Wittgenstein on equinumerosity and surveyability

Mathieu Marion, Mitsuhiro Okada

Research output: Chapter in Book/Report/Conference proceedingChapter


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.

Original languageEnglish
Title of host publicationThemes from Wittgenstein and Quine
Number of pages18
ISBN (Print)9789401211949, 9789042039124
Publication statusPublished - 2014 Dec 19

ASJC Scopus subject areas

  • Arts and Humanities(all)
  • Social Sciences(all)

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  • Cite this

    Marion, M., & Okada, M. (2014). Wittgenstein on equinumerosity and surveyability. In Themes from Wittgenstein and Quine (Vol. 89, pp. 61-78). Brill. https://doi.org/10.1163/9789401211949.006