It is a commonsense thesis that unactualized possibilities are not parts of actuality. To keep his modal realism in line with this thesis, David Lewis employed his indexical account of the term “actual.” I argue that the addition of counterpart theory to Lewis’s modal realism undermines his strategy for respecting the commonsense thesis. The case made here also reveals a problem for Lewis’s attempt to avoid haecceitism.
Thanks to Sam Cowling and Adam Podlaskowski for helpful feedback on earlier drafts of this paper.
Lewis, D. 1983. Philosophical Papers, Vol. I. Oxford: Oxford University Press.Search in Google Scholar
Lewis, D. 1986. On the Plurality of Worlds. Oxford: Basil Blackwell.Search in Google Scholar
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Skow, B. 2008. “Haecceitism, Anti-Haecceitism, and Possible Worlds.” The Philosophical Quarterly58:97–107.Search in Google Scholar
Sometimes (e.g. 1986, 99) Lewis does not explicitly include the qualification “unactualized.” It is evident from Lewis’s discussion of the thesis, however, that he is concerned with unactualized possibilities. Indeed, otherwise the thesis is plainly false. Clearly some possibilities can be parts of actuality, as is the case with respect to the possibility of you reading this paper. It is unactualized possibilities that are taken to be separate from actuality.
Lewis formally presents the postulate in the following way: P5: ∀x∀y∀z(Ixy & Izy & Cxz. ⊃ x = z). The English readings of the predicates Ixy and Cxy are “x is in possible world y” and “x is a counterpart of y,” respectively (Lewis 1968, 114).
Moreover, note that some possibilities might initially seem to require quantification over sets, when in fact they do not. For example, Lewis (1983, 44) applies counterpart theory to the issue of whether a pair of twin brothers might have been born not as twins but, rather, as unrelated inhabitants of separate planets. Instead of taking a set of which the brothers are members, Lewis takes the mereological sum of the pair of brothers (which is wholly in a possible world). Indeed, it would seem that Lewis’s general preference for counterpart theory is to quantify only over individuals that are wholly in a possible world: “The language of counterpart theory, and the modal language it replaces, had best be understood as quantifying only over possible individuals [i.e. individuals that are wholly in a possible world]. Modifications are called for if we wish to quantify over more of what there is” (1983, 40).
For a helpful discussion of various formulations of haecceitism, including Lewis’s, see Bradford Skow (2008).
For a recent attempt to make sense of a non-qualitative counterpart relation, see Cowling’s (2012) employment of substratum theory.
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