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{{Short description|1956 work by philosopher Ludwig Wittgenstein}}{{italic title}}File:RemarksOnTheFoundationsOfMathematics.jpg|thumb|First English-language edition(publ. Blackwell)]]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,BOOK, Ludwig, Wittgenstein, Georg Henrik, von Wright, Rush, Rhees, Gertrude Elizabeth Margaret, Anscombe, 1983, Remarks on the Foundations of Mathematics, 2nd, MIT Press, 978-0-262-73067-9, {{page needed|date=December 2013}} 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 reviewsBOOK, Marion, Mathieu, Wittgenstein, Finitism, and the Foundations of Mathematics, 2008, Oxford University Press, 978-0-19-955047-0, {{page needed|date=December 2013}} mostly from working logicians and mathematicians, among them Michael Dummett, Paul Bernays, and Georg Kreisel.JOURNAL, 10.1093/bjps/IX.34.135, Wittgenstein's Remarks on the Foundations of Mathematics, 1958, Kreisel, G., The British Journal for the Philosophy of Science, 34, 135–58, IX, Today Remarks on the Foundations of Mathematics is read mostly by philosophers sympathetic to Wittgenstein and they tend to adopt a more positive stance.Rodych V, Wittgenstein's Philosophy of Mathematics, SEPWittgenstein'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. Wittgenstein in the Remarks adopts an attitude of doubt in opposition to much orthodoxy in the philosophy of mathematics.{{anchor|Notorious}} Particularly controversial in the Remarks was Wittgenstein's "notorious paragraph", which contained an unusual commentary on Gödel's incompleteness theorems. Multiple commentators read Wittgenstein as misunderstanding Gödel. In 2000 Juliet Floyd and Hilary Putnam suggested that the majority of commentary misunderstands Wittgenstein but their interpretationJOURNAL, Juliet, Floyd, Hilary, Putnam, November 2000, A Note on Wittgenstein's 'Notorious Paragraph' about the Gödel Theorem, The Journal of Philosophy, 97, 11, 624–32, 2678455, 10.2307/2678455, has not been met with approval.Timothy Bays' disagreement (JOURNAL, Timothy, Bays, April 2004, On Floyd and Putnam on Wittgenstein on Godel, The Journal of Philosophy, 101, 4, 197–210, 3655690, 10.5840/jphil2004101422, 10.1.1.7.4931, ) was further commented by Putnam and Floyd and he wrote some more as Floyd, Putnam, Bays, Steiner, Wittgenstein, Gödel, Etc.; see also M. Plebani, The Key Problems of KC, Papers of the 31st IWS (eds. A. Hieke, H. Leitgeb), 2008JOURNAL, 10.1111/j.1746-8361.2003.tb00272.x, Misunderstanding Gödel: New Arguments about Wittgenstein and New Remarks by Wittgenstein, 2005, Rodych, Victor, Dialectica, 57, 3, 279–313, Wittgenstein wrote The debate has been running around the so-called Key Claim: If one assumes that P is provable in PM, then one should give up the "translation" of P by the English sentence "P is not provable".Wittgenstein does not mention the name of Kurt Gödel who was a member of the Vienna Circle during the period in which Wittgenstein's early ideal language philosophy and Tractatus Logico-Philosophicus dominated the circle's thinking; multiple writings of Gödel in his Nachlass contain his own antipathy for Wittgenstein, and belief that Wittgenstein wilfully misread the theorems.WEB, Rebecca Newberger, Goldstein,weblink Gödel And The Nature Of Mathematical Truth, Edge, June 8, 2005, December 13, 2013, Some commentators, such as Rebecca Goldstein, have hypothesized that Gödel developed his logical theorems in opposition to Wittgenstein.

References

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External links

• Sorin Bangu, Ludwig Wittgenstein: Later Philosophy of Mathematics, IEP
• Victor Rodych, Wittgenstein's Philosophy of Mathematics, The Stanford Encyclopedia of Philosophy

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