Notre Dame Journal of Formal Logic

Book Review: John P. Burgess and Gideon Rose. A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics.

Stewart Shapiro

Article information

Source
Notre Dame J. Formal Logic Volume 39, Number 4 (1998), 600-612.

Dates
First available in Project Euclid: 5 December 2002

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1039118873

Digital Object Identifier
doi:10.1305/ndjfl/1039118873

Citation

Shapiro, Stewart. Book Review: John P. Burgess and Gideon Rose. A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics. . Notre Dame J. Formal Logic 39 (1998), no. 4, 600--612. doi:10.1305/ndjfl/1039118873. http://projecteuclid.org/euclid.ndjfl/1039118873.


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References

  • [1] Alston, W., ``Ontological commitments,'' Philosophical Studies, vol. 9 (1958), pp. 8--17.
  • [2] Benacerraf, P., ``What numbers could not be,'' Philosophical Review, vol. 74 (1965), pp. 47--73. MR 30:1929
  • [3] Benacerraf, P., and H. Putnam, Philosophy of Mathematics, 2d edition, Cambridge University Press, Cambridge, 1983. Zbl 0548.03002 MR 85h:00015
  • [4] Boolos, G., ``To be is to be a value of a variable (or to be some values of some variables),'' Journal of Philosophy, vol. 81 (1984), pp. 430--49. Zbl 0972.03535 MR 86f:03048
  • [5] Boolos, G., ``Nominalist platonism,'' Philosophical Review, vol. 94 (1985), pp. 327--44. Zbl 0972.03514
  • [6] Burgess, J., ``Synthetic mechanics,'' Journal of Philosophical Logic, vol. 13 (1984), pp. 379--95. Zbl 0556.03009 MR 85i:03033
  • [7] Chihara, C., Constructibility and Mathematical Existence, Oxford University Press, Oxford, 1990. MR 91i:03007
  • [8] Field, H., Science Without Numbers, Princeton University Press, Princeton, 1980. Zbl 0454.00015 MR 82d:03008
  • [9] Field, H., Realism, Mathematics and Modality, Blackwell, Oxford, 1989. MR 92b:03003
  • [10] Hale, B., Abstract Objects, Basil Blackwell, Oxford, 1987.
  • [11] Hellman, G., Mathematics Without Numbers, Oxford University Press, Oxford, 1989. Zbl 0688.03001 MR 91a:03035
  • [12] Lewis, D., On the Plurality of Worlds, Basil Blackwell, Oxford, 1986.
  • [13] Maddy, P., Realism in Mathematics, Oxford University Press, Oxford, 1990. Zbl 0762.00001 MR 92h:00007
  • [14] Malament, D., ``Review of Hartry H. Field's Science Without Numbers'' Journal of Philosophy, vol. 79 (1982), pp. 523--34.
  • [15] Putnam, H., Philosophy of Logic, Harper Torchbooks, New York, 1971. MR 56:5201
  • [16] Shapiro, S., Foundations Without Foundationalism: A Case for Second-Order Logic, Oxford University Press, Oxford, 1991. Zbl 0732.03002 MR 93j:03005
  • [17] Shapiro, S., ``Modality and ontology,'' Mind, vol. 102 (1993), pp. 455--81. MR 95f:03007
  • [18] Shapiro, S., Philosophy of Mathematics: Structure and Ontology, Oxford University Press, New York, 1997. Zbl 0897.00004 MR 98m:00012
  • [19] Tennant, N., The Taming of the True, Oxford University Press, Oxford, 1997. Zbl 0929.03001 MR 98m:03007