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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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The Second Edition of Principia

The Second Edition of Principia

Chapter:
(p.195) 7 The Second Edition of Principia
Source:
Reason's Nearest Kin
Author(s):

Michael Potter (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199252619.003.0008

In the previous chapter, it was shown that the Tractatus accounted for only a limited part of arithmetic at best. When Russell read Wittgenstein's manuscript, he was convinced that this was a gap that needed to be filled. Curiously, it was not the omission of an account of real numbers that he found egregious, but that of a general account of cardinals. Russell was not willing simply to abandon the development of mathematics from the theory of types. He accepted, though, some of Wittgenstein's criticisms of the account he had given in Principia. He took the opportunity presented by the publication of a second edition of Principia to prepare a new Introduction indicating how mathematics could be based on a new theory of types consonant with the parts of Wittgenstein's account that Russell agreed with.

Keywords:   Tractatus, Wittgenstein, Russell, Principia Mathematica, atomism, empiricis, hierarchy of propositional functions, mathematical induction, identity

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