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 (2016)
Olga Hoppe-Kondrikova (Author)
Verburgt, Lukas M. (Author)
Historia Mathematica
Volume: 43
Issue: 4
Pages: 369-398
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. De Engelse vertaling van Aleksandr Yakovlevich Khinchins (1894–1959) artikel getiteld ‘Ideas of intuitionism and the struggle for a subject matter in contemporary mathematics’ wordt hier voor het eerst beschikbaar gemaakt. Khinchin presenteerde het beroemde grondslagendebat van de jaren ‘20 tussen L.E.J. Brouwer en David Hilbert in termen van een zoektocht naar een wiskunde met inhoud. Zijn hoofddoel lijkt te zijn geweest om het intuïtionisme ideologisch acceptabel te maken voor zijn publiek aan de Communistische Academie door middel van de claim dat voor zover Brouwers intuïtionisme een helder ‘onderzoeksobject’ had en Hilberts nieuwe programma een concessie was ten opzichte van het intuïtionisme, de vermeende overwinning van het intuïtionisme niet alleen het verlies van het ‘lege’ formalisme betekende, maar ook liet zien dat het marxisme verenigbaar was met de nieuwste ontwikkelingen binnen de moderne wiskunde en er een nauwe verwantschap mee vertoonde. Deze inleiding biedt een verkennend onderzoek naar de kwestie van wat tactisch (of te wijten aan ideologische druk) was en wat daadwerkelijke wetenschappelijke interesse (of te wijten aan onwetendheid) was (of beide) in Khinchins artikel uit 1926. Dit doet het in de vorm van een gedetailleerd commentaar op, met name, de tactische kant van zijn weergave van de posities van Brouwer en Hilbert.
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