Gerhard Heinzmann

According to a pragmatist, philosophical thought bears on the link between the construction and the description of mathematical objects. Thanks to his development of «theorematic reasoning», Peirce succeeded in bringing forward a pragmatic interpretation of a mathematical structure, exhibiting however an inherent vagueness with regard to the categoricalness of the structure. — In this matter, Gonseth's model of reconstruction of an axiomatic system can be resorted to: the logical genesis of a structure considered in his «Idoneism» corresponds to Peirce's program of explaining the meaning of a concept by means of a cumulative sequence of interpretants.

English summary: This ambitious study proposes an analysis of intuition that will allow us to understand it cognitive role in the justification of our beliefs and philosophical and mathematical reasoning. The book first demonstrates that the cognitive function of intuition passes through a semiotic system before situating the semantic treatment of intuition in the context of classic problems in philosophy, logic, and mathematics. French description: Proposer une symptomatique de l'intuition nous permettant de comprendre son fonctionnement cognitif dans la justification de nos croyances et de nos raisonnements philosophiques et mathematiques, tel est le defi releve dans ce livre. La premiere partie montre que la fonction cognitive de l'intuition dans la comprehension et la justification passe par l'utilisation d'un systeme semiotique. Un tel systeme est utilise intuitivement si, dans une action situee, les aspects significatifs et representatifs sont interdependants. Une demande de legitimation de ce qui est represente ne se place pas au meme niveau de reflexion que celui de l'intuition. Qu'elle puisse etre a la fois evidente et faillible n'a des lors rien de paradoxal. La deuxieme partie montre qu'envisager l'intuition dans une symptomatologie ne nous eloigne pas de la tradition philosophique. Au contraire, le traitement semantique de la question de l'intuition eclaire certains problemes classiques en philosophie, en logique et en mathematiques; et il permet de relire a nouveaux frais aussi bien Aristote, Descartes ou Kant, que Helmholtz, Poincare, Brouwer, Weyl, Beth et Cavailles.

"Dialogisches Handeln" ist eine Sammlung von philosophischen BeitrAgen zum dialogischen Konstruktivismus im Sinne von Kuno Lorenz, der Philosophie als eine Kommunikation mit Selbstreflexion versteht. Dabei umfaAt der Dialog in diesem Buch verschiedene Disziplinen der Philosophie - von der Anthropologie A1/4ber die Grundlagen von Logik und Sprachphilosophie bis hin zur Wissenschafts- und Erkenntnistheorie. Die Reflexion auf die kommunikativen Grundlagen wissenschaftlichen Austauschs schlieAt dabei Denkperspektiven verschiedener Wissenschaften - von der Psychologie bis zu Physik und Chemie - ebenso ein wie die philosophischen Disziplinen.

The 14th Congress of Logic, Methodology and Philosophy of Science will be held on July 19-26, 2011, in Nancy, France. In order to provide some historical background about DLMPS Congresses, we are honoured to have the opportunity to reissue a chapter of Anita Burdman Feferman and Solomon Feferman's Alfred Tarski : Life and Logic, dedicated to the early history of the DLMPS and the organization of the first Congress held in 1960 in Stanford. We are very grateful to the authors and the Cambridge University Press for their kind authorization to reissue this text.

ArgumentAccording to Hermann von Helmholtz, free mobility of bodies seemed to be an essential condition of geometry. This free mobility can be interpreted either as matter of fact, as a convention, or as a precondition making measurements in geometry possible. Since Henri Poincaré defined conventions as principles guided by experience, the question arises in which sense experiential data can serve as the basis for the constitution of geometry. Helmholtz considered muscular activity to be the basis on which the form of space could be construed. Yet, due to the problem of illusion inherent in the subject’s self-assessment of muscular activity, this solution yielded new difficulties, in that if the manifold is abstracted from rigid bodies which serve as empirical justification of the geometrical notion of space, then illusionary bodies will produce fictive manifolds. The present article is meant to disentangle these difficulties.