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.

In this paper, I raise the following problem: What terms are considered as syncategoremata in the Arabic logical texts? How are they defined? How do they determine the forms of the propositions and the inferences? To answer these questions, I focus on the analyses provided by al-Fārābī and Avicenna. Both authors apply the grammatical distinction between the particle, the noun and the verb to logic. They also state the semantic and the syntactic criterions, but their analyses of the particles are (...) different. For al-Fārābī devotes two treatises to the analysis of particles: al-musta‘malah fī l-maniq, where he provides a listing of particles that he classifies in the manner of the Greek grammarians and Kitāb al-urūf, where he analyzes some particles used in metaphysics; while Avicenna, despite the considerable amount of his logical corpus, does not devote a special book to the analysis of particles. He does not provide any listing either but characterizes each logical particle on its own, while analyzing the propositions, their elements and the inferences. In this paper, I argue that this treatment of particles in the two frames shows a significant difference between the two authors with regard to the relation between logic and grammar, and with regard to the characterizations of the logical particles themselves. For Avicenna is much less interested than al-Fārābī by the grammatical analysis and focuses much more on the logical particles, which he scrutinizes meticulously. This enriches his definitions of the logical constants and leads him in the final analysis to different and more various inferences than those hold by al-Fārābī. (shrink)

This paper explores a currently unnoticed argument used by John Buridan to defend his analysis of modal propositions and to reject the analysis of modal propositions of necessity put forward by William of Ockham. First, I explore this argument and, by considering possible responses of Ockham to Buridan, show some of the ways in which Ockham seems to be keeping closer to Aristotle's remarks about modal propositions in Prior Analytics, 18.

Peter Geach describes the 'doctrine of distribution' as the view that a term is distributed if it refers to everything that it denotes, and undistributed if it refers to only some of the things that it denotes. He argues that the notion, so explained, is incoherent. He claims that the doctrine of distribution originates from a degenerate use of the notion of ?distributive supposition? in medieval supposition theory sometime in the 16th century. This paper proposes instead that the doctrine of (...) distribution occurs at least as early as the 12th century, and that it originates from a study of Aristotle's notion of a term's being ?taken universally?, and not from the much later theory of distributive supposition. A detailed version of the doctrine found in the Port Royal Logic is articulated, and compared with a slightly different modern version. Finally, Geach's arguments for the incoherence of the doctrine are discussed and rejected. (shrink)