Gerhard Heinzmann

During a conference entitled “_Un logicien consciencieux. La philosophie de Evert Willem Beth_,” held in Nancy in 1998 and published in this journal, volume 3, cahier 4 [Barth, Heinzmann _et al._ 1998-1999], the participants regretted that a reasoned biography of Beth was not available. In view of the efforts made since then in this direction, in particular by Paul van Ulsen in his PhD thesis in Dutch [2000], this article attempts to provide an overview of Beth’s work for a broader community of philosophers of science. However, my focus is not so much on Beth’s widely discussed and important contributions to mathematical logic, where his most creative merits reside. My aim is to emphasize Beth’s philosophical and cultural background. Both are also discussed in the first two chapters of Ulsen’s thesis, which globally focuses on Beth’s work in logic. Of course, philosophical and scientific aspects cannot be systematically separated, but Beth’s influence on the philosophy of mathematics be...

There is no substantive agreement about the philosophical views of analytic philosophers. Nevertheless, for much of them logical analysis is widely recognized to be important. It is true that Poincare used no logical analysis but refused nevertheless the old metaphysics. Indeed, the analytic tradition of philosophy of science is perhaps better characterized by several overlapping similarities, which are the clincher for my main thesis: Analytic philosophy of science has one of its origins in the philosophical network in France around 1900 and, especially, in Poincare.

The goal of this paper is to answer the following question: Does it make sense to speak of thought experiments not only in physics, but also in mathematics, to refer to an authentic type of activity? One may hesitate because mathematics as such is the exercise of reasoning par excellence, an activity where experience does not seem to play an important role. After reviewing some results of the research on thought experiments in the natural sciences, we turn our attention to experiments and thought experiments in mathematics, especially in fundamental mathematics, and investigate what thought experiments can teach us there. If we accept the principle that mathematical practice can sometimes be best described by a pragmatist approach where the concept of experience in mathematics is considered from a new perspective, thought experiments can in some cases be a useful instrument different from both ‘mathematical experiments’ and ‘formal’ proofs: they are mathematical experiments using deviant methods.

This open access book examines the many contributions of Paul Lorenzen, an outstanding philosopher from the latter half of the 20th century. It features papers focused on integrating Lorenzen's original approach into the history of logic and mathematics. The papers also explore how practitioners can implement Lorenzen’s systematical ideas in today’s debates on proof-theoretic semantics, databank management, and stochastics. Coverage details key contributions of Lorenzen to constructive mathematics, Lorenzen’s work on lattice-groups and divisibility theory, and modern set theory and Lorenzen’s critique of actual infinity. The contributors also look at the main problem of Grundlagenforschung and Lorenzen’s consistency proof and Hilbert’s larger program. In addition, the papers offer a constructive examination of a Russell-style Ramified Type Theory and a way out of the circularity puzzle within the operative justification of logic and mathematics. Paul Lorenzen's name is associated with the Erlangen School of Methodical Constructivism, of which the approach in linguistic philosophy and philosophy of science determined philosophical discussions especially in Germany in the 1960s and 1970s. This volume features 10 papers from a meeting that took place at the University of Konstanz.

Hide Ishiguro, Leibniz’s philosophy of logic and language. 2nd ed. Cambridge:Cambridge University Press, 1990. x + 246pp. £27.50/$49.50 ; £10.95/$16.95 Massimo Mugnai, Leibniz’ theory of relations. Stuttgart:Franz Steiner Verlag, 1992. 291 pp. 96 DM W. A. Wallace, Galileo’s logic of discovery and proof The background, content, and use of his appropriated treatises on Aristotle’s posterior analytics. Dordrecht, Boston, and London:Kluwer, 1992. xxiii + 323 pp. £84, $139, DF1240 W. A. Wallace, Galileo’s logical treatises. A translation, with notes and commentary, of his appropriated Latin questions on Aristotle’s posterior analytics. Dordrecht, Boston, and London:Kluwer, 1992. xix + 239 pp. £65, $;99, DF1185 W. A. Wallace, Galileo’s early notebooks:the physical questions ; Prelude to Galileo: essays on medieval and sixteenth-century sources of Galileo’s thought ; Galileo and his sources: the heritage of the Collegio Romano in Galileo’s science ; and Galileo Galilei:Tractatio de Precognitionibus et Praecognitis and Tractatio de Démonstration Raymond M. Smullyan, GödeVs incompleteness theorems, New York, Oxford:Oxford University Press, 1992. xiii + 139. pp. $29.95 Raymond M. Smullyan, Recursion theory for metamathematics, New York, Oxford:Oxford University Press, 1993. xiv + 163 pp. $29.95 D. MiéVille, Kurt Gödel:Actes du Colloque, Neuchâtel 13-14 juin 1991. Neuchâtel, Switzerland: Centre de Recherches Sémiologiques, Université de Neuchâtel, 1992. iv +200pp. 15 Sfr Geoffrey Hellman, Mathematics without numbers. Oxford:Clarendon Press, 1989. xi + 154 pp. £22.50 Michael Detlefsen Proof, logic and formalization. London and New York:Routledge, 1992. x + 241 pp. £40.00 J. Cavaillès, Método axiomâtico y formalismo. Foreword by S. Ramirez. Translation from the French by C. Alvarez and S. Ramirez. Mexico:Servicios Editoriales de la Facultad de Ciencias, UNAM, 1992. 199pp. No price stated Roberto Poli, Ontologia formale. Genoa:Marietti, 1992, 542 pp. No price stated Jon Barwise and John Etchemendy, The language of first-order logic, 3rd edition, Stanford, CA:CLSI Lecture Notes No. 34, 1992, xiv + 329pp. US $34.95

"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.

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.