Francois Lepage

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

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

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

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.

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