Treatise on Consequences

By John Buridan

The rediscovery of Aristotle in the late twelfth century led to a fresh development of logical theory, culminating in Buridan’s crucial comprehensive treatment in the Treatise on Consequences. Buridan’s novel treatment of the categorical syllogism laid the basis for the study of logic in succeeding centuries.

This new translation offers a clear and accurate rendering of Buridan’s text. It is prefaced by a substantial Introduction that outlines the work’s context and explains its argument in detail. Also included is a translation of the Introduction (in French) to the 1976 edition of the Latin text by Hubert Hubien.

• Language: English
• Publisher: Fordham University Press
• Release date: Dec 15, 2014
• ISBN: 9780823257201

Book preview

TREATISE ON CONSEQUENCES

Introduction

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1. John Buridan

John Buridan was born in Béthune in Picardy, in northern France, in the late 1290s. He spent his entire academic career in the arts faculty at the University of Paris, dying around 1360. In this regard, his career was unusual. Most other scholars either joined one of the religious orders (John Duns Scotus and William Ockham were Franciscans, Paul of Venice an Augustinian), or at least proceeded from their studies in arts to one of the higher faculties, usually theology (Scotus and Ockham did, as did Walter Burley, Thomas Bradwardine, William Heytesbury, and many others). Many of their works on logic and other arts matters were composed while studying in the higher faculty (often as a source of income from teaching), but eventually their interests moved onto theological matters. Buridan remained resolutely an arts man throughout his career. As he writes in his Tractatus de Consequentiis (Treatise on Consequences), the subject of the present study, whether … syllogisms in divine terms are formally valid … I leave to the theologians, and … it is not for me, an Arts man, to decide regarding the foregoing beyond what was said (Book III, Part I, Chapter 4, first conclusion).

Our first firm evidence for Buridan’s career is when he was elected rector in 1327, in charge of all teaching at the University of Paris, a responsible post with a new incumbent elected every three months. He held it from mid-December 1327 until mid-March 1328. He must, therefore, have started his university studies some five or ten years earlier, for the rectorship was normally held by a young teaching master. He had not been a wealthy student, for we know that he held a benefice for needy students at the College of Lemoine. He continued to be supported by such benefices throughout his career, one of which, perhaps the main one, was that of the Collegiate Church of St Pol-sur-Ternoise at Arras. He seems to have held this benefice for life, which aids us in dating his death, since it was bestowed on his successor in 1361. There is evidence that he died on October 11, probably in 1360, and certainly no earlier than July 1358.¹

The University of Paris was divided by the origins of its students into four nations, the French comprising those from France roughly south of Paris, Spain, and Italy; the English (later English-German) made up of those from Britain, the German and Slavic-speaking countries, and Scandinavia; the Norman, those from Normandy; and the Picardian, those from an area running from what is now Picardy northeast through present-day Belgium up to the Meuse. Béthune and Arras lie centrally in this area. Teaching, and even social life, seems to have been heavily segregated between the nations. Buridan himself was involved in disputes among the nations; we know he was still active in Paris in 1358 since he was party to a dispute with the English nation over whose right it was to examine a certain student. Each nation, for example, had its own teaching rooms, and only in exceptional cases would a student from one nation study under a master from another. Thus it is highly unlikely that Albert of Saxony was a student of Buridan’s (as has sometimes been supposed), since Albert belonged to the English nation.² Albert shares certain doctrines with Buridan, but he has much more in common with English masters of the time such as Burley and Ockham and is highly critical of Buridan on several counts.

1.1. Buridan’s Works

By the time Albert arrived in Paris in 1351, Buridan had been teaching and writing there for perhaps twenty-five years. He was a prolific author, though given his secular interests, his writings are restricted almost entirely to commentaries on Aristotle and two logical treatises, the Treatise on Consequences and the Summulae de Dialectica. The Summulae is a mammoth work, running to some one thousand pages in its recent English translation.³ It clearly went through many revisions over the course of at least twenty years, and its nine component treatises survive in versions that are apparently from different periods, some as early as 1340, others probably revised as late as the mid-1350s. It is written ostensibly as a commentary on the Summulae (or Tractatus—literally, Treatises) of Peter of Spain, composed in the early to mid-thirteenth century. Indeed, Buridan seems to have rescued this work from obscurity by his commentary. In at least one of the component treatises, he replaced Peter’s text with a text of his own on which to comment. Buridan’s Summulae consists of eight main treatises (on propositions, predicables, categories, supposition, syllogisms, loci, fallacies, and demonstration). In addition, some manuscripts include a ninth treatise on sophismata, which also seems to have had a separate existence. The treatises on propositions and on syllogisms will particularly concern us in relation to our study of the Treatise on Consequences.

Hubien, in his introduction to his edition of the Latin text, dates the Treatise on Consequences to 1335. His argument is based on rather amusing internal evidence concerning a particular logical example Buridan uses. He wants to give an example of material consequence, one dependent on the meaning of the descriptive terms it contains. He writes: A white cardinal has been elected Pope, so a master of theology has been elected Pope (see Book I, Chapter 4), and from I see him, he infers, I see a deceitful man. Who was this white cardinal? So asks Hubien rhetorically, replying that it must be Jacques Fournier, famous as a scourge of the Cathars, a Cistercian (whose monastic cloak was consequently white), created cardinal in 1327 and elected Pope Benedict XII in December 1334. He had been a fierce opponent of Ockham in the late 1320s, when Ockham was summoned to the papal seat at Avignon to answer charges of heresy, and of the terminism that Ockham represented and Buridan admired.

Hubien is surely right in his identification of the white cardinal. It would be a brave, indeed foolhardy, cleric, however, who made quite so obvious his distaste for the current pope. We certainly have a terminus a quo in the election of Benedict XII; but would Buridan include this example before Fournier’s death in 1342? On the other hand, the treatise also contains evidence of a relatively early composition in Buridan’s career in his discussion of the liar paradox. Buridan’s diagnosis of the liar paradox has been much discussed in the past sixty years, at least since Moody’s Truth and Consequence in Medieval Logic of 1953. It has become clear that his view evolved over the years. In his Sophismata he describes a possible solution to the liar paradox as one he used to hold, a position we find in the Treatise on Consequences.

The liar paradox is an example of a type of proposition called an insoluble by the medievals. They were particularly difficult sophisms. For example, suppose I say, The proposition which I am uttering is false (see Book I, Chapter 5). According to Buridan’s account of truth (see Book I, Chapter 2), an affirmative subject-predicate proposition is true if subject and predicate supposit for the same. So, by an argument we find in his Quaestiones Elencorum,⁴ every proposition signifies, or as he says there, at least implies, its own truth. For an affirmative proposition signifies its subject and predicate to supposit for the same thing or things, and we will see later that this is the condition of its being true, so it signifies that it is true. (A similar argument, mutatis mutandis, applies to negative propositions.) Hence, The proposition which I am uttering is false signifies both that subject and predicate supposit for different things (that is what false means) and that they supposit for the same (since it is affirmative). So it signifies both that it is false and that it is true. Hence it is self-contradictory, and thus false. The important thing to note here regarding chronology is that in the present treatise, the Consequentiae, he speaks only of each proposition signifying that it itself is true, that is, the position he later described as an earlier view of his own. He later revised the view to say that each proposition implies (but does not signify) its own truth. The reason was his vehement opposition to any suggestion that there is anything in the world with propositional or proposition-like structure, an idea he rejected along with his nominalistic rejection of real universals. A particular articulation of such an idea, invoking complexly signifiables (complexe significabilia), was famously put forward in Paris in 1344 by Gregory of Rimini, drawing on ideas of Adam Wodeham’s, presented in Oxford in 1331.⁵ But it did not take thirteen years for Wodeham’s ideas to reach Paris from Oxford, as Tachau points out.⁶ It was almost certainly taken up by Nicholas of Autrecourt in his Sentences commentary, now lost, and partly led to the Condemnation at Paris in December 1340 of Autrecourt’s theses. That there is no mention of complexe significabilia, and Buridan’s rejection of them, in the Consequentiae would seem to support Hubien’s contention that Buridan’s treatise belongs to the mid-1330s.

However, Zupko argues that Buridan would not have found Wodeham’s version of the doctrine objectionable.⁷ Rather, it was Rimini’s reification of the complexly signifiables to which Buridan vehemently objected. In fact, a later date is strongly suggested by an issue that arises in Book II over the correct analysis of modal propositions. Buridan appears there to be rejecting claims made by an anonymous author known nowadays as Pseudo-Scotus, since his works appear in the Opera Omnia of Duns Scotus, first edited by Wadding in 1639 and reprinted by Vivès in the 1890s. In fact, there are arguably two authors deserving the epithet, since neither the Questions on the Prior Analytics nor the Questions on the Posterior Analytics printed there is by Scotus, though they are demonstrably not by the same author. The Questions on the Posterior Analytics is attributed in one manuscript to a John of Cornwall and may indeed date from the time of Scotus himself. The Questions on the Prior Analytics, however, shows knowledge (from a Parisian perspective) of the doctrine of complexly signifiables. It also shows knowledge of Buridan’s Questions on the Posterior Analytics, as we will see. Thus, the Consequentiae are not only later than Pseudo-Scotus’s treatise, but later than the Questions on the Posterior Analytics, an early work of Buridan’s itself dating from whenever the doctrine of complexly signifiables reached Paris. This does not categorically rule out a date for the Consequentiae in the 1330s, but it does favor a date in the 1340s, before Rimini provoked Buridan to give voice to his opposition to the complexe significabilia.

Buridan’s version of terminism, a more temperate and Aristotelian, and less Augustinian version than Ockham’s, had a huge influence in the century and a half following his death. Many of Buridan’s works were printed when the age of printing arrived in the late fifteenth century: the commentaries on Aristotle’s Physics, Metaphysics, Ethics, and Politics; the Sophismata, which was printed in 1496; and the Treatise on Consequences, printed at Paris in 1493, 1495, and 1499. It might seem that the whole of the compendious Summulae de Dialectica was published in 1499, from the title Perutile compendium totius logicae Joannis Buridani. But the title continues, "cum praeclarissime solertissimi viri Joannis Dorp expositione (with the most expert and brilliant commentary of master John Dorp"), and what we find is Dorp’s own commentary on the text (largely that of Peter of Spain) on which Buridan had commented, and hence almost nothing of Buridan’s survives in that work, apart from his influence on Dorp. The genuine Summulae has now been published in an outstanding English translation by Gyula Klima, but even today not all the Latin text has appeared in print. Moreover, there have been three English translations of the Sophismata, Klima’s, as part of the whole Summulae, another of just the Sophismata by Theodore Scott in 1966, and a third, of just Chapter 8, dealing with the semantic paradoxes, by George Hughes in 1982, all predating the publication in 2004 of Pironet’s edition of the Latin text.⁸

The text of the Treatise on Consequences was published in 1976, when Hubert Hubien produced a meticulous edition of the Latin text, based on the three surviving manuscripts and the incunabula, together with a brief introduction.⁹ An English translation was published in 1985, but is very unreliable;¹⁰ hence the occasion for this new translation. The English translation given here follows Hubien’s text with only a very small number of changes made after consulting the manuscripts. Hubien’s introduction, originally in French, is also translated here into English.

2. Truth

There were two great spurs to medieval logical theory. One was the rediscovery of Aristotle’s logic (the logica nova) in the twelfth century. This was preceded by the development of logical theories by Peter Abelard in the early decades of that century. Abelard was at first aware only of the logica vetus, that is, Porphyry’s Isagoge, Aristotle’s Categories and De Interpretatione, and the logical works of Boethius. The upshot was that when medieval scholars came to read the rest of Aristotle’s Organon, they read them under the influence of Abelard, while Abelard’s thought was allowed to roam free, given the relative paucity of logical theory in the logica vetus and the very elementary and unsophisticated introductions of Boethius’s, in comparison to the power of Abelard’s originality. For example, while Boethius’s De Syllogismo Categorico summarizes Aristotle’s reduction of the theory of the assertoric syllogism to the perfect moods of the first figure, it omits not only Aristotle’s further theory of the modal syllogism entirely but also Aristotle’s careful proofs of the invalidity of the other putative (assertoric) moods. Once faced with Aristotle’s own text in the Prior and Posterior Analytics, and his account of fallacy in the Sophistici Elenchi, the medievals went on to develop an increasingly sophisticated theory of consequence, a general theory by which the particular theories of assertoric and modal consequence could be underpinned and explained. In many ways, what we find in Buridan’s Consequentiae, even more than his Summulae, is the pinnacle of sophistication and development in medieval times of a general theory of logical consequence.

2.1. The Theory of Signification

In order to understand Buridan’s theory of consequence we need to look first at his theories of signification (meaning) and of truth. Along with other medievals, following Aristotle, Buridan recognizes three kinds of language: written, spoken, and mental. Written and spoken language is conventional by its conventional attachment to mental language, but mental language was taken to be natural, not conventional, because the constituents of mental language, concepts, are formed by a natural, or causal, process by similarity to external things. Hence, mental language or mental expressions (orationes) are primary and give meaning to spoken and written expressions by this conventional attachment. Any of these expressions can be simple or complex, and one type of complex expression is a proposition. It is important to realize, however, that all such expressions, including mental expressions, are for Buridan concrete contingent particulars. They exist only if they are uttered or inscribed (spoken or written down) or thought. In particular, things might be as some proposition signifies (e.g., Buridan might be running) but unless someone says or thinks that Buridan is running, the proposition that Buridan is running would not be true, since it would not exist. Absolutely everything is, for Buridan, a particular, and although some particulars exist of necessity (e.g., God), propositions, including mental propositions, do not, and depend for their existence on the contingency of someone uttering, inscribing or thinking them.

The view of signification that Aristotle adumbrates at the opening of De Interpretatione, as understood by Buridan, made spoken and written expressions signs of mental expressions and consequently signs of things. But note that, whereas for Ockham, mental expressions are signs of things, that is not Buridan’s view. For Ockham, both spoken and mental expressions are signs of things (and indeed, spoken expressions are not signs of mental expressions, but, as he puts it, conventionally subordinated to them). In contrast, for Buridan, mental expressions are naturally similar to things outside the mind, but they are not signs of them. Rather, spoken expressions are signs of mental expressions and so derivatively signs of external things.

But this is only true of simple expressions. Simple mental expressions—that is, concepts—are similar to things outside the mind, but, as mentioned before, Buridan does not believe there is propositional complexity in external things. Such complexity exists only in spoken, written or mental propositions themselves. Spoken and written terms get their meaning or signification by signifying mental terms (concepts), which are their immediate significates, and consequently their ultimate significates are the things conceived by and similar to those concepts. The spoken and written propositions get their meaning or signification by being compounded of meaningful parts, and so immediately signify complex compounds of concepts. But their ultimate significates are not themselves in that way complex, but are only the ultimate significates of the constituent terms. For example, the written proposition, A man is white, signifies the spoken proposition, which immediately signifies the concepts man and white and their combination, the mental proposition, but it ultimately signifies only men and white things. In particular, A man is white and A man is not white, and generally any proposition and its contradictory, have the same (ultimate) signification.

2.2. The Theory of Supposition

This aspect of Buridan’s theory of signification has important consequences for his theory of truth. We see this in Book I, Chapter 1. For if a proposition and its contradictory signify the same, then things being as it signifies cannot be a sufficient condition for a proposition to be true, on pain of contradiction. Yet things being as it signifies (ita est sicut significat) was a very common account of the truth of propositions in Buridan’s day; we find it in Thomas Bradwardine, Albert of Saxony, and many others.¹¹ But Buridan needs a different account of truth. It is not completely unrelated to his account of signification, but it needs to be mediated by his account of supposition. The theory of the supposition of terms was a peculiarly medieval notion, not matching any modern semantic one. The basic idea was to identify those among the things signified by a term that were in fact being spoken about in a particular proposition, that is, a particular utterance. For instance, in the above example, A man is white, when uttered, it is presently existing men and white things that are being spoken about—it is a present-tense proposition, so the subject supposits for the men there are at present and the predicate (for Buridan) for those things that are currently white. In A fat man was running, on the other hand, the subject is ampliated by the past tense of the verb, but at the same time restricted by the adjective fat, to supposit for those things that are or were fat men, while the predicate supposits for what was running at some past time. By Buridan’s account, such an affirmative subject-predicate proposition is true if subject and predicate supposit for the same thing or things—that is, for something in common. So if Socrates, for example, was at some time fat, but at another time thin and while thin went running one day, the proposition is true: Subject and predicate both supposit for Socrates, who was at some past time a fat man and at some, possibly other, past time was running.

Thus we can see how the doctrines of signification, supposition, ampliation, and restriction of terms combine to give the truth-conditions of subject-predicate propositions. Buridan spells them out at length in his Sophismata (Chapter 2, fourteenth conclusion). We have just stated the truth-conditions for affirmative particulars. There need also to be clauses for universal affirmatives (true when the predicate supposits for everything the subject supposits for), universal negatives (true when the predicate supposits for nothing the subject supposits for), and particular negatives (true when the corresponding universal affirmative, its contradictory, is false). Nonetheless, these clauses are sufficiently cumbersome that Buridan says (Book I, Chapter 1) that he will often say that a proposition is true if things are altogether as it signifies, provided this is understood as shorthand for the appropriate clause about the supposition of its terms and not literally about some supposed significate of the proposition.

2.3. Causes of Truth

One distinctive facet of Buridan’s account of truth in Treatise on Consequences and in Summulae de Dialectica is his talk of causes of truth. For example, we noted in the penultimate paragraph that Socrates having run at some time and having been a fat man at another—or the same—would make the proposition, A fat man was running, true, so it would be one cause of the truth of that proposition. Buridan writes (Book I, Chapter 2): I understand by a cause of truth of a proposition whatever is enough for the proposition to be true. Hubien, and Klima following him in his translation of Summulae de Dialectica 1.6.5 (56 n.), insert "propositio (i.e., proposition") here. Klima cites Book I, Chapter 2 of the Treatise on Consequences as saying: And by the causes of truth of a given proposition I understand propositions such that any of them would suffice for the truth of the given proposition. But construing the causes of truth of a proposition as themselves propositions is Hubien’s speculative addition. The word propositio does not occur here in the manuscripts. Indeed, it would be circular to claim that what makes propositions true are (the same or other) propositions—for what makes those further propositions true? There is a danger, of course, in suggesting that it is not propositions but something else that makes propositions true—things being thus and so, for example, Socrates having gone running. But that need not be construed as a fact or state of affairs or a truthmaker, a thing. Buridan