Remarks on the Foundations of Mathematics

Resumen

Remarks on the Foundations of Mathematics is a book of Ludwig Wittgenstein's notes on the philosophy of mathematics. It has been translated from German to English by G.E.M. Anscombe, edited by G.H. von Wright and Rush Rhees, and published first in 1956. The text has been produced from passages in various sources by selection and editing. The notes have been written during the years 1937-1944 and a few passages are incorporated in the Philosophical Investigations which were composed later. When the book appeared it received many negative reviews mostly from working logicians and mathematicians, among them Michael Dummett, Paul Bernays, and Georg Kreisel. Today Remarks on the Foundations of Mathematics is read mostly by philosophers sympathetic to Wittgenstein and they tend to adopt a more positive stance.
Wittgenstein's philosophy of mathematics is exposed chiefly by simple examples on which further skeptical comments are made. The text offers an extended analysis of the concept of mathematical proof and an exploration of Wittgenstein's contention that philosophical considerations introduce false problems in mathematics.