What exactly is the character of possible worlds and, more importantly, whence the ground of possibility for objects?
There are essentially two paths one might take of the character of possible worlds: concretism and abstractionism. The concretist, ala Lewis, understands possible worlds to be maximal collocations of spatio-temporally related objects. The abstractionist, ala Adams or Plantinga, understands possible worlds to be maximally consistent sets of propositions or states-of-affairs. Notice then that the abstractionist holds that there are two sorts of things in the Universe (where the term 'Universe' means the entirety of reality) - possible worlds and a concrete world to which these possible worlds might 'match-up'.
So, the concretist believes that all worlds are, so to speak, on the same playing field - each is just as 'real' as every other; hence the concretist's inherent commitment to an indexical analysis of actuality. The abstractionist however, believes that one possible world is privileged - only one world happens to match-up to the concrete world; of course, concretists have no need to have anything 'match-up' to anything else.
What then are these two conceptions' respective theories of the foundation of de re possibility? The concretists founds the de re possibilities of an object in its counterparts - those objects in different possible worlds which are qualitatively similar to the object in question. What makes it possible that an object x have a property P (one which it doesn't actually possess) is the fact that y, a qualitatively similar (but necessarily distinct) object existing in another possible world actually does have P.
The abstractionist, on the other hand, founds the de re possibilities of an object in a proposition which expresses a state of affairs containing the object actually possessing the property in question. What makes it possible that x possess P is that there (necessarily) exists a proposition which is part of a possible world of the form 'x has P'. This proposition being a part of a possible world just means, as Plantinga states, that if this possible world were actual (that is, if it did in fact match-up to the concrete world) then it would be the case that x would have P.
Now, although I think that there are plenty of problems for either view of possible worlds - I want to point out two pertinent ones here which I think go directly against our intuitional common sense.
The first is, why should we agree that the fact that some other object, wholly distinct from x and only related to it by way of it being merely qualitatively similar to it in certain respects, in virtue of it standing in some closed spatio-temporal relation to some other objects in another fully concrete world has any say whatsoever in the de re possibilities of x? The question is not the familiar objection to counterpart theory - namely "What's he got to do with me?" (though I think this is a valid and pertinent objection). Rather, the question is - what has concreteness and qualitative similarity in a counterpart have to do with grounding modal facts about objects?
Secondly, concerning abstractionism, why should we agree that a proposition in a 'Platonic Heaven' has any fundamental role in determining which things are possible for an object and which are not? The abstractionist seems to me rather to have things the wrong way around - it is the objects in the concrete world and their dispositional properties therein which ground whether or not there exist such propositions expressing states of affairs wherein they possess some certain property.
Besides this, why should we agree, with the abstractionist, that propositions which do not match-up with the concrete world even exist in any form whatsoever? Now, Plantinga certainly has independent motivation for holding this brand of abstractionism - his actualism entails, he thinks, the need to have an 'essence' which grounds the fact that there are propositions about non-existent individuals. But I am inclined to think, with Adams, that there are no singular propositions about non-actual individuals - these propositions supervene on actual existents. And I am also therefore inclined to think that propositions about an object x possessing a property P 'exist', but not, as it were, pre-objectually or extra-objectually.
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