Malezieu’s principle is that if the things exist, then the oset exists. If a exists (singular) and b exists (singular), then a and b exist (plural) , and the oset O (i.e. a and b) exists also. If some or all of the elements do not exist, or cease to exist then the oset does not exist, or ceases to exist, also. The reference of ‘that dozen eggs’ fails as soon as even one egg is broken. This contrasts with set theory, where we have to postulate the existence of a set containing the members.
Thus there cannot be two possible worlds, each of which contains a and b, such that the oset of a and b exists in one possible world, but not the other. This has the following corollary
(M) If an oset exists in one possible world but not another, it follows that at least one of its elements is in the first world, that is not in the other.This leads to the problem of the infinite universe where there is no oset corresponding to the infinitely many elements. If we allow the possibility at all, it follows from (M) above that there cannot be two possible worlds where any element one is identical with some element in the other, but where the oset of all of them exists in one, but not the other. Either such a world is impossible, or every infinite world is like this. If it is impossible, then Oxinf is not independent – if every finite oset excludes at least one thing, unlike set theory this guarantees the existence of infinite oset. But if it is possible, this rules out infinite osets.