Reasoning about Knowledge in Linear Logic: Modalities and Complexity

In a recent paper, Jean-Yves Girard commented that ”it has been a long time since philosophy has stopped intereacting with logic”[17]. Actually, it has no

L’anti-psychologisme de Bradley : idéalité de la signification, jugement et universaux

L’opinion est souvent exprimée que Bradley fut un des tout premiers critiques du psychologisme. Dans cet article, j’examine cette thèse en me penchant principalement sur ses Principles of Logic (1883). Je définis le psychologisme au sens étroit comme une thèse portant sur les fondements de la logique, et le psychologisme au sens large comme une thèse plus générale en théorie de la connaissance pour montrer que Bradley a rejeté les deux, même s’il n’avait pas grand chose à dire sur la version étroite. Sa critique de l’autre version est basée sur une distinction entre contenu psychologique et contenu logique, et sur sa défense de la thèse de l’idéalité du contenu logique, avant Frege et Husserl. Cependant, il tient encore à l’idée que le contenu logique provient de la perception. Après une brève présentation de ses critiques de la psychologie associationniste, je montre qu’il fait face à de véritables difficultés en essayant d’éviter de retomber dans le psychologisme en faisant appel à la distinction entre universel abstrait et universel concret. Je termine avec quelques remarques sur la place de Bradley dans l’histoire de la psychologie britannique.One often hears the opinion voiced that Bradley was an early critique of psychologism. In this paper, I investigate that claim, focussing on his Principles of Logic (1883). I define psychologism in the narrow sense as a thesis pertaining to the foundations of logic, and psychologism in the wide sense as a more general thesis concerning the theory of knowledge, and show that Bradley rejected both, although he had little to say on the narrow version. His criticism of the wider version is based on his distinguishing between psychological and logical content and on his defence of the ideality of logical content, before Frege and Husserl. Nevertheless, he still hung to the idea that the latter harks back to ordinary perception. I then review briefly his criticisms of associationism in psychology, to show that he faced some difficulties in trying to avoid lapsing back into psychologism, with an appeal to a distinction between abstract and concrete universals. I conclude with some remarks on the palace of Bradley in the history of British psychology

Wittgenstein, l’intentionnalité et les règles

Après avoir présenté les grandes lignes de la réflexion phénoménologique de Wittgenstein en 1929 et son abandon de Vidée d'un langage phénoménologique, je montre qu'il fait face à un dilemme à propos de la notion de règle. Si on regarde l'expression symbolique d'une règle sous le mode physicaliste, on ne peut pas voir le lien entre celle-ci et ses applications. Comment peut-elle, de par elle-même, servir de guide à nos actions ? Il faut une intention, une interprétation, ce qui fait de la règle un objet phénoménologique. L'abandon du langage phénoménologique doit cependant forcer Wittgenstein à reconnaître qu'une règle en tant qu'objet phénoménologique ne peut pas être comparée à ou être utilisée pour déclencher une action qui se déroule dans le monde physique. Je montre que c'est en tentant de sortir de ce dilemme que Wittgenstein en viendra aux conceptions exposées dans ses remarques sur « suivre une règle ». J'examine en dernier lieu quelques conséquences de cette interprétation sur celle de la philosophie des mathématiques de Wittgenstein.After presenting a broad sketch of Wittgenstein's phenomenology; in 1929, and of his abandonment of the idea of a phenomenological language, it is shown that the notion of a rule left him with a dilemma, if the symbolical expression of a rule is understood in a physicalist mode, one cannot see the link between it and its applications. How could it, of itself guide our actions? One needs an intention or interpretation, thus turning the rule into a phenomeno/ogica I object. The abandonment ofthe p he nojne no logical language must have foiled Wittgenstein to recognize that a rule, qua phenomenological object, cannot be compared to or used to trigger an action in the physical world. It is then shown how Wittgenstein reached, while trying to solve this dilemma, the conception of rules presented in the remarks on 'following a rule". Lastly, some of the consequences of this new reading on the interpretation of Wittgenstein's philosophy of mathematics are examined

La logique symbolique en débat à Oxford à la fin du XIXe siècle : les disputes logiques de Lewis Carroll et John Cook Wilson

The development of symbolic logic is often presented in terms of a cumulative story of consecutive innovations that led to what is known as modern logic. This narrative hides the difficulties that this new logic faced at first, which shaped its history. Indeed, negative reactions to the emergence of the new logic in the second half of the nineteenth century were numerous and we study here one case, namely logic at Oxford, where one finds Lewis Carroll, a mathematical teacher who promoted symbolic logic, and John Cook Wilson, the Wykeham Professor of Logic who notoriously opposed it. An analysis of their disputes on the topic of logical symbolism shows that their opposition was not as sharp as it might look at first, as Cook Wilson was not so much opposed to the « symbolic » character of logic, but the intrusion of mathematics and what he perceived to be the futility of some of its problems, for logicians and philosophers alike

L’idéalisme britannique : histoire et actualité

L’idéalisme britannique est un mouvement qui a dominé les universités britanniques (et celles de son empire) pendant une cinquantaine d’années à la fin du xixe siècle et au début du xxe siècle, mais qui est passé presque totalement inaperçu dans le monde francophone. Rejetés en bloc par les philosophes analytiques, ces auteurs ont aussi été ignorés pendant longtemps dans leur pays, mais certains d’entre eux, notamment Bradley et Collingwood, jouissent d’un regain d’intérêt à la faveur d’un renouveau des études sur les origines de la philosophie analytique. Ce texte est une introduction à l’idéalisme britannique, qui retrace, dans une première partie plus historique, les grandes lignes de sa genèse, son développement et son déclin. Dans une deuxième partie, nous donnons quelques arguments en faveur d’une étude plus approfondie de ce mouvement.British Idealism is a philosophical movement that dominated British universities (and those of its empire), for fifty years around the turn from the XIXth to the XXth century, but it went largely unnoticed in the French-speaking world. Condemned by analytic philosophers, these authors were also ignored in their own country, but some of them, notably Bradley and Collingwood, are now enjoying a newly found popularity within the larger trend towards a study of the origins of analytic philosophy. This text is an introduction to British Idealism that plots, in an historical first part, the outlines of its rise, development and decline. In the second part, we provide reasons for further studies of this movement

Antilogic

This paper is an interim report of joint work begun in (Castelnérac & Marion 2009) on dialectic from Parmenides to Aristotle. In the first part we present rules for dialectical games, understood as a specific form of antilogikê developed by philosophers, and explain some of the key concepts of these dialectical games in terms of ideas from game semantics. In the games we describe, for a thesis A asserted by the answerer, a questioner must elicit the answerer’s assent to further assertions B1, B2,…, Bn, which form a scoreboard from which the questioner seeks to infer an impossibility (adunaton); we explain why the questioner must not insert any of his own assertions in the scoreboard, as well as the crucial role the Law of Non Contradiction, and why the games end with the inference to an impossibility, as opposed to the assertion of ¬A. In the second part we introduce some specific characteristics of Eleatic Antilogic as a method of enquiry. When Antilogic is used as a method of inquiry, then one must play not only the game beginning with a given thesis A, but also the game for ¬A as well as for A & ¬A, while using a peculiar set of opposite predicates to generate the arguments. In our discussion we hark back to Parmenides’ Poem, and illustrate our points with Zeno’s arguments about divisibility, Gorgias’ ontological argument from his treatise On Not-Being, and the second part of Plato’s Parmenides. We also identify numerous links to Aristotle, and conclude with some speculative comments on the origin of logic

Editors\u27 Introduction

The idea of interpreting quantifiers in terms of a game between two players was first suggested at the end of the 19th century by one of the inventors of quantification theory, C. S. Peirce, but it laid buried in his papers until it was discovered in the 1980s. His idea was independently discovered in the 1950s, when Leon Henkin suggested a game semantics for infinitary languages. Paul Lorenzen introduced his Dialogspiele at the same time, while his student Kuno Lorenz introduced the vocabulary of game theory that led to our modern conception of game semantics shortly after. The idea is to provide an explanation of the meaning of the logical connectives and quantifiers in terms of rules for non-collaborative, zero-sum games between two agents, one of whom argues for the validity of the claim against moves from the other, and to define truth in terms of the existence of a winning strategy for the defender

Jogando o bebê junto com a água do banho: Wittgenstein, Goodstein e o cálculo equacional

Reuben Louis Goodstein (1912-1985) was a student of Wittgenstein atCambridge in 1931-1934. In this paper, I provide an brief overview of his work inmathematical logic that shows the influence of Wittgenstein's ideas, including thereplacement in his equation calculus of mathematical induction by a rule ofuniqueness of a function defined by a recursive function. The latter is found inWittgenstein's Big Typescript. I also show that the fundamental ideas of the equationcalculus are found not only in the middle period but, in nuce, in the remarkson mathematics in the Tractatus Logico-Philosophicus and I use this to develop anargument against a fashionable reading of that book, the so-called 'New Wittgenstein'.Another link with Wittgenstein is the rejection of quantification theory; inthe last part of the paper use Goodstein's critical remarks on the Law of ExcludedMiddle, which also include a critique of Brouwer's half-way rejection, to shed lighton Wittgenstein's.Reuben Louis Goodstein (1912-1985) foi aluno de Wittgenstein em Cambridge de1931 a 1934. Neste artigo, faço uma breve descrição de seu trabalho na lógica matemática,no qual se percebe a influência das idéias de Wittgenstein, inclusive a substituição,em seu cálculo equacional, da indução matemática por uma regra de unicidade de umafunção definida por uma função recursiva. Esse último aspecto se encontra no Big Typescriptde Wittgenstein. Também mostro que as idéias fundamentais do cálculo equacionalpodem ser encontradas não apenas no período intermediário, mas, in nuce, nas observaçõessobre matemática do Tractatus Logico-philosophicus. A partir disso, procuro desenvolverum argumento contra uma leitura corrente daquele livro, o assim chamado “NovoWittgenstein”. Outra conexão entre Goodstein e Wittgenstein se encontra na rejeição dateoria da quantificação; na parte final do artigo, recorro às observações críticas de Goodsteinsobre a Lei do Terceiro Excluído (que também incluem uma crítica a Brouwer e à suarejeição “pela metade” dessa lei) para lançar luz sobre as observações do próprioWittgenstein a esse respeito