Materia prima CHÍA (Salvia Hispánica L.) 2

Our main focus in this chapter will be on Buridan’s Treatise on Consequences. From time to time we will supplement this with passages from the Summulae De Dialetica when they will help clarify Buridan’s meaning. Hubert Hubien, in his introduction to the critical edition of the Treatise, dates the work to around 1334[4, p. 9-10] based on allusions made to a ‘white cardinal’. However this dating is somewhat questionable. The main concern is that the ‘white cardinal’ was actually the Pope at the time that this work was written. Given that Buridan makes some unflattering comments about this ‘white cardinal’ it would be a brave move by Buridan to be insulting the current Pope. 1. Buridan distinguishes between two kinds of propositions, subject–predicate propositions and compos- ite propositions, where composite propositions are composed of several subject–predicate propositions along with an expression such as ‘if’. We shall see shortly what it means for a proposition to be modal.

To this end, I say that propositions are divided into subject–predicate and compound propo- sitions. Now a consequence is a compound proposition; for it is constituted from several propositions conjoined by the expression “if” or the expression “therefore” or something equivalent.[51, p.66]

Buridan’s Treatise on Consequences is divided into four books. Each of these books follows a general format.

The book opens with a preamble.

A number of definitions are given, remarked on, proved, or agreed to. A number of conclusions are proved based on the definitions laid down.

The first book outlines Buridan’s general theory of consequence. Here ‘consequence’ is defined and then divided into a number of different kinds. The notions of ampliation and supposition are introduced and defined for various kinds of propositions. Buridan also outlines the various causes of truth for propositions and explains when different kinds of propositions are true and false. Most of the conclusions are fairly standard results about consequences, including Ex Impossibile Quodlibet (this is one of the medieval phrases used to express the principle of explosion2; literally ‘from an impossibility anything follows’)3 transitivity of consequence4 and how consequence relates to the truth and possibility of truth.5

Buridan’s second book provides an analysis of modal consequences where the an- tecedent and conclusion are simple expressions.6 In this chapter, Buridan provides an analysis of modality using the theory of ampliation and supposition. He then gives a number of definitions about propositions in which modals occur. In particular, he iden- tifies two ways that a modal can occur in a proposition. These give rise to two senses: the composite sense and the divided sense.7 From these definitions and the previous results in the first book, Buridan proves a number of interesting results about such propositions. The conclusions are separated into three sections. First he proves con- clusions for divided propositions. Second he offers some more remarks about composite modal propositions and proves some conclusions. Finally, he proves conclusions about the relationship between divided and composite modal propositions.

Buridan’s third book provides a discussion of assertoric syllogisms. The book is divided into two parts. The first part concerns syllogisms between direct terms.8 The second part 2. Formally, the principle of explosion says for any formulaeφ,ψfromφand¬φone may inferψ. 3. See Book One Conclusions 1 and 7. See [51, p.75] and [51, p.79] respectively.

4. See Book One Conclusion 4

5. See Book One Conclusion 5. See [p.77]sr:10.

6. We will define simple expressions when we introduce the book in more detail. For now, it is easiest to think of these as terms with nothing modifying them.

7. This is a standard medieval distinction used to cover a number of differences in scope that occur with various kinds of operations.

8. The distinction between direct and oblique terms is an important one. Buridan explains what oblique terms are in the following passage

Accordingly, it will first be explained what an oblique term is when it is used with a direct term that is governed by it as a determination of that direct term, just as an adjective is a determination of a substantive [term]. For just as when saying ‘A white horse is running,’ the expression ‘white’ determines the expression ‘horse’ to supposit only for white ones, so if I say ‘Socrates’s horse is running,’ the expression ‘Socrates’s’ restricts the expression

concerns syllogisms with oblique terms. In this book he discusses the usual Aristotelian moods, however, he displays considerable originality both in his presentation of these moods and in his discussion of additional, non-Aristotelian syllogisms involving oblique terms. He discusses non-standard forms of the various propositions, as well as syllogisms with oblique terms. Oblique terms are terms that are modified by a genitive or an accusative construction. For example, in the proposition the term ‘Everything that is a man’s ass is running’ the term ‘man’s’ is an oblique term since ‘man’ is in the genitive and in this context implies possession of an ass. Oblique terms are technically interesting (at least) because they can be seen as a medieval attempt to treat relations within the context of syllogisms.

Buridan’s fourth and final book brings together the results from the previous three books. Here he develops his theory of the modal syllogism using the resources proven in the other three books. All of the English translations given here are drawn from a recent book by Professor Read, [51].