Notre Dame Journal of Formal Logic

Logics of Relative Identity

Paweł Garbacz


This paper is the first part of an exploration into the logical properties of relative identity. After providing the semantic grounds for various monadic logics of relative identity, I define the minimal system and its nine extensions. It is suggested that despite their purely formal origin at least some of them may contain nontrivial philosophical insights. All logics are axiomatized by means of sound and complete sequent calculi. I show their affinities with existing formalizations.

Article information

Notre Dame J. Formal Logic Volume 43, Number 1 (2002), 27-50.

First available in Project Euclid: 15 December 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B60: Other nonclassical logic
Secondary: 03B80: Other applications of logic

relative identity indiscernibility


Garbacz, Paweł. Logics of Relative Identity. Notre Dame J. Formal Logic 43 (2002), no. 1, 27--50. doi:10.1305/ndjfl/1071505768.

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  • [1] Blizard, W. D., "Multiset theory", Notre Dame Journal of Formal Logic, vol. 30 (1989), pp. 36--66.
  • [2] Deutsch, H., "Identity and general similarity", pp. 177--99 in Philosophical Perspectives, XII, Language, Mind, and Ontology, edited by J. E.Tomberline, Blackwell Publishers, Cambridge, 1998.
  • [3] Ebbinghaus, H.-D., J. Flum, and W. Thomas, Mathematical Logic, 2d edition, Undergraduate Texts in Mathematics. Springer-Verlag, New York, 1994. Translated from the German by Margit Meß mer.
  • [4] Geach, P., "Identity", Review of Metaphysics, vol. 21 (1967), pp. 3--13.
  • [5] Geach, P., "Replies", pp. 276--99 in Peter Geach: Philosophical Encounter, edited by H. Lewis, Kluwer, Dordrecht, 1991.
  • [6] Griffin, N., Relative Identity, Clarendon Press, Oxford, 1977.
  • [7] Krause, D., "On a quasi-set theory", Notre Dame Journal of Formal Logic, vol. 33 (1992), pp. 402--11.
  • [8] Noonan, H. W., Objects and Identity: An Examination of the Relative Identity Thesis and its Consequences, Martinus Nijhoff Publishers, The Hauge, 1980.
  • [9] Noonan, H. W., "Relative identity: A reconsideration", Analysis, vol. 46 (1986), pp. 6--10.
  • [10] Noonan, H. W., "Relative identity", pp. 634--52 in A Companion to the Philosophy of Language, edited by B. Hale and C. Wright, Blackwell Publishers, Cambridge, 1996.
  • [11] Routley, R., and N. Griffin, "Towards a logic of relative identity", Logique et Analyse. Nouvelle Série, vol. 22 (1979), pp. 65--83.
  • [12] Stevenson, L., "A formal theory of sortal quantification", Notre Dame Journal of Formal Logic, vol. 16 (1975), pp. 185--207.
  • [13] Strawson, P., Individuals: An Essay in Descriptive Metaphysics, Methuen, London, 1959.
  • [14] van Inwagen, P., "And yet they are not three Gods but one God", pp. 222--59 in God, Knowledge, and Mystery, edited by P. van Inwagen, Cornell University Press, Ithaca, 1989.
  • [15] Wiggins, D., Sameness and Substance Renewed, 2d edition, Cambridge University Press, Cambridge, 2001.
  • [16] Zemach, E. M., "Schematic objects and relative identity", Noûs, vol. 16 (1982), pp. 295--305.
  • [17] Zemach, E. M., "In defence of relative identity", Philosophical Studies, vol. 26 (1974), pp. 207--18.
  • [18] Zemach, E. M., "Identity and open texture", Philosophia, vol. 13 (1983), pp. 255--62.