Abstract
On the one hand, philosophers have presented numerous apparent examples of indeterminate individuation, i.e., examples in which two things are neither determinately identical nor determinately distinct. On the other hand, some have argued against even the coherence of the very idea of indeterminate individuation. This paper defends the possibility of indeterminate individuation against Evans’s argument and some other arguments. The Determinacy of Identity—the thesis that identical things are determinately identical—is distinguished from the Determinacy of Distinctness—the thesis that distinct things are determinately distinct. It is argued that while the first thesis holds universally and there is no case of indeterminate identity, there are reasons to think that the second thesis does not hold universally, and that there are cases of indeterminate distinctness.
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Notes
The issue of vague identity is discussed in the papers in Akiba and Abasnezhad (2014, Sect. 5).
Thus, we have changed our mind on this issue.
In an admissible manner—but this qualification is henceforth omitted for the sake of simplicity.
In fact, there is a simple quasi-Evans argument against indeterminate distinctness that uses not Axiom B but Axiom 5: \(\lnot {\Delta } p\rightarrow {\Delta } \lnot {\Delta } p\), which is supported by the euclidean accessibility relation: \(wR{w}'\wedge wR{w}''\Rightarrow {w}'R{w}''\). Take any precisification \(w\) (possibly @). If, for some \(a\) and \(b\), \(\lnot {\Delta } a=b\wedge \lnot {\Delta } \lnot a=b\) at \(w\), then there is a precisification \({w}'\) of \(w\) (i.e., \(wR{w}'\)) at which \(a=b\), and there is a precisification \({w}''\) of \(w\) (i.e., \(wR{w}''\)) at which \(\lnot a=b\). But, by DI, \({\Delta } a=b\) at \({w}'\). By the euclidean accessibility relation, \({w}'R{w}''\); thus, \(a=b\) at \({w}''\), contradicting \(\lnot a=b\). QED. However, this argument does not hold up because the ‘is a precisification of’ relation cannot be euclidean, as we just saw. We thank Ali Abasnezhad (in correspondence) for showing us a similar reductio proof in the modal system K45.
This interpretation is adopted most explicitly by Williamson (1999), although he does not commit himself exclusively to it and considers other possibilities. Some, such as Dummett (1975), Salmon’s (1981), and Greenough (2003), adopt the same interpretation or similar interpretations. Our interpretation is close to Fine (1975), though we develop it in a different direction.
Nor shall we decide between our interpretation and the interpretation given in Barnes and Williams (2011), which sets forth a generally ontic theory of indeterminacy but embraces S5 modality as the logic of ‘determinately’.
Williamson (2002, p. 293) gives a proof that uses Axioms K and T (i.e., in the modal system KT), but K is in fact not necessary.
References
Akiba, K. (2000a). Vagueness as a modality. Philosophical Quarterly, 50, 359–370.
Akiba, K. (2000b). Identity is simple. American Philosophical Quarterly, 37, 389–404.
Akiba, K. (2004). Vagueness in the world. Noûs, 38, 407–429.
Akiba, K. (2014). Introduction. In Akiba and Abasnezhad (2014, pp. 1–21).
Akiba, K., & Abasnezhad, A. (Eds.). (2014). Vague objects and vague identity. Dordrecht: Springer.
Barcan, R. (1947). The identity of individuals in a strict functional calculus of second order. Journal of Symbolic Logic, 12, 12–15.
Barnes, E. (2009). Indeterminacy, identity and counterparts: Evans reconsidered. Synthese, 168, 81–96.
Barnes, E., & Williams, J. R. G. (2011). A theory of metaphysical indeterminacy. In K. Bennett & D. W. Zimmerman (Eds.), Oxford studies in metaphysics (Vol. 6, pp. 103–148). Oxford: Oxford University Press.
Bobzien, S. (2012). If it’s clear, then it’s clear that it’s clear, or is it? Higher-order vagueness and the S4 axiom. In B. Morison & K. Ierodiakonou (Eds.), Episteme, etc.: Essays in honor of Jonathan Barnes (pp. 189–212). Oxford: Oxford University Press.
Dummett, M. (1975). Wang’s paradox. Synthese, 30, 301–324.
Edgington, D. (2000). Indeterminacy de re. Philosophical Topics, 28, 27–44.
Evans, G. (1978). Can there be vague objects? Analysis, 38, 208.
Field, H. (2000). Indeterminacy, degree of belief, and excluded middle. Noûs, 34, 1–30.
Fine, K. (1975). Vagueness, truth and logic. Synthese, 30, 265–300.
Geach, P. (1962). Reference and generality. Ithaca, NY: Cornell University Press.
Gibbard, A. (1975). Contingent identity. Journal of Philosophical Logic, 4, 187–222.
Greenough, P. (2003). Vagueness: A minimal theory. Mind, 112, 235–281.
Hawley, K. (2002). Vagueness and existence. Proceedings of Aristotelian Society, 102, 125–140.
Hughes, G. E., & Cresswell, M. J. (1996). A new introduction to modal logic. London: Routledge.
Kripke, S. (1971). Identity and necessity. In M. Munitz (Ed.), Identity and individuation (pp. 135–164). New York: New York University Press.
Lewis, D. (1988). Vague identity: Evans misunderstood. Analysis, 48, 128–130.
Lewis, D. (1993). Many, but almost one. In K. Campbell, J. Bacon, & L. Reinhardt (Eds.), Ontology, causality, and mind (pp. 23–38). Cambridge: Cambridge University Press.
Marcus, R. (1961). Modality and intensional languages. Synthese, 13, 303–322.
Parsons, T. (1987). Entities without identity. Philosophical Perspectives, 1, 1–19.
Parsons, T. (2000). Indeterminate identity. Oxford: Oxford University Press.
Parsons, T., & Woodruff, P. (1995). Worldly indeterminacy of identity. Proceedings of the Aristotelian Society, 95, 171–191.
Salmon, N. (1981). Reference and essence. Princeton: Princeton University Press.
Shoemaker, S. (1963). Self-knowledge and self-identity. Ithaca, NY: Cornell University Press.
Shoemaker, S., & Swinburne, S. (1984). Personal Identity. Oxford: Blackwell.
Smith, N. J. J. (2008). Why sense cannot be made of vague identity. Noûs, 42, 1–16.
van Inwagen, P. (1988). How to reason about vague objects. Philosophical Topics, 16, 255–284.
Weatherson, B. (2003). Many, many problems. Philosophical Quarterly, 53, 481–501.
Williams, J. R. G. (2008). Multiple actualities and ontically vague identity. Philosophical Quarterly, 58, 134–154.
Williamson, T. (1996). The necessity and determinacy of distinctness. In S. Lovibond & S. G. Williams (Eds.), Essays for David Wiggins: Identity, truth and value (pp. 1–17). Oxford: Blackwell.
Williamson, T. (1999). On the structure of higher-order vagueness. Mind, 108, 127–143.
Williamson, T. (2002). Vagueness, identity and Leibniz’s law. In A. Bottani, M. Carrara, & P. Giaretta (Eds.), Individual essence and identity (pp. 273–304). Dordrecht: Kluwer.
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Akiba, K. A defense of indeterminate distinctness. Synthese 191, 3557–3573 (2014). https://doi.org/10.1007/s11229-014-0462-x
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DOI: https://doi.org/10.1007/s11229-014-0462-x