The aim of this paper is to investigate the problem of existential import in Abelard's modal logic, and to ask whether the system of logical relationships that he proposes for modal propositions ma...

The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic ; analytical philosophy, philosophy of science, philosophy of mathematics and decision theory and foundations of economics. (...) Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic. (shrink)

The recovery of Aristotle’s logic during the twelfth century was a great stimulus to medieval thinkers. Among their own theories developed to explain Aristotle’s theories of valid and invalid reasoning was a theory of consequence, of what arguments were valid, and why. By the fourteenth century, two main lines of thought had developed, one at Oxford, the other at Paris. Both schools distinguished formal from material consequence, but in very different ways. In Buridan and his followers in Paris, formal consequence (...) was that preserved under uniform substitution. In Oxford, in contrast, formal consequence included analytic consequences such as ‘If it’s a man, then it’s an animal’. Aristotle’s notion of syllogistic consequence was subsumed under the treatment of formal consequence. Buridan developed a general theory embracing the assertoric syllogism, the modal syllogism and syllogisms with oblique terms. The result was a thoroughly systematic and extensive treatment of logical theory and logical consequence which repays investigation. (shrink)

In this article, the author studies some central concepts in Avicenna's and sī's modal logics as presented in Avicenna's Al-Ish r t wa'l Tan īh t ( Pointers and Reminders ) and in sī's commentary. In this work, Avicenna introduces some remarkable distinctions in order to interpret Aristotle's modal syllogistic in the Prior Analytics . The author outlines a new interpretation of absolute sentences as temporally indefinite sentences and argues on the basis of this that Avicenna seems to subscribe to (...) the Principle of Plenitude. He also shows that he has no valid proof of the modal conversion rules and that he uses some rather ad hoc distinctions to show that Aristotle's modal syllogistic is correct. The author also notes some interesting differences between Avicenna's and sī's approaches to modal logic. (shrink)

In this paper, we provide a historical exposition of John Buridan's theory of divided modal propositions. We then develop a semantic interpretation of Buridan's theory which pays particular attention to Buridan's ampliation of modal terms. We show that these semantics correctly capture his syllogistic reasoning.

Thomas Bradwardine (d. 1349) was an English philosopher, logician, and theologian of some note; but though recent scholarship has revived an interest in much of his work, little attention has been paid to an early treatise he wrote on the topic of future contingents, entitled De futuris contingentibus. In this thesis I aim to address this deficit, arguing in particular that the treatise makes original use of the divine power distinction to resolve the apparent conflict between God’s foreknowledge on the (...) one hand, and human free will on the other. Bradwardine argues that God’s foreknowledge operates in accord with God’s ordained power, and so relative to God’s ordained power, our actions are indeed compelled; however, because of Bradwardine’s appeal to the distinction in power, he is able to maintain that our actions remain free relative to God’s absolute power, and are thus free, absolutely speaking. This solution is, I argue, unique to Bradwardine, although it seems to be abandoned in his later writing. Bradwardine’s approach to the problem is heavily influenced by three figures in particular — Boethius, Anselm of Canterbury, and John Duns Scotus — each of whose solutions I discuss in some detail. Furthermore, Bradwardine explicitly places his own solution in opposition to that of William Ockham, and so I give substantial attention to examining Ockham’s position. But while I agree with Bradwardine’s assessment that Ockham’s position undermines God’s foreknowledge in ways that should be untenable to someone of 14th-century Christian commitments, I argue that Bradwardine’s solution amounts to an equally untenable determinism. An appendix contains excerpts from my own English translation of the De futuris contingentibus (the first into any modern language), in parallel with the original Latin. (shrink)