Clement Lion

Cet article récuse l’idée qu’intervenir dans l’espace public revienne, pour la philosophie, à y formuler des propositions, supposées être éclairantes en vertu même de leur caractère philosophique. Envisageant plutôt qu’il puisse y avoir une tension irréductible entre les exigences propres à l’espace public (lisibilité, transmissibilité, etc.) et celles propres à la philosophie (rigueur conceptuelle, sens de la complexité, etc.), nous questionnons la possibilité de définir un espace commun entre les deux. Si une philosophie réduite à ce qu’elle est selon sa reconnaissance publique cesse d’être philosophique, en revanche, un espace public qui explicite sa propre spatialité, de façon immanente, tendra à devenir philosophique à mesure que sa propre publicité se dévoilera problématique, faute de pouvoir être enclose dans un discours suffisamment univoque. Plutôt que d’interroger les modes possibles d’intervention de la philosophie dans l’espace public, il s’agit ici de montrer comment l’espace public est lui-même philosophant par les tensions qui le constituent nécessairement en tant qu’espace, c’est-à-dire en tant qu’ensemble défini par des relations d’extériorité mutuelle. Le philosophique apparaît comme ce que soutient un effort continuel de résistance à toute structuration inertielle de l’espace public à travers des routines discursives, tendanciellement consensuelles, dont la philosophie elle-même offre souvent l’exemple.

It is thought that the fact that the processes of intuitionism come into conflict with certain laws of classical logic justifies reforming the latter to remove the reasons for this conflict and associate intuitionistic mathematics with a logic. Contrary to this way of apprehending the relationship between intuition and logic, we propose to develop the idea that the conflict between a properly intuitionist mathematics and the classical logic does not have to be suppressed, insofar as it is the expression of a dynamic tension, which is the very essence of intuitionism. We then show that the idea of such a dialogical tension opens us new perspectives on the very concept of phenomenological reduction.

“Logic and Agon” is the text of a lecture given in Rome in 1958 by the German philosopher and mathematician Paul Lorenzen. In this inaugural text are laid the foundations of the dialogic logic, which represents an alternative approach to the question of meaning and logical truth, based on a dynamic formalism. Through the enrichment of the standard approach to logic with original tools, it allows a philosophical explanation of the foundations of the concept of formal validity. Clément Lion proposes an unpublished French translation of this text as well as a presentation, in which he tries to show that the initial ambition of Paul Lorenzen was not so much to propose a new logical formalism as to question in principle any enterprise based on the use of such a formalism.

“Logic and Agon” is the text of a lecture given in Rome in 1958 by the German philosopher and mathematician Paul Lorenzen. In this inaugural text are laid the foundations of the dialogic logic, which represents an alternative approach to the question of meaning and logical truth, based on a dynamic formalism. Through the enrichment of the standard approach to logic with original tools, it allows a philosophical explanation of the foundations of the concept of formal validity. Clément Lion proposes an unpublished French translation of this text as well as a presentation, in which he tries to show that the initial ambition of Paul Lorenzen was not so much to propose a new logical formalism as to question in principle any enterprise based on the use of such a formalism.

Avec l’article « Aristotle’s natural deduction system », publié en 1974, J. Corcoran a contribué à diffuser une nouvelle perspective sur les écrits logiques d’Aristote et sur la théorie du syllogisme en particulier. Dans cet article, Corcoran affirme que, dans les premiers chapitres des Premiers Analytiques, Aristote ne propose pas un système axiomatique, qui supposerait une logique sous-jacente, ainsi que le pensait Łukasiewicz, mais plutôt un système de déduction naturelle, avec des dimensions métalogiques. Notre propos est ici basé sur une courte monographie de Kurt Ebbinghaus, intitulée Ein formales Model der Syllogistik des Aristoteles (1964), où est fixé le canon de cette nouvelle perspective mentionnée plus haut et qui a été développé dans le cadre conceptuel de la « logique opérative » de Paul Lorenzen. Ebbinghaus développe une reconstruction formelle montrant que l’approche d’Aristote relève de la « théorie de la preuve », non seulement pour ce qui concerne le système d’inférence sous-jacent, mais aussi pour ce qui concerne les éléments métalogiques. C’est notamment à travers ce dernier aspect que se manifeste une différence majeure par rapport à la reconstruction de Corcoran. Alors que celui-ci pose que le système d’inférence d’Aristote est enraciné dans une sémantique de théorie des modèles (élaborée par Corcoran lui-même), Ebbinghaus comprend que la théorie du syllogisme a été développée à partir d’une approche de la signification par des règles (« rule based »), semblables aux règles d’un jeu. En fait, la reconstruction d’Ebbinghaus offre une lecture pragmatiste de la syllogistique d’Aristote, qui, tel est notre propos, paraît non seulement beaucoup plus proche du point de vue d’Aristote que ne l’est la sémantique de théorie des modèles proposée par Corcoran, mais qui, de plus, permet de saisir l’unité systématique de la théorie du syllogisme.

We argue that the recent developments of the dialogical framework towards the incorporation of materiality within dialogues certainly enables one to extend its possible applications beyond the domain of logic. We ask the question of linking Bakhtin’s criticism of literary formalism, based on advocating dialogical features within novels, and the dialogical sight on formalism, in order to assess the program of constituting a dynamical formalism as a means towards literary analysis, enabling to speak of subjectivity without falling into psychologism. By the way, we propose a dialogical reading of the alleged non constructivity of Kripke’s schema in and we indicate a new path towards another understanding of its constructive content.

The present paper aims at integrating the phenomenological reading of Brouwerian intuitionism into the domain of semantics, by challenging the claim that the very meaning of mathematical expressions—expressions of free choice sequences included—is invariable and objectively determinable and that, accordingly, any deictic expression should be removed from mathematics. By introducing constructability into the constitution of meaning itself and by considering meaning as a “social act”, we try to map another route into intersubjectivity, based on the distinction between the play-level and the strategic level, which has been further developed in the dialogical framework, following the work of Paul Lorenzen. It is suggested that the steps towards such a route can be retraced from Oskar Becker’s original “Cartesian” approach to intersubjectivity, which facilitates a new reading of Brouwer’s own way of conceptualizing “mutual understanding”. In doing so, our general purpose is therefore to promote an insertion of dialogical constructivism into Mark van Atten’s take on the intuitionist Creating Subject.

We argue that no attempt of reducing meaning to a systematic set of rules, according to which the role of linguistic expressions is to be normatively defined, can be abstracted from an irreducibly decisional compound. By comparing Lorenzen ’s project of building an Ortho-language and Brandom ’s inferentialist take on meaning, we distinguish two ways of acknowledging this fact, while claiming that Lorenzen ’s take is more genuinely constructive, insofar as choices be thought of as genuine features of constructions. It brings into a new perspective the relation between dialogical constructivism and Brouwer ’s intuitionism. Finally we bring up a philosophical argument for the claim that interaction rules should be indexed on players and on their choices, when providing deontic bases to semantics.

We argue that no attempt of reducing meaning to a systematic set of rules, according to which the role of linguistic expressions is to be normatively defined, can be abstracted from an irreducibly decisional compound. By comparing Lorenzen’s project of building an Ortho-languageand Brandom’s inferentialist take on meaning, we distinguish two ways of acknowledging this fact, while claiming that Lorenzen’s take is more genuinely constructive, insofar as choices be thought of as genuine features of constructions. It brings into a new perspective the relation between dialogical constructivism and Brouwer’s intuitionism. Finally we bring up a philosophical argument for the claim that interaction rules should be indexed on players and on their choices, when providing deontic bases to semantics.