By Benedikt Paul Göcke (auth.)
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Extra info for A Theory of the Absolute
We based our understanding of metaphysical possibility on the intuition that one and the same particular, at least sometimes, could have had properties other than the ones it actually exemplifies. ’ Our answer was that particulars could indeed have exemplified different properties if another possible world had been actual. One could object to this that it begs the question against Lewis’s account of possible worlds. If Lewis’s modal realism is a correct representation of possible worlds, it follows that this intuition concerning contingent property exemplification is mistaken, because there is no transworld identity and particulars could not have exemplified properties other than the ones they in fact exemplify.
This in turn is because it is difficult to express the ‘extra’ (or ‘more of’ being or existence) which is given by the obtaining of a state of affairs in contrast to and ‘over and above’ what is given in by the non-obtaining of a state of affairs. The difference between obtaining and non-obtaining states of affairs cannot be that we cannot think about non-obtaining states of affairs. I think about the non-actual tree with four branches as well as the actual tree with three branches. The reason this is possible is that, insofar as they are both objects of the understanding, obtaining and non-obtaining states of affairs are both accessed under a particular conceptual grasp that does not differentiate between the actual and the merely possible existence of the particular in question.
Formally: ڿx (p=x)ۀ. ‘Peter exists’ is true if and only if there is an object in the universe of discourse that is identical with Peter. If we deploy this approach to the putative non-existence of Santa Claus, prima facie we dissolve the contradiction: the assertion that Santa Claus does not exist no longer means that there exists an object which exemplifies non-existence. Rather, 40 A Theory of the Absolute it means that it is not the case that there is at least one object in the universe of discourse, which is identical with Santa Claus: ¬ڿx (x=s)ۀ.