At the end of the 1980s, Tennant invented a logical system that he called “intuitionistic relevant logic”. Now he calls this same system “Core logic.” In Section 1, by reference to the rules of natural deduction for $\mathbf{IR}$, I explain why $\mathbf{IR}$ is a relevant logic in a subtle way. Sections 2, 3, and 4 give three reasons to assert that $\mathbf{IR}$ cannot be a core logic.

Ce livre developpe une theorie de la negation qui rend compte de maniere complete des trois significations naturelles et fondamentales de la negation: rejet, absence et denegation. L'auteur adopte une theorie intuitionniste de la negation, parce qu'il considere que celle-ci offre une comprehension a la fois plus riche et plus fine de la negation que celle qui est donnee par la logique classique. La premiere partie de l'ouvrage commence avec des remarques qui relevent de la psychologie, la seconde traite de (...) la negation d'un point de vue logique, et la troisieme donne un apercu critique sur quelques metaphysiques de la negation, c'est-a-dire sur certains systemes philosophiques (ceux de Platon, de Spinoza et de Hegel) qui ont tire des consequences ontologiques a partir d'une definition specifique de la negation. Cette troisieme partie trouve une suite naturelle dans le commentaire des reflexions sur la question de la negation developpees par Spinoza (proposition 49 de la seconde partie de l'Ethique) et par Kant (Essai pour introduire en philosophie le concept de grandeur negative). Ces deux commentaires sont respectivement prolonges par une critique de l'analyse spinoziste de la negation et par l'explication de l'interet que presente la logique intuitionniste a la fois pour la comprehension de l'analyse kantienne et pour les lecons que l'on peut tirer du celebre carre des oppositions logiques, ou la negation joue un role crucial. (shrink)

Vuillemin a écrit un article concis sur la Théorie de la justice de Rawls où son propos se concentre uniquement sur la justice comme convention, c’est-à-dire sur le contrat qui définit une société juste selon Rawls. Après avoir analysé la nature du « contrat explicite » puis celle du « contrat implicite » dans cette théorie, Vuillemin critique la définition de la justice que donne Rawls et soutient que celui-ci«s’est trompé d’ancêtres » en considérant que sa philosophie politique est dans (...) la filiation de la morale kantienne alors qu’elle est, selon Vuillemin, l’expression d’un scepticisme comparable à celui de Carnéade. On réfute dans cet article l’interprétation que Vuillemin donne de la théorie de Rawls en montrant que celle-ci est fondée sur une lecture à la fois partielle et partiale de la Théorie de la Justice. (shrink)

Etudie la notion de paradoxe en philosophie en s'intéressant notamment aux paradoxes logiques (paradoxes, solutions ensemblistes et sémantiques). En deuxième partie, deux textes (de B. Russell et W.V.O. Quine) sont commentés.

Vuillemin a écrit un article concis sur la Théorie de la justice de Rawls où son propos se concentre uniquement sur la justice comme convention, c’est-à-dire sur le contrat qui définit une société juste selon Rawls. Après avoir analysé la nature du « contrat explicite » puis celle du « contrat implicite » dans cette théorie, Vuillemin critique la définition de la justice que donne Rawls et soutient que celui-ci«s’est trompé d’ancêtres » en considérant que sa philosophie politique est dans (...) la filiation de la morale kantienne alors qu’elle est, selon Vuillemin, l’expression d’un scepticisme comparable à celui de Carnéade. On réfute dans cet article l’interprétation que Vuillemin donne de la théorie de Rawls en montrant que celle-ci est fondée sur une lecture à la fois partielle et partiale de la Théorie de la Justice. (shrink)

En 2004, la famille de Jules Vuillemin lègue aux Archives Henri-Poincaré (Université de Lorraine) un fonds constitué par les ouvrages, les tirés à part et les manuscrits du célèbre philosophe français, décédé aux Fourgs (Doubs) le 16 janvier 2001. Dans le cadre de la conservation et de la valorisation de ce fonds très riche, les Archives Henri-Poincaré organisent chaque année, au mois de décembre, une journée d’études autour d’un texte ou d’un aspect de la pensée de Jules Vuillemin, afin de (...) d... (shrink)

Ce numéro spécial, édité à l’occasion du centenaire de la naissance d’Alan Turing, est le fruit d’une double collaboration : d’une part une collaboration internationale qui exprime via internet l’importance de l’année Turing, d’autre part une collaboration locale régulière entre des chercheurs de l’équipe TYPES du Laboratoire Lorrain de Recherche en Informatique (LORIA) qui s’intéressent à la logique, la théorie de la preuve et la programmation, et des philosophes et logiciens du Laboratoire...

En 2004, la famille de Jules Vuillemin lègue aux Archives Henri-Poincaré un fonds constitué par les ouvrages, les tirés à part et les manuscrits du célèbre philosophe français, décédé aux Fourgs le 16 janvier 2001. Dans le cadre de la conservation et de la valorisation de ce fonds très riche, les Archives Henri-Poincaré organisent chaque année, au mois de décembre, une journée d’études autour d’un texte ou d’un aspect de la pensée de Jules Vuillemin, afin de d...

Free logic, an alternative to traditional logic, has been seen as a useful avenue of approach to a number of philosophical issues of contemporary interest. In this collection, Karel Lambert, one of the pioneers in, and the most prominent exponent of, free logic, brings together a variety of published essays bearing on the application of free logic to philosophical topics ranging from set theory and logic to metaphysics and the philosophy of religion. The work of such distinguished philosophers (...) as Bas van Fraassen, Dana Scott, Tyler Burge, and Jaakko Hintikka is represented. Lambert provides an introductory essay placing free logic in the logical tradition beginning with Aristotle, developing it as the natural culmination of a trend begun in the Port Royal logic of the 1600s, and continuing through current predicate logic--the trend to rid logic of existence assumptions. His Introduction also provides a useful systematic overview of free logic, including both a standard syntax and some semantical options. (shrink)

As well as aiming to revive interest in Meinong's thought, this book challenges many of the most widespread assumptions of philosophical logic.

Free logic is an important field of philosophical logic that first appeared in the 1950s. J. Karel Lambert was one of its founders and coined the term itself. The essays in this collection explore the philosophical foundations of free logic and its application to areas as diverse as the philosophy of religion and computer science. Amongst the applications on offer are those to the analysis of existence statements, to definite descriptions and to partial functions. The volume contains a (...) proof that free logics of any kind are non-extensional and then uses that proof to show that Quine's theory of predication and referential transparency must fail. The purpose of this collection is to bring an important body of work to the attention of a new generation of professional philosophers, computer scientists and mathematicians. (shrink)

The essays in this volume are based on addresses presented during a colloquium on free logic, modal logic and related areas held at the University of California at Irvine, in May of 1968. With the single exception of Dagfinn F011esdal, whose revised address is included in a recent issue of Synthese honoring W. V. Quine, all of the speakers at the Irvine colloquium are contributors to this volume. Thanks are due to Professor A. I. Melden, Chairman of the Department of (...) Philosophy at Irvine, for his enthusiastic support of the colloquium, and to Drs. Gordon Brittan and Daniel Dennett for their help in the administration of the colloquium. Finally. I should also like to thank Professor Ralph W. Gerard, Dean of the Graduate Division of the University of California at Irvine, for the financial support which made the colloquium possible. KAREL LAMBERT Laguna Beach, California, 1969 TABLE OF CONTENTS PREFACE V KAREL LAMBERT and BAS C. VAN FRAASSEN/ Meaning Relations, Possible Objects, and Possible Worlds 1 JAAKKO HINTIKKA / Existential Presuppositions and Uniqueness Presuppositions 20 RICHMOND H. THOMASON / Some Completeness Results for Modal Predicate Calculi 56 H. LEBLANC and R. K. MEYER / Truth-Value Semantics for the Theory of Types 77 J. M. VICKERS / Probability and Non Standard Logics 102 PETER W. WOODRUFF / Logic and Truth Value Gaps 121 DANA SCOTT / Advice on Modal Logic 143 INDEX OF NAMES 175 KAREL LAMBER T AND BAS C. (shrink)

The essays in this volume are based on addresses presented during a colloquium on free logic, modal logic and related areas held at the University of California at Irvine, in May of 1968. With the single exception of Dagfinn F011esdal, whose revised address is included in a recent issue of Synthese honoring W. V. Quine, all of the speakers at the Irvine colloquium are contributors to this volume. Thanks are due to Professor A. I. Melden, Chairman of the Department of (...) Philosophy at Irvine, for his enthusiastic support of the colloquium, and to Drs. Gordon Brittan and Daniel Dennett for their help in the administration of the colloquium. Finally. I should also like to thank Professor Ralph W. Gerard, Dean of the Graduate Division of the University of California at Irvine, for the financial support which made the colloquium possible. KAREL LAMBERT Laguna Beach, California, 1969 TABLE OF CONTENTS PREFACE V KAREL LAMBERT and BAS C. VAN FRAASSEN/ Meaning Relations, Possible Objects, and Possible Worlds 1 JAAKKO HINTIKKA / Existential Presuppositions and Uniqueness Presuppositions 20 RICHMOND H. THOMASON / Some Completeness Results for Modal Predicate Calculi 56 H. LEBLANC and R. K. MEYER / Truth-Value Semantics for the Theory of Types 77 J. M. VICKERS / Probability and Non Standard Logics 102 PETER W. WOODRUFF / Logic and Truth Value Gaps 121 DANA SCOTT / Advice on Modal Logic 143 INDEX OF NAMES 175 KAREL LAMBER T AND BAS C. (shrink)

The expression ‘free logic,’ coined by the author in 1960, is an abbreviation for ‘logic free of existence assumptions with respect to its terms, singular and general, but whose quantifiers are treated exactly as in standard quantifier logic.’ In more traditional language, such logics do not presume that either singular or general terms — the two distinct categories of terms emphasized in modern logical grammar — have existential import. A singular term ‘t’ has existential import just in case t exists (...) (or, equivalently, there exists an object the same as t) and a general term (or predicate) ‘G’ has existential import just in case G exist (or, equivalently, there exists an object that is G).1 Examples from colloquial English customarily taken to be singular terms are expressions such as ‘Socrates’, ‘the planet causing perturbations in the orbit of Mercury’, ‘5’, ‘5/0’, ‘the square of 3’ and ‘having a heart’. Some of these do not have existential import — in particular, ‘5/0’ and ‘the planet causing perturbations in the orbit of Mercury’. Examples from colloquial English customarily taken to be general terms are expressions such as ‘is a philosopher’, ‘is a planet causing perturbations in the orbit of Mercury’, ‘number’, ‘is divisible by 0’, and ‘has a heart’. Some of these general terms do not have existential import — in particular, ‘is a planet causing perturbations in the orbit of Mercury’ and ‘is divisible by 0’. To say that the quantifers are treated exactly as in standard quantifier logic is to say, roughly, that the operator symbol ‘∃’ (the existential quantifier) reads: ‘There exists an object’, and the operator symbol ‘∀’ (the universal quantifier) reads: ‘Every existent object’. (shrink)

Those who want to interpret the quantifier ? (3 x) (. . .x. . .)'as having no existence commitment often fail to distinguish between this objective and that of merely changing the values of the variables. The confusion vitiates solutions of the singular existence anomalies which purport to be based on a non?existential interpretation of the quantifier. An example of one who makes the distinction but still interprets the particular quantifier non?existentially is offered by Czeslaw Lejewski. Objection to the classical (...) interpretation of the quantifiers often runs hand in hand with aversion to extensional logic. However, it is at least arguable that such an aversion is the result of underestimating the resources of extensional logic. These points arc discussed in the wake of Professor Marcus's recent paper in this journal ?Interpreting Quantification? (shrink)

This note is a comment on Suppes's essay on the limits of rationality. The substantial point is that if a theory of rationality is conceived as a structure plus scope, then, contra Suppes, intuitive judgement is part of the theory of rationality because it is part of the scope of that theory. The point is supported by analogy with a learning theory. Finally, intuitive judgement and informal knowledge is suggested to be evidence of the irreducible vagueness of theory as opposed (...) to irreducible limits on theory. (shrink)

The essay outlines the character of free logic, and motivation for its construction and development. It details some technical achievements of high philosophical interest, but urges that the role of existence assumptions in logic is still not fully understood, that unresolved old problems, both technical and philosophical, abound, and presents some new problems of considerable philosophical import in free logic.

This essay lays out the leading principles of the theories of definite descriptions advocated by Frege, Russell, and Hilbert and Bernays, and discusses various difficulties, philosophical and otherwise, with each treatment, fixing especially on the treatment of singular existence claims. Then the leading principles of free (definite) description theory are presented and it is shown how it resolves difficulties confronting the more traditional approaches. Finally, a pair of technical problems in free (definite) description theory are addressed. They help to show (...) the fecundity of this treatment of definite descriptions. (shrink)

The authors contend that most contemporary logic textbooks fail the average student because they emphasize the evaluation of arguments over their clarification, assuming that the student already understands what motivations underlie logic.

The authors contend that most contemporary logic textbooks fail the average student because they emphasize the evaluation of arguments over their clarification, assuming that the student already understands what motivations underlie logic.