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Can Identity Be Relativized?

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The Road to Universal Logic

Part of the book series: Studies in Universal Logic ((SUL))

Abstract

What is the scope of identity? The intuitive response is that it applies everywhere, since every object is identical to itself. In this sense, identity is a general concept. In this chapter, I argue for the generality of identity by critically examining some attempts at relativizing it. I argue that each alleged instance of relativization ultimately presupposes identity, and as a result, identity still stands – in all of its un-relativized glory.

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Notes

  1. 1.

    Considerations in support of the unsubstantial character of identity can be found in [1].

  2. 2.

    The assumption is not unreasonable. Consider a physical magnitude, such as gravitational potential in field theories, and suppose that each value of this magnitude is a particular property. In this case, as one moves away from the source of the field, the field intensity decreases continuously. As a result, there would be uncountably many properties (see [10]). A far more controversial illustration would be this: Consider the properties identical to the real number 0, identical to the real number 1, identical to the real number 2, and so on. Note that each property of this kind is a property only of the corresponding number: identical to 0 is a property of 0, and 0 alone; identical to 1 is a property of 1, and 1 alone, etc. Since there are uncountably many real numbers, there are uncountably many properties. Identity already figures here, as it should, as an extremely general (relational) property; in fact, it is arguably the most general one. It may be complained that identity is not a property, but a relation of an object to itself and to no other object (see, for instance, [11]). But this clearly presupposes identity [2]: the reference to “no other object” requires that there is no object distinct (that is, not identical to) the one under consideration. And it is unclear what else identity could be.

  3. 3.

    For discussions of absolute generality, see the papers in [7].

References

  1. Bueno, O.: Why Identity is Fundamental. Am. Philos. Q. 51, 325–332 (2014)

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  2. Deutsch, H.: Relative identity. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (Winter 2008 Edition). (2008). http://plato.stanford.edu/archives/win2008/entries/identity-relative

  3. French, S. Krause, D.: Identity in Physics: A Historical, Philosophical, and Formal Analysis. Clarendon Press, Oxford (2006)

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  4. Krause, D., Béziau, J.-Y.: Relativizations of the Principle of Identity. Log. J. Interest Group Pure Appl. Log. 5, 327–338 (1997)

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  5. McGinn, C.: Logical Properties. Clarendon Press, Oxford (2000)

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  6. Mendelson, E.: Introduction to Mathematical Logic, 4th edn. Chapman and Hall, London (1997)

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  7. Rayo, A., Uzquiano, G. (eds.): Absolute Generality. Clarendon Press, Oxford (2006)

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  8. Savellos, E.: On Defining Identity. Notre Dame J. Form. Log. 31, 476–484 (1990)

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  9. Shapiro, S.: Foundations without Foundationalism. Oxford University Press, Oxford (1991)

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  10. Swoyer, C., Orilia, F.: Properties. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (Fall 2014 Edition). (2014). http://plato.stanford.edu/archives/fall2014/entries/properties

  11. Zalabardo, J.: Introduction to the Theory of Logic. Westview Press, Boulder (2000)

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Acknowledgment

My thanks go to Jean-Yves Béziau, Newton da Costa, Steven French, Décio Krause, and Alan Weir for extremely helpful discussions. It is a pleasure to offer this paper to Jean-Yves on the occasion of his 50th birthday. It still feels as though it was only yesterday that he arrived for the first time in Brazil to change so much of the logical landscape in the country – and elsewhere. It’s surprising that two decades have already passed since then!

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Authors and Affiliations

  1. Department of Philosophy, University of Miami, Coral Gables, USA

    Otávio Bueno

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  1. Otávio Bueno
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Correspondence to Otávio Bueno .

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Editors and Affiliations

  1. City University of New York, New York, New York, USA

    Arnold Koslow

  2. Federal University of Santa Catarina, Florianópolis, Santa Catarina, Brazil

    Arthur Buchsbaum

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To Jean-Yves Béziau

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Bueno, O. (2015). Can Identity Be Relativized?. In: Koslow, A., Buchsbaum, A. (eds) The Road to Universal Logic. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-15368-1_11

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