Wittgenstein and Brouwer

In this paper, I present a summary of the philosophical relationship betweenWittgenstein and Brouwer, taking as my point of departure Brouwer's lecture onMarch 10, 1928 in Vienna. I argue that Wittgenstein having at that stage not doneserious philosophical work for years, if one is to understand the impact of thatlecture on him, it is better to compare its content with the remarks on logics andmathematics in the Tractactus. I thus show that Wittgenstein's position, in theTractactus, was already quite close to Brouwer's and that the points of divergence are the basis to Wittgenstein's later criticisms of intuitionism. Among the topics of comparison are the role of intuition in mathematics, rule following, choice sequences, the Law of Excluded Middle, and the primacy of arithmetic over logic.

[1]  M. Walker,et al.  Ludwig Wittgenstein: The Duty of Genius , 1993 .

[2]  L. Wittgenstein.  Tractatus Logico-Philosophicus , 2021, Nordic Wittgenstein Review.

[3]  Paolo Mancosu,et al.  From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s , 1997 .

[4]  H. Rose.  R. L. Goodstein , 1988 .

[5]  Ray Monk,et al.  Ludwig Wittgenstein: The Duty of Genius , 1991 .

[6]  T. Crilly.  From Kant to Hilbert: a sourcebook in the foundations of mathematics , William Ewald (ed.). 2 vols. Pp. 1340. 1999. £50 (Paperback). ISBN 0 19 850537 X (Oxford University Press). , 2000, The Mathematical Gazette.

[7]  H. Feigl,et al.  Inquiries and Provocations , 1980 .

[8]  Jacques-Paul Dubucs.  L.J.E. Brouwer : Topologie et constructivisme , 1988 .

[9]  M. Marion.  Wittgenstein, finitism, and the foundations of mathematics , 1998 .

[10]  P. Frascolla.  Wittgenstein's philosophy of mathematics , 1994 .

[11]  J. Roger Hindley,et al.  Introduction to combinators and λ-calculus , 1986, Acta Applicandae Mathematicae.

[12]  SIGNE, PROPOSITION, SITUATION : ÉLÉMENTS POUR UNE LECTURE DU TRACTATUS LOGICO-PHILOSOPHICUS (") , 2002 .

[13]  A. Church.  A Set of Postulates for the Foundation of Logic , 1932 .

[14]  J. Hintikka.  Die Wende der Philosophie: Wittgenstein’s New Logic of 1928 , 1996 .

[15]  Alexandroff.,et al.  Elementary concepts in Topology , 1932 .

[16]  H. Feigl.  The Wiener Kreis in America , 1981 .

[17]  George Pitcher,et al.  The Philosophy of Wittgenstein. , 1965 .

[18]  Cora Diamond,et al.  Wittgenstein's Lectures on the Foundations of Mathematics. , 1977 .

[19]  Ludwig Wittgenstein,et al.  Notebooks, 1914-1916 , 1961 .

[20]  R. Read,et al.  The New Wittgenstein , 2000 .

[21]  D. van Dalen,et al.  The War of the frogs and the mice, or the crisis of themathematische annalen , 1990 .

[22]  Eric T. Bell,et al.  The Philosophy of Mathematics , 1950 .

[23]  Pasquale Frascolla.  The Tractatus System of Arithmetic , 2004, Synthese.

[24]  Jaakko Hintikka,et al.  Ludwig Wittgenstein: Half-Truths and One-and-a-Half-Truths , 1996 .