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The sortal resemblance problem

Published online by Cambridge University Press:  01 January 2020

Joongol Kim
Joongol Kim*
Affiliation:
Department of Philosophy, Gyeongsang National University, Jinju, Korea
*
*Email: joongolk@gnu.ac.kr
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Abstract

Is it possible to characterize the sortal essence of Fs for a sortal concept F solely in terms of a criterion of identity C for F? That is, can the question ‘What sort of thing are Fs?’ be answered by saying that Fs are essentially those things whose identity can be assessed in terms of C? This paper presents a case study supporting a negative answer to these questions by critically examining the neo-Fregean suggestion that cardinal numbers can be fully characterized as those things whose identity can be assessed in terms of one-one correspondence between concepts.

Keywords

criteria of identitycriteria of applicationcategoriesneo-Fregeanismthe Caesar Problem
Type
Articles
Information
Canadian Journal of Philosophy , Volume 44 , Issue 3-4 , August 2014 , pp. 407 - 424
Copyright
Copyright © Canadian Journal of Philosophy 2014

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References

Boolos, G. 1986. “Saving Frege from Contradiction.” In Logic, Logic and Logic, edited by Burgess, John P. and Jeffrey, Richard, 171–182. Cambridge, MA: Harvard University Press.Google Scholar
Boolos, G. 1987. “The Consistency of Frege’s Foundations of Arithmetic.” In Logic, Logic and Logic, edited by Burgess, John P. and Jeffrey, Richard, 183–201. Cambridge, MA: Harvard University Press.Google Scholar
Dummett, M. 1981. Frege: Philosophy of Language. 2nd ed.Cambridge, MA: Harvard University Press.Google Scholar
Dummett, M. 1991. Frege: Philosophy of Mathematics. Cambridge, MA: Harvard University Press.Google Scholar
Frege, G. 1980 [1884]. The Foundations of Arithmetic [Die Grundlagen der Arithmetik]. 2nd. rev. ed.Translated by Austin, J. L..Oxford: Blackwell.Google Scholar
Frege, G. 1906. “On the Foundations of Geometry: Second Series.” In Collected Papers on Mathematics, Logic, and Philosophy, edited by McGuinness, Brian, 293–340. New York: Basil Blackwell.Google Scholar
Frege, G. 1962. Grundgesetze der Arithmetik, I/II. Hildesheim: Georg Olms.Google Scholar
Hale, B. 2000. “Reals by Abstraction.” In The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics, by Hale, B. and Wright, C., 399–420. Oxford: Clarendon Press.Google Scholar
Hale, B., and Wright, C.. 2000. “Implicit Definition and the A Priori.” In The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics, by Hale, B. and Wright, C., 117–150. Oxford: Clarendon Press.Google Scholar
Hale, B., and Wright, C.. 2001a. The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics. Oxford: Clarendon Press.CrossRefGoogle Scholar
Hale, B., and Wright, C.. 2001b. “To Bury Caesar ….” In The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics, by Hale, B. and Wright, C., 335–396. Oxford: Clarendon Press.CrossRefGoogle Scholar
Hale, B., and Wright, C.. 2005. “Logicism in the Twenty-First Century.” In The Oxford Handbook of Philosophy of Mathematics and Logic, edited by Shapiro, S., 166–202. Oxford: Oxford University Press.CrossRefGoogle Scholar
Hale, B., and Wright, C.. 2008. “Abstraction and Additional Nature.” Philosophia Mathematica 16 (2): 182–208.CrossRefGoogle Scholar
Kim, J. 2011. “A Strengthening of the Caesar Problem.” Erkenntnis 75 (1): 123–136. 10.1007/s10670-011-9272-4.CrossRefGoogle Scholar
Kim, J. 2014. “Euclid Strikes Back at Frege.” Philosophial Quarterly 64 (254): 20–38. 10.1093/pq/pqt009.Google Scholar
Kim, J. forthcoming. “A Logical Foundation of Arithmetic.” Studia Logica. 10.1007/s11225-014-9551-6.Google Scholar
Lowe, E. J. 1997. “Objects and Criteria of Identity.” In A Companion to the Philosophy of Language, edited by Hale, B. and Wright, C., 613–633. Oxford: Blackwell.Google Scholar
Shapiro, S. 2003. “Prolegomenon to Any Future Neo-Logicist Set Theory: Abstraction and Indefinite Extensibility.” British Journal for the Philosophy of Science 54: 59–91.CrossRefGoogle Scholar
Stevens, S. S. 1946. “On the Theory of Scales of Measurement.” Science 103 (2684): 677–680.CrossRefGoogle ScholarPubMed
Williamson, T. 1990. Identity and Discrimination. Oxford: Basil Blackwell.Google Scholar
Wright, C. 1983. Frege’s Conception of Numbers as Objects. Aberdeen: Aberdeen University Press.Google Scholar
Wright, C. 1997. “On the Philosophical Significance of Frege’s Theorem.” In The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics, by Hale, B. and Wright, C., 272–306. Oxford: Clarendon Press.Google Scholar