Armstrong's Number-of-Parts Essentialism
Here's an odd passage from Armstrong's A Combinatorial Theory of Possibility, p.116:
[Hume's Distinct Existences Principle], as we shall uphold it, may be stated thus:
If A and B are wholly distinct existences, then it is possible for A to exist while no part of B does (and vice versa).The principle applies straightforwardly to individuals, properties and relations. [...]
It is interesting to notice that the converse of Hume's principle also seems to be true:
If it is possible for A to exist while no part of B does (and vice versa), then A and B are wholly distinct existences.
These two principles appear to entail a rather interesting form of essentialism.
The first principle entails that nothing is essentially related to anything else (because it could exist without that other thing). So origin etc. aren't essential. Armstrong accepts this; in fact, on pp.51-53, he argues that Russell (qua thin particular) has no non-trivial essential properties at all.
The second principle seems to contradict that: it entails that everything has all its parts essentially: if B is part of A, then A and B are not wholly distinct, so by the second principle, it is impossible for A to exist without B (or for B to exist without A).
But if these parts don't have any non-trivial essential properties, this isn't much of a constraint: Russell's nose is an essential part of Russell, but since Russell's nose could have been a trumpet, it doesn't follow that Russell essentially had a nose. His only non-trivial essential property would have been the number of his parts.
(OK, this almost certainly isn't (and wasn't) Armstrong's real view. For one, there's also Russell qua thick particular who has all his non-relational properties essentially. More importantly, I think Armstrong was just careless here and forgot to formulate the first principle in terms of duplicates. Not sure what he meant by the second one, though: I can't believe he wanted to endorse mereological essentialism.)
Armstrong isn't averse to mereological essentialism: some recent stuff appears to endorse m.e., with counterpart theory presented not as an analysis of de re modalizing, but as a way of finding something in the vicinity of de re modalizing that has a chance of being true. Pretty natural attitude if you buy the Humphrey argument I guess (and aren't too fussed about charity).
But I think the stuff you quote is earlier, anyway.
cheers