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Wittgenstein, Finitism, and the Foundations of Mathematics$
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Mathieu Marion

Print publication date: 2008

Print ISBN-13: 9780199550470

Published to Oxford Scholarship Online: September 2011

DOI: 10.1093/acprof:oso/9780199550470.001.0001

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Strict Finitism

Strict Finitism

(p.213) 8 Strict Finitism
Wittgenstein, Finitism, and the Foundations of Mathematics

Mathieu Marion (Contributor Webpage)

Oxford University Press

The philosophical world outside Cambridge discovered the later Ludwig Wittgenstein's philosophy of mathematics with the publication in the 1956 of the Remarks on the Foundations of Mathematics, a selection from manuscripts dating from 1938 to 1944. In his 1958 survey paper, Hao Wang promoted strict finitism, which he then called anthropologism, to the rank of a foundational thesis alongside finitism, intuitionism, predicativism, and Platonism, with the later Wittgenstein being enrolled as its most important representative. This has been by far the prevailing view ever since, with some exceptions. A useful preliminary step would be to give a brief characterization of strict finitism. Various strict finitist programmes have been devised in the past, and they do not show much homogeneity: contrary to intuitionism, there is no orthodoxy.

Keywords:   Ludwig Wittgenstein, finitism, mathematics, Hao Wang, logic, anthropologism, predicativism, Platonism

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