Antoine Arnauld and Pierre Nicole were philosophers and theologians associated with Port-Royal Abbey, a centre of the Catholic Jansenist movement in seventeenth-century France. Their enormously influential Logic or the Art of Thinking, which went through five editions in their lifetimes, treats topics in logic, language, theory of knowledge and metaphysics, and also articulates the response of 'heretical' Jansenist Catholicism to orthodox Catholic and Protestant views on grace, free will and the sacraments. In attempting to combine the categorical theory of the (...) proposition with a Cartesian account of knowledge, their Logic represents the classical view of judgment which inspired the modern transformation in logic and semantic theory by Frege, Russell, Wittgenstein and recent philosophers. This edition presents a new translation of the text, together with a historical introduction and suggestions for further reading. (shrink)

In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is deducible (...) by means of a formal deduction in the system. Review of the system makes the first point obvious. The purpose of the present article is to prove the second. Strong completeness is demonstrated for the Aristotelian system. (shrink)

This volume is the first annotated translation in any language of the entire text of the Summulae de dialectica, by the Parisian master of arts John Buridan (1300-1358). One of the most influential works in the history of late medieval philosophy, the Summulae is Buridan's systematic exposition of his nominalist philosophy of logic. Buridan's doctrine spread rapidly and for some two hundred years was dominant at many European universities. His work is of increasing interest today not only to historians of (...) medieval philosophy but also to modern philosophers, several of whom find in Buridan's ideas important clues to problems of contemporary philosophy. Gyula Klima provides a substantial introduction to Buridan's life and work and discusses his place in the history of logic. Through extensive notes Klima assists philosopher and medievalist alike to read Buridan with understanding and insight. Those with a philosophical interest in the relations among the structures of language, thought, and reality will find much to ponder in the Summulae. (shrink)

John Corcoran’s natural deduction system for Aristotle’s syllogistic is reconsidered.Though Corcoran is no doubt right in interpreting Aristotle as viewing syllogisms as arguments and in rejecting Lukasiewicz’s treatment in terms of conditional sentences, it is argued that Corcoran is wrong in thinking that the only alternative is to construe Barbara and Celarent as deduction rules in a natural deduction system.An alternative is presented that is technically more elegant and equally compatible with the texts.The abstract role assigned by tradition and Lukasiewicz (...) to Barbara and Celarent is retained.The two ‘ perfect syllogisms’ serve as ‘basic elements’ in the construction of an inductively defined set of valid syllogisms.The proposal departs from Lukasiewicz, and follows Corcoran, however, in construing the construction as one in natural deduction.The result is a sequent system with fewer rules and in which Barbara and Celarent serve as basic deductions.To compare the theory to Corcoran’s, his original is reformulated in current terms and generalized.It is shown to be equivalent to the proposed sequent system, and several variations are discussed.For all systems mentioned, a method of Henkin‐style completeness proofs is given that is more direct and intuitive than Corcoran’s original. (shrink)

In this article, we discuss the notion of merely confused supposition as it arose in the medieval theory of suppositio personalis. The context of our analysis is our formalization of William of Ockham's theory of supposition sketched in Mind 86 (1977), 109-13. The present paper is, however, self-contained, although we assume a basic acquaintance with supposition theory. The detailed aims of the paper are: to look at the tasks that supposition theory took on itself and to use our formalization to (...) relate them to more modern ideas; to explain the notion of merely confused supposition and to defend it against certain criticisms; and to discuss two issues closely related to the idea of merely confused supposition which we could not broach in a shorter article: the mode of supposition of terms in intensional contexts, and the possible existence of a fourth mode, often called suppositio copulatim. (shrink)

This book shows otherwise. John Martin rehabilitates Neoplatonism, founded by Plotinus and brought into Christianity by St. Augustine.

The paper explores the existential import of universal affirmative in Descartes, Arnauld and Malebranche. Descartes holds, inconsistently, that eternal truths are true even if the subject term is empty but that a proposition with a false idea as subject is false. Malebranche extends Descartes? truth-conditions for eternal truths, which lack existential import, to all knowledge, allowing only for non-propositional knowledge of contingent existence. Malebranche's rather implausible Neoplatonic semantics is detailed as consisting of three key semantic relations: illumination by which God's (...) ideas cause mental terms, creation by which God's ideas cause material substances by a kind of ?ontic privation?, and sensation in which brain events occasion states of mental awareness. In contrast, Arnauld distinguishes two types of propositions ? necessary and contingent ? with distinct truth-conditions, one with and one without existential import. Arnauld's more modern semantics is laid out as a theory of reference that substitutes earlier causal accounts with one that adapts the medieval notion of objective being. His version anticipates modern notions of intentional content and appeals in its ontology only to substances and their modes. (shrink)

Le concept d'un logique des idees, qui pose son objet comme une realite historique et culturelle, est un element important pour la comprehension du developpement de la logique. Toutes les histoires de la discipline mentionne la logique de Port-Royal (au reste, rarement pour en donner une evaluation positive). Peu s'interessent a ce qu'on appelle la logique classique qui va de la parution de Port-Royal (1662) jusqu'aux travaux de Boole et De Morgan, c'est-a-dire jusqu'au milieu du XIXe siecle. L'objet de ce (...) livre est de fournir une representation realiste de la logique classique a partir d'une modelisation qui en permette la comprehension. La logique des idees doit etre concue comme un moment dans l'histoire de la logique et, plus globalement, comme un element d'une certaine conception des operations cognitives humaines. D'autres conceptions de la logique sont possibles et il y a moyen de se representer autrement la cognition. Dans tous les cas, on s'efforce de mettre en place un cadre general de discussion pour ces questions. Ce sont, en effet, des reponses specifiques qui determinent les limites et les points forts de la logique des idees dans ce domaine de ce que l'on appelle aujourd'hui les sciences cognitives. (shrink)