What is time? Don't ask me, and I know. Ask me, and I don't know. (Augustine). The same goes, in my case at least, for presentism, as Peter Lupu made clear to me Christmas night. Don't ask me what it is, and I know. Ask me, and I don't know.
The rough idea, of course, is that the temporally present -- the present time and its contents -- alone exists. The only items (events, individuals, properties, etc.) that exist are the items that presently exist. Past and future items do not exist. But surely it is trivial and not disputed by any anti-presentist that the present alone now exists. (Obviously, the past does not now exist, else it would not be past, and similarly with the future.) If the presentist is forwarding a substantive metaphysical thesis then it cannot be this triviality that he is hawking. So what does the thesis of presentism amount to?
It seems obvious that the presentist must invoke a use of 'exist(s)' that is not tensed in order to formulate his thesis. For this is a rank tautology: The only items that exist (present tense) are the items that exist (present tense). It is also tautologous to affirm that the only items that exist (present tense) are the items that presently exist. So it seems that if presentism is to be a substantive thesis of metaphysics, then it must be formulated using a temporally unqualified use of 'exist(s).' So I introduce 'exist(s) simpliciter.' Accordingly:
P. The only items that exist simpliciter are items that presently exist.
(P) is a substantive thesis. The presentist will affirm it, the antipresentist will deny it. Both, of course, will agree about such Moorean facts as that James Dean existed. But they will disagree about whether Dean exists simpliciter. The presentist will say that he does not, while the anti-presentist will say that he does. Again, both will agree that Dean does not exist now. But whereas the presentist will say that he does not exist at all, the anti-presentist will say that he does exist, though not at present. The anti-presentist can go on to say that, because Dean exists simpliciter, there is no problem about how he can stand in relations to things that presently exist. The presentist, however, faces the problem of how the existent can stand in relation to the nonexistent.
My mother is dead. But I am her son. So I stand in the son of relation to my mother. If the dead are nonexistent, then I, who exist, stand in relation to a nonexistent object. But how the devil can a relation obtain between two items when one of them ain't there? This is a problem for the presentist, is it not? But it is not a problem for the anti-presentist who maintains that present and past individuals both exist simpliciter. For then the relation connects two existents.
The antipresentist, however, needs to tell us what exactly existence simpliciter is, and whether it is the same or different than tenseless existence (whatever that is).
But nota bene: the presentist must also tell us what existence simpliciter is since he needs it to get his thesis (P) off the ground.
In my experience, the problems associated with time are the most difficult in all of philosophy.