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Reason's Nearest KinPhilosophies of Arithmetic from Kant to Carnap$
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Michael Potter

Print publication date: 2002

Print ISBN-13: 9780199252619

Published to Oxford Scholarship Online: May 2007

DOI: 10.1093/acprof:oso/9780199252619.001.0001

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(p.206) 8 Ramsey
Reason's Nearest Kin

Michael Potter (Contributor Webpage)

Oxford University Press

Frank Ramsey was involved in preparing the English translation of the Tractatus as an undergraduate at Cambridge. He developed an account of the theory of types which avoided the difficulties associated with the axiom of reducibility by following what he took to be Wittgensteinian principles. In December 1924, he wrote an essay which was eventually published under the title ‘The foundations of mathematics’. The material in the essay that is relevant here falls into three distinct parts: in the first Ramsey showed how to develop a theory of types on Wittgensteinian principles that had no need of the problematic axiom of reducibility; in the second he dealt with the derivation of the theory of classes from the theory of types; and in the third he addressed the problematic dependence of the theory on the axiom of infinity.

Keywords:   Frank Ramsey, Wittgenstein, propositions, identity, propositional functions, axiom of infinity

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