rhetoric is present in the original.

PAR. 4-7

19

(practise sicut est), nevertheless falsifies itself, for which reason it cannot be true.9 6 (4va55) But there is also another opinion on the matter. It is secured on a deeper foundation than it is effectively ruled by reason.10 It asserts that in the case of insolubles no contradictory is either true or false, for the reason that no insoluble is a sentence according to this opinion. For although each insoluble is an indicative expression (oratio) signifying as is the case or as is not the case, nevertheless its signification does not suffice for it to be called a "sentence."11 7 (4vb4) A third opinion takes the following conclusion as its maxim. 12 Otherwise perhaps I would quietly consider it worth a laugh. that each insoluble is true or false, and yet no insoluble is true, nor is any false. For, since each insoluble is a sentence, and every sentence is true or false, it follows that every insoluble is true or false. But it is not required by the fact that something is a sentence that it be true, 9

This is Roger Swyneshed's position. See the discussion in section 2 of the study, below, and the edition in Spade [38]. 10 That is, although it is hard to refute, it is nevertheless not a reasonable position. In his general refutation of the assumption shared by the first three opinions (pars. 10-18), Heytesbury employs a special trick to get at the "deep foundation" of this second opinion. See section 2 of the study, below. 11 Note the difference between the first part of this sentence and Boethius' classic definition, De differentiis topicis, PI. 64, 1174s: "A sentence is an expression signifying what is true or what is false." 12 "Tenet sibi... pro maxima." This seems a better translation than "as its greatest," even though it is perhaps odd to speak of a conclusion as a "maxim." See, e.g., Boethius, In Topica Ciceronis, PI. 64, 105ID: "Maxims, therefore, that is, the universal and best known sentences, from which the conclusion of syllogisms descends...."

20

PREVIOUS OPINIONS

nor that it be false. And so, although each insoluble is true or false, it does not follow from this that any is true or that any is false. That is what this opinion argues and concedes.13 8 (4vbl 3) The fourth and last opinion to be reviewed sets up the following as a principle, that no casus14 is possible which in any way includes anything that is absolutely (simpliciter) insoluble. Hence the following casus is not possible, that the sentence "A falsehood exists" (Falsum est), or any one like it, should be every sentence,15 and that it should precisely signify that a falsehood exists.16 For it follows from this that a falsehood is true and that two contradictories are false at the same time. Many other such inconsistencies (inconvenientia) follow too, but there is no point in reciting them now. Therefore, these are enough for the moment. 9 (4vb20) I shall argue first of all in a single way (per unum medium) against the first three opinions taken together, then against the individual ones individually, and afterwards 13 On this strange view, see the discussion in section 2 of the study, below. 14 On this term, see section 1 of the study, below. 15 A "sentence" in this context is an individual utterance or inscription - the sentence-token, not the sentence-type. As such, its existence is a contingent affair. 16 The Latin "Falsum est" might more naturally be translated "It is false." But I think that translation has a disadvantage in the present context. To say "The sentence 'It is false' precisely signifies that it is false" suggests a situation that is paradoxical even without assuming that the sentence is the only one in existence; the natural referent for the second occurrence of "it" is the quoted sentence "It is false" itself. The translation "A falsehood exists," although less strict, avoids this difficulty.

PAR. 8 - 1 1

21

against the fourth < opinion >, which I think ought to be maintained among the others. But I do not claim that it or any < opinion > is altogether satisfactory, because I do not see that that is possible. Nevertheless, I rate this one among all of them to be nearer the truth. 10 (4vb24) I argue therefore as follows. Each of those three opinions admits the main thing,17 that Socrates may be saying only the sentence "Socrates is saying what is false" (Sortes dicit falsum], which precisely signifies that Socrates is saying what is false. Then the first of those opinions says that the sentence so uttered by Socrates, "Socrates is saying what is false," is false because it falsifies itself, and its contradictory is false because it signifies entirely as is not the case. The second opinion denies under that casus that the expression so uttered by Socrates is a sentence, because it is inconsistent (non stat) with its signification and the circumstances posited in the assumed casus that it should be true or false. Therefore it follows that it is not a sentence when the casus is admitted. The third opinion, under the same casus, says that what is so uttered by Socrates is true or false, but denies that it is true and says it is not false. 11 (4vb36) From all this I argue as follows. If it is possible that Socrates is saying only the sentence "Socrates is saying what is false," which precisely signifies in that way, therefore it is possible that Socrates is saying only that he is saying what is 17

The Venice edition has "primarium" ("the main thing") here, which perhaps ought to be read "primarum" ("first"), modifying "opinions." The MSS omit the word.

22

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false. The inference is argued as follows:18 Since he is saying only the sentence "Socrates is saying what is false," which precisely signifies that he is saying what is false, it follows both that Socrates is saying that he is saying what is false and that he is not saying anything else. And if so, then Socrates is saying only that he is saying what is false. The inference is a good one, and the antecedent is possible. Therefore, the consequent too. 12 (4vb43) Now by the same reasoning by which it is possible, or should be admitted, that Socrates is saying only that he saying what is false, it is also possible and should be admitted that Socrates is saying only that he is saying what is not the case (sicut non est) or that it is not the case as Socrates is saying (non est ita sicut Sortes dicit). I prove the inference . Let it be posited that Socrates is saying only the sentence "It is not the case as Socrates is saying," and let it precisely so signify.19 It follows, by an argument like the earlier one in the first casus,20 that Socrates is saying only that it is not the case as he is saying. The antecedent is possible, as before. Therefore, the consequent too.21

18

The point of the inference is to eliminate the quotation of the sentence Socrates is uttering in favor of a "that"-clause expressing the sentence's precise signification. 19 Namely, that it is not the case as Socrates is saying. 20 See par. 11. 21 See section 2 of the study, below, for the reason Heytesbury shifts from arguing in terms of "Socrates is saying what is false" to "It is not the case as Socrates is saying."

PAR. 12-14

23

13 (4vb49) Let it be posited then that Socrates is saying only that it is not the case as Socrates is saying. When this has been posited, either it is the case as Socrates is saying or it is not. If not, then let it be posited that Plato is saying only that it is not the case as Socrates is saying. And then I argue as follows: It is not the case as Socrates is saying; and Plato is saying only that (solummodo sic dicii)\ therefore, it is the case as Plato is saying. Then it follows: It is the case as Plato is saying; and Socrates is saying just what Plato is saying, and only that (dicit totaliter sicut Plato, et solummodo sic); therefore, it is the case as Socrates is saying.22 14 (4vb55) Similarly, one argues thus: It is not the case as Socrates is saying; therefore, it is true that it is not the case as Socrates is saying. This inference is argued as follows: It follows "If God exists, therefore it is true that God exists," "If man is not an ass, it is true that man is not an ass." Likewise, "You are sitting, it is true that you are sitting." The inference is valid in this way for cases like these. Otherwise the following would hold at the same time (starent simul), "God exists" and "It is not true that God exists." 23 It follows also that if no sentence existed, it would not be possible for anything to exist, which every intellect shrinks from admitting. 24 22 Contrary to the hypothesis. Hence it follows by reductio that it is the case after all as Socrates is saying. But see par. 16. 23 That is, if arguments of the form "p-, therefore, it is true thatp" were not in general valid, it would be possible to have a case where "p and it is not true that p" holds. Using "God exists" for "77" simply yields a particularly striking example. 24 The argument in pars. 14-15 yields, by a different route, the same conclusion as the argument in par. 1 3. The last sentence of par. 14, however.

24

PREVIOUS OPINIONS

15 (5ra4) Therefore, one argues as follows. It is true that it is not the case as Socrates is saying;25 and Socrates is saying so;26 therefore, Socrates is saying what is truly the case (sicut verum est esse)\ therefore, Socrates is saying what is the case. And furthermore: therefore, it is the case as Socrates is saying.27 16 (5ra6) So, if this28 is conceded as following in the assumed casus, to the contrary: Let it be posited29 that Cicero is saying only that it is not the case as Socrates is saying. Then I argue as follows: It is the case as Socrates is saying;30 and Cicero is saying only that it is not the case as Socrates is saying; therefore, it is not the case as Cicero is saying. The inference is apparent enough. Then let me argue further: It is not the case as Cicero is saying; and Cicero is saying just what Socrates is saying, and vice versa; therefore, it is not the case as Socrates is saying.31 suggests that Heytesbury himself does not accept this mode of argumentation because of the consequences it entails. For instance, if God exists, then if such consequences ("/?; therefore, it is true that p") are in general valid, it would follow that it is true that God exists, and so that a truth exists - i.e., that some utterance or inscription exists. But, if creation is a free act, it must be possible for God to exist without there existing any utterances or inscriptions. 25 See the first sentence of par. 14. 26 See the beginning of par. 13. 27 See n. 24. 28 Namely, that it is the case as Socrates is saying, whether one argues for this by the argument in par. 13 or by the more dubious argument in pars. 14-15. 29 Together with what was posited in par. 1 3. 30 That has just been conceded. 31 Contrary to the conclusion in par. 1 3. The moral is drawn in par. 18.

PAR. 15-18

25

17 (5ral 2) Similarly, it follows: It is the case as Socrates is saying;32 therefore, it is false that it is not the case as Socrates is saying. This inference is proved exactly as was argued earlier in the other deduction.33 Then one argues thus: It is false that it is not the case as Socrates is saying; and Socrates is saying only that; therefore, Socrates is saying what it is false is the case (sicut falsum est esse). And if so, it follows that it is not the case as Socrates is saying.34 18 (5ral7) Thus, when the assumed casus35 is admitted, it seems that both contradictories follow.36 The same argument appears when it is posited that any man you pick is saying only that it is not the case as any man is saying (non est ita sicut aliquis homo dicit).31 Therefore, by positing that two contradictories are false at the same time, the first opinion 32 33

34

That has been conceded. See par. 16. See par. 14.

Once again. Heytesbury uses a second argument to derive the same conclusion as was reached in par. 16. In virtue of the remarks at the end of par. 14, Heytesbury would perhaps not accept this mode of argumentation. 35 In par. 13. 36 Namely, the conclusion of par. 1 3 (and par. 15), and the conclusion of par. 16 (and par. 1 7). 37 Literally, "it is not the case as some man is saying." But medieval logicians would read this so that the "some" falls within the scope of the "not." Thus the phrase does not amount to "some man is saying what is not the case." but rather to "this is not so, namely, that it is the case as some man is saying" - which is to say, "it is not the case as any man is saying." Heytesbury's claim here is wrong. If man A says "It is not the case as any man is saying," it cannot be the case as he himself is saying. Hence, it is the case after all as some man somewhere is saying. But it does not follow that it is the case as this man A is saying. In order to get a parallel argument, and so a paradox, we should have to add the (quite possible) assumption that no one else in the world is at that time saying anything that is the case.

26

PREVIOUS OPINIONS

was able to maintain whatever follows under the casus. And if the second opinion knew how to strike a medium between contradictories, it could perhaps feign some sort of response. But let the third opinion say whatever it pleases; it will have no path by which to flee. 19 (5ra24) Now I shall argue against these opinions one at a time, and first of all against the first one. Let it be posited that the sentence "This sentence signifies otherwise than is the case" (aliter quam est), indicating itself, is a. And let it precisely so signify.38 When this has been posited, either the case is entirely as a signifies or else it is not. If not, then to the contrary: The case is not entirely as the sentence a signifies; and it signifies the case to be somehow (aliqualiter esse); therefore, the sentence a signifies otherwise than is the case. The inference is a familiar one. Then let it be posited that b is a sentence which precisely signifies that this sentence indicating the sentence a - signifies otherwise than is the case. Let its contradictory be c, which precisely signifies that this sentence39 does not signify otherwise than is the case. When these things have been posited, it follows that if the sentence a signifies otherwise than is the case, and the sentence b signifies precisely that the sentence a signifies otherwise than is the case, then the case is entirely as the sentence b signifies. And it follows < further >: The case is entirely as the sentence b signifies; and a signifies entirely as b does, and vice versa; therefore, the case is entirely as a signifies. And if so, therefore a does not signify otherwise than is the case. 38

case.

39

That is, that this sentence, namely, a, signifies otherwise than is the Namely, a.

PAR. 19-21

27

20 (5ra38) So if it is said that the case is entirely40 as the sentence a signifies in the assumed casus,41 to the contrary: Then c is true. For then c is a sentence which does not falsify itself, and it signifies precisely as is the case;

therforititturueiffoo

b are contradictories; therefore, b is false.43 And it follows: b is false, and does not falsify itself; therefore, b signifies otherwise than is the case.44 And it follows : b signifies otherwise than is the case; and a signifies entirely as b does, and vice versa; therefore, a signifies otherwise than is the case. The inference is evident enough from the casus. Therefore, it is evident that two contradictories follow from the casus.45 21 (5ra46) Now if someone should say perhaps that the casus is not a possible one, to the contrary: Let a be this particular sentence46 "Some sentence signifies otherwise than is the case." And let b be one like it in all respects.47 Let each of these signify precisely that some sentence signifies 40 Reading "ita est totaliter" with the MSS rather than "ista est totaliter" with the edition. 41 This is the other alternative left from the fourth sentence of par. 19. 42 See Roger Swyneshed's definition of truth, quoted below in section 2 of the study. 43 Swyneshed would accept this conclusion. For him, two contradictories may be false at the same time, but not true at the same time. See section 2 of the study. 44 See Swyneshed's definition of falsehood quoted in section 2 of the study. 45 Namely, the conclusion of par. 19 and that two sentences before in par. 20. 46 "Particular" in the technical sense of having a "particular" (existential) quantifier "some." 47 That is. a and b are two tokens of the same type.

28

PREVIOUS OPINIONS

otherwise than is the case. And let there be many other false sentences, each one of which signifies otherwise than is the case. Then let us posit that, with the sentences a and b remaining and signifying precisely as before, the other sentences are destroyed one after another, until there are no sentences but a and b. Once this has been posited, either there will be some sentence which signifies otherwise than is the case, or there will not. If not, therefore no sentence signifies otherwise than is the case; and the sentence a signifies that some sentence signifies otherwise than is the case; therefore, the case is not as the sentence a signifies. And it follows: The case is not as the sentence a signifies; and the sentence a signifies the case to be somehow; therefore, the sentence a signifies otherwise than is the case. And if so, therefore some sentence signifies otherwise than is the case.48 22 (5rb2) If that is conceded, then I argue as follows. Some sentence signifies otherwise than is the case; and the sentences, a as much as /?, precisely signify so;49 therefore, the case is as a signifies; and b signifies entirely as a does, and vice versa; therefore, the case is entirely as b signifies; and there is no sentence which is not either a or b, by the casus; therefore, there is no sentence which signifies otherwise than is the case. Now he who posits that two contradictories are false at the same time is not in a position to deny that this casus is possible. For he himself proves in this way that it is possible for some sentence to falsify itself.50 48

Contrary to the hypothesis. That is, that some sentence signifies otherwise than is the case. 50 Heytesbury is arguing against a straw man here. Swyneshed considers a series of five objections to his claim that some sentences falsify themselves. 49

PAR. 22-23

29

23 (5rb9) Again, I argue thus: It follows from this position that a falsehood follows from a truth in a valid (bond} formal inference where the antecedent is a simple sentence and the consequent likewise.51 This is argued as follows: According to this position, when it is posited that the sentence 'This is false" signifies precisely thus, namely, that this is false, indicating itself, then the sentence 'This is false" would be false, because it falsifies itself. Its contradictory would also be false, because it would signify as is not the case.52 Let it be posited, therefore, that a is a sentence which signifies itself to be false;53 and let b be another sentence like this: "This is false," which precisely signifies that this is false, indicating a. When this has been posited, a follows from b in a valid formal inference, because it follows 'This is false; therefore, this is false," indicating the same thing. That inference is argued thus: The contradictory of the consequent is inconsistent (non stat) with the antecedent, since these do not hold at the same time (ista non slant simul) "This is false" and "This is not false," indicating precisely the same thing. 54 Then I argue as follows: a follows The fifth of these objections is based on the sentence "This <sentence> signifies otherwise than is the case." Swyneshed rejects the argument but admits the casus. (See Spade [38].) Hence the argument in pars. 21-22 is superfluous. Despite Heytesbury's remark, Swyneshed does not argue on the basis of the casus in pars. 21-22. 51 See Swyrieshed's second conclusion, quoted below in section 2 of the study. On the significance of Heytesbury's including the proviso about "simple" sentences, see section 3 of the study. 52 See Swyneshed's definition of falsehood, quoted below in section 2 of the study. 53 That is, a is the sentence "This is false," indicating itself. See the next sentence. 54 A common test of validity was to ask if the contradictory of the consequent was inconsistent with the antecedent.

30

PREVIOUS OPINIONS

from b in a valid formal inference. And b is true, because b is a sentence signifying precisely as is the case, and it does not falsify itself, and so b is true. And a is false. Therefore, a falsehood follows from a truth in a valid formal inference. And we note that a as well as b are simple sentences.55 Therefore, what we proposed56 follows. It is usually abandoned as impossible. 24 (5rb26) Likewise, I argue that a truth is convertible with a falsehood, and that the same simple sentence contradicts a false sentence and a true one. Now it is apparent at once that a and b57 are convertible, because a and b formally imply one another. For b follows from a formally, and vice versa, as was argued before;58 therefore, a and b are convertible.59 Also the same thing that contradicts b contradicts a. For one such "This is false" signifies no more than do two, indicating always the same thing; therefore, there is no reason why, by that in virtue of which it would contradict a, it would not also contradict b.™ Therefore, the <second> claim follows.61 55

See section 3 of the study. At the beginning of the paragraph. 57 From par. 23. 58 Par. 23. 59 "Conversion" here applies to any logical equivalents, not just to the "simple" and "per accidens' conversions of the syllogistic. This sentence in the text establishes the first of the two claims in this paragraph. Recall from par. 23 that a is false and b is true. 60 Heytesbury seems to have reversed a and b here. In the previous sentence, we start by contradicting b, and ask whether the same thing contradicts a, not, as here, the other way around. 61 Actually, the second claim of the paragraph requires a "simple" sentence as the contradictory of a and b. See section 3 of the study. 56

PAR. 24-25

31

25 (5rb33) I argue in a different way that, on the given view, something other than the necessary contradicts the impossible, and that there are two sentences, each one of which contradicts the same impossible sentence, and yet one of them is necessary and the other contingent and not necessary. For let it be posited that the sentence 'This sentence is not necessary" is a. And let it precisely signify that this sentence is not necessary, indicating in both cases the very same sentence a. Let b be its contradictory, namely, "This sentence is necessary," which precisely signifies that this sentence is necessary, indicating the same one as before, just as it should, since a and b are62 contradictories. Once these things have been posited, it follows that b is impossible. For it includes opposites, namely, that this sentence is necessary which precisely signifies that this sentence is not necessary, as is apparent to anyone who looks at it.63 But a is not necessary, by the same argument, , that if a, signifying in this way, were necessary, it would include opposites, as is obvious and evident.64 Therefore, it follows that a is not necessary. But a contradicts the impossible b. Therefore, what is not necessary contradicts the impossible, which is what we wanted insofar as the first part of the conjunction (copulativae)65 is concerned.

62

Reading "sint" with the MSS, rather than "sit" with the edition. If b is possible, then suppose it is so. I.e., suppose a is in fact necessary. Arguing ab necesse ad esse, we can conclude a - i.e., we can conclude that a is not necessary. Hence, by reductio, b is impossible after all. 64 If a is necessary, then arguing again ab necesse ad esse, we can conclude a - i.e., we can conclude that a is not necessary. By reductio, then, a is not necessary. 65 That is. the two claims at the beginning of the paragraph. 63

32

PREVIOUS OPINIONS

26 (5rb47) The second part66 is argued forthwith, as follows. Positing that c is a sentence like a,67 namely, "This is not necessary," which precisely signifies that this is not necessary, indicating the sentence a in both cases, then it follows, as was noted, that c is necessary68 - but with the proviso that it precisely signifies in this way. When this has been assumed, it follows that there are two sentences, namely, a and c, each one of which contradicts the same impossible < sentence >, namely b, and yet one of them is necessary, namely, c, and the other contingent and not necessary, namely, a. For one cannot posit that the sentence a is impossible when it signifies in this way, because the sentence a precisely signifies as is the case and does not falsify itself;69 therefore, a is true.70 The proposed conclusion71 follows, therefore, in each of its parts. 27 (5rb56) Likewise, I argue that there is some true sentence which is72 neither necessary nor contingent. From this it also follows that the sentence a under the casus we have 66

The second of the two claims in par. 25. That is, a second token of the same type as a. 68 If c is not necessary, then the case might not be as c precisely signifies. I.e., a might be necessary, which is to say b is possible. The argument then proceeds exactly as in n. 63. This is why Heytesbury says "as was noted." 69 It follows from a that a is not necessary - insofar as a follows from itself. But it does not follow that a is false - i.e., a does not falsify itself. 70 See Swyneshed's definition of truth quoted below in section 2 of the study. And since a is true, it cannot be impossible. Thus, since it is neither necessary (see n. 69) nor impossible, it must be contingent. 71 That is, the twofold claim at the beginning of par. 25. 72 Reading "sit" with the Vatican MSS, rather than the edition's "scit." The Padua MS has "est." 67

PAR. 26-27

33

treated,73 although it is true, is neither necessary nor contingent, the opposite of which was just now correctly argued. I argue this conclusion as follows: Let it be posited that the sentence "This sentence is not necessary" is a. And let it precisely signify thus, namely, that this is not necessary. And let it be unable to signify otherwise.74 Let its contradictory be b, namely, this LThis sentence is necessary," which likewise is unable to signify otherwise than that this is necessary, indicating the sentence a. When this has been posited, it follows, as was observed, that a is true, because it precisely signifies as is the case and does not falsify itself.75 But a is not necessary, because then b would be true in virtue of the same argument by which it was proved that a is true,76 and if that is so, it follows that two contradictories are true at the same time. 77 Therefore, it follows that a is true and that a is not necessary. But neither is it a contingent sentence, because the sentence a precisely signifies as is necessarily the case (sicut necesse est esse)1* and does not falsify itself; therefore it is necessary.79 73

In pars. 25-26. Note that this crucial added stipulation does not affect the reasoning in pars. 25-26. 75 See par. 26. 76 I.e.. h would signify precisely as is the case and would therefore, it would be true. 77 Contrary to Swyneshed's view. See above, n. 43. 78 As long as a precisely signifies as it does, it will precisely signify as is the case, as was argued in par. 25. But, by the hypothesis of the paragraph, a cannot precisely signify otherwise than in fact it does. Hence a in fact precisely signifies as is necessarily the case. 79 And not contingent, thus completing the proof. If a were not necessary, then it might be false. But, by Swyneshed's definition of falsehood (see section 2 of the study), it could be false only if either it precisely signifies 74

34

PREVIOUS OPINIONS

28 (5val6) Likewise, I argue as follows. Some sentence convertible with this a*° is necessary; therefore, a itself is necessary.81 The inference is clear, and I prove the assumption: Let c be another sentence like a, which precisely signifies that this is not necessary, indicating the sentence a. Then, since c follows from a formally, and vice versa - because the contradictory of c contradicts a and vice versa, as was argued before in a similar argument82 - it follows that a and c are convertible. Now c is a necessary sentence.83 Therefore, a is a necessary

s e n t e n c e a f i o f t h a t i s s s s s s s s e i s o84 contingent nor a necessary sentence, which is what I wanted.

29 (5va25) But perhaps someone will say here either that the truth of the matter is that the casus is impossible, or that the otherwise than is the case (and this has been ruled out as impossible - see n. 78 above), or else it falsifies itself. But it does not falsify itself (see n. 69, above), and cannot falsify itself since in order to do that its signification would have to change (and that has been ruled out too). Swyneshed might reply here that the assumption that a cannot change its signification is not to be admitted - it is impossible since it violates the conventional nature of language. This would require Swyneshed to say not only that language is in fact conventional, but that it must be. This reply would avoid Heytesbury's criticism in par. 31. 80 Where a is as in par. 27. 81 Only necessary sentences are logically equivalent to a necessary sentence. 82 See par. 24. 83 See par. 26. 84 Par. 28 is a second argument that a is not contingent. As in par. 27, the argument proceeds by proving that a is necessary, and so cannot be contingent. The claim that a is not necessary is the conclusion of an independent argument in par. 26. Heytesbury simply imports that conclusion here. The fact that the two conclusions, although validly derived, are inconsistent is exactly what Heytesbury is trying to show.

PAR. 28-30

35

inference "The sentences a and c are convertible; and c is necessary; therefore, a is necessary" is not valid, just as it does not follow "a and c are convertible; and c is true; therefore, a is true," because although perhaps the case is as a entirely signifies, yet a perhaps falsifies itself, and so it does not follow that a is true. Perhaps likewise someone will say about the example before us that, although a and c are convertible, each signifying precisely as is necessarily the case, and c is necessary, nevertheless a is not necessary, because the sentence a denies that it is necessary, or signifies that it is not necessary, which amounts to the same thing. 30 (5va36) But this is no reply, because by changing the terms a little, there follows an inconsistency just as bad. For, when it is posited that the sentence a signifies that a does no signify as is necessarily the case, and that it is unable to signify otherwise, it follows that the sentence a is true, and it does not signify as is necessarily the case, or as is contingently not the case (sicut contingent est non esse).*5 85 The last phrase perhaps ought to be emended to "as is contingently the case." with Vat. lat. MS 2136. But if contingency here is contingency ad iitrumlibet (i.e., possibly so a n d possibly not so), it makes no difference, although the text is startling as it stands. The point of this paragraph is to bypass the argument in par. 29. Just as Swyneshed would deny that a true sentence can be converted only with truths, since on the contrary a true sentence can be converted in special cases with a sentence that falsifies itself, so too he might deny that a necessary sentence can be converted only with necessary sentences, since on the contrary a necessary sentence can be converted in special cases with a sentence that "unnecessitates" itself (here the analogue of "falsifies"). Heytesbury bypasses this argument by descending from the level of truth and necessity to the level of signification. It is indeed the case, presumably, that if a and c are converted, then they both signify precisely the same way. And so the following inference holds: "a and

36

PREVIOUS OPINIONS

31 (5va41) But if someone says that this last casus is impossible, just like the first,86 and so none of the impossible sentences follows, except from the impossible, then , on the contrary: To deny in any way the casus of an insoluble is nothing but an evasion of the argument, as those who uphold this position as true themselves bear witness.87 Moreover, if the term "sentence signifying otherwise than is the case" is put in place of the term "false" so that, where it is usually assumed that the sentence "This is false" signifies precisely that it itself is false, it is posited that it 88 signifies precisely that it signifies otherwise than is the case, and where it is posited that the sentence "A falsehood exists" is every sentence, and that it precisely signifies just that,89 it is posited that this is every sentence "There is some sentence signifying otherwise than is the case," and that it precisely signifies just that,90 and in general, in place of such simple terms there are put terms like this compounded out of adverbs, which according to a sound understanding are convertible with those simple terms (for it follows according to a sound underc are convertible; and c precisely signifies as is necessarily the case; therefore, so does a." Hence the entire argument in the preceding paragraphs can be reconstructed in a way that meets the objection. 86 See the first alternative in par. 29. 87 See perhaps Spade [38], par. 47: "But, as will appear later, that is no reason except for those vacuous quibblers who do not know how to reply to insolubles other than by holding that the possible is impossible." Swyneshed is replying here to an attempt to deny an insoluble casus as impossible. 88 Or rather, the sentence "This is a sentence signifying otherwise than is the case." 89 Namely, that a falsehood exists. 90 Namely, that there is such a sentence.

PAR. 31-33

37

standing: 'This sentence is false; therefore, it signifies otherwise than is the case," and vice versa, "This sentence is necessary; therefore, it signifies what is necessarily the case." and so on in similar cases) then, when the terms are changed, you will see what that twofacedness amounts to, namely, of admitting the one casus and denying the other, as long as they do not give any cause or reason for the difference except that "two contradictories are false at the same time," which carries meager evidence for many people. Many other things could be added, as is evident to one who wishes to inquire into the matter. But it would be superfluous to linger on these things any longer. 32 (5vb8) I argue in two ways against the second opinion, which posits that no insoluble is a sentence. First, it follows from that opinion that there are two expressions each of which signifies entirely as the other of them does, and yet one of them is a true sentence and the other is not a sentence. For let a be "This is not true." which precisely signifies that this is not true, indicating a. And let b be another <sentence> entirely like a, which also precisely signifies that this is not true, indicating a. It follows that then b is true, because b is an expression precisely signifying as is the case, and also it does not falsify itself; therefore, it is true. But a is not a sentence, according to this position. Therefore, under this casus the conclusion follows. 33 ( 5 v b l 7 ) It would follow also that there is an expression that signifies precisely as is not the case, and is not a sentence, and it would become a true sentence just because another sentence signified

38

PREVIOUS OPINIONS

in a manner precisely opposite to it. For let it be posited that these two are all the sentences : "A falsehood exists" and "This is true." Let the first of these be a. signifying precisely that a falsehood exists, and the second be b, signifying precisely that this is true, indicating a. When these things have been posited, it follows, according to the given view,91 that neither of those expressions is a sentence.92 And just because there should come to exist an expression c, precisely signifying that this is not true, b would become a true sentence and so would a, as is apparent to one who looks at it.93 Also if under that casus94 we posit that a stops existing, then b wou begin to be a sentence.95 But that does not conform to any understanding, whatever a person says outwardly with his mouth. Moreover, if we change the simple terms into composite terms, as was shown above in arguing against the first opinion, 96 this <second> position has no point at all. We 91

That is, the second opinion. The casus gives us a "cyclic" insoluble. Presumably in such a case this opinion says that both pseudo-sentences are to blame, so that neither one of them is a sentence. On such cyclic paradoxes, see Spade [28]. 93 I.e., if we suppose now that, in addition to the two sentences a and b, a third sentence c comes into existence, precisely signifying that a is not true, this new casus is no longer an insoluble one. Sentence b cannot be consistently made false, any more than it could under the original casus. For then a falsehood would exist, and so a would be true. But then b would be true and not false. On the other hand, under the new casus, b can consistently be made true. Then a is true and c is false. No paradox arises. 94 The original casus, not including sentence c. 95 The paradox would dissolve, and b would be straightforwardly false in virtue of its being affirmative and having a non-denoting subject term. 96 See par. 31. The second opinion, although it denies that insolubles are either true or false, nevertheless admits that they either signify as is the case or signify otherwise than is the case. See par. 6. 92

PAR 34-35

39

therefore abandon the second position, like a void without a plenum. 97 34 (5vb33) Against the third position, which says that each insoluble is absolutely true or false and yet none is true and none is false, I can argue in many ways. First, in a manner entirely like what was just argued against the second opinion, 98 that is, by deducing that there are two convertible sentences, one of which is true and the other neither true nor false. Let a be the sentence 'This is not true," which precisely signifies that this is not true, indicating a. And let b be another <sentence> completely like it, which also precisely so signifies, namely, that this is not true, indicating a. Then it follows according to this view that a is neither true nor false, since it is insoluble. But b is true, because it is a sentence signifying as is the case, and it is not insoluble; therefore, b is true. But b is convertible with a, because a and b formally imply each other. Therefore, what I proposed follows. 35 (5vb7) It follows also that there is a pair of contradictories neither of which is true, nor is one of them false, or else that one of them is true and the remaining one neither true nor false. For let a be the insoluble 'This is false," which precisely signifies itself to be false. Then according to this view, neither is a true nor is it false. It follows therefore that its contradictory is neither true nor false, or else if it is true, it follows at least that a is neither true nor false. But nevertheless. 97

The point is that the former is as abhorrent to us as the latter is to nature. 98 See par. 32.

40

PREVIOUS OPINIONS

if we posit that the contradictory of a is true, a contradicts that truth which contradicts a itself." 36 (4vb56) Also, this position is inconsistent with itself (sihi ipsi repugnat). For it unquestionably includes contradictories that something is a man or an ass, and that it neither is a man nor is an ass. Thus the position is refuted. One part of it manifestly disproves the other. 37 (6ra3) Leaving the above opinions behind, the fourth opinion is next. I want to argue against it. Then, when the counterinstances (instantia) brought up in opposition to it have been resolved, there will follow certain conclusions or rules by means of which a respondent will be able to reply more quickly to every casus that <ever> has been or will be posited. Now this opinion denies every casus that in any way includes anything absolutely insoluble, as was said above.100 to the contrary: It is possible that the sentence "A falsehood exists" is every sentence, and that it precisely signifies that a falsehood exists. This is proven because it is possible that the sentence "A falsehood exists" signifies precisely that a falsehood exists, provided that there are many other false sentences. Therefore, let it be posited that 99 One might argue that since a is neither true nor false, neither is its contradictory. Alternatively, one might argue that a is neither true nor false only because it is insoluble and paradoxical, but that its contradictory, "This is not false." indicating a, is not insoluble or paradoxical but quite straightforwardly true. There is nothing especially paradoxical about a's contradicting that truth which contradicts a, at the end of the paragraph. Any false sentence will be like that. 100 Par. 8.

PAR. 36-38

41

it is so, 101 and that every false sentence begins not to be, so that immediately after this, there will not be any false sentence other than "A falsehood exists." But let that one remain as before. When this has been posited, either that <sentence> will signify immediately after this only that a falsehood exists, or it will not. If so, I have what I wanted. If not, to the contrary: This <sentence> in no way signifies the case to be (nullo modo signified! esse) except by imposition. But neither is it imposed, nor will it ever be imposed, nor was it ever imposed, to signify otherwise than as it now signifies. And immediately after this it will signify in some way. Therefore, immediately after this it will precisely signify just as it now signifies. The inference is a familiar one, and the major is clear. The minor follows from the casus. For I assume that no one imposes or imposed or will impose it to signify otherwise than it now signifies. It follows therefore that immediately after this it will signify entirely as it now signifies; and it now signifies precisely that a falsehood exists; therefore, it will signify then precisely that a falsehood exists. But then there will not be any false sentence other than this one; therefore, etc. 102 38 (6ra28) Moreover, let it be posited that no one but you thinks about this sentence, and by means of it you form the conception only that a falsehood exists, so that it does not signify to you except only that a falsehood exists. When this has been posited, I argue as follows: The sentence "A falsehood 101

That there are many other false sentences. I.e.. therefore the casus denied as impossible in par. 8 must be admitted after all. The case considered in this paragraph is very similar to one considered by Swyneshed. See Spade [38], par. 44. 102

42

PREVIOUS OPINIONS

exists" signifies to you only that a falsehood exists; and to no one else but you does it signify the case to be in any way; therefore, to no one else does it signify otherwise than that a falsehood exists: and if so, therefore it does not signify otherwise than that a falsehood exists. For if to no one else does it signify otherwise, it does not signify otherwise. 39 (6ra36) Moreover if, given this casus, it will signify otherwise than it now signifies, then to the contrary: Then it will signify the case to be in some way that it does not now signify. Pick such a <way>, therefore. No matter which <way> is picked, there will be no reason why the < sentence > will signify that the case is that way rather than that a stick stands in the corner, or something like that. from the fact that no one will form such a conception, given the casus, or impose the sentence to signify that way. 40 (6ra41) I do not see any way to reply to this other than to deny the antecedents from which there follows the consequent that has already been denied.103 For to the first <argument>, 104 when I argued that as long as many falsehoods exist it is possible that the sentence "A falsehood exists" precisely signifies that a falsehood exists, one can say that literally (de virtute sermonis) that has to be denied, because if it signifies that a falsehood exists, it follows that it signifies that a sentence exists, and that a sentence that is not true exists. 103

The consequent is that the casus described in par. 8 is possible. This was denied in par. 8. 104 Par. 37.

PAR. 39-41

43

and so on like that. 105 But according to a common understanding it is generally conceded that such a sentence signifies precisely that a falsehood exists. For it signifies that a falsehood exists, and howsoever it signifies the case to be, it follows from the fact that a falsehood exists that the case is so.l06 Therefore, speaking in this way, I concede the whole of the antecedent107 up to where it is assumed that all false sentences stop existing, so that no <sentence> other than <"A falsehood exists"> is false, and that no man imposes that one to signify otherwise , or conceives otherwise by means of it, and so on for the other circumstances, and that it remains signifying that a falsehood exists. For all these things are jointly impossible. Thus, as was shown in the second line of reasoning, 108 there would be no reason why this <sentence> would signify the case to be this way or that, rather than that a stick stands in the corner or that the king is sitting. Hence, when all those parts are added on, the aggregate antecedent has to be denied as impossible. And when the antecedent is so denied, the arguments based on it do not run. 41 (6rb4) But perhaps someone will argue against this view as follows: Nothing inconsistent follows when it is 105

And so. since it signifies in these additional ways, it does not signify precisely that a falsehood exists. Heytesbury does not take this argument very seriously, and rejects it in the next sentence. In n. 14 to the study, below, I argue that the way Heytesbury rejects it does not conform well with his own usual doctrine. But the point stands: Heytesbury does not take the argument very seriously. His real argument begins three sentences below with "therefore." 106 See n. 14 of the study, below. 107 In par. 37. 108 Par. 39. Heytesbury never explicitly replies to the argument in par. 38.

44

PREVIOUS OPINIONS

posited that Socrates sees nothing and that the sentence "Socrates sees a falsehood" signifies precisely that Socrates sees a falsehood. Therefore, let Socrates close his eyes so that he sees nothing, and let this sentence be written before his eyes "Socrates sees a falsehood," which precisely so signifies. When this has been posited, let Socrates open his eyes and see the inscription - let it be a - not thinking about it or in any other way conceiving by means of it. And let no one else do so, then or at any time before. It follows according to the given view 109 that Socrates with a single glance - and indeed even an ass - would bring it about that a would not signify as before and would not remain a sentence. 42 (6rbl5) I concede this to be possible. For under this casus a would not signify as before. On the other hand, since no reason can be assigned why a would signify in this way or that, it follows that it would signify precisely as before.110 But this together with the casus is inconsistent. Therefore, under this casus a would not remain a sentence - unless someone wanted to impose that a should then signify precisely that Socrates sees a sentence, so that as soon as a is seen by Socrates, it would be convertible with a sentence like "Socrates sees such a sentence or expression/' 111 But that is less reasonable than before.

109

That is, the fourth opinion, now under review. That is, if it signifies at all. 111 The particular imposition Heytesbury chooses is only by way of example. The point is that a would not be a sentence unless someone suddenly imposed a new and innocuous signification on it at just the crucial moment. 110

PAR. 42-43

45

43 (6rb22) Therefore, I concede the conclusion that was deduced." 2 Hence just as it is possible that, without Plato's hearing. Socrates says only "Plato hears that Socrates says otherwise than is the case,"113 and yet it is not possible that Socrates say only that when Plato is hearing, so too it is possible that the sentence #, without Socrates' seeing anything, signifies precisely that Socrates sees a falsehood, but it is not possible that it precisely so signifies when Socrates sees only that. Many objections of this sort can be raised against this view, which it would be difficult or impossible to answer to complete satisfaction. Instead we have to concede the inference, 114 and confirm by a repetition using composite terms, like those with which we argued against the earlier opinions. 115 112

In par. 41. "Plato audit quod Sortes dicit aliter quam est" in both the edition and the MSS. This example does not seem to be well put. It would be clearer if Socrates had said "Plato hears Socrates say otherwise than is the case" (Plato audit Sortem dicere aliter quam est). 114 That is. we have to concede that the objections raise real difficulties. 115 Pars. 31. 33. 113

< Assumptions and Rules>

44 (6rb34) We still have to look at some rules, mentioned above.116 But first two assumptions must be set out, in order to understand two terms. One is that a "casus of an insoluble" is one in which mention is made of some sentence such that if in the same casus signifies precisely as its words commonly pretend, from its being true it follows that it is false, and vice versa. 45 (6rb40) The other is this: An "insoluble sentence" is one of which mention is made in an insoluble casus, such that if in the same casus it signifies precisely as its words commonly pretend, from its being true it follows that it is false, and vice versa. 46 (6rb43) For example, if it is posited that Socrates says a sentence like "Socrates is saying what is false" and no other, or like "Socrates is not saying what is true," or like "Socrates is saying otherwise than is the case," or that a sentence like "A falsehood exists" is every sentence, or that this is every sentence "No sentence is true," and so on like that, each of these casus is called the casus of an insoluble. And the sentence "Socrates is saying what is false" in such a casus is called an

116

Par. 37.

PAR. 44-48

47

insoluble sentence, because if in that casus it signifies precisely that Socrates is saying what is false, from its being true it follows that it is false, and vice versa. 47 (6rb52) A casus of an insouble can be constructed in another way too, by positing that Socrates says only a sentence like "God exists," which precisely signifies that Socrates is saying what is false, or that the sentence "A chimera exists" is every sentence, and that it signifies precisely that a falsehood exists, or that no sentence is true, and so on in similar cases. But that is not the usual way of assuming these casus. Also, they are clearly convertible with a casus of an insoluble in which the insoluble signifies precisely as its terms commonly pretend, and so in effect the same thing happens as before. Therefore, to return to our program, let us set out the following division. 48 (6va5) If someone constructs a casus of an insoluble, either he posits how that insoluble should signify, or he does not. If not, then when the insoluble is proposed, one should respond to it exactly as one would respond when the casus is not assumed. For instance, when it is assumed that Socrates says the sentence "Socrates is saying what is false" and no other, and together with this it is not posited how the sentence "Socrates is saying what is false" should signify, then when it is proposed in the first position (primo loco)111 one should respond

117

The "first position" is occupied by the sentence proposed first after the casus has been admitted. Sometimes the order in which sentences are proposed makes a difference in the required replies. See the discussion of obligationes in section 1 of the study, below, and also Spade [37].

48

ASSUMPTIONS AND RULES

to it exactly as one would respond outside the casus. For it is consistent (stat) with the casus that it be true, and also that118 it be false. Therefore,s consistent with the casus that Socrates, in saying this, is saying what is true, and also consistent <with the casus> that he is saying what is false. And so, since the insoluble sentence is irrelevant (impertinens)119 to the casus, therefore when it is proposed in the first position one should not because of the casus respond to it otherwise than before the casus <was posited>. 12° One should also do the same thing when the casus is posited that the sentence "A falsehood exists" is every sentence, and it is not assumed how it signifies. When the <sentence> is proposed to you, you must respond to it in the first position exactly as you would without the casus. 49 (6va21) Second, notice that if a casus of an insoluble is posited, and together with that it it assumed that the insoluble precisely signifies just as its terms commonly pretend, the casus may in no way be admitted. Thus, when it is assumed that the sentence "A falsehood exists" is every sentence and signifies precisely that a falsehood exists, this casus and any one convertible with it has to be denied forthwith. For instance, if it is assumed that Socrates is saying only a sentence like "Socrates is saying what is false," and together with this it is also assumed that the sentence precisely signifies that Socrates

118

Reading "etiam quod" with the Padua MS, rather than "quod etiam" with the edition. The Vatican MSS have "et quod." 119 A sentence S is irrelevant to a casus C if and only if S neither from nor is inconsistent with C. See Spade [39], pars. 4 and 8. 120 See Spade [39], par. 24.

PAR. 49-51

49

is saying what is false, such a casus can in no way be admitted, nor can any one convertible with it, because of the many impossible things that follow. 50 (6va32) Third, if someone constructs a casus of an insoluble, and together with that it is assumed that the insoluble signifies as its terms pretend, but not precisely, then when this casus is admitted, the insoluble has to be conceded as following, in whatever position it is proposed, but that it is true has to be denied as being inconsistent (repugnans). For instance, when it is assumed that Socrates is saying only the sentence "Socrates is saying what is false," and that it so signifies, but not precisely, then when it is proposed, one has to concede it as following, but that it is true has to be denied as being inconsistent. For it follows: Socrates is saying the sentence "Socrates is saying what is false," which so signifies; therefore, Socrates is saying what is false. But since Socrates is saying no sentence but "Socrates is saying what is false," it follows that this one is false, and from that it follows that it is not true. It has to be conceded, therefore, as following from the casus, that Socrates is saying what is false. And it has to be denied, as being inconsistent with the same , that the sentence "Socrates is saying what is false" is true. The same thing happens in general in any similar casus whatever, as will be apparent to one who runs through individual cases. 51 (6va47) But if someone asks under this casus what the sentence uttered in this way by Socrates signified other than that Socrates is saying what is false, I say to him that the respondent does not have to solve or to give his determination for (determinare) that question. For from the casus it follows

50

ASSUMPTIONS AND RULES

that the sentence signifies otherwise than that Socrates is saying what is false, but the casus does not specify (certificat) what that is; hence, the respondent does not have to give any further determination for that question. 52 (6va55) But because casus of insolubles, like this one, are admitted where it is posited that the insoluble signifies as its words pretend, although it does not precisely so signify, but also otherwise than the words are usually understood , someone could assume perhaps that Socrates is saying only the sentence "Socrates is saying what is false," and that it precisely signifies that Socrates is saying what is false and that God exists, and that man is an animal, or something necessary like that. As to this, it has to be noted and observed as a rule that if someone constructs a casus of an insoluble, and together with that it is assumed that the insoluble signifies conjunctively (copulative) precisely as its words pretend - call that a - and that b, or something else whatever it may be, exists, if the opposite of that conjunct121 is inconsistent with the whole casus, the casus has to be denied as formally including contradictories. For instance, when it is assumed that Socrates is saying only the sentence "Socrates is saying what is false," and that it precisely signifies that Socrates is saying what is false and that God exists, from the fact that the opposite of the conjunct, namely, "No God exists," when it so signifies, is inconsistent with the whole assumed casus, it follows that the casus is utterly impossible. For it follows formally from the

.e., the (contradictory) opposite of "b exists."

PAR. 52-53

51

casus that the sentence "Socrates is saying what is false/' said in this way by Socrates, would be true and also that it would be false, as is immediately apparent to anyone who looks at it. Also, when it is assumed that Socrates is saying only the sentence "Socrates is saying what is false," and that it precisely signifies that Socrates is saying what is false and that Socrates is speaking, because the opposite of the conjunct, namely, "Socrates is not speaking," is inconsistent with the casus. neither this casus nor any one like it can be admitted. In this context, I say generally that those things are inconsistent (non stare simul) one of which formally opposes (repugnat) the other or one of which is impossible in itself. For there are many things that are inconsistent but nevertheless are not formally opposed. The <sentences> "You are an ass," and "You are not a goat" or "The king sits" are inconsistent, and yet they are not formally opposed.122 Just as two contradictories are not consistent with any third thing, so neither is a sentence that is impossible itself consistent with any other, because it is as it were universally included as an opposite. 53 (6vb28) But if someone constructs a casus of an insoluble, and together with that it is assumed that the insoluble signifies precisely disjunctively, as its words pretend or that a is b, or something of this sort, , unless what is disjoined with the insoluble is consistent with the whole casus. the casus is not to be admitted. Hence, when it is posited that Socrates is saying only the sentence "Socrates is saying what is false." and that it precisely signifies that Socrates is 122

Presumably. "You are an ass" is impossible in itself because it would violate your human nature.

52

ASSUMPTIONS AND RULES

saying what is false or that man is an ass, , because the disjunct "Man is an ass" is inconsistent with the casus, therefore the casus is impossible. Similarly, if someone constructs a casus like this, that Socrates is saying only the sentence "Socrates is saying what is false" and that it precisely signifies that Socrates is saying what is false or that Socrates is not saying a sentence, or that <Socrates is saying what is false or> Socrates is not saying what is true, the casus is not to be admitted, because of the inconsistency mentioned earlier.123 54 (6vb40) Just as in every casus where it is posited together with the casus of an insoluble that it signifies conjunctively as its terms commonly pretend and that this or that is the case (sic esse vel sic), wherever it is proposed it has be conceded, and it has to be denied that it is true, so too conversely, when a casus of an insoluble is posited and together with that it is posited that the insoluble signifies disjunctively precisely as its words pretend or that this or that is the case, the insoluble has to be denied as many times as it is proposed, and it has to be conceded that it is true. For instance, when it is posited that the sentence "A falsehood exists" is every sentence and that is precisely signifies that a falsehood exists or that God exists, when "A falsehood exists" is proposed it has to be denied, and it has to be conceded that it is true. Hence always in such a casus one must concede the disjunct to be true, just as in the other casus one must deny that the conjunct is true. For when a casus like this is constructed, that the sentence "A falsehood exists" is every sentence and

See par. 52.

PAR. 54-56

53

that it precisely signifies that a falsehood exists or that you run at Belmont (in hello monte), you have to concede it as following, however much you may know that it is false. The same thing happens in every similar case. 55 ( 7 r a l ) But conversely, when it is assumed that the sentence "A falsehood exists" is every sentence and that it precisely signifies that a falsehood exists and that you are a man, when "You are a man" is proposed, you have to deny it and anything else that is antecedent to it. 124 The reason for this will be apparent immediately to one who looks at it. 56 (7ra5) Sometimes however when a casus of an insoluble is constructed, it is hard to see quickly which is the insoluble sentence, as for instance when a casus like the following is posited, that every man who says what is true responds correctly (bene), and only such a man, and that each man who says what is false responds wrongly (male), and only such a man. and that Socrates says only the sentence "Some one of these responds wrongly." indicating Socrates and Plato, and that so signifies, and that Plato says the sentence "Socrates responds correctly." and that it so signifies. Then in this casus. each of the sentences125 can be insoluble. But when it is posited that the sentence so uttered by Socrates signifies precisely together with the whole casus that some one 124 I.e.. anything else that can be an antecedent of a valid inference having "You are a man" as its consequent. 125 I.e., Socrates' or Plato's. The other sentences are used in stating the casus. but are not mentioned in it.

54

ASSUMPTIONS AND RULES

of these responds wrongly, then that uttered by Plato is insoluble, and it will signify then otherwise than that Socrates responds correctly. For it is not consistent with the whole casus that it should then signify precisely that Socrates responds correctly. But if in the first casus, the <sentence> uttered by Plato precisely signifies that Socrates responds correctly, it follows that that uttered by Socrates is insoluble, and that it not only signifies that some one of these, indicating Socrates and Plato, responds wrongly, but also otherwise <signifies> what it is false is the case. For it is inconsistent with the casus that it should then precisely signify that some one of these responds wrongly, just as it is not consistent with any casus that the sentence which is insoluble signifies precisely as its words pretend, as was said from the beginning. Thus in such a casus the respondent should pay diligent attention to which is the insoluble sentence and which is not. 57 (7ra27) But because it was said as the basis that it is not possible for any insoluble sentence to signify precisely as its words commonly pretend, together with the whole casus of that insoluble, perhaps an antagonist will raise a quibbling argument against this as follows: It is possible that Socrates is saying only the sentence "Socrates is saying what is false" and that the sentence "Socrates is saying what is false" signifies precisely as its words commonly pretend. For at the outset I posit to you the conjunction 126 "The sentence 'Socrates is saying what is false' and every such sentence signifies precisely as its words commonly pretend and give to 126 This sentence is not strictly a conjunction (copulativa), although it has a conjunctive subject term.

PAR. 57-58

555 55

understand (dant intellegere)." This conjunction, we observe, is possible, because it is possible that every such sentence signify by the common understanding of its terms that Socrates runs at Belmont. When this is posited, let it be posited that Socrates is saying only "Socrates is saying what is false" and no other <sentence >. and that it signifies precisely as its words commonly pretend. And the opposite of the basis follows. 58 (7ra42) But this objection and reasoning is too trilling, and can well be called sophistical, because it goes only to the words and not to the understanding. For all the things that have been posited above are understood in the divided sense; but this quibbler argues for the contrary in the composite sense. 127 It would be too drawn out in words to press on so far 127 Heytesbury denies that it is possible that Socrates is saying only "Socrates is saying what is false" and that that sentence signifies precisely as its words commonly pretend. He denies this, however, in the "divided sense." That is. in effect, he denies the following: There is some replacement for "77" such that both (a) "Socrates is saying what is false" in fact pretends to signify that p. and (b) it is possible that both (i) Socrates is saying only "Socrates is saying what is false" and (ii) "Socrates is saying what is false" precisely signifies that p. This is the "divided" sense, or as modern logicians would say, it involves quantification into an opaque context. The objector, however, argues for the following conclusion: It is possible that, for some replacement of "/?." (a) "Socrates is saying what is false" pretends to signify that p. and (b) Socrates is saying only "Socrates is saying what is false," and (c) "Socrates is saying what is false" precisely signifies that p. This is the "composite" sense; the modal operator "it is possible that" governs all three conjuncts. And since this is not what Heytesbury is denying, and does not imply what Heytesbury is denying, the objection fails. On the distinction between composite and divided senses, see Heytesbury's De sensu composite et diviso, printed on fols. 2ra-4rb in the Venice, 1494, edition of Heytesbury's "Rules."

56

ASSUMPTIONS AND RULES

that nothing would be said that could not be attacked by a quibbler. Therefore, refer the argument not only to the naked words, but to the judgment (sententiam), and you will see how powerfully conclusive it is. 59 (7ra50) Likewise, someone could raise an objection on the grounds that it was frequently admitted earlier that Socrates is saying only the sentence [and]128 "Socrates is saying what is false," although literally that is quite impossible. I prove , because this sentence is impossible "Socrates is saying this sentence," so signifying about the present. For there neither is nor can there be any sentence so short that Socrates can suddenly and all at once say it in its totality, or any part of it, because since every utterance (vox) is divisible, no one suddenly or in an instant can bring forth (profert) one . 60 (7vbl) Likewise, given that Socrates says the whole sentence "Socrates is saying what is false," it follows that Socrates would say "Socrates is saying" which is the first part, and so Socrates would be saying not only the former. 61 (7vb4) Nevertheless, because quibbles like this do not deal with the subject, and neither do other literal objections of this sort, one should not carry on any further about them. 62 (7vb6) Often, however, a casus of an insoluble is constructed in terms that do not immediately concern the truth

This word should be deleted, following the MSS.

PAR. 59-63

57

or falsehood of a sentence, but rather mediately. Thus for instance, when it is posited that Socrates believes only the sentence "Some man is deceived" and that this [precisely]129 so signifies, and that everyone other than Socrates believes only what is the case, then we note that the sentence "Some man is deceived," which Socrates believes, is insoluble, and that it signifies otherwise than that some man is deceived. For if some man is deceived, he believes some sentence signifying 13° otherwise than is the case, because if some man is deceived, he believes otherwise than is the case; and if someone believes otherwise than is the case, he believes a false sentence, because a sentence signifying otherwise than is the case - unless someone would want to posit or say that howsoever some man believes the case to be, it does not follow that he believes some sentence, and howsoever he knows the case to be, it is not required that some sentence be known, or that there be knowledge of it. which I think could be probably maintained. But since that truth is scarcely apparent to us, < there fore > when the former casus is posited, you may respond as was set out earlier, and in any similar casus of an insoluble, you may draw your judgment (indicium) by what was said earlier. 63 (7rb24) There are many casus of this kind which are too drawn out and useless, in which one must diligently

129 This word should also be deleted, following the MSS. See the argument later in the paragraph for justification. "° The edition has "significare." Read "significantem." The emendation is required by the sense of the argument. The MSS omit the passage "some sentence ... he believes."

58 ASSUMPTIONS AND RULES

calculate and run through one sentence after another until it becomes apparent which of them is insoluble. Let no one be troubled when such a casus is posited, even if the first time he does not see what or how he should reply. For in a similar casus, or the same one changed a little bit, the opponent would not do it either. 64 (7rb29) Therefore, let these things said about insolubles serve for the introduction and drill of the young, so that when it is seen that insolubles, as their name implies, cannot be solved without evident objection, everyone may quickly go beyond them to a more useful study, pursuing it the more diligently.

Study

1. PRELIMINARY NOTIONS AND THE DEFINITION OF AN INSOLUBLE In the preceding text, I have chosen to leave the technical term "casus" (plural also "casus") untranslated. 1 In Heytesbury's usage, which is not at all an unusual one, the word has a double sense. It means first of all a situation assumed or "posited" as obtaining for the duration of an argument. But in an extended sense it means also a description of such a situation. For practical purposes, when Heytesbury speaks of positing a casus. or of constructing a casus, we can regard the casus as a set of sentences describing a situation. If the set of sentences is not satisfiable - i.e., if it is impossible for them to be jointly true - the casus has to be denied (rejected) as impossible. This is the import of the fourth previous opinion Heytesbury discusses (see paragraph 8), and of his own second rule (par. 49). The term "casus" is used throughout the tract in the technical sense it has in the medieval treatises on obligationes. The obligationes also explain some other points of terminology in Heytesbury's text. A "disputatio de obligationibus" was a disputation of a special kind, involving two parties, an "opponent" (opponent) and a "respondent" (respondent. There 1 See n. 3. below.

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were several kinds of such disputations; the list varied from author to author. All authors, however, agreed that one kind was called "positing" (positio). In a "positing," the opponent lays down (posits) a casus. This casus is to be assumed to hold (to be true) for the duration of the disputation. The respondent can either admit or deny the posited casus, according to certain rules set out in the tracts on obligationes. Once a casus has been posited and admitted, the opponent then "proposes" certain sentences. To each of these the respondent must reply either "I concede it," "I deny it," or "I doubt it," again according to certain rules. Sometimes during the course of the disputation, the opponent will add (posit) new clauses to his original casus. In the context of these obligationes, it is important to keep in mind the distinctions between "positing" a casus and "proposing" a sentence, and between "admitting" a casus and "conceding" a sentence. The rules are not the same in each case. Although a detailed knowledge of the rules of obligationes is not required for a general understanding of Heytesbury's tract, I have scrupulously adhered to these terminological distinctions in the translation.2 A word should be added here on the translation of the phrase "sicut est" and similar phrases. I have translated these difficult idioms by using the English "the case," as in "such and such is the case."3 It should be emphasized that the Latin phrases have no noun. There is nothing literally answering to the term "the case." The proper question, in this tradition, is to 2 For more on the obligationes-literature, which is still largely unexplored, see Angelelli [2], Brown [6], De Rijk [10], Green [16], Hamblin [17], Spade [34], Spade [37] and Spade [39]. 3 It was in part to avoid confusion here that I chose to leave the term "casus" untranslated.

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ask of a sentence not "What does it signify?" but rather "How does it signify?" It either signifies as is the case or signifies otherwise than as is the case. The phrases are adverbial and not nominal in the Latin. The distinction is important. For Heytesbury in this tract is a nominalist to this extent at least, that there exists nothing besides individual occurrences of sentences to serve as the bearers of truth or falsehood.4 There are then no "propositions" in the modern sense, no "complexe significabilia," as Gregory of Rimini called them, 5 for sentences to signify. Now "to signify" in the Middle Ages meant to "establish an understanding of - or. more perspicuously perhaps, "to bring to mind." 6 What then does a sentence signify? What does it bring to mind when heard? For the nominalists at least, the categorematic terms of a sentence (its proper or common nouns and predicate expressions) signify individual substances and their individual qualities. Moreover, there is nothing else in a nominalist ontology to be signified. Hence, "what" a sentence signifies is just the sum total of what its categorematic terms signify. 7 4 This is the import of the last sentence of par. 14, which presupposes that the bearer of truth-value is an existing sentence. That it is the individual occurrence - the "token" and not the "type" - is clear from several of Heytesbury's arguments in which he appeals to two utterances of the same sentence, and then argues from the truth-value of the one to the truth-value of the other. 5 See Elie [12]; and Nuchelmans [24], chs. 14-15. For John Buridan's nominalist criticism of the "complexe significabile" doctrine, see also Scott's "Introduction" to Scott [26]. 6 On this notion, see Spade [40]. 7 Thus. e.g.. John Buridan, Sophismata n. conclusion 5, translated by Scott in Scott [26]. p. 89: '... all that is signified by the terms or by some term

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There was a common medieval definition of truth according to which a sentence is true if and only if "howsoever it signifies, so it is the case" (qualitercumque significat ita est}. Some authors construed this definition in terms of suppositiontheory. For them, the truth-conditions of a sentence were fixed by the reference or "supposition" of its categorematic terms. And since, for the nominalists, terms in what was called "personal" supposition, the usual kind referred to or supposited for what they signify, the truth-conditions of most sentences were fixed ultimately by the significations of their categorematic terms.8 This view, however, had a problematic consequence. For most medievals held that spoken or written language was through and through conventional (ad placitum). Signification could be assigned entirely at will. 9 It would seem to follow from this, in particular, that the truth-conditions of sentences of a proposition is signified by that proposition. Indeed the proposition is not itself imposed as a whole alongside of the signification of its [categorematic] terms." (The word in brackets is Scott's insertion. Scott translates "propositio" by "proposition." whereas I use "sentence." The latter translation avoids the temptation to identify the medieval nominalist "propositio" with the modern notion of "proposition," which the nominalists denied.) That is, a sentence signifies everything signified by any of its categorematic terms, and nothing else in addition. This principle has important applications in some versions of nominalist connotation-theory. See Spade [32]. 8 See John Buridan, Sophismata n, translated in Scott [26], pp. 83-96. Scott's "Introduction," [26], pp. 29-42, also provides a good summary of the main points of supposition-theory. 9 Mental language, on the contrary, was natural and not conventional. The assigning of signification to spoken and written language amounted to setting up a conventional correlation between spoken or written linguistic units and linguistic units in the natural mental language. See Spade [32], especially section i, p. 57 n. 8; and William of Ockham [50], i, 3.

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need not be fixed by the signification of their categorematic terms. If one were willing to push the conventional character of spoken and written language to an extreme, one could hold that the terms "man" and "animal" by convention signify men and animals, respectively, and nevertheless at the same time the sentence "Every man is an animal" would by convention be true if and only if God does not exist. There is nothing inconsistent in maintaining both these conventions at once. If the signification of spoken and written language is really as thoroughly conventional as is claimed, then the signification of a whole sentence need not be a function of the significations of its parts. A nominalist who held such an extreme view of conventionality 10 would be forced to reject the construal of the traditional "howsoever" definition of truth in terms of supposition-theory. "Howsoever a sentence signifies" could not then be parsed in terms of "what" a sentence signifies - i.e., what its categorematic terms signify. The adverbial notion of signification implicit in this definition of truth would then take its place beside the nominal notion; the former would not be reducible to the latter. There is still of course the problem of making independent ontological sense out of an adverbial notion of signification. In any case, Heytesbury seems to have adopted just such a view. In his "On the truth and falsehood of a sentence" (De veritate et falsitate propositionis) he adopts essentially the "howsoever" definition of truth, independent of suppositiontheory." This suggests that Heytesbury took very seriously the 10 As for instance. Robert Fland did (although it is not clear that Fland was a nominalist). See Spade [35], p. 59. pars. 9-10. 11 See Maieru [22]. pp. 54-56. and especially the text quoted at p. 55.

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conventional character of spoken and written language. If so, it is ironical that Heytesbury's own position on insoluble sentences entails, as we shall see, a strange restriction on the arbitrariness of the conventions. Although in the text translated above, Heytesbury never gives an explicit definition of truth, we can gather one from what he does say: If a sentence S "precisely signifies" that p, then S is true if an only if p. This is a general rule, and holds for any choice of a sentence to replace "p." Given this general rule, let us assume that every sentence "precisely signifies" somehow. That is, for every sentence 5", there is some choice of a sentence to replace "p" such that S "precisely signifies" that p. This seems a reasonable assumption in the context in which Heytesbury is working. For sentences are not just utterances or inscriptions, but rather significant utterances or inscriptions. In any case, given this assumption, the above general definition of truth turns out to be logically equivalent to the following, alternative, general definition of truth: A sentence S is true if and only if, for whatever sentence replaces "/?," if S precisely signifies that p, then p.n

n. 59. Heytesbury's De veritate el falsitate propositions, from which the quotation is taken, may be found printed on fols. 183va-l 88rb of the Venice, 1494, edition used for the translation above. 12 The proof proceeds by elementary quantification theory. I am using a substitution interpretation of the quantifier in order to avoid any ontological commitment to propositions or "complexe significabilia" by quantifying over "p." On the substitution interpretation, see Dunn and Belnap [11].

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This links Heytesbury's implicit definition, given above, with the traditional definition according to which a sentence is true if and only if "howsoever it signifies, so it is the case." To say that "for whatever sentences replaces "p\ if S precisely signifies that p, then /?" is just to say that "howsoever S (precisely) signifies, so it is the case." Although Heytesbury does sometimes use the "howsoever it signifies" locution, there is nevertheless a good reason for his preference for the terminology of "precise signification." For the "howsoever" terminology would suggest that if a sentence S1 is true, and if 5* signifies (but not necessarily "precisely") that p. then p. But Heytesbury would deny this. For Heytesbury, if a sentence S is true, and if S signifies that p, it need not always follow that /?. 13 Heytesbury's motivation here appears to go back to the notion of signification as "bringing to mind." Just as "what" a sentence signifies is the sum total of what its categorematic terms signify, so that if a sentence signifies an individual substance or quality, that substance or quality must be signified by one of the categorematic terms of the sentence, so too, by parity of reasoning, it would seem that if in general we are asked "how" (not "what") a sentence S signifies, and we answer that it signifies that q, and if S "precisely signifies" that p, then the sentence replacing "g" must be a (not necessarily atomic) constituent of the sentence replacing "/?." (We allow that any sentence is, trivially, a constituent of itself.) For instance, if 5 signifies precisely that q or r, then when we hear that sentence, it brings to mind that q or r. Now just as we 13 This is a consequent of his fifth rule. par. 53. We shall discuss this rule more fully below.

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cannot bring to mind that man is an animal without bringing to mind men and animals, so too we cannot bring to mind that q or r without bringing to mind that q or without bringing to mind that r. Hence, 5" signifies that q and S signifies that r. But if S is true - i.e., if it is the case as S precisely signifies - it does nbt follow in general that q, nor does it follow in general that r. The "howsoever" definition of truth, unless one is careful, would suggest that it does follow. Hence, perhaps, Heytesbury's preference for the terminology of "precise signification." These considerations allow us to take "precise signification" as a (relatively) primitive notion, and to define "signification" (simpliciter) in terms of it: For whatever sentences replace "p" and "g," if a sentence S precisely signifies that /?, then 5 "signifies" (simpliciter) that q if and only if the sentence replacing "g" is a constituent of the sentence replacing "p." Alternatively, we can take "signification" (simpliciter} as the primitive notion, and define "precise signification" in terms of it as follows: For whatever sentence replaces "p," S "precisely signifies" that p if and only if, for whatever sentence replaces "g," S signifies that q if and only if the sentence replacing "
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Finally, Heytesbury uses a third locution that must be explained. He sometimes says that a sentence signifies "as its words pretend," or "as its terms pretend," or "as its words (terms) commonly pretend," etc. This notion of "pretended signification" is based on the normal or ordinary (the "common") signification of a sentence, the signification it replacing "p." This notion of precise signification, while it does indeed conform to a "common understanding." as Heytesbury says in par. 40, and while it does answer the spurious argument he considers there, nevertheless is not an extension of Heytesbury's usual notion of precise signification. For according to that usual notion, as we have seen above, if S precisely signifies that q or r. then it also signifies that r. But it need not then be necessary that q or r only if r. Nevertheless, the spirit of Heytesbury's remarks in par. 40 can be accommodated to his own usual notion of precise signification. Taking "signification" (simpliciter) as a primitive notion, we can define precise signification in Heytesbury's usual sense as follows: For whatever sentence replaces "p," S precisely signifies that p if and only if, for whatever sentence replaces "q." S signifies that q if and only if the sentence replacing "q" is a member of the smallest class .Y containing all the constituent sentences of the sentence replacing "p." (This definition is equivalent to the one just given in the study. X is the "smallest" such class in the sense that it is set-theoretically included in all such classes.) This definition can be accommodated to the spirit of Heytesbury's remarks in par. 40 by adding the stipulation that the class X be "closed" under logical consequence - i.e., that X contain the logical consequents of all its members. There are two reasons why this modification of his usual notion of precise signification would not be to Heytesbury's advantage. First, it requires that whenever a person brings to mind that p, he also brings to mind whatever follows from p. This requires an ideal mind, able to see all the logical consequents of everything it brings to mind. This kind of signification, then, would be signification only for an ideal mind - only for God. Second, since Heytesbury is going to base logical inference on the preservation of what we shall call "firmness" (see below, section 3 of the study), and since "firmness" will be defined in terms of "pretended signification." and since the "pretended signification" of a sentence will be just the precise signification it would have under the usual or normal conventions, therefore if precise signification is defined in terms of logical inference, we have an obvious circularity.

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conventionally has in ordinary, day to day discourse. Since the signification of a sentence is entirely arbitrary, however, it need not always in practice have its normal or ordinary signification; it need not signify as its words pretend. Indeed, in a "disputatio de obligationibus," the opponent sometimes arbitrarily stipulates at the outset how certain sentences are to signify for the duration of the disputation. Some authors reserved a separate species of obligatio, called "imposition" (impositio), for this kind of stipulation.15 Others regarded it as simply a subcategory of the species "positing" (positio).16 Heytesbury appears to have done the latter.17 There is a certain ambiguity in Heytesbury's usage here. Is the "pretended signification" of a sentence the "signification" (simpliciter) it would have under the ordinary conventions, or is it rather the "precise signification" it would have under those conventions? If the latter, then if a sentence S in fact precisely signifies that /?, and if S also commonly pretends to signify that p, then the conventions actually in force are just exactly the normal or ordinary conventions. If the former, on the other hand, this need not be so. For let S in fact precisely signify th p, and suppose that S commonly pretends to signify that p, in the sense that, under the usual conventions, S would signify (simpliciter) that p. Then it is still possible that, under the 15

It was also customary to say that sentences acquired their original or ordinary signification by "imposition"; they were "imposed to signify." In order to distinguish these two notions of imposition, some authors spoke of the imposition of sentences in the special context of an obligatio as a "new" imposition. 16 Roger Swyneshed was one of those who distinguished impositio as a separate species. See Spade [38]. On the other hand. Peter of Ailly, Paul of Venice and Paul of Pergula did not. See Spade [38], n. 60 to par. 69. 17 See the opening words of par. 48, above.

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normal or ordinary conventions, S would precisely signify, say, that p or q, so that the conventions actually governing S are not the same as those that normally or ordinarily govern S. This possibility follows from the relation, described above, between signification (simpliciter) and precise signification. Heytesbury is unclear which of these two he intends, but I think it more plausible to suppose that the pretended signification of a sentence is the same as the precise signification it would have under normal conventions. Indeed, this interpretation is required if the reconstruction of Heytesbury's position, below, is going to work. Given these notions, we are now in a position to see the import of Heytesbury's crucial definitions in pars. 44-45: the definitions of an insoluble casus (casus of an insoluble) 18 and of an insoluble sentence. Beginning with the latter, what par. 45 says in effect is that a sentence S is an insoluble sentence if and only if for some casus C, if we assume both that C is satisfied and that 5" signifies precisely as its words commonly pretend, then 5"s being true is equivalent to its being false.19

18

In par. 44 we find "casus of an insoluble" (casus de insolubili); in par. 45 we find "insoluble casus" (casu insolubili'}. The meaning appears to be the same. 19 This definition, in order to capture the cases Heytesbury wants to treat, must presuppose bivalence: every (declarative) sentence is either true or false. There is still a problem, however, with this attempt to define the paradoxes. It works well only for vicious cycles involving a single sentence. In cases involving more than one sentence, the definition is inadequate to Heytesbury's intent. See. e.g.. par. 56 of the translation. See also Spade [28]. Note also par. 47, in which Heytesbury considers an alternative definition of an insoluble casus.

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For instance, suppose someone says, "What I am now saying is false," and that alone. That will be our casus. Now if we suppose further that the sentence in question signifies precisely as its terms commonly pretend, then it follows that the sentence is true if and only if it is false, just as we argued above in the Introduction. Hence the sentence "What I am now saying is false" is an insoluble sentence.20 Given this definition of an insoluble sentence, we can define a casus of an insoluble as follows (par. 44): A casus C is a casus of an insoluble if and only if C mentions a sentence S such that, if we assume both that C is satisfied and that 5" signifies precisely as its words commonly pretend, then 5"s being true is equivalent to its being false.21 On the basis of these definitions, it is contradictory to assume both that the casus of an insoluble is satisfied and that the insoluble sentence in question signifies precisely as its words commonly pretend. This yields an embarrassing consequence for Heytesbury's theory. For in many cases at least, the casus is clearly quite possible. If it should happen to be satisfied, therefore, the insoluble sentence would no longer be able to signify precisely as its words commonly pretend. But why not? 20

Note that on this definition, a sentence is not said to be insoluble with respect to a certain casus. I.e., insolubility is not a relative notion. If a sentence is insoluble, it is insoluble in all casus - although the contradiction will not in general be derivable from all casus. See the definition of a casus of an insoluble, below, and also n. 21. 21 If we allow the notion of insolubility with respect to a given casus, in an obvious way, then this definition may be simplified to read: A casus C is a casus of an insoluble if and only ifC mentions some sentence that is insoluble with respect to C.

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Because, of course, that would yield a contradiction. But does this not amount to a major and strange restriction on the arbitrary conventionality of language? If someone should say, for instance, "Every sentence now being uttered by anyone anywhere in the world is false," that sentence can signify precisely as its words commonly pretend provided that, somewhere in the world, someone is uttering at the same time some other, true sentence - but not, for instance, if by chance and unknown to the speaker, everyone else in the world should happen to be silent at that moment. In the latter case, the man's sentence could not signify precisely as its words commonly pretend, but must signify somehow otherwise. But how ? There seems to be no way to answer this. Since sentences get their signification by imposition - i.e., by being imposed by the speaker to perform a certain significative duty - what are we to say? That, unknown to himself and solely on the basis of the chance and unknown fact that everyone else is silent at the crucial moment, the man secretly intends that his sentence signify otherwise than he thought? This is an unacceptable consequence. Heytesbury considers cases like this in pars. 37-43, and gives no satisfactory answer to them. Indeed, in par. 9, Heytesbury admits in advance that his own theory is not perfect, and he does not think any theory of the insolubles can be. This is a significant admission, as I have discussed in the Introduction. 2. PREVIOUS OPINIONS After a rather pompous prologue (pars. 1-3), Heytesbury turns to consider four previous opinions. 22 The fourth is the 22

Cajetan of Thiene. in his commentary printed with the "Rules" in the

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one he will ultimately defend and adopt.23 The first position is Roger Swyneshed's (par. 5). 24 For our purposes, the main principles of Swyneshed's position are these:25 Definitions

Asentence is a well-formed (congrua) indicative (DAA expression, significative either naturally, or by imposition, or by impositions, by which imposition or impositions it was last (ultimo) imposed to signify complexly. (2) A true sentence is a sentence that does not falsify itself and signifies principally as is the case, either naturally, or by imposition, or by impositions, by which imposition or impositions it was last imposed to signify. (3) A false sentence is an expression that falsifies itself, or an expression that does not falsify itself and principally signifies otherwise than is the case, either naturally, or by imposition, or by impositions, by which imposition or impositions it was last imposed to signify. (4) An insoluble, for our purposes, is a sentence signifying principally as is the case or otherwise than is the case, relevant Venice edition of 1494, says (fol. 7va): "The first of these positions is Swyneshed's; the second is posited by Dumbleton; the third is Richard Kilvington's in his Soplnsmata." See below on these attributions. 23 See n. 6 to par. 3 of the translation, above. 24 See Spade [30], item i.xui. Swyneshed's tract appeared between 1330 and 1335. It is edited in Spade [38]. 25 For the Latin text, and for the Latin of Swyneshed's other principles, see Spade [30], item i.xui, and Spade [38]. Note that, where Swyneshed seems to have "signifies principally," Heytesbury often quotes him as having "signifies precisely." There is some justification for this in the manuscript tradition of Swyneshed's text.

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to inferring that it is false or unknown or believed, and so on for the individual cases.26 Assumptions (1) Every sentence that is relevant to inferring that it is false is one that falsifies itself. Conclusions (1) Some false sentence signifies principally as is the case. (2) In some valid (bona) formal inference, a falsehood follows from a truth. (3) two contradictories that are mutually contradictory are false at the same time. 27 The second previous opinion holds that insolubles are not really sentences, and so are neither true nor false (par. 6). 28 The 26 Here a sentence S is "relevant to inferring that it is false" if and only if "5 is false" follows from S. This is a somewhat unusual usage. In general, a sentence S is usually said to be "relevant" (pertinens) to a casus C if and only if S either follows from C or is inconsistent with C. See n. 119 to par. 48 of the translation, above. 27 The restriction to "mutual" contradictories rules out the spurious case in which we say that P is false, the contradictory of not-P. and Q is false, the contradictory of not-Q, and so two contradictories. P and Q. are false at the same time. Swyneshed's claim is stronger than this. 28 Cajetan attributes this opinion to John Dumbleton. But since Dumbleton himself mentions Heytesbury's position as the fourth in his list of previous opinions, it appears that this attribution is wrong. (See Weisheipl [47], pp. 202f.) Weisheipl [47], p. 203, nevertheless says that Dumbleton defended a position similar to the second in Heytesbury's list. This too appears to be wrong. (See Spade [30], item xxxvi. where the relevant texts of Dumbleton are quoted. Dumbleton's text is dated 1335-1340.) Although it is

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third says that, although insolubles are sentences, and so are either true or false, nevertheless none of them is true and none of them is false (par. 7). The (fallacious) argument for this curious position seems to be that, in general, from "A is B or C" it does not follow that "A is B," nor does it follow that"A is

c;,29

thus not clear just whose position Heytesbury is rejecting here, Cajetan gives us some help in interpreting the position. He says (fol. 8rb): "For the groundwork of this position, it has to be premissed that a sentence is an indicative and well-formed expression, determinately signifying what is true or what is false." He goes on to explain that, since insolubles refer to themselves, they do not signify determinately what is true or what is false. The notion of "determinateness" here seems to be roughly as follows. If "<7 or b" is a disjunctive term (as distinct from a disjunctive sentence), then we can truly say that "a or b is determinately F" if and only if either a is For b is F. Here, what is true or what is false (a or b) is not determinately "signified by an insoluble" (not determinately F). 29 Cajetan attributes this position to Richard Kilvington. But Heytesbury's formulation is at best a misleading way of putting Kilvington's position, which seems to be a straightforward attempt to solve the paradoxes in terms of the Aristotelian distinction between attribution secundum quid and attribution simpliciter. (See Spade [30], item i.v for the relevant texts and a discussion. See also Bottin [4], pp. 86-91. I date Kilvington's Sophismata circa 1 330 (Spade [30], p. 92, n. 167.) The last sophism, the forty-ninth in the collection, contains the discussion of insolubles. It is edited in Bottin [5]. A complete edition and translation, with a commentary, is being prepared by Norman and Barbara Ensign Kretzmann.) Cajetan comments on these paragraphs of Heytesbury's (fol. 8va): "Nevertheless, in order to uphold this < position >, first it is granted that the disjunction (disjunctum) 'true or false' is convertible with the term 'sentence'. This is clear, because <'true or false'> posits the primary attribute (prima passio) of . Furthermore, let us grant that every true sentence is absolutely (simpliciter) true and every false sentence is absolutely false. This is clear, because 'true' and 'absolutely true' are convertible, and likewise 'false' and 'absolutely false' are convertible, just like 'white' and 'absolutely white' - from which what is white in a certain respect (secundum quid) is not absolutely (absolute) white. Assuming these things to hold, it follows first

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Heytesbury argues that these first three opinions have a single basis in common: they all grant that in an insoluble casus the insoluble sentence in question can signify precisely as its words commonly pretend (par. 10). Heytesbury argues in a long, convoluted passage that this is impossible (pars. 11-18). From the above considerations, we can already anticipate how the argument will go in general, and so do not need to review the details here. Nevertheless, one point should be noted. Heytesbury's argument does not proceed in terms of truth or falsehood, but rather in terms of signifying as is the case or signifying otherwise than is the case. The insoluble sentence is "It is not the case as Socrates is saying," not "Socrates is saying what is false." I suggest that one reason Heytesbury adopts this strategy is to include the second previous opinion in his refutation. 30 For that opinion denies that insolubles are either true or false, since they are not sentences at all. But it admits that insolubles signify either as is the case or as is not the case (par. 6). If Heytesbury's argument had started from "Socrates is saying what is false," and concluded that the expression is true if and only if it is false, an upholder of the second position might reply that this just goes to show that such insolubles are neither true nor false, which is just what he had been

that every insoluble is true or false, because every insoluble is a sentence. It follows second that none is true, because none is true absolutely (simpliciter), but only in a certain respect. It follows third that no insoluble is false, because no insoluble is false absolutely, but only in a certain respect. For, as was said above, an insoluble sentence, insofar as it asserts itself to be false, is false at least in a certain respect. <But> insofar as it is the case that it is false, it is true at least in a certain respect. In virtue of these considerations one may reply to the opposing arguments." 30 See n. 10 to par. 6 of the translation.

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maintaining all along. By shifting the grounds of the argument, Heytesbury avoids this possible reply. Note that Heytesbury's argument does not quite succeed in refuting Swyneshed - at least not without pushing the argument further than Heytesbury does in these paragraphs as Heytesbury himself admits (par. 18). For Swyneshed would be quite willig to grant Heytesbury's conclusions. He would say that it is false that what Socrates is saying is the case, and also false that what he is saying is not the case. He can say this because he allows that in the case of insoluble sentences two mutual contradictories are both false at the same time. (See his third conclusion, above.) One might object that this is not enough. For since both contradictories were deduced by valid arguments from a casus admitted as true, Swyneshed ought to allow also that two contradictories can be true at the same time. But Swyneshed does not allow this. He tries to avoid the problem by claiming that in certain cases a valid inference can lead from truth to falsehood. (See his second conclusion, above.)31 Heytesbury addresses this point in par. 23. Curiously, 31 For Swyneshed, an inference is valid if and only if it preserves, not necessarily truth, but rather the property of "signifying as is the case." See Spade [38], par. 35: "If from some sentences, each of which signifies principally as is the case, there follows some sentence, then it signifies as is the case. But if from some sentences, one of which signifies otherwise than is the case and all the others as is the case, there follows some sentence, it does not follow that it signifies as is the case." The role of the adverb "principally" is not entirely clear in Swyneshed's doctrine. Swyneshed's three conclusions are not as strange as they sound. In effect, they amount to a separation of "truth-conditions" from "correspondence-conditions." Compare Herzberger [19]. Nevertheless, the conclusions were the topic of much controversy in the Middle Ages. See Spade [30], items in (p. 22), vn (p. 30), xxvi (Anthony de Monte, p. 52, second conclusion), xi.n (John of Wesel, p. 72, first question).

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he does not attempt to refute this contention there. He just observes that it is indeed required by Swyneshed's position, and apparently considers it unacceptable on the face of it. (But see below, section 3, for a qualification.) After treating the first three opinions together, Heytesbury considers them one by one. And. since he realizes that more needs to be said about Swyneshed's position, he appropriately devotes most of his discussion to it (pars. 19-31). Many of Heytesbury's arguments in these paragraphs are inconclusive - at least without pushing them further than Heytesbury does. His first argument (pars. 19-20) again consists of concluding two contradictories from an admitted casus, a conclusion that Swyneshed would accept, as we have seen. Heytesbury then argues (pars. 21-22) that one cannot get out of this by denying the casus as impossible. But Swyneshed never intended to do that. Next, Heytesbury argues (par. 23) that Swyneshed's second conclusion would follow. Swyneshed would hardly deny that. Fourth (par. 24), Heytesbury argues that a true sentence would be "convertible"32 with a false one, and that the same simple sentence would contradict both a false sentence and a true one. Although Swyneshed did not explicitly list these among his conclusions, there is no reason to think he would not have accepted them. Fifth (par. 25), Heytesbury argues that an impossible sentence could be contradicted by something other than a necessary sentence. Once again, Swyneshed might well have accepted this.

xi.ix (Paul of Pergula. p. 82), i, (Paul of Venice, p. 84). i.m (Ralph Strode, pp. 88-90). and i.xn (Roger Roseth, p. 101). 12 Here two tokens of the same type are said to be "convertible" - i.e.. each follows from the other.

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More interesting are Heytesbury's sixth and seventh arguments. His sixth argument (par. 26) concludes that two sentences may contradict the same impossible sentence, and yet the first of them be necessary and the second contingent. His example is that, if S is the sentence "5 is not necessary," S* the sentence "S is necessary," and S** is also the sentence "S1 is not necessary" (a different token of the same type as S), then S is contingently true, S* is impossible, and S** is necessary. Both S and 5**, however, contradict S*. In his seventh argument (pars. 27-28), Heytesbury adds the assumption that S be unable to signify otherwise than in fact it does. It is important to note that this does not affect the reasoning in par. 26. For on the basis of this added assumption, Heytesbury goes on to argue that S is not contingent, contradicting the conclusion of his sixth argument, as Heytesbury points out.33 I suggest that, by his involved sixth and seventh arguments, Heytesbury is trying to push his objection further than he did in his previous arguments. I suggest that what he has perhaps implicitly in mind is a point that could have been made much earlier (as early as his first arguments, in pars. 19-20), but that Heytesbury never clearly formulated - namely, that Swyneshed's attempt to allow two contradictories to be deducible from an admissible casus by providing that a valid inference may sometimes lead from truth to falsehood will not work. For if Swyneshed's principles validly yield a contradiction, then we may set up the following argument. Let R be the conjunction of Swyneshed's principles. Then from R we can, trivially,

33 For the details of these difficult arguments, see the notes to pars. 26-28 of the translation.

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conclude R by a valid inference. Furthermore, as Heytesbury has shown, from R we can also validly conclude a contradiction. But then, by reductio ad absurdum - a valid argument form - we can conclude the negation of/?: not-R. Hence from R we can validly conclude both R and not-R, which are contradictories. Swyneshed would be required to say in this case that both sides of the contradiction are false. In particular, he would have to say that R itself is false. That is, he would be forced to deny his own principles. And it does no good to say that a valid inference can start from a truth and lead to a falsehood, since we have just shown it does not start from a truth. In short, Swyneshed's own position is committed to saying that that very position is false. Heytesbury's arguments against the second and third positions are relatively brief, and need not be examined in detail here. 34 The discussion of the fourth previous position has been referred to above, at the end of section 1 of this study. 3. HEYTESBURY'S OWN VIEW After these preliminaries, Heytesbury sets out the definitions and rules governing his own position. We have already examined his definitions of an insoluble casus and of an insoluble sentence (pars. 44-45). After these, Heytesbury gives five rules. These rules became famous in the later literature. The first two rules (pars. 48-49) are quite straightforward, and need not be examined further here. The third rule, however, is important (pars. 50-51). It says, in effect, that if C is a casus of

See the notes to pars. 32-36 of the translation.

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an insoluble, and S is the insoluble sentence in question in C, then if the opponent posits both that C is satisfied and that S signifies as its terms (words) pretend - but note, the opponent does not posit that 5* "precisely" signifies as its terms pretend - then the respondent has to admit the casus. Then if the opponent proposes S in any subsequent step of the disputation, the respondent has to concede it, since it follows from what has been admitted. But if the opponent should propose "5" is true," the respondent has to deny that, since it is inconsistent with what has been admitted. Heytesbury's example illustrates the rule. Furthermore, if the respondent is asked in such a case just how the insoluble S signifies otherwise than as its words commonly pretend, he is not required to answer that question. For any one of a number of alternatives would do, and none of them is required by what has been admitted. Heytesbury's position here is perhaps motivated by the difficulties he discussed in pars. 37-43. This aspect of Heytesbury's view was the subject of much criticism in the later literature. The third rule will ultimately require some additional provisos, in virtue of the fifth rule. For the moment, however, let us observe that Heytesbury is saying here that sometimes we ought to concede sentences that are not true - and this because they follow validly from a casus which was assumed to be true. In effect, then, Heytesbury is allowing that a valid inference may lead from a truth to a falsehood. It may seem odd, therefore, that Heytesbury objected to Swyneshed on just this point (par. 23). On the other hand note that, strictly speaking, Heytesbury puts his argument in par. 23 in terms of inferences the components of which are simple sentences. A simple sentence seems to be a categorical which is not

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"exponible." 35 The difference between simple sentences and others is perhaps important here, since the cases in which Heytesbury allows a falsehood to follow validly from a truth seem always to be cases which do not start from simple sentences but from conjunctions. For Heytesbury, then, a valid inference does not necessarily preserve truth. It does, however, preserve "concedability." But just when is a sentence "concedable"? The rules of obligatio usually state that the respondent may - and indeed must concede whatever validly follows from what has been admitted, and also whatever neither follows from nor is inconsistent with what has been admitted, but is otherwise known to be so.36 This shows that the valid inferences cannot be simply identified with the "concedability"-preserving inferences. I suggest nevertheless that there is another property that some sentences have, preservation of which may be taken to define validity for Heytesbury. That property is its being the case as the sentence commonly pretends to signify. For convenience, we shall call this property "firmness." A sentence S. then, is "firm" if and only if, for whatever sentence replaces

35 See, e.g.. William of Ockham [50], n, 1 1 : "Having spoken about categoricals. simple ones as it were, we have to speak about sentences that are equivalent to hypotheticals." These sentences that are "equivalent" to hypotheticals are the so-called "exponibles." On exponibilia see Spade [29], pp. 83-93: and. for the later period, Ashworth [3]. 36 Or, for some authors, whatever validly follows from what has been admitted together with what hs already been conceded, and also whatever neither so follows from nor is inconsistent with what has been admitted, together with what has already been conceded, but is otherwise known to be so. See the distinction between the "old" and the "new" positions in Spade [37].

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"p," ifS commonly pretends to signify that p, then p.31 Then an inference is "valid" if and only if it cannot lead from a firm sentence to an infirm one-i.e., if and only if it "preserves firmness." Such an approach has, as we shall see, the distinct advantage of making good sense out of Heytesbury's position, and moreover seems to conform to standard views in the obligationes-\iterature. Note first that if one compares the definition of firmness with the second or alternative definition of truth given above in section 1 of the study, it is clear that the only difference lies in the substitution of "commonly pretends to signify" for "precisely signifies." The firmness of a sentence, then, rests only on its original or ordinary imposition; its truth, on the other hand, may rest on a second or "new" imposition,38 which the sentence acquires in the context of an obligatio. Since validity is based on firmness and not on truth, it follows that the validity of an inference is not affected by any "new" imposition in the context of an obligatio. Hence, insofar as a respondent's replies in a disputation are determined by what follows validly from what has been admitted, the respondent must reply according to the original or normal significations of the sentences proposed to him, and not according to any special significations they may be imposed to have for the duration of the disputation. I.e., he must reply according to the pretended significations of the proposed sentences.

37

The plausibility of taking Heytesbury to have had such a notion as the basis of validity will rest on our taking the "pretended signification" of a sentence to be the same as the precise signification it would have under normal conventions. See the discussion above in section 1 of the study. 38 See above, n. 15 to the study.

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This interpretation conforms to what is said elsewhere in the obligationes-litemture. Robert Fland, for instance, says "Hence one must always respond to sentences according to their primary significations, and never according to secondary ones/' 39 "Primary signification," for Fland, appears to be the same as "pretended signification" for Heytesbury, and "secondary signification" seems to be the same as "signification acquired by a new or special imposition."40 Again, Roger Swyneshed adopts the following as one of the principles of his own discussion of obligationes: "One's response to a sentence is not to be changed because of its composition"41 - i.e., because of the "new" imposition it acquires in that species of obligatio known as impositio.42 The motivation behind this rule appears to have been in effect a concern to keep object-language and metalanguage distinct.43 For instance, if the opponent should posit that the sentence "God exists" precisely signifies that man is not rational, the respondent should admit that casus, since it is 39

See Spade [37], par. 73. This terminology will be discussed in a forthcoming study of Robert Fland's doctrine. 41 See Spade [39], par. 21. 42 This rule, a common one in the obligationes-literature, was nevertheless not universally accepted. See, e.g., John Buridan, Sophismata, vi, conclusion 5, translated in Scott [26], p. 60: "Still, another case commonly occurs in required disputations in the schools. The master states that for the time of those disputations, this term 'ass' signifies for them exactly the same as what the term 'animal' signifies for us, according to its common significations. And if the respondent and others agree, then the proposition 'A man is an ass' is for them true and to be conceded. And yet without such an obligation, a similar one in wording would normally be false and impossible, even if it should be stated in church by the Blessed Mary." 43 On this distinction, see Tarski [43] and [44]. 40

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possible because of the arbitrariness of linguistic conventions. Then if the opponent proposes the sentence "God exists," the respondent might think that he should deny it on the basis of the new or secondary signification it has acquired. But not so, according to the rule. The respondent must concede the sentence on the basis of its pretended signification. To do otherwise would in effect be to confuse object-language and metalanguage. The distinction between the new or secondary significations of sentences and their original or normal significations parallels the modern distinction between metalanguage and object-language. The reason for the rule can perhaps be made clearer if we use two obviously distinct languages. Let us consider, then, the case in which the opponent says (in English): "I posit that the sentence 'Deus esf signifies precisely that man is not rational." The respondent admits the casus. Then the opponent says: "I propose that God exists." The respondent must concede it. Here the temptation to think that the respondent must deny the proposed sentence is removed. The argument proceeds in English, but is, in part at least, about a Latin sentence. The same kind of distinction is being made when the medievals say that a disputatio de obligationibus proceeds according to the pretended or normal signification of its sentences, even though it may be in part about some new or secondary signification. How does Heytesbury's third rule, interpreted according to the above considerations, disarm the "insoluble" paradoxical sentences? Consider the following example, paralleling the one Heytesbury himself gives in par. 50. Take a sentence S that pretends to signify that S is not true. (I.e., S is the sentence "5 is not true.") Then let the casus be: The sentence S signifies that S is not true. Note that the casus does not stipulate that S

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"precisely" signifies that S is not true. This casus fits the conditions in the antecedent of the third rule (par. 50). We reason now as follows: Suppose, for reductio, that (1) S is true. Now (2) S signifies that S is not true, by the casus. Hence (3) S is not true, from (1) and (2). But this contradicts (1). Thus, by reductio. (4) S is not true. At this point, let us interrupt to observe that step (3), as it stands, is a fallacy. For, as argued above in section 1 of the study, it is wrong to think that if a sentence S is true and signifies that p, then it follows that p. The counterexample that was given there concerned a sentence that precisely signifies disjunctively. Such counterexamples must somehow be ruled out if the third rule is to do the job Heytesbury wants. I suggest we proceed as follows. In Heytesbury's statement of the rule, the opponent posits that 5 signifies as its words pretend, but he does not posit that S signifies precisely as its words pretend. It is clear, however, from par. 51, that Heytesbury intends more than this. Not only does the opponent refrain from positing that 5 signifies precisely as its terms pretend, he also refrains altogether from positing how S precisely signifies. Let us then include this explicitly in the antecedent of the third rule. Then what that rule, together with Heytesbury's example, tells us is that in such a case, where the precise signification is not specified, we have a right to proceed on the assumption that it will not provide a counterexample to the kind of inference employed in step (3) above. Unless explicitly prevented by the casus, Heytesbury is saying, the respondent may legitimately adopt a certain bias toward the easier possibility. What happens when the opponent does specify the precise signification is discussed in Heytesbury's fourth and fifth rules. Returning now to the argument, step (4) must be conceded,

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since it follows from the casus (and the legitimate "bias" we have just mentioned) by a valid inference. But step (4) is just the original insoluble sentence S that was mentioned in the casus. Hence the insoluble is to be conceded.44 On the other hand, the second half of the paradox cannot be derived. The respondent must concede the insoluble, but he does not have to concede that it is true - indeed, he has to deny that it is true, since that would be inconsistent with the casus, as proved in the deduction of (4). He does not have to concede that it is true, because that does not follow validly from the casus (and the legitimate "bias"). If we try to make it follow, we should have to proceed like this: (4) S is not true. But (5) S signifies that S is not true, from the casus. Hence (6) S is true after all. Here step (6) is a fallacy. Given that p and that S signifies that p, it does not necessarily follow that S is true. It would follow, of course, if we were given that S precisely signified that p. But we are not given that. It would also follow if we supposed that 5 precisely signified that p or q. But in virtue of the legitimate "bias" mentioned above, that possibility can be ruled out. Hence the respondent does not have to concede - indeed, he must deny - that S is true. Heytesbury, unlike Swyneshed, 44

Strictly, of course, (4) need not be S itself, but only a token of the same type as S. Some authors try to turn this fact to philosophical advantage. (See, e.g.. Robert Fland in Spade [36], pars. 5-6. Fland. it should be noted, recognizes that there are cases where this device is not available. See Spade [36], par. 7.) Heytesbury's position, however, does not rest on this. For him, all tokens of the same type as an insoluble sentence are to be treated alike with respect to concedability (unless perhaps, although Heytesbury does not explicitly consider this case, they contain indexical words like "I" or "now").

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does not have to concede both sides of a contradiction. Note also that normally, where S is for instance the sentence "The king is sitting," we may infer: 'The king is sitting; therefore, S is true" and also "51 is true; therefore, the king is sitting." These inferences correspond to the so-called Tarski-biconditionals.45 Heytesbury's position has the effect of disallowing inferences like the first of these in cases governed by his third rule. To this extent, Heytesbury stands in the tradition I have elsewhere called the "tradition of the weakened Tarski biconditionals."46 Heytesbury's third rule is problematic, of course, because of the notion of "legitimate bias" that seems to be required to make it work the way it is supposed to. The implications of this notion may perhaps be made clearer by looking at his fourth and fifth rules (pars. 52-54). The third rule covers situations in which the opponent does not posit how the insoluble sentence is precisely to signify. The fourth and fifth rules cover two kinds of situations in which the opponent does posit how the insoluble precisely signifies. The fourth rule concerns cases in which the insoluble is posited as precisely signifying conjunctively, as its words commonly pretend and that such and such is so. Let us examine such a case. Take a sentence S that pretends to signify that S is not true. (I.e.. S is the sentence "5 is not true.") Then let the casus be: S precisely signifies that S is not true and p. Then we argue just as before: Suppose for reductio that (1) S is true. Now (2) S precisely signifies that S is not true and /?, from the casus. Hence (3) S is not true and p. This follows straightforwardly from the definition of truth given above, and does not require 45 46

See Tarski [43] and [44]. See Spade [27], pp. 1-3.

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any special "bias." Now from (3) by simplification we can get (4) S is not true, which contradicts the assumption in (1). Hence by reductio, (5) S is not true. But step (5) is just the insoluble sentence S itself. Hence the insoluble must be conceded, just as under the third rule. Similarly, it does not follow further that S is true, and so one does not have to concede that S is true - indeed, one must deny it. If we try to make it follow, we would argue thus: (5) 5 is not true. And (6) S precisely signifies that S is not true and /?, by the casus. Hence (7a) it is not the case that S is not true - i.e., 5" is true after all. Step (7a) is a fallacy - and again, no special "bias" is necessary to make it a fallacy. All we can legitimately infer from (5) and (6) is that (7b) either 5" is true or it is not the case that p. But we already known that S is not true, from (5). Hence (8) it is not the case that p. In this case, then, the respondent must concede the insoluble, deny that it is true, and deny that p. This is why Heytesbury says (par. 52) that if, in such a situation, the sentence replacing "/?" is such that its (contradictory) opposite is inconsistent with the original casus, then the casus must not be admitted to begin with, since one could derive both sides of a contradiction from it. Under the fourth rule, then, the respondent must reply to the insoluble, and to the claim that the insoluble is true, exactly as he must under the third rule. The fifth rule, however, presents a different situation, one in which the insoluble is posited as precisely signifying disjunctively, as its words pretend or that such and such is the case. Once again, take a sentence S that pretends to signify that S is not true. (I.e., S is the sentence "5" is not true.") Let the casus be: S precisely signifies that S is not true or p. Then we argue, somewhat differently than before: Suppose for reductio that (1) S is not true. Now (2) S precisely

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signifies that S is not true or /?, from the casus. Hence (3) it is not the case that either S is not true or p - i.e., S is true and it is not the case that p. Once again, this follows quite straightforwardly from the definition of truth, and requires no special "bias." From (3) by simplification we can get (4) S is true, which contradicts the assumption in (1). Hence by reductio, (5) S is true. Hence one must in this case, unlike the cases governed by the third and fourth rules, concede that the insoluble S is true. Accordingly, one must deny the sentence "S is not true," which is just the insoluble S itself. Whereas formerly one had to concede the insoluble and deny that it is true, in the present case one must deny the insoluble and concede that it is true. Nor does the other half of the contradiction follow - namely, that S is not true. If we try to make it follow, we would argue thus: (5) S is true. And (6) S precisely signifies that 5" is not true or p. by the casus. Hence (7a) S is not true after all. Step (7a) is a fallacy, and once again no special "bias" is required to make it a fallacy. All we can legitimately argue from (5) and (6) is that (7b) either S is not true or p. But we already know that S is true, from (5). Hence we conclude that (8) p. In this case, then, the respondent must deny the insoluble, concede that it is true, and concede that p. This is why Heytesbury says (par. 53) that in such a case, if the sentence replacing "/?" is inconsistent with the original casus, then the casus must not be admitted to begin with, since one could derive both sides of a contradiction from it. Heytesbury considers only two kinds of cases in which an insoluble is posited to signify as its words commonly pretend, but not precisely so, and in which the precise signification is nevertheless stipulated: cases in which it precisely signifies conjunctively and cases in which it precisely signifies dis-

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junctively. Presumably there are yet other ways in which an insoluble can precisely signify when it signifies (but not precisely) as its words commonly pretend. For instance, there seems to be no reason to suppose - given the arbitrariness of linguistic convention - that the insoluble could not signify "causally1 (e.g., "Because S is not true, the king is sitting") or "conditionally" (e.g., "If the king is sitting, then S is not true'"), and so on. Some of these modes can perhaps be reduced to the ones Heytesbury explicitly considers, but others cannot. Heytesbury thus does not give us a complete account. Nevertheless, what he does say is enough to shed some light perhaps on the notion of "legitimate bias" that seemed required for the third rule. It is striking that the respondent's replies to an insoluble 5, and to the sentence "5 is true," are the same on the fourth rule as they are on the third. This suggests - and it is only a suggestion - that when the precise signification of an insoluble is not specified, as in the third rule, the respondent is justified in assuming that it precisely signifies conjunctively in such a way that the contradictory of the second conjunct is consistent with the original casus. The more "bizarre" kinds of precise signification are to be taken as serious alternatives only when they are explicitly specified in the original casus. The respondent has a right to assume the most plausible alternative consistent with what he has admitted by admitting the casus. And the most plausible alternative appears to be conjunctive signification. But why should conjunctive signification seem any more plausible, any less 'bizarre," than the other modes? One possible answer comes from another tradition in the mso/wM/a-literature. According to this tradition, an insoluble

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sentence precisely signifies conjunctively, as its words pretend and that it itself is true. Indeed, some authors held that all sentences signify in part that they themselves are true.47 On this view, where S is an insoluble sentence "5 is not true," S precisely signifies that S is not true and S is true. Given the definition of truth, this means that S is true if and only if both S is not true and also S is true. It follows of course that S is false, since it precisely signifies in a contradictory way. The details of this position need not detain us here. Suffice it to say that it was a very common view. Heytesbury, of course, by saying that in a case governed by his third rule the respondent does not have to specify the precise signification of an insoluble, avoids committing himself to this position.48 Nevertheless, these considerations may explain why Heytesbury seems to have thought that in the absence of any stipulation about the precise signification of an insoluble, conjunctive precise signification was a more plausible alternative than disjunctive precise signification or precise signification in one of the other modes. Heytesbury's position, then, avoids the problems that Swyneshed's position had. Heytesbury agrees with Swyneshed that valid inferences need not preserve truth. For Heytesbury, they preserve what we have called "firmness."49 Unlike 47

See. e.g., Albert of Saxony, quoted in Spade [30], item xxiv. The roots of this tradition go back at least to Bonaventure. See Spade [30], item xxvn. See also the first of the two "acceptable" positions distinguished by Fland, Spade [30], item i.vm. (See also Spade [36]. The second of the two positions is Heytesbury's.) 48 Some later revisionists touched up Heytesbury's rules in a way that did commit them to this view. See, e.g.. the anonymous (Pseudo-Heytesbury) text discussed as item xn in Spade [30]. 49 Swyneshed's position does not rely on any claim that insolubles must

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Swyneshed, however, Heytesbury avoids the conclusion that both sides of a contradiction may be concedable, and the correlative difficulties that go with that. Nevertheless, Heytesbury's position is not without its own difficulties. Take a sentence 5" that pretends to signify that it is not the case as S pretends to signify - in our terminology, that S is "infirm." (I.e., S is the sentence "It is not the case as S pretends to signify," or "5" is infirm.") Now either S is firm or it is infirm. Suppose for reductio that (1) S is firm. Then (2) 5 pretends to signify that S is infirm. Hence (3) -S is infirm, which contradicts the assumption in (1). Step (3) follows from steps (1) and (2) and the definition of firmness, insofar as the respondent is always to reply according to the pretended significations of sentences. Hence, by reductio, we get (4) S is infirm. But again (5) S pretends to signify that 5" is infirm. Hence (6) it is not the case that S is infirm - i.e., S is firm, which contradicts (4). Step (6) follows from steps (4) and (5) and the definition of firmness, just as step (3) followed from steps (1) and (2) and that definition. Steps (4) and (6) show that Heytesbury's position yields a contradiction.50

signify otherwise than as their words pretend. For practical purposes, then, Heytesbury's notion of validity, in terms of what we have called "firmness," may be identified with Swyneshed's notion of validity in n. 31, above. Indeed, in virtue of the discussion in the study at n. 41, it appears that, when Swyneshed does take into account the possibility of a sentence's signifying otherwise than as its words pretend, his notion of validity agrees with Heytesbury's and not with his own as formulated in n. 31. 50 A similar objection is argued in the anonymous text discussed as item xn in Spade [30]. There the author uses the sentence "This sentence is not to be conceded," which yields a contradiction in a parallel, but more complicated, fashion.

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The only way for Heytesbury to avoid this paradox is to deny that there is any sentence S that pretends to signify that it is not the case as S pretends to signify - that S is infirm. But how could such a denial be maintained? What about the sentence "It is not the cae as this sentence pretends to signify"? Does it not pretend to signify just as is required ? If not, why not? Would not such a denial require an important and strange restriction on the original or normal imposition of sentences - thus compromising the arbitrariness of those conventional impositions? We have seen this problem before. Heytesbury, as he himself admits in another context, has no satisfactory answer. 51 One can perhaps draw a general lesson from Heytesbury's experience in this tract. The insolubles, it seems, constitute a refutation of the view that spoken and written language is altogether conventional (ad placitum] in the way Heytesbury thinks. It is quite true, of course, that in normal circumstances, in circumstances that do not give rise to the paradoxes, one can evaluate sentences of spoken and written language in accordance with the conventions imposed on them by the 51

It is interesting to point out that Heytesbury's position, although it is certainly not the same, bears interesting similarities to the position sketched by Hans G. Herzberger in [20], and elaborated in [19]. Both resolve the Liar paradox by distinguishing truth from another property which serves as the basis for valid inferences. In [20], Herzberger calls this property "security"; in [19] he calls it "correspondence." Both seem to be what we have called "firmness." Herzberger takes the theory he develops in these two places to be suggested not by Heytesbury but by John Buridan. In fairness, it should be pointed out that Herzberger, no more than Heytesbury, takes his theory to be a final and adequate solution to the paradoxes. Herzberger's theory allows the paradox "This sentence is not secure." just as Heytesbury's allows "This sentence is infirm."

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linguistic community. What the paradoxes show, however, is that in certain special circumstances, those that give rise to the paradoxes, those normal or ordinary conventions or "rules" cannot be consistently applied. It is this fact, I suggest, that accounts for the "shock" of the insolubles, for the fact that we find them "paradoxical." This much of what Heytesbury has to say seems to be quite correct. What gets him into trouble, however, is his insistence that in all cases, sentences are to be evaluated as true or false in terms of their "precise signification," where "precise signification" (and "signification" simpliciter) is construed in epistemological terms, in terms of what the sentence "brings to mind" when it is heard. Furthermore, Heytesbury contends that in all cases, what a sentence "brings to mind" in this way is a matter of the conventions imposed on the sentence, either the normal or ordinary conventions of the linguistic community, or else a special or new "imposition" or convention adopted for particular purposes. Heytesbury, then, links the semantic notions of truth and falsehood with the epistemological notion of "bringing to mind," and construes the latter in terms of more or less explicitly adopted conventions. This linkage, I suggest, is responsible for the failure of Heytesbury's approach. For it is a simple fact that a person can utter a sentence under circumstances which, unknown to himself, render the sentence an "insoluble" or paradoxical one. And he can utter that sentence under those circumstances in complete innocence, fully intending that his sentence be taken in the usual way, according to the normal or ordinary conventions. The epistemology of such a situation would be exactly the same as it would be under normal circumstances, where the sentence

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would not be a paradoxical one and where the normal or ordinary conventions would apply consistently. This is just the kind of case that constitutes a problem for Heytesbury's approach. What such cases show, I suggest, is that an adequate account of the paradoxes, if indeed one is possible, would require that the notions of truth and falsehood be severed from the epistemological notion of signification or "bringing to mind." What is needed is an account of truth and falsehood built on a different basis. Heytesbury fails to give us such an account.

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Bibliography [1] Albert of Saxony. Perutilis logica. Venice: Petrus Aurelius Sanutus Venetus, 1518. (Copy at Paris, Bibliotheque nationale, Imprimes. Res. R. 183.) [2] Angelelli, Ignacio. "The Techniques of Disputation in the History of Logic." The Journal of Philosophy 67 (1970): 800815. [3] Ashworth, E. J. "The Doctrine of Exponibilia in the Fifteenth and Sixteenth Centuries." Vivarium 11 (1973): 137-167. [4] Bottin, Francesco. Le antinomic semantiche nella logica medievale. Padua: Editrice Antenore, 1976. [5] . "L'Opinio de insolubilibus' di Richard Kilmyngton." Rivista critica di storia delta filosofia 28 (1973): 408-421. [6] Brown, Mary Anthony. "The Role of the Tractatus de obligationibus in Mediaeval Logic." Franciscan Studies 26 (1966): 2635. [7] Clagett, Marshall. The Science of Mechanics in the Middle Ages. University of Wisconsin Publications in Medieval Science, 4. Madison: University of Wisconsin Press, 1959. [8] Dales, Richard C. The Scientific Achievement of the Middle Ages. Philadelphia: University of Pennsylvania Press, 1973. [9] De Rijk, Lambert M. "Some Notes on the Mediaeval Tract De insolubilibus with the Edition of a Tract Dating from the End of the Twelfth Century." Vivarium 4 (1966): 83-115. [10] . "Some Thirteenth Century Tracts on the Game of Obligation." i: Vivarium 12 (1974), 94-123; 11: Vivarium 13 (1975): 22-54; m: Vivarium 14(1976): 26-49. [11] Dunn, J. Michael, and Nuel D. Belnap, Jr. "The Substitution Interpretation of the Quantifiers." Nous 2 (1968): 177-185.

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[12] Elie, Hubert. Le Complexe significabile. Paris: Librairie philosophique J. Vrin, 1936. [13] Emden, A. B. A Biographical Register of the University of Oxford to a.d. 1500. 3 vols. Oxford: Clarendon Press, 1957-1959. [14] Grabmann, Martin. Die Sophismatalitteratur des 12. und 13. Jahrhunderts mil Textausgabe eines Sophisma des Boetius von Dacien. Beitrage zur Geschichte der Philosophie und Theologie des Mittelalters, 36, 1. Miinster i.W.: Aschendorffsche Verlagsbuchhandlung, 1940. [15] Grant, Edward. A Source Book in Medieval Science. Source Books in the History of Science. Cambridge, Mass.: Harvard University Press, 1974. [16] Green, Romuald. The Logical Treatise "De obligationibus": An Introduction with Critical Texts of William of Sherwood and Walter Burley. St. Bonaventure: Franciscan Institute (forthcoming). [17] Hamblin, C. L. Fallacies. London-. Methuen, 1970. [18] Heidingsfelder, Georg. Albert von Sachsen: Sein Lebensgang und sein Kommentar zur nikomachischen Ethik des Aristoteles. Beitrage zur Geschichte der Philosophie des Mittelalters, 22, 34. Miinster i.W.: Aschendorffsche Verlagsbuchhandlung, 1927. [19] Herzberger, Hans G. "Dimensions of Truth." Journal of Philosophical Logic 2 (1973): 535-556. [20] . "Truth and Modality in Semantically Closed Languages." In [23], pp. 25-46. [21] Linsky, Leonard, ed. Reference and Modality. Oxford Readings in Philosophy. Oxford: University Press, 1971. [22] Maieru, Alfonso. "II problema della verita nelle opere di Guglielmo Heytesbury." Studi medievali, serie terza, 7 (1966): 40-74. [23] Martin, Robert L., ed. The Paradox of the Liar. New Haven, Conn.: Yale University Press, 1970. [24] Nuchelmans, Gabriel. Theories of the Proposition: Ancient and

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[31] [32] [33] [34]

[35]

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Medieval Conceptions of the Bearers of Truth and Falsity. North-Holland Linguistic Series. Amsterdam: North-Holland Publishing Company, 1973. Roure, Marie-Louise. "La problematique des propositions insolubles au xm e siecle et au debut du xiv e , suivie de 1'edition des traites de W. Shyreswood, W. Burleigh et Th. Bradwar dine.' Archives d histoire doctrinale et litteraire du moyen age 37 (1970): 205-326. Scott, Theodore Kermit. John Buridan: Sophisms on Meaning and Truth. Century Philosophy Sourcebooks. New York: Appleton-Century-Crofts, 1966. Spade, Paul Vincent. "An Anonymous Tract on Insolubilia from Ms Vat. lat. 674: An Edition and Analysis of the Text." Vivarium 9(1971): 1-18. . "On A Conservative Attitude toward Some Naive Semantic Principles." Notre Dame Journal of Formal Logic 15 (1975): 597-602. . "Five Logical Tracts by Richard Lavenham." In Essays in Honour of Anton Charles Pegis, ed. J. R. O'Donnell, pp. 70-124. Toronto: The Pontifical Institute of Mediaeval Studies, 1974. . The Mediaeval Liar: A Catalogue of the InsolubiliaLiterature. Subsidia Mediaevalia, 5. Toronto: Pontifical Institute of Mediaeval Studies. 1975. . "Ockham on Self-Reference." Notre Dame Journal of Formal Logic 15 (1974): 298-300. . "Ockham's Distinction between Absolute and Connotative Terms." Vivarium 13 (1975): 55-76. . "The Origins of the Mediaeval Insolubilia-Literature." Franciscan Studies 33 (1973): 292-309. . "Richard Lavenham's Obligationes: Edition and Comments." Rivista critica di storia della filosofia 33 (1978): 225242. . "Robert Fland's Consequentiae-. An Edition." Mediaeval Studies 38 (1976): 54-84.

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[36]

[37] [38] [39]

[40] [41 ]

[42] [43]

[44]

[45]

[46]

[47] [48]

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. "Robert Fland's Insolubilia: An Edition, with Comments on the Dating of Fland's Works." Mediaeval Studies 39 (1978): 56-80. . "Robert Fland's Obligationes: An Edition." Mediaeval Studies (forthcoming). . "Robert Swyneshed's Insolubilia: Edition and Comments." (Forthcoming). . "Roger Swyneshed's Obligationes: Edition and Comments." Archives d'histoire doctrinale et litteraire du moyen age 44(1977): 243-285. . "Some Epistemological Implications of the BurleyOckham Dispute." Franciscan Studies 35 (1975): 212-222. . "The Treatises On Modal Propositions and On Hypothetical Propositions by Richard Lavenham." Mediaeval Studies 35 (1973): 49-59. . "William Heytesbury's Position on "Insolubles": One Possible Source." Vivarium 14(1976): 114-120. Tarski, Alfred. "The Concept of Truth in Formalized Languages." In Logic, Semantics, Metamathematics: Papers from 1923 to 1938, tr. J. H. Woodger, pp. 152-278. Oxford: Clarendon Press, 1969. . "The Semantic Conception of Truth and the Foundations of Semantics." Philosophy and Phenomenological Research 4 (1944): 341-376. Wallace, William A. Causality and Scientific Explanation, vol. 1: Medieval and Early Classical Science. Ann Arbor: University of Michigan Press, 1972. Weisheipl, James A. "Developments in the Arts Curriculum at Oxford in the Early Fourteenth Century." Mediaeval Studies 28 (1966): 151-175. . "Ockham and Some Mertonians." Mediaeval Studies 30 (1968): 163-213. . "Repertorium Mertonense." Mediaeval Studies 31 (1969): 174-224.

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101

[49] Whitehead, Alfred North, and Bertrand Russell. Principia Mathematica. 2nd ed. Cambridge: University Press, 1927. [50] William of Ockham. Guillelmi de Ockham Summa logicae. Eds. Philotheus Boehner, Gedeon Gal and Stephen F. Brown. Guillelmi de Ockham Opera philosophica et theologica: Opera philosophica, 1. St. Bonaventure, N.Y.: The Franciscan Institute. 1974. [51 ] Wilson, Curtis. William Heytesbury. Medieval Logic and the Rise of Mathematical Physics. University of Wisconsin Publications in Medieval Science, 3. Madison: University of Wisconsin Press, 1956.

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Index of Names

Albert of Saxony 8 & nn. 20 & 22, 91 n. 47. Angelelli, I. 60 n. 2. Angelo of Fossambrone 6. Anthony de Monte 76 n. 31. Aristotle ("the Philosopher") 4, 10, 18 & n. 7. Ashworth, E. J. 81 n. 35. Belnap. N. D., Jr. 64 n. 12. Boethius 19 nn. 11-12. Bonaventure 91 n. 47. Bottin, F. 6 n. 15, 74 n. 29. Brown, M. A. 60 n. 2. Cajetan of Thiene 6, 1 1 , 7 1 n. 22, 73 n. 28, 74 n. 29. Clagett. M. 4 nn. 9 & 12. Dales, R C. 4 n. 9. De Rijk L. M. 7 n. 17, 60 n. 2. Dunn, J. M. 64 n. 12. Elie, H. 61 n. 5. Emden, A. B. 1 nn. 1-2. Galileo 4. Grabmann, M. 3 n. 7, 7 n. 17. Grant, E. 4 n. 12. Green, R. 60 n. 2. Gregory of Rimini 61. Hamblin, C. L. 60 n. 2. Heidingsfelder, G. 8 n. 19.

Herzberger, H. G. 10 n. 26, 76 n. 31, 93, n. 51. John Buridan 3 n. 7, 61 nn. 5 & 7, 62 n. 8, 83 n. 42, 93 n. 51. John of Constance 6. John Dumbleton 1 & n. 1, 6, 72 n. 22, 73 n. 28. John of Holland 6. John Hunter (Venator) 6 & n. 16. John of Wesel 6, 76 n. 31. John Wycliff 6. Kretzmann, N. and B. E. 3 n. 7, 74 n. 29. Linsky, L. 2 n. 5. Maierii, A. 63 n. 11. Martin R. L. 6 n. 14. Moody, E. A. 4 n. 12. Nuchelmans, G. 61 n. 5. Paul of Pergula 6, 68 n. 16, 77 n. 31. Paul of Venice 6, 68 n. 16, 77 n. 31. Peter of Ailly 68 n. 16. Ralph Strode 4 n. 10, 6, 77 n. 31. Richard Kilvington 3 n. 7, 72 n. 22, 74 n. 29. Richard Lavenham 8 & nn. 21-22. Robert Fland 6, 63 n. 10, 83 & n. 40, 86 n. 44, 91 n. 47.

104

INDEX OF NAMES

Roger Roseth 77 n. 31. Roger Swyneshed 18-19 & n. 9, 25-37, 41 n. 102, 68 n. 16, 72-73, 76-79, 83, 86, 91-92 & n. 49. Roure, M.-L. 7 n. 17, 9 n. 25. Russell, B. 9. Scott T. K. 3 n. 7,61 nn. 5 & 7, 62 n. 8, 83 n. 42. Spade, P. V. 4 n. 10, 6 nn. 15-16, 7 n. 17, 8 n n . 18 & 20-22, 9 n. 25, 16 n. 6, 19 n. 9, 29 n. 50, 36 n. 87, 38 n. 92,41 n. 102, 47 n. 117,48nn. 119120, 60 n. 2 , 6 1 n. 6, 62 nn. 7 & 9, 63 n. 10, 68 n. 16, 69 n. 19, 72 nn. 24-25,73 n. 28, 74 n. 29, 76 n. 31, 81 nn. 35-36, 83 nn. 39 & 41, 86 n. 44, 87 n. 46, 91 nn. 47-48, 92 n. 50. Tarski, 1. 83 n. 43, 87 & n. 45. Thomas Bradwardine 3, 4 n. 10, 9 n. 25.

Wallace, W. A. 4 n. 9. Weisheipl, J. A. 1 nn. 1-3, 2 n. 4, 3 n. 8, 4 n . 9, 6 n. 16, 15 n. 1 , 7 3 n. 28. Whitehead, A. N. 9 n. 24. William Heytesbury: life 1; works: dates 1-2; "Rules for Solving Sophisms" 1-7, 11, chapters, 4-5, 1617, date 2 & n. 4, 4; Sophismata 3 & n. 8; De sensu composite et diviso 55 n. 127; De veritate etfalsitate propositionis 63 & n. 11; two wrongly ascribed Insolubilia 1 n. 3, 6 n. 16 (see also 91 n. 48). Pseudo-William of Heytesbury 91 n. 48. See also 1 n. 3, 6 n. 16. William of Ockham 7-9 & nn. 18 & 23, 62 n. 9, 81 n. 35. William of Sherwood 7 n. 17. Wilson, C. 1 n. 2, 3 n. 8, 5 n. 13, 15 n. 3.

Index of Topics

Certain technical expressions occur in the translation so frequently that it would be pointless to index all their occurrences. In such cases I have listed only the most important occurrences and those where the expression is introduced or explained. Ab necesse ad esse arguments 31 nn. "case," use of term in translating Latin 63-64. adverbial phrases 60-61. Absolutely: casus including something Casus: assumed true for duration of a. insoluble 20, 40; true or false 39, disputation 60; explanation of term 74 n. 29. 59; impossible 20, 34, 36 & n. 87, Acceleration 4. 77; including something absolutely Admit casus in disputatio de obligatioinsoluble 20, 40; of insoluble, Heynibus 60. tesbury's definition 46, 69 & n. 19, Ad utrumlibet contingency 35 n. 85. 70 & nn. 20-21, 79, alternative Adverbial notion of signification 61-63, construction 49, 69 n. 19; term left 65. untranslated 59, 60 n. 3. Adverbs, terms compounded of 36-37. Categorematic term 61-62 & n. 7, 63, See also 38, 45. 65. "A falsehood exists" (Falsum est) 20 & Categorical sentence 80, 81 n. 35. n. 16, 36, 38, 40-43, 46, 48, 52-53. Causal signification 90. Antecedent, contradictory of conse- Circle, square the 10, 18 & n. 7. quent inconsistent with 29 & n. 54. Closed under logical consequence 67 n. Assumptions: Heytesbury's two 46 (see 14. also Definition); Roger Swyneshed's Complexe significabile 61 & n. 5, 64 n. 73. 12. Attribute, primary of sentence 74 n. 29. Composite: sense 55 & n. 127; terms convertible with simple terms 36"Begins," sophisms involving 4, 17. 37, 38, 45. Believe without believing a sentence 57. Concedability 81, 86 n. 44; preservation Belmont, run at 53, 55. of 81. Bias, legitimate 85-91. Concede; insoluble (as following) 49, Bivalence 69 n. 19. See also 19. 52-53, 80, 86, 88; proposed sentence in disputatio de obligationibus 60; "Calculators," Merton 3 & n. 7, 4 & n. that insoluble is true 52, 89. 9. Conceive by means of sentence 41, 42,

106

INDEX OF TOPICS

43, 44. Conclusions, Roger Swyneshed's 73, 76 n. 31; his first 73; his second 29 & n. 51, 30, 73, 76-77, 78-79, 80-81; his third 18-19, 20, 25,27 n. 43,28,37, 73, 76, 79. Conditional signification 90. Conjunctive signification 50-51, 52, 8788, 89, 90-91. Connotation-theory 62 n. 7. Consequent: contradictory of inconsistent with antecedent 29 & n. 55; signification 66 n. 14. Constituent of sentence 65-66 & n. 14. Contingent: ad utrumlibet 35 n. 85; contradicts impossible 31-32, 78; true sentence neither necessary nor 32-34. Contradictories: false at same time (Roger Swyneshed's 3rd conclusion) 18-19, 20, 25, 27 n. 43, 28, 37, 73, 76, 79; necessary and contingent are both c. of impossible 31-32, 78; neither of pair is true and neither false 39, 40 n. 99; neither true nor false 19; not true at same time 27 n. 43, 33 & n. 77. Contradictory: of consequent inconsistent with antecedent 29 & n. 54; of impossible is contingent 31-32, 78; of impossible is other than necessary 31, 77; same sentence c. of falsehood and truth 30, 77. Conventional signification 34 n. 79, 6264, 71, 83-84,90, 93-95. Conversion: of logical equivalents 30 n. 59; necessary sentences only with one aother 34 & n. 81, 35 & n. 85; simple/per accidens 30 n. 59; simple terms with terms compounded of adverbs 36-37 (see also 38, 45); truth

with falsehood 30, 77; truth with non-truth 35 & n. 85, 39. Correspondence 93 n. 51. Correspondence-conditions separated from truth-conditions 76 n. 31. Creation, free act of 24 n. 24. Definition of: casus of insoluble, Heytesbury's 46, 69 & n. 19, 70 & nn. 20-21, 79; falsehood, Roger Swyneshed's 27 n. 44, 29 n. 52, 33 n. 79, 72; firmness 81-82; insoluble sentence Heytesbury's 46, 69-70, 79, Roger Swyneshed's 72-73; sentence 19 & n. 11, 72, 74 n. 28; truth, Heytesbury's implicit 64, 82, "howsoever it signifies, so it is the case" 62-66, in terms of supposition 62, 63, Roger Swyneshed's 27 & n. 42, 32 n. 70, 72. Demonstratives 4. Deny: casus in disputatio de obligationibus 27-28, 48-49, 59, 60, 77; insoluble 52, 89; proposed sentence in disp. de oblig. 60; that insoluble is true 49, 52, 80, 86, 88. Determinateness 74 n. 28. Determinate signification 74 n. 28. Disjunctive: signification 51-52, 85, 86, 88-90, 9 1 ; t e r m 7 4 & n n . 28-29. Disputatio de obligationibus. See Obligationes. Divided sense 55 & n. 127. Division, Heytesbury's 47. See also Rules, Heytesbury's. Doubt proposed sentence in disputatio de obligationibus 60. "Doubt," sophisms involving 4, 17. Epistemic logic 4. Epistemological notion of signification

INDEX OF TOPICS

61, 65, 94-95. Erfurt: MS Amplon. 2° 135 (Heytesbury's "Rules") 2; MS Amplon. 4° 270, fols. 37rl-39r30(John Hunter's Insolubilia) 6 n. 16. "Every sentence now being uttered by anyone anywhere in the world is false" 71. Exercitatio 15. Exponible sentences 81 & n. 35. Falsehood: absolute 39, 74 n. 29; and truth contradicted by same sentence 30, 77; can validly follow from truth (see Roger Swyneshed's 2nd conclusion) 29 & n. 51, 30, 73, 76-77, 7879, 80-81; signifies principally as is the case (Roger Swyneshed's first conclusion) 73; Swyneshed's definition 26 n. 44, 28 n. 52, 33 n. 79, 72; truth convertible with 30, 77. Falsifies itself, sentence 1 9 , 2 1 , 2 7 , 2 8 & n. 50,29, 32 & n. 69, 33 & n. 76, 34 n. 79, 35 & n. 85, 37, 72-73. Firmness 67 n. 14, 81-82, 91, 92 & n. 49. 93 n. 51. First position in disputatio de obligationibus 46 & n. 117. 47. "Howsoever it signifies, so it is the case," definition of truth 62-66. Hypotheticals, sentences equivalent to 81 n. 35. Ideal mind 67 n. 14. Imposition: new 68 n. 15, 82-83, 94; signification by 40, 41, 42, 68 & n. 15, 71, 72, 82-83; species of obligatio 68 & nn. 15-16, 83. Impossible: casus 20, 34, 36 & n. 87, 77: contradicted by both necessary

107

and contingent 31-32, 78; contradicted by other than necessary 31, 78; everything follows from 36; inconsistent with any other sentence 51; universally included as opposite 51. Inconsistent, ways of being 51. Indexical words 86 n. 44. Insolubilia, two works wrongly ascribed to Heytesbury 1 n. 3, 6 n. 16. See also 92 n. 48. Insolubilia-literature, medieval 6-11; stages in 7-11. See also Liar Paradox. Insoluble: additional signification of 4950, 80 (see also 6 n. 16); can be solved 7-9, 10-11, 18; cannot be solved without evident objection 11, 58; casus including something absolutely i. 20, 40; casus of, Heytesbury's definition 46, 69 & n. 19, 70 nn. 20-21, 79, alternative construction 47, 69 n. 19; cyclic 38 & n. 92, 69 n. 19; does not signify precisely as words commonly pretend 48-49, 54, 70-71, 75; explanation of problem 5; Heytesbury's confidence there is solution 10-11, 18; Heytesbury's recognition of no satisfactory solution 10-11, 21, 45, 58, 71; is a sentence 19, 74 & n. 29; not a sentence 19, 21, 37-39, 73, 75; not immediately concerning truth or falsehood 56-58; not relative to casus 70 n. 20; sentence, Heytesbury's definition 46, 69-70. 79, Roger Swyneshed's definition 7273; stages in medieval discussion 711; true-or-false but not true and not false 19-20, 21, 39-40, 74 & n. 29. See also Liar Paradox. Irrelevant (impertinent to casus 48 & n.

108

INDEX OF TOPICS

119. "It is not the case as any man is saying" 25 & n. 37. "It is not the case as Socrates is saying" 22 &n. 21, 75. "It is not the case as S pretends to signify" 92-93. "It is not the case as this sentence pretends to signify" 93. Know without knowing a sentence 57. "Know," sophisms involving 4, 17.

ble only with necessary 34 & n. 81, 35 & n. 85; something other than n. contradicts the impossible 31, 77; true sentence neither n. nor contingent 32-34. Nominalism 61 & n. 5, 62 & n. 7, 63 & n. 10. Nominal notion of signification 61-63, 65. "No sentence is true" 46.

Maxim 19 & n. 12. "Maximum," sophisms involving 4, 17. Mental language 62 n. 9. Merton College, Oxford 1, 3-4 & n. 9; Merton "Calculators" 3 & n. 7, 4 & n. 9. Metalanguage 83-84. Mind, ideal 67 n. 14. "Minimum," sophisms involving 4, 17. Modal: arguments against first previous opinion 31-35, 77-79; logic 2; operator, position of 55 n. 127. Motion. See Acceleration, Velocity.

Object-language 83-84. Obligations, disputation 47 n. 117; 5960 &n. 2 , 6 8 & n . 15,81 &n. 35,8284; old and new views 81 n. 36. Opaque contexts 2, 55 n. 127; quantification into 55 n. 127. Opinions, Heytesbury's list of previous 11,18-20; first (Roger Swyneshed's) 18-19 & n. 9, 21, 25-26, 72-73; against it 26-37, 38, 76-79; self refuting 79; second 19, 21, 26, 73, 75; attributed to John Dumbleton 72 n. 22, 73 n. 28; against it 37-39, 79; third 19-20, 21, 26, 74; attributed to Richard Kilvington 72 n. 22, 74 n. 29; against it 39-40, 79; first three together 11, 20 n. 10; arguments against them 20 n. 10, 20-26, 75-76; fourth 11, 20, 21, 59, 71, 79; against it 11, 21, 40-45. Opponent in disputatio de obligationibus 59-60. Originality, Heytesbury's disclaimer of 16 & n. 6 Oxford Bodl., MS Canon. Misc. 219, fols. 7ra-9rb (John Hunter's Insolubilia) 6 n. 16. See also University of Oxford.

Necessary: and contingent both contradict impossible 31-32, 78; converti-

Padua: Bibl. Anton., Cod. N. 407, fols. 26ra-30ra (Ch. 1 of Heytesbury's

Language: mental 62 n. 9; (spoken or written) is conventional 34 n. 79, 62-64,71, 83-84, 90, 93-95. Liar Paradox: medieval literature 6-11; modern literature 6 & n. 14. See also Insoluble. Logic: epistemic 4; modal 2; study of at Oxford 15 n. 1. London, British Library, MS Sloane 3899, fol. 73r (passage from Richard Lavenham's Insolubilia) 8 n. 22.

INDEX OF TOPICS

"Rules") 12; Bibl. univ., MS 1123, fols. 22vb-24rb (anonymous Insolubilia) 6 n. 16. Per accidens conversion 30 n. 59. Place, velocity and acceleration in 4. "Plato hears Socrates say otherwise than is the case" 45 n. 113. "Plato hears that Socrates says otherwise than is the case" 45. Plenum, void without 39. Positing (positio), species ofobligatio 60, 68. Position in disputatio de obligationibus 49; propose in first 47 & n. 117, 48. Precise signification 64-66 & 14, 68-69, 82 & n. 37, 94. Preservation of: concedability 81; firmness 67 n. 14, 81-82, 9 1 , 9 2 n. 49, 93 n. 51; signification as is the case 76 n. 31 (see also 92 n. 49); truth 76 n. 31, 81, 91. Pretended signification 67-69 & n. 14, 81-84, 92-93. "Principally," role of word in Roger Swyneshed's doctrine 72 n. 25, 76 n. 31. Principle/ Mathematica 9 & n. 24. Propose sentence in disputatio de obligationibus 60; in first position 47 & n. 117, 48. Proposition in modern sense 61, 62 n. 7, 64 n. 12. Quality, velocity and acceleration in 4. Quantification: into opaque contexts 55 n. 127; substitution interpretation 64 n. 12; theory 64 n. 12. Quantity, velocity and acceleration in 4. Queen's College, Oxford 1.

109

Relative pronouns, sophisms involving 4, 17. Relevant (pertinens): to casus 73 n. 26; to inferring that it is false 72-73 & n. 26. Respondent in disputatio de obligationibus 59-60, 81 & n. 36; need not give additional signification of insolubles 49-50, 80 (see also 6 n. 16). Rules for insolubles, Heytesbury's: first 47-48, 79; second 48-49, 59, 79; third 49-50, 79-80, 84-87, 88, 89, 90-91; fourth 50-51, 85, 87-88, 89, 90; fifth 51-52, 65 n. 13, 80, 85, 87, 88-90. "Rules for Solving Sophisms" (Regulae solvendi sophismata), Heytesbury's 1-7, 11; chapters 4-5, 16-17; date 2 & n. 4, 4. Secundum quid and simpliciter 74 n. 29. Security 93 n. 51. Sense, composite and divided 55 & n. 127. Sentence: as translation of 'propositio' 62 n. 7; constituent of 65-66 & n. 14; definition 74 n. 28, Boethius' 19 n. 11, Roger Swyneshed's 72; every s. is true or false 19; insoluble (see also Insoluble, Liar Paradox), Heytesbury's definition 46, 69-70, 79, Roger Swyneshed's definition 7273; insoluble is as. 19, 74 & n. 29; insoluble is not 19, 21, 37-39, 73, 75; signification of 19 n. 11, 61-69, 91; signifies that it is true 91; simple 29 & n. 51, 30 & n. 61, 77, 80-81 & n. 35; token/type 61 n. 4, 77 n. 32, 86 n. 44.

10

INDEX OF TOPICS

Set-theory 67 n. 14. "Sicut est," translation of 60. Signification: adverbial notion of 61-63, 65; as is the case, preservation of 76 n. 31 (see also 92 n. 49); by imposition 41, 42, 43, 68 & n. 15, 71, 72, 82-83; causal 90; conditional 90; conjunctive 50-51, 52, 87-88, 89, 90-91; consequent 66 n. 14; conventional 34 n. 79, 62-64, 71, 83-84, 90, 93-95; determinate 74 n. 28; disjunctive 51-52, 85, 86, 88-90, 91; establishing an understanding or bringing to mind 61, 65, 94-95; insoluble's additional 49-50, 80 (see also 6 n. 16); nominal notion of 6163, 65; precise 64-66 & n. 14, 68-69, 82 & n. 37, 94; pretended 67-69 & n. 14, 81-84, 92-93; primary/secondary 83-84; sentence's 20 n. 11, 6169, 91, sentences signifying that they are true 91; simpliciter 66, 67 n. 14, 68-69, 94. Simple: conversion 30 n. 59; sentences 29 & n . 51, 30 & n. 61, 77, 80-81 & n. 35; terms convertible with terms compounded of adverbs 36-37 (see also 38, 45). Simpliciter and secundum quid 74 n. 29. "S is infirm" 92-93. "Socrates is not saying what is true" 46. "Socrates is saying otherwise than is the case" 46. "Socrates is saying what is false" (Sortes dicitfalsum) 21, 22 & n. 21, 46-52, 54-55, 56, 75. "Socrates responds correctly" 53. "Socrates sees a falsehood" 44-45. "Some one of these responds wrongly" 53.

"Some sentence signifies otherwise than is the case" 27-28. Sophismata-Mterature 3 & n. 7. Sophism: explanation of notion 2-3; hidden from any logician 15 & n. 2. Sophistry (sophistical) in pejorative sense 2 & n. 6, 55. Square the circle 10, 18 & n. 7. "Stops," sophisms involving 4, 17. Substitution interpretation of quantification 64 n. 12. Supposition: definiton of truth in terms of 62, 63; personal 62; theory of 62 & n. 8, 63. Tarski-biconditionals, weakened 87. Term: composite 36-37, 38, 45; disjunctive 74 nn. 28-29; signification of categorematic 61-62 & n. 7; simple, convertible with term compounded of adverbs 36-37 (see also 38, 45). "The number of planets is necessarily greater than seven" 2. Theory of types 9. "There is a sentence signifying otherwise than is the case" 36 n. 88. "There is some sentence signifying otherwise than is the case" 36. "This is false" 29 & n. 53, 30, 36, 39. "This is not true" 37, 39. "This sentence is infirm" 93 n. 51. "This sentence is not necessary" 31-35. "This sentence is not to be conceded" 92 n. 50. "This sentence signifies otherwise than is the case" 26-27, 29 n. 50. Tokens, sentence 61 n. 4, 77 n. 32, 86 n. 44. Truth: absolute 41, 74 n. 29; and falsehood contradicted by same sentence 30, 77; can lead validly to

INDEX OF TOPICS

falsehood (see Roger Swyneshed's 2nd conclusion) 29 & n. 51, 30, 73, 76-77, 78-79, 80-81; convertible with falsehood 30, 77; convertible with non-truth 34 & n. 85, 38; definition, Heytesbury's implicit 64, 82, "howsoever it signifies, so it is the case" 62-66, in terms of supposition 62, 63, Roger Swyneshed's 27 n. 42, 32 n. 70, 72; neither necessary nor contingent 32-34; preservation of 76 n. 31, 81, 91. Truth-conditions separated from correspondence-conditions 76 n. 31. Truth-value, bearer of is sentence-token 61 & n. 4. Types: sentence 61 & n. 4, 77 n. 32, 86 n. 44; theory of 9. Understanding: common, of precise signification 43; sound, of adverbial phrases 36-37. University of Oxford: Merton college 1, 3-4; Merton "Calculators" 3 & n. 7, 4 & n. 9; Queen's College 1; study of logic at 1 5 n. 1. "Unnecessitates" itself, sentence 35 n. 85.

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Utterance, every is divisible 56. Validity: can lead from truth to falsehood (see Roger Swyneshed's 2nd conclusion) 29 & n. 51, 30, 73, 7677, 78-79, 80-81; cannot lead from truth to falsehood 5; common test of, contradictory of consequent inconsistent with antecedent 29 & n. 54; notion of, Heytesbury's (preservation of firmness) 80-82, 91, 92 & n. 49, Roger Swyneshed's (preservation of signification as is the case) 76 n. 31, 92 n. 49; of"/?; therefore, it is true that p" 23 & n. 24. Vatican: MSS Vat. lat. 2136, fols. lra-5rb (Ch. 1 of Heytesbury's "Rules") 12; Vat. lat. 2138, fols. 89ra-91va(Ch. 1 of Heytesbury's "Rules")! 2; Vat. lat. 3065, fols. 28r-30r (John Hunter's Insolubilia) 6 n. 16. Velocity 4, 17. Venice 1494 edition of Heytesbury 3 n. 8, 11, 55 n. 127, 64 n. 11, 71 n. 22. Void without plenum 39. "What I am now saying is false" 5, 70. Wiltshire, Salisbury diocese 1.