This paper shows that Aristotle's De Interpretatione does not separate syntax from semantics. Linguistic sentences are not syntactic entities, and non-linguistic meanings are not semantic propositions expressed by linguistic sentences. In fact, Aristotle resorts to a mental conception of meaning, distinguishing linguistic meanings in a given language from non-linguistic mental contents in relation to actual things: while the former are not the same for all, the latter are shared by everyone. Aristotle is not a modern logician, like Boole, Frege, or (...) Russell, in so far as a mental conception of meaning does not reveal an abstract semantics for a syntactic language. (shrink)

Jean-Louis Gardies. AVANT-PROPOS En plaçant ici Pascal entre Eudoxe et Cantor, il va de soi que nous le mettons d'une certaine manière au centre de notre propos ; non cependant que nous prétendions faire converger toutes les lignes de ...

Aristotle’s Prior Analytics identifies deductions simpliciter with inferential necessity, so that a deduced conclusion is necessarily inferred from some premises. Modern logical reconstructions claim that inferential necessity in Aristotle corresponds to logical validity. However, this logical reconstruction fails on two accounts. First, logical validity does not highlight Aristotle’s distinction between inferential necessity and predicative necessity, meaning that the inferential necessity of a deduction is not of the same kind as the predicative necessity of a non‑deductive argument. Second, logical validity does (...) not explain the relevance of Aristotle’s distinction between complete and incomplete deductions. Logicians speak of complete deduction by adding the term “obvious” or “transparent” to logical validity, and then criticize Aristotle’s view for being unclear. However, Aristotle’s position is not confronted with this difficulty. There is nothing to add to inferential necessity, which already means complete deducibility, as opposed to incomplete deducibility, deemed to be potentially complete. Accordingly, the Prior Analytics reduces the incomplete deductions to the complete deductions in order to prove the potential, inferential necessity of the incomplete deductions. Logical validity would have been faithful to Aristotle’s text, if it had been possible to coin a notion of potential validity, distinct from both validity and invalidity. (shrink)

Inλ-calculus, the strategy of leftmost reduction (“call-by-name”) is known to have good mathematical properties; in particular, it always terminates when applied to a normalizable term. On the other hand, with this strategy, the argument of a function is re-evaluated at each time it is used.To avoid this drawback, we define the notion of “storage operator”, for each data type. IfT is a storage operator for integers, for example, let us replace the evaluation, by leftmost reduction, ofϕτ (whereτ is an integer, (...) andϕ anyλ-term) by the evaluation oftτϕ. Then, this computation is the same as the following: first computeτ up to some reduced formτ 0, and then applyϕ toτ 0. So, we have simulated “call-by-value” evaluation within the strategy of leftmost reduction.The main theorem of the paper (Corollary of Theorem 4.1) shows that, in a second orderλ-calculus, using Gödel's translation of classical intuitionistic logic, we can find a very simple type (or specification) for storage operators. Thus, it gives a way to get such operators, which is to prove this type in second order intuitionistic predicate calculus. (shrink)

, which uses the intuitionistic propositional calculus, with the only connective →. It is very important, because the well known Curry-Howard correspondence between proofs and programs was originally discovered with it, and because it enjoys the normalization property: every typed term is strongly normalizable. It was extended to second order intuitionistic logic, in 1970, by J.-Y. Girard [4], under the name of system F, still with the normalization property.More recently, in 1990, the Curry-Howard correspondence was extended to classical logic, following (...) Felleisen and Griffin [6] who discovered that the law of Peirce corresponds to control instructions in functional programming languages. It is interesting to notice that, as early as 1972, Clint and Hoare [1] had made an analogous remark for the law of excluded middle and controlled jump instructions in imperative languages.There are now many type systems which are based on classical logic; among the best known are the system LC of J.-Y. Girard [5] and the λμ-calculus of M. Parigot [11]. We shall use below a system closely related to the latter, called the λ c -calculus [8, 9]. Both systems use classical second order logic and have the normalization property.In the sequel, we shall extend the λ c -calculus to the Zermelo-Frænkel set theory. The main problem is due to the axiom of extensionality. To overcome this difficulty, we first give the axioms of ZF in a suitable (equivalent) form, which we call ZF ɛ. (shrink)

We describe here a simple method in order to obtain programs from proofs in second-order classical logic. Then we extend to classical logic the results about storage operators proved by Krivine for intuitionistic logic. This work generalizes previous results of Parigot.

The biological function of human reasoning abilities cannot be to improve shared knowledge. This is at best a side effect. A more plausible function of argumentation, and thus of reasoning, is to advertise one's ability to detect lies and errors. Such selfish behavior is closer to what we should expect from a naturally selected competence.

The immemorial and recollection -- The reserve of forgetting -- The unforgettable -- The sudden and the unhoped for -- Retrospection.

Episodic memory is certainly a unique endowment, but its primary purpose is something other than to provide raw material for creative synthesis of future scenarios. Remembered episodes are exactly those that are worth telling. The function of episodic memory, in my view, is to accumulate stories that are relevant to recount in conversation.

Les douze etudes ici proposees jalonnent un parcours s'etalant sur une vingtaine d'annees et s'etant ordonne autour d'une question centrale: et si nous n'avions rien entendu de la difference introduite par le logos entre l'homme et l'animal ...

un essai de reconstitution Jean-Louis Gardies. n'avait, dans cette voie, cherché et réussi à en éviter qu'une seule. Le disciple ici va plus loin que le maître dans la voie que ce dernier avait ouverte, puisqu'il ne présuppose pas, mais ...

Many logicians have tried to formalize a modal logic from the Prior Analytics, but the general view is that Aristotle has failed to offer a consistent modal logic there. This paper explains that Aristotle is not interested in modal logic as such. Modalities for him pertain to the relations of predication, without challenging the assertoric system of deductions simpliciter. Thus, demonstrations or dialectical deductions have modal predicates and yet are still deductions simpliciter. It is a matter of distinguishing inferential necessity (...) that applies to every deduction from the modal predicates in the two premises and conclusion. The modality of demonstrations can be either necessary or possible. The necessity is predicative, i.e., independent of inferential necessity. While the possible demonstration challenges the predicative necessity of the necessary demonstration, it preserves the inferential necessity of the deduction simpliciter. (shrink)

Jean-Louis Vieillard-Baron | : La recherche pour déterminer ce qu’est une spiritualité philosophique s’appuie sur les oeuvres de Bergson et de Lavelle. Il y a une sensibilité aux choses de l’âme dans cette spiritualité qui n’est pas spécifiquement religieuse. La réalisation personnelle d’une vocation est au coeur de toute spiritualité philosophique, en tant qu’elle est la vie spirituelle d’un homme parmi d’autres hommes. Le spiritualisme est la philosophie qui intègre en elle la demande d’une vie spirituelle. | : (...) This attempt to determine the nature of a philosophical spirituality is based on the works of Bergson and Lavelle. There is sensitiveness to matters of the soul in that spirituality which is not specifically religious. The personal realization of a vocation is at the heart of any philosophical spirituality in so far as it is the spiritual life of a man amongst other men. Spiritualism is the philosophy which integrates within itself the demand for a spiritual life. (shrink)

A modular analysis of spontaneous language use provides support for the existence of an identifiable step in language evolution, protolanguage. Our suggestion is that a grammarless form of expression would have evolved to signal unexpected events, a behavior still prevalent in our species. Words could not be so specific as to refer to whole, non-recurring, situations. They referred to elements such as objects or locations, and the communicated event was inferred metonymically. Compositionality was achieved, without syntax, through multi-metonymy, as words (...) referring to elements of the same situation were concatenated into proto-utterances. (shrink)

Book review of Jean-Louis Schefer's The Ordinary Man of Cinema (2016) with particular attention to Schefer's conception of affect and its influence on Deleuze.

La sémiologie générale étant avant tout une description des systèmes signifiants, le problème qu'elle soulève au lieu même de sa formation, est celui de la transcription dans un code linguistique de données extra-linguistiques. Ce problème se pose dans toutes les branches de la sémiologie. mais il est plus aisément inaperçu ou passé sous silence lorsqu'il s'agit d'une sémio logie formalisant les systèmes signifiants élaborés dans les langues naturelles. Or, une fois touchés les systèmes signifiants représentatifs qui s'orga nisent sans recours (...) explicite au langage naturel, le problème de la lexicali sation de ces systèmes et de la formalisation de cette lexicalisation, surgit avec tout son poids épistémologique et sémiologique. C'est la question du " triptyque image-langue-discours" : c'est ici que nous trouvons la notion de lexie qu'élabore l'étude de Jean-Louis Schefer, " Lecture et système du tableau ". Traité par un spécialiste à propos d'un objet qui paraitra restreint, la peinture, le concept de lexie et la manière dont il est présenté jette, cependant, un pont entre le texte et les pratiques sociales non textuelles. En ce sens, cette étude pourra introduire, à nos yeux, à une réflexion générale sur l'expansion de la démarche sémiotique vers toutes les pratiques signifiantes non discursives de la société. D'autre part, la notion de lexie telle qu'elle est étudiée par Schefer, étend la problématique soulevée par l'article de Gérard Genette " Langage poé tique, poétique du langage" concer nant l'aspect sémiotique des rapports norme-anomalie dans les systèmes signifiants irréductibles à la langue parlée. La lexie propose un point de vue qui dépasse une telle distinction dans la mesure où, traitant du texte, elle passe outre la ligne et la surface, et pense dans l'espace de la permutation signifiante. Cette réflexion se situe de même, on le verra, dans le champ ouvert par la philosophie de J. Derrida exposée brièvement dans ce numéro. (shrink)