Against quidditism

modal realism is incompatible with quidditism, for we cannot have two structures which are structurally indistinguishable but nevertheless distinct. (Lewis argues this in some detail [10, pp. 158-65], though of course he takes it as a reason for rejecting abstract modal realism.) Must, conversely, the concrete modal realist be a quidditist? I think not. One could regard other possible worlds as concrete while rejecting any identity of fundamental properties across possible worlds---either by insisting that questions about the identity of properties only make sense within a world or, probably more easily, by insisting that no fundamental property is found in more than one world, the other possible worlds containing only counterparts of this-worldly properties, just as, for the anti-haecceitist, they contain only counterparts of this-worldly individuals. (Alternatively, work with tropes, and deny that there is any cross-world matching of tropes.) A concrete modal realism of this kind would work in almost exactly the same way as abstract modal realism, since on this view two possible worlds which share the same abstract structure become indiscernible. 18 Now it is (and ought to be felt as) an embarrassment for concrete modal realism, both in quidditist and antiquidditist versions, that it allows indiscernible worlds. Given a concrete possible world, how many exact copies of it are there out there in logical space? An arbitrary answer like 'seventeen' seems ruled out by the thought that there could have been (and therefore are) more but also by the same argument there could have been (and therefore are) fewer! The only two non-arbitrary answers would appear to be 'one' and 'proper-class many'. And here even these look arbitrary, for i f there is only one, why couldn't there have been more, and if proper-class many, why couldn't there have been fewer? 19 If, however, we are talking about abstract structures, this problem disappears, since identity of indiscernibles applies. If we are talking not about worlds, but about types of world, then it is trivial that there is exactly one type of each type. Thus the move fi'om concrete to abstract modal realism in this respect provides a cleaner and more elegant theory. I am inclined to think that in almost all respects it provides a cleaner and more elegant theory. For example, just as the antihaecceitist can avoid having to give straight answers to unanswerable questions such as whether the Queen could have come from a different sperm and egg ([6, pp. 112-3]; cf. [10, pp. 251-2]), so the antiquidditist can avoid giving straight answers to unanswerable questions such as whether gravitational attraction is necessarily inverse-square (if we accept a force obeying Newtunian laws except that the exponent is -2.1 rather than -2 as a counterpart of gravity, then no; i f we insist that any counterpart must arise as the limiting case of an Einstein-type theory, then probably yes). There is perhaps one advantage which Lewis claims for concrete modal realism and which I cannot claim for the abstract form, namely a reductive analysis of modality. I cannot claim it, because what mathematical structures there are is a matter of what is logico-mathematically possible. So logico-mathematical necessity/possibility has to be in ~8 I am using this term, as Lewis does, to deny difference, not to deny perceptible difference. 19 Lewis concedes [10, p. 224 fn. ] that the question shouldn't have an arbitrary answer, but he doesn't, at least to my satisfaction, explain how any answer could fail to be arbitrary.