Jean-Yves Beziau

In a first section, we discuss Quine’s claim according to which identity is a logical notion. We point out that Quine mixes up various types of identities: trivial (or diagonal) identity, Leibniz identity, etc.; and this leads him to commit several mistakes. In a second section, we review Quine’s criticisms to various philosophers (Wittgenstein, Whitehead, Leibniz, etc.), who ac-cording to him made confusion between names and objects in defining identity. We show that in fact only Korzybski can be accused of such confusion. In a third section, we analyze the relation between identity and entity. We notice that for Quine a river is the result of the identification of river stages, but that he admits it as an entity by opposition to squareness, which according to him is a result of an identification process of higher abtraction.

We present the logic K/2 which is a logic with classical implication and only the left part of classical negation.We show that it is possible to define a classical negation into K/2 and that the classical proposition logic K can be translated into this apparently weaker logic.We use concepts from model-theory in order to characterized rigorously this translation and to understand this paradox. Finally we point out that K/2 appears, following Haack's distinction, both as a deviation and an extension of K.

This is a volume containing papers honoring Patrick Suppes (1922-2014). All contributors have worked directly with Suppes or/and with his ideas. The book also contains one of the last papers by Suppes (co-authored by two of his collaborators). The work of Suppes touches many different areas, ranging from meteorology to physics, through logic, mathematics, psychology, neuroscience, education, painting, but he was first of all and above all a philosopher, always questioning, but not in vain. There are not many philosophers who can be proud of having written influential math textbooks, contributed decisively to the philosophical foundations of science, helped to develop research in real labs, promoted new forms o education (computer-assisted learning and the EGPY – Education Program for Gifted Youth). Since the range of interest of Suppes was very broad, so is the variety of topics dealt with in this volume. The work of a researcher is certainly not limited to his own writings, but also has to be appreciated through the work of the people he has been working with and influenced. From this point of view the work of Suppes is very impressive, and the present book contributes to show that. This is a follow up of a special issue of the journal Synthese, New Directions in the Foundations of Science, edited by Béziau and Krause, after a meeting they organized with Suppes in Florianópolis (Brazil) in 2002 for his 80th birthday. Jean-Yves Béziau worked with Suppes at Stanford University for two years (2000 and 2001) and has been continuously working in the Suppes tradition of logic, methodology and philosophy of science, which emphasizes structures and models. Décio Krause has used Suppes’ approach to the axiomatization of scientific theories in many fields. With J.C.M. Magalhães, he presented a ``Suppes predicate” for genetics and natural selection and with S. French he developed a Suppes predicate for quantum field theories via Fock spaces.

A collection of papers from Paul Hertz to Dov Gabbay - through Tarski, Gödel, Kripke - giving a general perspective about logical systems. These papers discuss questions such as the relativity and nature of logic, present tools such as consequence operators and combinations of logics, prove theorems such as translations between logics, investigate the domain of validity and application of fundamental results such as compactness and completeness. Each of these papers is presented by a specialist explaining its context, import and influence.

The present book discusses all aspects of paraconsistent logic, including the latest findings, and its various systems. It includes papers by leading international researchers, which address the subject in many different ways: development of abstract paraconsistent systems and new theorems about them; studies of the connections between these systems and other non-classical logics, such as non-monotonic, many-valued, relevant, paracomplete and fuzzy logics; philosophical interpretations of these constructions; and applications to other sciences, in particular quantum physics and mathematics. Reasoning with contradictions is the challenge of paraconsistent logic. The book will be of interest to graduate students and researchers working in mathematical logic, computer science, philosophical logic, linguistics and physics.

Dans un texte désormais célèbre, Ferdinand de Saussure insiste sur l’arbitraire du signe dont il vante les qualités. Toutefois il s’avère que le symbole, signe non arbitraire, dans la mesure où il existe un rapport entre ce qui représente et ce qui est représenté, joue un rôle fondamental dans la plupart des activités humaines, qu’elles soient scientifiques, artistiques ou religieuses. C’est cette dimension symbolique, sa portée, son fonctionnement et sa signification dans des domaines aussi variés que la chimie, la théologie, les mathématiques, le code de la route et bien d’autres qui est l’objet du livre La Pointure du symbole. -/- Jean-Yves Béziau, franco-suisse, est docteur en logique mathématique et docteur en philosophie. Il a poursuivi des recherches en France, au Brésil, en Suisse, aux États-Unis (UCLA et Stanford), en Pologne et développé la logique universelle. Éditeur-en-chef de la revue Logica Universalis et de la collection Studies in Universal Logic (Springer), il est actuellement professeur à l’Université Fédérale de Rio de Janeiro et membre de l’Académie brésilienne de Philosophie. SOMMAIRE -/- PRÉFACE L’arbitraire du signe face à la puissance du symbole Jean-Yves BÉZIAU La logique et la théorie de la notation (sémiotique) de Peirce (Traduit de l’anglais par Jean-Marie Chevalier) Irving H. ANELLIS Langage symbolique de Genèse 2-3 Lytta BASSET -/- Mécanique quantique : quelle réalité derrière les symboles? Hans BECK -/- Quels langages et images pour représenter le corps humain? Sarah CARVALLO Des jeux symboliques aux rituels collectifs. Quelques apports de la psychologie du développement à l’étude du symbolisme Fabrice CLÉMENT Les panneaux de signalisation (Traduit de l’anglais par Fabien Shang) Robert DEWAR Remarques sur l’émergence des activités symboliques Jean LASSÈGUE Les illustrations du "Songe de Poliphile" (1499). Notule sur les hiéroglyphes de Francesca Colonna Pierre-Alain MARIAUX Signes de vie Jeremy NARBY Visualising relations in society and economics. Otto Neuraths Isotype-method against the background of his economic thought Elisabeth NEMETH Algèbre et logique symboliques : arbitraire du signe et langage formel Marie-José DURAND – Amirouche MOKTEFI Les symboles mathématiques, signes du Ciel Jean-Claude PONT La mathématique : un langage mathématique? Alain M. ROBERT.