We present a paraconsistent logic, called Z, based on an intuitive possible worlds semantics, in which the replacement theorem holds. We show how to axiomatize this logic and prove the completeness theorem.

The hexagon of opposition is an improvement of the square of opposition due to Robert Blanché. After a short presentation of the square and its various interpretations, we discuss two important problems related with the square: the problem of the I-corner and the problem of the O-corner. The meaning of the notion described by the I-corner does not correspond to the name used for it. In the case of the O-corner, the problem is not a wrong-name problem but a no-name (...) problem and it is not clear what is the intuitive notion corresponding to it. We explain then that the triangle of contrariety proposed by different people such as Vasiliev and Jespersen solves these problems, but that we don’t need to reject the square. It can be reconstructed from this triangle of contrariety, by considering a dual triangle of subcontrariety. This is the main idea of Blanché’s hexagon. We then give different examples of hexagons to show how this framework can be useful to conceptual analysis in many different fields such as economy, music, semiotics, identity theory, philosophy, metalogic and the metatheory of the hexagon itself. We finish by discussing the abstract structure of the hexagon and by showing how we can swing from sense to non-sense thinking with the hexagon. (shrink)

Consequence is at the heart of logic, and an account of consequence offers a vital tool in the evaluation of arguments. This text presents what the authors term as 'logical pluralism' arguing that the notion of logical consequence doesn't pin down one deductive consequence relation; it allows for many of them.

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

La logique de Leibniz: d'apres des documents inedits / par Louis Couturat,...Date de l'edition originale: 1901Sujet de l'ouvrage: Leibniz, Gottfried Wilhelm (1646-1716)Logique moderneCollection: Collection historique des grands philosophesCe livre est la reproduction fidele d'une oeuvre publiee avant 1920 et fait partie d'une collection de livres reimprimes a la demande editee par Hachette Livre, dans le cadre d'un partenariat avec la Bibliotheque nationale de France, offrant l'opportunite d'acceder a des ouvrages anciens et souvent rares issus des fonds patrimoniaux de la BnF.Les (...) oeuvres faisant partie de cette collection ont ete numerisees par la BnF et sont presentes sur Gallica, sa bibliotheque numerique.En entreprenant de redonner vie a ces ouvrages au travers d'une collection de livres reimprimes a la demande, nous leur donnons la possibilite de rencontrer un public elargi et participons a la transmission de connaissances et de savoirs parfois difficilement accessibles.Nous avons cherche a concilier la reproduction fidele d'un livre ancien a partir de sa version numerisee avec le souci d'un confort de lecture optimal. Nous esperons que les ouvrages de cette nouvelle collection vous apporteront entiere satisfaction.Pour plus d'informations, rendez-vous sur www.hachettebnf.frhttp: //gallica.bnf.fr/ark: /12148/bpt6k110843d. (shrink)

Cognitive science is a child of the 1950s, the product of a time when psychology, anthropology and linguistics were redefining themselves and computer science and neuroscience as disciplines were coming into existence. Psychology could not participate in the cognitive revolution until it had freed itself from behaviorism, thus restoring cognition to scientific respectability. By then, it was becoming clear in several disciplines that the solution to some of their problems depended crucially on solving problems traditionally allocated to other disciplines. Collaboration (...) was called for: this is a personal account of how it came about. (shrink)

Preface of Festschrift on the occasion of Professor Rohit Parikh's 60th birthday.

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found already (...) in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)

Au printemps 1996, une revue américaine fort respectée - Social Text - publiait un article au titre étrange : "Transgresser les frontières : vers une herméneutique transformative de la gravitation quantique". Son auteur, Alan Sokal, étayait ses divagations par des citations d'intellectuels célèbres, français et américains. Peu après, il révélait qu'il s'agissait d'une parodie. Son but était de s'attaquer, par la satire, à l'usage intempestif de terminologie scientifique et aux extrapolations abusives des sciences exactes aux sciences humaines. Plus généralement, il (...) voulait dénoncer le relativisme postmoderne pour lequel l'objectivité est une simple convention sociale. Ce canular a déclenché un vif débat dans les milieux intellectuels, en France et à l'étranger. Dans ce livre, les auteurs ont rassemblé et commenté des textes illustrant les mystifications physico-mathématiques de Jacques Lacan, Julia Kristeva, Luce Irigaray, Bruno Latour, Jean Baudrillard, Gilles Deleuze, Félix Guattari et Paul Virilio, auteurs qui jouissent tous d'une grande notoriété aux Etats-Unis. Ils montrent que, derrière un jargon imposant et une érudition scientifique apparente, le roi est nu. Après les vives polémiques suscitées par la version initiale d'Impostures intellectuelles, cette nouvelle édition, revue et enrichie d'une préface inédite (1999), procure aux auteurs l'occasion d'une nécessaire mise au point. Ils y précisent leur point de vue. Ils écartent les idées voire les arrière-pensées qui leur ont été à tort attribuées. (shrink)

Jean-Yves Béziau Abstract In this paper I relate the story about the new rising of the square of opposition: how I got in touch with it and started to develop new ideas and to organize world congresses on the topic with subsequent publications.

In the general theory of logic built up by Whitehead and Russell to furnish a basis for all mathematics there is a certain subtheory which is unique in its simplicity and precision; and though all other portions of the work have their roots in this subtheory, it itself is completely independent of them. Whereas the complete theory requires for the enunciation of its propositions real and apparent variables, which represent both individuals and propositional functions of different kinds, and as a (...) result necessitates- the introduction of the cumbersome theory of types, this subtheory uses only real variables, and these real variables represent but one kind of entity—which the authors have chosen to call elementary propositions. The most general statements are formed by merely combining these variables by means of the two primitive propositional functions of propositions Negation and Disjunction; and the entire theory is concerned with the process of asserting those combinations which it regards as true propositions, employing for this purpose a few general rules which tell how to assert new combinations from old, and a certain number of primitive assertions from which to begin. (shrink)

The displacement of the idea that facts and evidence matter by the idea that everything boils down to subjective interests and perspectives is -- second only to American political campaigns -- the most prominent and pernicious manifestation of anti-intellectualism in our time.

In this paper we discuss the difference between (...) proliferations of logic systems, the questions of relativity and universality of logic and the position and interaction of logic with regards to other sciences such as physics, biology, mathematics and computer science. (shrink)

Le but principal de la communication est d’esquisser les traits essentiels de la méthode appliquée dans les sciences déductives.1. A quoi tend la méthode déductive? Termes primitifs et définis ; axiomes et théorèmes. Les sciences antérieures à une science donnée. La méthode déductive considérée comme propriété caractéristique des mathématiques.2. Liberté dans le choix des termes primitifs et des axiomes ; notion d’équivalence de deux systèmes de termes ou de propositions.Postulats d’indépendance des termes primitifs et des axiomes.3. Postulats de la formalisation (...) des définitions et des démonstrations. Règles de définition et de démonstration ; les démonstrations complètes ; les sciences déductives formalisées. Le rôle de la logique mathématique au point de vue des nouvelles exigences méthodologiques.4. Les notions de science non-contradictoire et complète. L’importance théorique de ces notions ; leur rapport avec le problème de la vérité des mathématiques. Pourquoi les notions en question n’exercent pas en pratique une grande influence sur la construction des sciences mathématiques.5. Certaines propriétés des sciences mathématiques découlant d’une application conséquente de la méthode déductive.ion du sens des termes primitifs dans la construction de la science. Modèles et interprétations du système d’axiomes. Concept de système formel. Valeur de la méthode déductive du point de vue de l’économie de la pensée. (shrink)

Le progrès d’une science comme la physique détermine dans la logique un mouvement correspondant ; elle aussi est en devenir. Dans le monde atomique en particulier, les relations d’incertitude d’Heisenberg et l’existence de valeurs quantifiées conduisent à la construction d’une logique mieux adaptée à ce genre de recherches, logique trivalente, et de genre doux, c’est-à-dire dans laquelle les couples de propositions peuvent être soit composables, soit incomposables, par rapport à l’opération produit.

For several years I have been developing a general theory of logics that I have called Universal Logic. In this article I will try to describe how I was led to this theory and how I have progressively conceived it, starting my researches about ten years ago in Paris in paraconsistent logic and the broadening my horizons, pursuing my researches in Brazil, Poland and the USA.