It is shown that counterpart theory and the duplication account of intrinsicality—two key pieces of the Lewisian package—are incompatible. In particular, the duplication account yields the result that certain intuitively extrinsic modal properties are intrinsic. Along the way I consider a potentially more general worry concerning certain existential closures of internal relations. One conclusion is that, unless the Lewisian provides an adequate alternative to the duplication account, the reductive nature of their total theory is in jeopardy.
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This is not to say Perfect is the better formulation, for it relies on the contentious notion of perfect naturalness, whereas Disjunctive can get away with the less contentious notion of comparative naturalness.
Whether the example is of a highly theoretical sort depends on whether the notion of duplication is, and for the DA proponent (e.g. Lewis), it must be since she cannot define duplication as one ordinarily would in terms of the sharing of intrinsic properties (as that would be circular). I don’t know of any ordinary sense of duplication that does not appeal to intrinsicality, so the DA proponent can only be working with a theoretical notion. (Lewis’s proposal is obviously very theory-laden.)
One axiom of Lewis’s counterpart theory of Lewis (1968) (viz. P5) is that nothing is a counterpart of a distinct worldmate. Though Lewis speaks of the counterpart relation as being internal, P5 rules it out. I don’t think this affects what I have to say since there are strong, independent reasons for doing away with P5. Lewis himself later rejects the axiom (see [Lewis (1986, fn. 22)]) to get a cheap alternative to haecceitism. From hereon I reject P5 from having axiom status, though I don’t deny that some contexts will determine a counterpart relation satisfying the axiom.
To reemphasize, I see the problem I raise as involving properties picked out by our ordinary vernacular, unlike theoretical properties such as being a duplicate of at least one non-overlapping individual (on which, see footnote 2). It should be made clear, then, that the problem I’m about to raise does not rest on examples like being possibly bent-qua-merely-shaped-object. All that is needed is that there is a context and some x such that a property like being possibly bent involves only counterpart relations that are internal, when restricted to x and its counterparts. Under some contexts, e.g. those where we care only about the shapes of things, even being possibly bent will involve only internal counterpart relations. A nice feature of being possibly bent-qua-merely-shaped-object is that the relevant counterpart relations will always be internal, restricted or not, no matter the context. Thanks to an anonymous referee for getting me to clarify these matters.
The necessary property of being such that every number has two successors is intuitively extrinsic but deemed intrinsic according to DA. Instead of saying that it is harmless to apply DA more widely to cover necessary properties, which it certainly is not, Langton and Lewis should have said that it is harmless to restrict the account by excluding necessary and impossible properties.
Non-transitivity of the counterpart relation allows the possibility for there being x, y, and z such that (i) y is x’s counterpart while z is y’s but not x’s; (ii) y has \(\phi \) and hence x has \(\Diamond \phi \); (iii) none of y’s counterparts has \(\phi \) and hence x doesn’t have \(\Box \Diamond \phi \). I take the example just given of possibly having fewer atoms to be a legitimate instance of \(\phi \), but here is another example perhaps more plausible for some. Consider the property had by a mere lump or sum x of many atoms. Plausibly x has a one-atom counterpart y—imagine a scenario in which the lump could’ve been reduced to a single atom. Then x could have had fewer atoms, but one of its counterparts, y, could not have had fewer atoms. So x has a modal property non-essentially. This example requires (plausibly I think) denying mereological essentialism.
See [Lewis (1986, pp. 202–206)] for discussion.
Thanks to an anonymous referee for pressing this point.
Regarding the ‘consists in’ relation, he says: “I propose that we view the consists-in relation as being nothing less than identity; the event or state, x’s having F, consists in the event or state, x’s having G, just in case x’s having F is the very same event or state as x’s having G” [Francescotti (1999, p. 599)].
Francescotti uses ‘x is distinct from y’ to mean ‘x is not a (possibly improper) part of y’. I’ve chosen to use the latter so as to make this clear without introducing another definition.
In general, a property \(\phi \) is independent of another \(\psi \) iff it is possible for: (i) a \(\phi \) to have \(\psi \), (ii) a \(\phi \) to lack \(\psi \), (iii) a \(\psi \) to lack \(\phi \), (iv) something to lack both \(\phi \) and \(\psi \).
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I would like to thank the audiences at Utrecht University, SIFA 2012 (Italy), the Northern Institute of Philosophy, and the University of St Andrews. I would also like to thank, in particular, Ralph Bader, Julia Langkau, Thomas Müller, and Elia Zardini, for very helpful discussion. This research was funded by the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement nr 263227.
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De, M. Intrinsicality and counterpart theory. Synthese 193, 2353–2365 (2016). https://doi.org/10.1007/s11229-015-0847-5
- Counterpart theory