Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T20:48:05.393Z Has data issue: false hasContentIssue false
  • English
  • Français

IDENTITY AND INDISCERNIBILITY

Published online by Cambridge University Press:  07 June 2011

JEFFREY KETLAND
JEFFREY KETLAND*
Affiliation:
Department of Philosophy, University of Edinburgh
*
*JEFFREY KETLAND DEPARTMENT OF PHILOSOPHY UNIVERSITY OF EDINBURGH EDINBURGH UNITED KINGDOM. E-mail:[email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The notion of strict identity is sometimes given an explicit second-order definition: objects with all the same properties are identical. Here, a somewhat different problem is raised: Under what conditions is the identity relation on the domain of a structure first-order definable? A structure may have objects that are distinct, but indiscernible by the strongest means of discerning them given the language (the indiscernibility formula). Here a number of results concerning the indiscernibility formula, and the definability of identity, are collected and a number of applications discussed.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 4 , Issue 2 , June 2011 , pp. 171 - 185
Copyright
Copyright © Association for Symbolic Logic 2011

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

BIBLIOGRAPHY

Black, M. (1962). The identity of indiscernibles. Mind, 61, 153–164.Google Scholar
Burgess, J. P. (1999). Review of Shapiro 1997. Notre Dame Journal of Formal Logic, 40, 283–291.Google Scholar
Cortes, A. (1976). Leibniz’s principle of identity of indiscernibles: A false principle. Philosophy of Science, 45, 466–470.Google Scholar
Frege, G. (1891). Review of E. Husserl 1891, Philosophie der Arithmetik. Extracts reprinted in Geach, & Black, (eds.) 1980; Translations from the Philosophical Writings of Gottlob Frege (third edition). New Jersey, NJ: Barnes and Noble.Google Scholar
French, S., & Redhead, M. (1988). Quantum physics and the identity of indiscernibles. British Journal for the Philosophy of Science, 39, 233–246.CrossRefGoogle Scholar
Hilbert, D., & Bernays, P. (1934). Grundlagen der Mathematik, Vol. 1. Berlin: Springer.Google Scholar
Hodges, W. (1997). A Shorter Model Theory. Cambridge, MA: Cambridge University Press.Google Scholar
Keränen, J. (2001). The identity problem for realist structuralism. Philosophia Mathematica, 3, 308–330.CrossRefGoogle Scholar
Ketland, J. (2006). Structuralism and the identity of indiscernibles. Analysis, 66, 303–315.CrossRefGoogle Scholar
Ladyman, J. (2005). Mathematical structuralism and the identity of indiscernibles. Analysis, 62, 218–221.CrossRefGoogle Scholar
Leitgeb, H., & Ladyman, J. (2008). Criteria of identity and structuralist ontology. Philosophia Mathematica, 16, 388–396.CrossRefGoogle Scholar
Manzano, M. (1996). Extensions of First-Order Logic. Cambridge Tracts in Theoretical Computer Science. Cambridge, MA: Cambridge University Press.Google Scholar
Quine, W. V. (1960). Word and Object. Cambridge, MA: MIT Press.Google Scholar
Quine, W. V. (1962). Reply to Professor Marcus. Synthese, 20. Page references are to the reprint in W. V. Quine 1976, The Ways of Paradox (revised edition). Cambridge, MA: Harvard University Press.Google Scholar
Quine, W. V. (1976). Grades of Discriminability. Journal of Philosopy, 73. Reprinted in W. V. Quine 1981, Theories and Things (Cambridge, MA: Harvard University Press), pp. 129–133.Google Scholar
Quine, W. V. (1986). Philosophy of Logic (second edition). Cambridge, MA: Harvard University Press.CrossRefGoogle Scholar
Saunders, S. (2002). Indiscernibles, general covariance and other symmetries: The case for non-eliminativist relationism. In Ashtekar, A., Howard, D., Renn, J., Sarkar, S., & Shimony, A., editors. Revisiting the Foundations of Relativistic Physics: Festschrift in Honour of John Stachel. Dordrecht, The Netherlands: Kluwer.Google Scholar
Saunders, S. (2003). Physics and Leibniz’s principles. In Castellani, E., and Brading, K., editors. Symmetries in Physics: Philosophical Reflections, Cambridge, MA: Cambridge University Press.Google Scholar
Savellos, E. (1990). On defining identity. Notre Dame Journal of Formal Logic, 31, 476–484.CrossRefGoogle Scholar
Shapiro, S. (1991). Foundations without Foundationalism: A Case for Second-Order Logic. Oxford: Oxford University Press.Google Scholar
Shapiro, S. (1997). Philosophy of Mathematics: Structure and Ontology. Oxford: Oxford University Press.Google Scholar
Shapiro, S. (2008). Identity, indiscernibility and ante rem structuralism: The tale of i and – i. Philosophia Mathematica, 16, 285–309.CrossRefGoogle Scholar
Tarski, A. (1959). What is elementary geometry? In Henkin, L., Suppes, P., and Tarski, A., editors. The Axiomatic Method, Amsterdam, The Netherlands: North Holland, pp. 16–29. Page references are to the reprint in J. Hintikka (ed.) 1968, Philosophy of Mathematics. Oxford: Oxford University Press.CrossRefGoogle Scholar
van Dalen, D. (1994). Logic and Structure. Berlin: Springer.CrossRefGoogle Scholar