Abstract
It is widely assumed that the identity relation is, among other things, transitive. Some have proposed that the identity relation might hold between objects contingently or occasionally. If, on those proposals, identity is shown to not be transitive, then there is reason to reject such proposals. One such argument attempts to show that the identity relation on such proposals violates transitivity in cases of ‘simultaneous’ fissions and fusion. I argue that, even in those cases, contingent identity and occasional identity are transitive.
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Notes
See Gallois (1998, pp. 69–70) for an argument that Occasional Identity implies Contingent Identity.
Names of objects are typeset in small-caps throughout. Principles and views are monospaced when first mentioned or defined.
A relation is said to be reflexive when every object stands in the relation to itself. More precisely and with respect to the identity relation:
- Reflexivity of Identity::
-
\(\forall x (x = x)\)
A relation is said to be symmetric when, for two objects, the first stands in the relation to the second just in case the second stands in it to the first. More precisely and with respect to identity:
- Symmetry of Identity:
-
\(\forall x \forall y (x = y \rightarrow y = x)\)
See, for example, Griffin (1977) for an argument that identity is relative, rather than absolute. See, for example, Parsons (2000) for an argument that identity is indeterminate, rather than absolute. See, for example, Cotnoir and Baxter (2014), Wallace (2011a) and Wallace (2011b) for discussions of the view that identity is composition, and as such is a many-one relation.
Here I do not say whether Leibniz’s Law is one of the Logical Principles of Identity or Metaphysical Principles of Identity. I think there are good reasons for either categorization. Elsewhere, I claimed that, when it comes to theory choice, it functions like the Logical Principles of Identity (de Araujo, 2021, chap. 1).
By “a case of Occasional Identity/Contingent Identity” I mean a case that, if it were true, would be sufficient for the truth of Occasional Identity or Contingent Identity, respectively.
The opponent of Contingent Identity would justify 1.3 and 1.4 by Reflexivity of Identity. Gallois (1998, pp. 76–77) would agree that 1.3 and 1.4 are true by the particulars of the case, but not in virtue of Reflexivity of Identity. While not discussed in Gallois (1998), an Occasional Identity theorist would, for reasons similar to relativizing Transitivity of Identity, only accept a reformulation of Reflexivity of Identity that fixes the principle to the same time. See Gallois (1998, pp. 91–92) for a discussion of reflexivity.
The argument has been adapted. The original uses descriptions instead of names to illustrate a different point.
Where @ is the actual world.
See above for a discussion of the justification for 2.3 and 2.4.
See Gilmore (2009) for an example of relativizing transitivity for his view that the parthood relation is four-place.
See van Inwagen (1981) for an argument against the assumption underlying this view.
It is also the case that by transitivity, amoeba is to the north of amoeba. This is because amoeba is pond which is to the north of tree which is to the north of slide which is identical to amoeba.
The particular formulation of this is given on p. 129. And for structurally similar reasons, he argues that necessary properties should be understood relative to (i) the world at which the object is said to have the necessary property and to (ii) all worlds (Gallois, 1998, Chap. 6).
When presented (on p. 84), this is considered along with a variation that replaces the existential quantifier that binds the y variable in the right-hand side of the biconditional with a universal quantifier. On this understanding of temporally indexed properties, to have such a property is for everything that an object is identical to at that time to have the property at another time. Arguably, while objects might have temporally indexed properties in this sense, these construals cannot capture some temporally indexed properties that Occasional Identity theorists might want to capture. Gallois officially accepts that there might be some properties that are best captured under this formulation. However, in the case of eternal properties, he argues that the formulation with an existential quantifier best captures what it means for an object to have eternal properties. Further, he suggests that his interpretations of eternal properties and temporally indexed properties naturally come together. If this is so, then there is reason to accept the existential formulation rather than the universally quantified one.
Such defenses are given in Chaps. 3 and 5.
I have argued (de Araujo, 2021, chap. 2) that Gallois could harmonize the response I propose here with his preferred view of instantiation (Gallois, 1998, p. 38). Thank you to an anonymous reviewer for this journal for pointing out that the particular proposal presented there could be separated from the response to Bader’s objection.
It might be suggested that we should also bind \(x_1\) and \(x_2\) to the same quantifier, and further, bind \(z_1\) and \(z_2\) to the same quantifier. Although I do not think a counterexample demonstrating the inadequacy of this current formulation is forthcoming, I do not see why such a reformulation that binds those variables would be objectionable. Such a formulation was in fact suggested by an anonymous reviewer for this journal.
References
Bader, R. M. (2012). The non-transitivity of the contingent and occasional identity relations. Philosophical Studies, 157, 141–52.
Cotnoir, A. J., & Baxter, D. L. M. (Eds.). (2014). Composition as identity. Oxford University Press.
Frege, G. (1892). Über Sinn und Bedeutung. Zeitschrift fur Philosophie und philosophische Kritik, 100, 25–50. Translated as “On Sinn and Bedeutung" by Max Black in Translations from the Philosophical Writings of Gottlob Frege, Peter Geach and Max Black (Eds.). Oxford: Blackwell, 1952. Reprinted in Micheal Beaney (Ed.), The Frege Reader, pp. 151–71. Oxford: Blackwell (1997).
Gallois, A. (1998). Occasions of identity: A study in the metaphysics of persistence, change, and sameness. Clarendon Press.
Gibbard, A. (1975). Contingent identity. Journal of Philosophical Logic, 4, 187–222.
Gilmore, C. (2009). Why parthood might be a four-place relation, and how it behaves if it is. In L. Honnefelder, E. Runggaldier, & B. Schick (Eds.), Unity and time in metaphysics (pp. 83–133). Walter de Gruyter.
Griffin, N. (1977). Relative identity. Clarendon Press.
Hawthorne, J. (2003). Identity. In M. J. Loux & D. W. Zimmerman (Eds.), The Oxford handbook of metaphysics (pp. 99–130). Oxford University Press.
Kripke, S. A. (1971). Identity and necessity. In M. K. Munitz (Ed.), Identity and individuation (pp. 135–64). New York University Press.
Parsons, T. (2000). Indeterminate identity: Metaphysics and semantics. Clarendon Press.
van Inwagen, P. (1981). The doctrine of arbitrary undetached parts. Pacific Philosophical Quarterly, 62, 123–37.
Wallace, M. (2011). Composition as identity: Part 1. Philosophy Compass, 6, 804–16.
Wallace, M. (2011). Composition as identity: Part 2. Philosophy Compass, 6, 817–27.
de Araujo, Eric (2021). Distinct samenesses: Essays on non-standard views of identity. Dissertation, The Ohio State University.
Acknowledgements
Thank you to Ben Caplan, Julia Jorati, Kevin Scharp, and William Taschek for helpful comments on and discussions of previous versions of this paper, and to the anonymous reviewers for this journal for their helpful comments.
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de Araujo, E. Transitivity When the Same are Distinct. Erkenn 88, 2893–2909 (2023). https://doi.org/10.1007/s10670-021-00482-x
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DOI: https://doi.org/10.1007/s10670-021-00482-x