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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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From Truth-Functional Logic to a Logic of Equations

From Truth-Functional Logic to a Logic of Equations

(p.110) 5 From Truth-Functional Logic to a Logic of Equations
Wittgenstein, Finitism, and the Foundations of Mathematics

Mathieu Marion (Contributor Webpage)

Oxford University Press

In order to appreciate fully the depth of Ludwig Wittgenstein's commitment to finitism, one ought to look for the causes of his change of mind on quantification. They are to be found in underlying changes in the notion of analysis which took place in the first steps away from Tractatus Logico-Philosophicus in the manuscripts of 1929. Upon his return to Cambridge in January of that year, Wittgenstein immediately started writing extensively. This was a period of intense intellectual fervor. Early entries in his notebooks indicate that he had started to think afresh some of the problems even before his arrival in Cambridge and that he moved in new directions very quickly. This indicates that Wittgenstein had already given up or was about to give up one of the cental claims of the Tractatus Logico-Philosophicus.

Keywords:   finitism, quantification, Ludwig Wittgenstein, Tractatus Logico-Philosophicus, logic, colour exclusion

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