Exploration de concepts avancés en logique formelle, notamment la logique modale, la logique partielle, la logique probabiliste et la logique intuitionniste.

The aim of the paper is to develop the notion of partial probability distributions as being more realistic models of belief systems than the standard accounts. We formulate the theory of partial probability functions independently of any classical semantic notions. We use the partial probability distributions to develop a formal semantics for partial propositional calculi, with extensions to predicate logic and higher order languages. We give a proof theory for the partial logics and obtain soundness and completeness results.

In this paper, we introduce a Hilbert style axiomatic calculus for intutionistic logic with strong negation. This calculus is a preservative extension of intuitionistic logic, but it can express that some falsity are constructive. We show that the introduction of strong negation allows us to define a square of opposition based on quantification on possible worlds.

This paper presents a generalization of a proposal of van Benthem’s who has shown how to provide a canonical name for any object in propositional type theory. Van Benthem’s idea is to characterize any function in the hierarchy by the Boolean values the function takes for any sequence of arguments. The recursive definition of canonical names uses only the abstraction, functional application, the identity operator and the fact that we have a name for the true and the false. We show (...) that this result can be extended to the finite theory of types by the introduction of an algebra on individuals. (shrink)

RésuméOn montre d'abord que la technique de révision des probabilités appelée « imagerie », qui a été introduite par Lewis pour la logique des conditionnels de Stalnaker, peut être généralisée à la sémantique des systèmes de sphères de Lewis si l'on permet aux énoncés conditionnels d'avoir des valeurs de vérité fractionnaires. Un système est proposé.

This paper is composed of two independent parts. The first is concerned with Russell’s early philosophy of mathematics and his quarrel with Poincaré about the nature of their opposition. I argue that the main divergence between the two philosophers was about the nature of definitions. In the second part, I briefly present Le!niewski’s Ontology and suggest that Le!niewski’s original treatment of definitions in the foundations of mathematics is the natural solution to the problem that divided Russell and Poincaré.

Dans la partie de la philosophic que l'on appelle habituellement philosophie du langage, la vieille opposition entre le réalisme et le nominalisme est toujours actuelle. D'un côté, les thèses nominalistes trouvent de nouveaux défenseurs qui apportent quelquefois des arguments originaux ou qui reprennent d'anciennes argumentations. D'un autre côté le réalisme est violemment attaqué sur tous ses flancs.

SummaryIn this paper I will strive towards three main objectives. First of all, I will try to show that a very commonplace property of knowledge, that of yielding truth, can be used to characterize an ideal and radical notion of knowledge. It will be argued that this property generates a basic and autonomous concept of knowledge, i.e., a purely logical concept of knowledge that can be clearly separated from the psychological, intentional or epistemological aspects of knowledge. What results can thus (...) be regarded as a kind of reduction of the concept of knowledge to that of truth. This reduction will be expressed by means of a criterion which a relation between an agent and a sentence must satisfy in order to be interpreted as exemplifying the relation of knowing.Secondly, 1 will offer an analysis of presuppositional knowledge which shows how the very strong and ideal notion of knowledge previously developed can be useful in interpreting the ordinary use of “knowing”.My third and last objective will be to use this criterion to characterize formally the semantic interpretation associated to a rational and competent agent, i.e. the space of his knowledge. (shrink)

Foundations of Illocutionary Logic de John Searle et Daniel Vanderveken constitue, à ma connaissance, la première suggestion sérieuse d'un cadre formel destiné à l'élaboration d'une logique de l'illocutoire. Les phénomènes illocutoires sont en effet d'une telle com-plexité que, souvent, les schèmes explicatifs proposés n'ont qu'une valeur très locale et ne constituent une explication que pour quelques exemples bien précis, ceux qui justement ont servi de base empirique sur laquelle ces schèmes se sont élaborés. La prévention de FIL est tout autre. (...) On ne saurait en aucun cas faire un reproche de provincialisme aux auteurs dont le but explicite est d'élaborer un véritable cadre théorique général à l'intérieur duquel tous les phénomènes illocutoires pourront trouver une explication. (shrink)

La théorie des types que Bertrand Russell proposa en 1908 ne se voulait pas une solution ad hoc au problème des contradictions, elle prétendait plutôt être la solution naturelle, celle que tout le monde reconnaîtra comme la solution attendue. En fait, il s'agit d'une théorie philosophique qui concrétise un projet grandiose: réduire les mathématiques à la logique. Le présent texte se propose d'examiner les thèses russelliennes et la dynamique de leur évolution de 1903 à 1907, c'est-à-dire des Principles à la (...) naissance de la théorie des types.The theory of types that Bertrand Russell proposed in 1908 didn't present itself as an ad hoc solution to the problem of contradictions. Rather it pretended to be the natural solution, the one that everybody would recognize as the expected solution. In fact, it is a philosophical theory materializing an imposing project: to reduce mathematics to logic. This paper examines the russellian theses and their evolution from 1903 to 1907 i.e. from the Principles to the birth of the theory of types. (shrink)

Le but de cette intervention est tout d'abord de caractériser un concept de sémantique d'un point de vue suffisamment général pour que l'on puisse l'interpréter comme celui de sémantique universelle. Dans un deuxième temps, il sera question de la caractérisation des contextes extensionnels et un critère général d'identification de tels contextes sera proposé. La thèse suivante, assez surprenante, sera avancée : selon ce critère, les contextes d'attitudes propositionnelles sont extensionnels. La solution que l'on proposera pour sortir de cette situation apparemment (...) paradoxale sera justement de l'interpréter comme un indice du caractère non sémantique du problème des attitudes propositionnelles. Finalement, une voie de solution au puzzle de Kripke sera proposée.The aim of this paper is first to characterize a concept of semantics from such a general point of view that it could be considered as the concept of universal semantics. Extensional contexts will then be characterized and a general identification criterion for such contexts will be given. The following rather surprising thesis will be put forward : According to this criterion, propositional attitude contexts are extensional. The proposed solution to this seemingly paradoxical situation will be to consider propositional attitude contexts as non semantic. Finally, a way out to Kripke's puzzle is propounded. (shrink)

Le dernier ouvrage d'Yvon Gauthier, son quatrième, n'est certes pas d'une lecture des plus faciles. Le bon lecteur devrait à la fois être familier du formalisme de la mécanique quantique et des labyrinthes lacaniens, connaître la théorie des modéles êt etre revenu de Heidegger.Tout cela rend la tâche d'un critique de Gauthier ardue et périlleuse; aussi je prierai le lecteur de m'excuser à l'avance si, dans le foisonnement philosophique de l'ouvrage, j'ai dû restreindre mon attention à certains aspects particuliers.

This paper has four parts. In the first part, I present Leniewski's protothetics and the complete system provided for that logic by Henkin. The second part presents a generalized notion of partial functions in propositional type theory. In the third part, these partial functions are used to define partial interpretations for protothetics. Finally, I present in the fourth part a complete system for partial protothetics. Completeness is proved by Henkin's method [4] using saturated sets instead of maximally saturated sets. This (...) technique provides a canonical representation of a partial semantic space and it is suggested that this space can be interpreted as an epistemic state of a non-omniscient agent. (shrink)

Parmi l'ensemble de toutes les propositions à propos desquelles un agent rationnel entretient des croyances et des désirs, certaines correspondent à des actes que l'agent juge faisables. Le but de mon intervention est de caractériser ce sous-ensemble de propositions en termes de leur probabilité et de leur désirabilité.Among the set of all propositions on which a rational agent entertains beliefs and desires, some express acts considered as possible options for the agent. The aim of this paper is to characterize this (...) subset of propositions in terms of their probability and their desirability. (shrink)

La théorie des descriptions de Bertrand Russell est sans aucun doute l'une des thèses philosophiques qui, au vingtième siècle, ont donné lieu au plus grand nombre de commentaires, de critiques, voire de querelles. Portée aux nues par certains-Ramsey l'a qualifiée de ‘paradigme de philosophie’-elle sera violemment contestée par d'autres, en particulier par Strawson qui s'avisera, quelque quarantecinq ans plus tard, qu'elle comporte des ‘erreurs fondamentales.’.

Cet article se veut une critique de la thèse défendue par [Cleland 1993], laquelle soutient que la thèse de Church doit être rejetée puisque les limites du calcul dépendent de la structure physique du monde. Dans un premier temps, nous offrons un (très) bref aperçu de la thèse de Church puis nous présentons l argument de Cleland. Par la suite, nous proposons une analyse critique de son argument, ce qui nous amènera à faire quelques distinctions conceptuelles par rapport aux notions (...) qui concernent la calculabilité. Finalement, nous montrons que les limites du calcul ne sont pas physiques mais bien logiques. En résumé, notre argument est que les limites du calcul sont déterminées en partie par le fait qu’une procédure effective doit pouvoir être décrite de manière finie. (shrink)

Cet article se veut une critique de la thèse défendue par [Cleland 1993], laquelle soutient que la thèse de Church doit être rejetée puisque les limites du calcul dépendent de la structure physique du monde. Dans un premier temps, nous offrons un bref aperçu de la thèse de Church puis nous présentons l argument de Cleland. Par la suite, nous proposons une analyse critique de son argument, ce qui nous amènera à faire quelques distinctions conceptuelles par rapport aux notions qui (...) concernent la calculabilité. Finalement, nous montrons que les limites du calcul ne sont pas physiques mais bien logiques. En résumé, notre argument est que les limites du calcul sont déterminées en partie par le fait qu’une procédure effective doit pouvoir être décrite de manière finie.Even though Church’s thesis is widely accepted among mathematicians, it is nonetheless controversial. In this paper, we argue against the position of [Cleland 1993], which defends that Church s thesis must be rejected because the limits of computation depend upon the physical structure of the world. We first give a brief overview of Church’s thesis and then we present Cleland s argument. We then propose a critical analysis of Cleland s argu­ment, which will involve some conceptual distinctions regarding the notion of computability, and finally we will show that the limits of computation are not physical but logical. In short, we argue that computation is limited by the fact that an effective procedure must be described in a finite way. (shrink)

Cet article se veut une critique de la thèse défendue par [Cleland 1993], laquelle soutient que la thèse de Church doit être rejetée puisque les limites du calcul dépendent de la structure physique du monde. Dans un premier temps, nous offrons un (très) bref aperçu de la thèse de Church puis nous présentons l argument de Cleland. Par la suite, nous proposons une analyse critique de son argument, ce qui nous amènera à faire quelques distinctions conceptuelles par rapport aux notions (...) qui concernent la calculabilité. Finalement, nous montrons que les limites du calcul ne sont pas physiques mais bien logiques. En résumé, notre argument est que les limites du calcul sont déterminées en partie par le fait qu’une procédure effective doit pouvoir être décrite de manière finie. (shrink)

The aim of this paper is to present a strongly complete first order functional predicate calculus generalized to models containing not only ordinary classical total functions but also arbitrary partial functions. The completeness proof follows Henkin’s approach, but instead of using maximally consistent sets, we define saturated deductively closed consistent sets . This provides not only a completeness theorem but a representation theorem: any SDCCS defines a canonical model which determine a unique partial value for every predicate symbol and any (...) function symbol. Any SDCCS can thus be interpreted as an epistemic state. (shrink)

Parallel to the New Left, whose influence on French public opinion is so pronounced today, a new academic movement has grown up in the United States in the last fifteen years. Its ideas are the portents of an intellectual and scientific revolution whose importance for the economic and political future of western society should be almost as great as the Keynesian revolution of the ‘30s.

Common sense has it that animals matter considerably less than humans; the welfare and suffering of a cow, a chicken or a fish are important but not as much as the welfare and suffering of a human being. Most animal ethicists reject this “speciesist” view as mere prejudice. In their opinion, there is no difference between humans and other animals that could justify such unequal consideration. In the opposite camp, advocates of speciesism have long tried to identify a difference that (...) would fit the bill, but they have consistently seemed to fail. In light of this, some naturally began to appeal to Moorean arguments: the case against speciesism must be flawed somehow, these philosophers maintain, because speciesism is supported by a strong and widespread intuition. This chapter draws on recent findings in social psychology to criticize this defence of speciesism. It argues that the strong and widespread intuition that humans count more than animals is epistemically defective because it is causally shaped by a pair of irrelevant influences: cognitive dissonance and tribalism. Accordingly, it is no suitable basis for a Moorean argument. (shrink)

Our societies are marked by anthropocentrism: most people treat animals in ways in which they would by no means treat fellow humans. One might nonetheless expect this prejudice to be much less prevalent in animal shelters since these places are created for the very sake of non-humans and generally managed by people who truly care about animal welfare. This chapter questions this expectation. It discusses three practices that are widespread in animal shelters and yet could be suspected of anthropocentrism: killing (...) animals for lack of resources, partnering with the livestock industry, and feeding animals meat. Drawing on the distinction between ideal and non-ideal theory, the chapter argues that management euthanasia and cooperation with animal agriculture are acceptable in non-ideal theory even though they would be condemned by ideal theory. Then it argues that meat-based pet food should be rejected even in the non-ideal circumstances faced by animal shelters. (shrink)

We propose a new approach to the study of introspection. Instead of asking what form introspection actually takes in humans or other animals, we ask what forms it could take, in natural or artificial minds. What are the dimensions along which forms of introspection could vary? This is a relatively unexplored question, but it is one that has the potential to open new avenues of study and reveal new connections between existing ones. It may, for example, focus attention on possible (...) forms of introspection radically different from the human one and help to integrate competing theories of human introspection in a non-adversarial manner. We introduce and motivate the project, provide a preliminary mapping of the space of possible forms of introspection, and sketch a programme for interdisciplinary research on the topic. (shrink)

The philosophical tradition in the West has always subjected life to conceptualdivisions and questions about meaning. In Vital Nourishment, François Jullien contends that althoughthis process has given rise to a rich history of inquiry, it proceeds too fast. In their anxietyabout meaning, Western thinkers since Plato have forgotten simply to experience life. In thisinstallment of his continuing project of plumbing the philosophical divide between Eastern andWestern thought, Jullien slows down, and, using the third and fourth century B.C.E. Chinese thinkerZhuanghi (...) as a foil, begins to think about life from a point outside of Western inquiry.The questionof how to "feed life," or nourish it, is the point of departure for the Chinese traditionthat Jullien locates in Zhuanghi. Life passes through each of us, and we have a duty to becomeamenable to its ebbs and flows. We must cultivate a sense of being adequate to it so that we canhouse it. Exploring notions of breath, energy, and immanence, Jullien reopens a vibrant space ofintellectual exchange between East and West. In doing so, he refuses to commit to a rigid frameworkof meaning, and his text unfolds as an elegant process that mirrors the very type of thought heexplores. Pointing out that it seems intellectually and politically imperative today to reinvigorateWestern thought with ideas from the East, Jullien seeks to create a space of mutual inquiry thatmaintains the integrity of both Eastern and Western thinking. Vital Nourishment is both a richintellectual historical journey and a text very much attuned to the philosophical politics of thepresent.François Jullien is Professor at the Université Paris VII-Denis Diderot and director at theInstitut de la Pensée Contemporaine. He is the author of Detour and Access: Stratgies of Meaning inChna and Greece, The Propensity of Things: Toward a History of Efficacy in China, and In Praise ofBlandness: Proceeding from Chinsese Thought and Aesthetics, all published by Zone Books. (shrink)

In this highly insightful analysis of Western and Chinese concepts of efficacy, François Jullien subtly delves into the metaphysical preconceptions of the two civilizations to account for diverging patterns of action in warfare, politics, and diplomacy. He shows how Western and Chinese strategies work in several domains (the battlefield, for example) and analyzes two resulting acts of war. The Chinese strategist manipulates his own troops and the enemy to win a battle without waging war and to bring about victory (...) effortlessly. Efficacity in China is thus conceived of in terms of transformation (as opposed to action) and manipulation, making it closer to what is understood as efficacy in the West. Jullien’s brilliant interpretations of an array of recondite texts are key to understanding our own conceptions of action, time, and reality in this foray into the world of Chinese thought. In its clear and penetrating characterization of two contrasting views of reality from a heretofore unexplored perspective, A Treatise on Efficacy will be of central importance in the intellectual debate between East and West. (shrink)