Skip to main content Accessibility help
×
Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-20T10:28:29.360Z Has data issue: false hasContentIssue false

5 - On Nominalism

from Part I - Structuralism, Extendability, and Nominalism

Published online by Cambridge University Press:  26 January 2021

Geoffrey Hellman
Affiliation:
University of Minnesota
Get access

Summary

Probably there is no position in Goodman’s corpus that has generated greater perplexity and criticism than Goodman’s “nominalism.” As is abundantly clear from Goodman’s writings, it is not “abstract entities” generally that he questions – indeed, he takes sensory qualia as “basic” in his Carnap-inspired constructional system in Structure [Goodman, 1977]] – but rather just those abstracta that are so crystal clear in their identity conditions, so fundamental to our thought, so prevalent and seemingly unavoidable in our discourse and theorizing that they have come to form the generally accepted framework for the most time-honored, exact, sophisticated, refined, central, and secure branch of human knowledge yet devised, mathematics itself! Of all the abstracta to question, why sets? Of course, Goodman gave his “reasons,” the unintelligibility of “generating” an infinitude of “constructed objects” automatically from any given object or objects.

Type
Chapter
Information
Mathematics and Its Logics
Philosophical Essays
, pp. 74 - 87
Publisher: Cambridge University Press
Print publication year: 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Boolos, G. [1985] “Nominalist Platonism,” Philosophical Review 94: 327344.CrossRefGoogle Scholar
Boolos, G. [1998] Logic, Logic, and Logic, Jeffrey, R., ed. (Cambridge, MA: Harvard University Press).Google Scholar
Burgess, J. [1984] “Synthetic mechanics,” Journal of Philosophical Logic 13: 379395.CrossRefGoogle Scholar
Burgess, J. and Rosen, G. [1997] A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics (Oxford: Oxford University Press).Google Scholar
Burgess, J., Hazen, A., and Lewis, D. [1991] “Appendix,” in Lewis, D., Parts of Classes (Oxford: Blackwell), pp. 121149.Google Scholar
Carnap, R. [1956] “Empiricism, semantics, and ontology,” in Meaning and Necessity (Chicago, IL: University of Chicago Press), pp. 205221.Google Scholar
Chihara, C. [1973] Ontology and the Vicious Circle Principle (Ithaca, NY: Cornell University Press).Google Scholar
Chihara, C. [1990] Constructibility and Mathematical Existence (Oxford: Oxford University Press).Google Scholar
Colyvan, M. [1999] “Contrastive empiricism and indispensability,” Erkenntnis 51: 323332.CrossRefGoogle Scholar
Feferman, S. [1998] In the Light of Logic (Oxford: Oxford University Press).CrossRefGoogle Scholar
Field, H. [1980] Science without Numbers (Princeton, NJ: Princeton University Press).Google Scholar
Frege, G. [1884] The Foundations of Arithmetic (Oxford: Blackwell, 1950), translation by J. L. Austin of Die Grundlagen der Arithmetik (Breslau: Wilhelm Koebner, 1884).Google Scholar
Goodman, N. [1972] “A world of individuals,” in Problems and Projects (Indianapolis, IN: Bobbs-Merrill), pp. 155172.Google Scholar
Goodman, N. [1977] The Structure of Appearance, 3rd edn. (Dordrecht: Reidel).CrossRefGoogle Scholar
Goodman, N. and Quine, W. V. [1947] “Steps toward a constructive nominalism,” Journal of Symbolic Logic 12: 105122.CrossRefGoogle Scholar
Harrington, L. A., Morley, M., Scedrov, A., and Simpson, S. G. (eds.) [1985] Harvey Friedman’s Research on the Foundations of Mathematics (Amsterdam: North-Holland).Google Scholar
Hellman, G. [1989] Mathematics without Numbers: Towards a Modal-Structural Interpretation (Oxford: Oxford University Press).Google Scholar
Hellman, G. [1998] “Maoist mathematics? Critical study of John Burgess and Gideon Rosen, A Subject with No Object: Strategies for Nominalist Interpretation of Mathematics (Oxford, l997),” Philosophia Mathematica 6(3): 357368.Google Scholar
Hellman, G. [1999] “Some ins and outs of indispensability,” in Cantini, A., et al., eds., Logic and Foundations of Mathematics (Dordrecht: Kluwer), pp. 2539.CrossRefGoogle Scholar
Lewis, D. [1991] Parts of Classes (Oxford: Blackwell).Google Scholar
Maddy, P. [1990] Realism in Mathematics (Oxford: Oxford University Press).Google Scholar
Maddy, P. [1992] “Indispensability and practice,” Journal of Philosophy 89: 275289.Google Scholar
Richman, F. [1996] “Interview with a constructive mathematician,” Modern Logic 6: 247271.Google Scholar
Simpson, S. [1999] Subsystems of Second Order Arithmetic (Berlin: Springer).CrossRefGoogle Scholar
Sober, E. [1993] “Mathematics and indispensability,” Philosophical Review 102: 3557.CrossRefGoogle Scholar
Wright, C. [1983] Frege’s Conception of Numbers as Objects (Aberdeen: Aberdeen University Press).Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • On Nominalism
  • Geoffrey Hellman, University of Minnesota
  • Book: Mathematics and Its Logics
  • Online publication: 26 January 2021
  • Chapter DOI: https://doi.org/10.1017/9781108657419.006
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • On Nominalism
  • Geoffrey Hellman, University of Minnesota
  • Book: Mathematics and Its Logics
  • Online publication: 26 January 2021
  • Chapter DOI: https://doi.org/10.1017/9781108657419.006
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • On Nominalism
  • Geoffrey Hellman, University of Minnesota
  • Book: Mathematics and Its Logics
  • Online publication: 26 January 2021
  • Chapter DOI: https://doi.org/10.1017/9781108657419.006
Available formats
×