Skip to main content
SpringerLink
Log in

A Critique of Resnik’s Mathematical Realism

  • Published:
Erkenntnis Aims and scope Submit manuscript

Abstract

This paper attempts to motivate skepticism about the reality of mathematical objects. The aim of the paper is not to provide a general critique of mathematical realism, but to demonstrate the insufficiency of the arguments advanced by Michael Resnik. I argue that Resnik’s use of the concept of immanent truth is inconsistent with the treatment of mathematical objects as ontologically and epistemically continuous with the objects posited by the natural sciences. In addition, Resnik’s structuralist program, and his denial of relational properties, is incompatible with a realist metaphysics about mathematical objects.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • C. Chihara (1990) Constructability and Mathematical Existence Oxford University Press Oxford

    Google Scholar 

  • D. Davidson (1974) ‘On the Very Idea of a Conceptual Scheme’. in Inquiries into Truth and Interpretation Clarendon Press Oxford

    Google Scholar 

  • D. Davidson (1977) ‘Reality without Reference’. in Inquiries Into Truth and Interpretation Clarendon Press Oxford

    Google Scholar 

  • D. Davidson (1979) ‘The Inscrutability of Reference’. in Inquiries Into Truth and Interpretation Clarendon Press Oxford

    Google Scholar 

  • M. Devitt (1991) Realism and Truth Princeton University Press Princeton

    Google Scholar 

  • M. Dummett (1977) Elements of Intuitionism Oxford University Press Oxford

    Google Scholar 

  • H. Field (1980) Science Without Numbers Princeton University Press Princeton

    Google Scholar 

  • G. Hellman (1989) Mathematics Without Numbers Oxford University Press Oxford

    Google Scholar 

  • W.V. Quine (1990) Pursuit of Truth Harvard University Press Cambridge

    Google Scholar 

  • W.V. Quine (1969) ‘Ontological Relativity’. in Ontological Relativity and Other Essays Columbia University Press New York

    Google Scholar 

  • W.V. Quine (1960) Word and Object MIT Press Cambridge

    Google Scholar 

  • M.D. Resnik (1997) Mathematics as a Science of Patterns Oxford University Press Oxford

    Google Scholar 

  • M.D. Resnik (1981) ArticleTitle‘Mathematics as a Science of Patters: Ontology and Reference’ Nous 15 529–550

    Google Scholar 

  • S. Shapiro (1997) Philosophy of Mathematics: Structure and Ontology Oxford University Press Oxford

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Massachusetts, Philosophy Dartmouth, 285 Old Westport Road North Dartmouth, Massachusetts, 02747, United States

    Timothy John Nulty

Authors
  1. Timothy John Nulty
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Timothy John Nulty.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nulty, T.J. A Critique of Resnik’s Mathematical Realism. Erkenntnis 62, 379–393 (2005). https://doi.org/10.1007/s10670-004-6883-z

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10670-004-6883-z

Keywords

Search

Navigation