Compare: Is there such a thing as the number 2? Does the number 2 exist?
This is arguably not a valid argument: It is possible for the the premise to be true and the conclusion false. In fact, the premise is true and the conclusion is false. If this argument is not valid, then perhaps the first one is not valid either.
First note that among the claims below, (1) entails but is not entailed by (2), (3) and (4); and (2) and (3) entail but are not entailed by (4):
Then the argument goes like this:
If this is to help us understand what it is for two sets to be identical, then it should not assume a prior understanding of what it is for two sets to be indentical (i.e. it should not be circular). This does seem to be the case: even if, when comparing the members of two sets, some of those members are themselves sets, we can just apply the criterion again, with no fear of an infinite regress.
Lowe offers a counterexample: Three opposing armies are fighting pair-wise with each other in the same location at the same time. So three distinct battles (and thus events) are occurring in the same location at the saand me time.
And another one: Three point particles collide, so there are three distinct collisions (and thus events) occurring at the same location and at the same time.
But if the causes and effects of an event are themselves events then this proposal seems to be circular: checking whether the causes (or effects) of one event are identical to the causes (effects) of another event assumes an understanding of what it is for two events to be identical (perhaps even the original two events themselves), and appealing to the criterion again will start us on an infinite regress. Is this right?
And we might also have trouble with the following world: there are just five events; e1 causes e3 and e4, e2 causes e4 and e5. The concern is that this only distinguishes event e4; it does not distinguish e1 from e2, and it does not distinguish e3 from e5.
(Note that this gives us a criterion of identity: