Chapter

Strict Finitism

Mathieu Marion

in Wittgenstein, Finitism, and the Foundations of Mathematics

Published in print August 2008 | ISBN: 9780199550470
Published online September 2011 | e-ISBN: 9780191701559 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199550470.003.0008
Strict Finitism

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  • History of Western Philosophy
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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

Chapter.  10365 words. 

Subjects: History of Western Philosophy ; Philosophy of Mathematics and Logic

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