Wittgenstein on equinumerosity and surveyability

Mathieu Marion, Mitsuhiro Okada

研究成果: Chapter

2 被引用数 (Scopus)

抄録

This paper aims to connect two of Wittgenstein's arguments against Logicism. The 'modality argument' is directed at the Frege/Russell-definition of numbers in terms of one-one correlations. According to this argument, it is only when the Fs and Gs are few in number that one can know that they can be one-one correlated without knowing their numbers. Wittgenstein's 'surveyability argument' purports to show that only a limited portion of arithmetic can actually be proven within Principia Mathematica. For proof-constructions within this system quickly become unsurveyable and thereby loose their cogency. As we shall argue, the role of visualisation in proofs plays a fundamental role in both arguments.

本文言語English
ホスト出版物のタイトルThemes from Wittgenstein and Quine
出版社Brill
ページ61-78
ページ数18
89
ISBN(電子版)9789401211949
ISBN(印刷版)9789042039124
DOI
出版ステータスPublished - 2014 12月 19

ASJC Scopus subject areas

  • 人文科学(全般)
  • 社会科学(全般)

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