Frege’s Context Principle and Reference to Natural Numbers
Frege proposed that his Context Principle—which says that a word has meaning only in the context of a proposition—can be used to explain reference, both in general and to mathematical objects in particular. I develop a version of this proposal and outline answers to some important challenges that the resulting account of reference faces. Then I show how this account can be applied to arithmetic to yield an explanation of our reference to the natural numbers and of their metaphysical status.
KeywordsNatural Number Singular Term Proper Part Physical Body Unity Relation
Unable to display preview. Download preview PDF.
- 1.George Boolos. To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables). Journal of Philosophy, 81(8):430–449, 1984. Reprinted in .Google Scholar
- 3.Michael Dummett. Frege: Philosophy of Language. Harvard University Press, Cambridge, MA, second edition, 1981.Google Scholar
- 4.Michael Dummett. Frege: Philosophy of Mathematics. Harvard University Press, Cambridge, MA, 1991.Google Scholar
- 5.Gareth Evans. Varieties of Reference. Oxford University Press, Oxford, 1982.Google Scholar
- 7.Gottlob Frege. Foundations of Arithmetic. Blackwell, Oxford, 1953. Transl. by J.L. Austin.Google Scholar
- 8.Bob Hale. Grundlagen Section 64. Proceedings of the Aristotelian Society, 97(3):243–61, 1997. Reprinted with a postscript in .Google Scholar
- 11.Øystein Linnebo. Plural Quantification, 2004. In Stanford Encyclopedia of Philosophy, available at http://plato.stanford.edu/entries/plural-quant/.
- 13.Øystein Linnebo. To Be Is to Be an F. Dialectica, 59(2):201–222, 2005.Google Scholar
- 14.Øystein Linnebo. Sets, Properties, and Unrestricted Quantification. In Agustín Rayo and Gabriel Uzquiano, editors, Unrestricted Quantification: New Essays, pp. 149–178. Oxford University Press, Oxford, 2006.Google Scholar
- 16.Charles Parsons. Mathematics in Philosophy. Cornell University Press, Ithaca, NY, 1983.Google Scholar
- 17.John Perry. The Two Faces of Identity. In Identity, Personal Identity, and the Self. Hackett, Indianapolis, IN, 2002.Google Scholar
- 18.Robert Stalnaker. On Considering a Possible World as Actual. Proceedings of the Aristotelian Society, Suppl. vol. 65:141–156, 2001.Google Scholar
- 20.Timothy Williamson. Identity and Discrimination. Blackwell, Oxford, 1990.Google Scholar
- 21.Crispin Wright. The Philosophical Significance of Frege’s Theorem. In Richard Heck, editor, Language, Thought, and Logic. Essays in Honour of Michael Dummett. Clarendon, Oxford, 1997. Reprinted in .Google Scholar
- 22.Crispin Wright. Response to Michael Dummett. In Matthias Schirn, editor, Philosophy of Mathematics Today. Clarendon, Oxford, 1998.Google Scholar
- 23.Crispin Wright. The Harmless Impredicativity of N= (Hume’s Principle). In Matthias Schirn, editor, Philosophy of Mathematics Today. Clarendon, Oxford, 1998.Google Scholar