Ludwig Wittgenstein's philosophy of mathematics
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ToursExplore Lably’s 3D toursHis Remarks on the Foundations of Mathematics contains his compiled views, notably a controversial repudiation of Gödel's incompleteness theorems.
Tractatus
Wittgenstein's initial conception of mathematics was logicist and even formalist. The Tractatus described the propositions of logic as a series of tautologies derived from syntactic manipulation, and without the pictorial force of elementary propositions depicting states of affairs obtaining in the world.
Wittgenstein asserted that “[t]he logic of the world, which is shown in tautologies by the propositions of logic, is shown in equations by mathematics” (6.22) and further that “Mathematics is a method of logic” (6.234).
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Philosophy of mathematics, post-1929
During the 1920s, Wittgenstein turned away from philosophical matters, but his interest in mathematics was rekindled when he attended a lecture in Vienna by the intuitionist L. E. J. Brouwer. After 1929, his primary mathematical preoccupation entailed resolving the account of logical necessity he had articulated in the Tractatus Logico-Philosophicus—an issue that had been fiercely pressed by Frank P. Ramsey. Wittgenstein's initial response, Some Remarks on Logical Form, was the only academic paper he published during his lifetime, and it marked the beginnings of a departure from the ideal language philosophy and correspondence theory of truth of the Tractatus.
The Lectures on the Foundations of Mathematics
During the two terms of 1938/39 Wittgenstein lectured without any notes before students for two hours twice a week. From four sets of notes made during the lectures a text has been created, presenting Wittgenstein's views at that time.
The Remarks on the Foundations of Mathematics (1937–44)
An editorial team prepared the edition of Wittgenstein's Remarks on the Foundations of Mathematics from the manuscript notes he made during the years 1937–44. The material has been arranged in chronological order, allowing to observe some changes of emphasis or interest in Wittgenstein's views over the years.