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On A.Ya. Khinchin's paper ‘Ideas of intuitionism and the struggle for a subject matter in contemporary mathematics’ (1926): A translation with introduction and commentary
- Source :
- Historia Mathematica. 43:369-398
- Publication Year :
- 2016
- Publisher :
- Elsevier BV, 2016.
-
Abstract
- The translation into English of Aleksandr Yakovlevich Khinchin's (1894–1959) 1926 paper entitled ‘Ideas of intuitionism and the struggle for a subject matter in contemporary mathematics’ is made available for the first time. Here, Khinchin presented the famous foundational debate between L.E.J. Brouwer and David Hilbert of the 1920s in terms of a search for a mathematics with content. His main aim seems to have been to make intuitionism ideologically acceptable to his audience at the Communist Academy by means of the claim that insofar as Brouwer's intuitionism had a clear ‘subject matter’ and Hilbert's new program was a concession to intuitionism, the alleged victory of intuitionism not only implied the defeat of ‘empty’ formalism, but also showed the compatibility and affinity of Marxism with the newest developments in modern mathematics. This introduction provides a tentative exploration of the issue of what was tactical (or due to ideological pressure) and what was real scientific interest (or due to ignorance) (or what was both) in Khinchin's 1926 paper in the form of a detailed commentary, especially, on the tactical side of his presentation of the positions of Brouwer and Hilbert.
- Subjects :
- History
General Mathematics
media_common.quotation_subject
010102 general mathematics
Victory
Ignorance
06 humanities and the arts
0603 philosophy, ethics and religion
01 natural sciences
Epistemology
Subject matter
Formalism (philosophy of mathematics)
Intuitionism
060302 philosophy
Calculus
Ideology
0101 mathematics
Communism
media_common
Mathematics
Subjects
Details
- ISSN :
- 03150860
- Volume :
- 43
- Database :
- OpenAIRE
- Journal :
- Historia Mathematica
- Accession number :
- edsair.doi...........6c4645928263b5d6ef265f12628efe1a