(For David Brightly, whom I hope either to convince or argue to a standoff.)
Suppose God creates ex nihilo a bunch of TinkerToy pieces at time t suitable for assembly into various (toy) artifacts such as a house and a fort. A unique classical mereological sum -- call it 'TTS' -- comes into existence 'automatically' at the instant of the creation ex nihilo of the TT pieces. (God doesn't have to do anything in addition to creating the TT pieces to bring TTS into existence.) Suppose further that God at t assembles the TT pieces (adding nothing and subtracting nothing) into a house. Call this object 'TTH.' So far we have: the pieces, their sum, and the house. Now suppose that at t* (later than t) God annihilates all of the TT pieces. This of course annihilates TTS and TTH. During the interval from t to t* God maintains TTH in existence.
I set up the problem this way so as to exclude 'historical' and nonmodal considerations and thus to make the challenge tougher for my side. Note that TTH and TTS are spatially coincident, temporally coincident, and such that every nonmodal property of the one is also a nonmodal property of the other. Thus they have the same size, the same shape, the same weight, etc. Surely the pressure is on to say that TTH = TTS? Surely my opponents will come at me with their battle-cry, 'No difference without a difference-maker!' There is no constituent of TTH that is not also a constituent of TTS. So what could distinguish them?
Here is an argument that TTH and TTS are not identical:
1. NecId: If x = y, then necessarily, x = y.
2. If it is possible that ~(x = y), then ~(x = y). (From 1 by Contraposition)
3. If it is possible that TTS is not TTH, then TTS is not TTH. (From 2, by Universal Instantiation)
4. It is possible that TTS is not TTH. (God might have assembled the parts into a fort instead of a house or might have left them unassembled.)
5. TTS is not TTH. (From 3, 4 by Modus Ponens)
The gist of the argument is that if x = y, then they are identical in every possible world in which both of them exist. But there are possible worlds in which TTS and TTH both exist but are not identical. (E.g., a world in which the pieces are assembled into a fort instead of a house.) Therefore, TTS andf TTH are not identical.
If you are inclined to reject the argument, you must tell me which premise you reject. Will it be (1)? Or will it be (4)?
Your move, David.