Presentism in the philosophy of time is the thesis that the present moment enjoys an ontological privilege over the other two temporal modi. The basic idea is that only (temporally) present items (individuals, events, times) exist. If so, past and future items do not exist. What is no longer is not, and what is not yet is not. Presentism presupposes the A-theory of time according to which pastness, presentness, and futurity are monadic properties irreducible to the B-relations earlier than, simultaneous with, and later than. Presentness is an absolute property. To say of an event that it is present is not to say that it is simultaneous with a reference to it or perception of it.
Presentism, then, is the claim all that exists is present, or
P) Nothing exists that is not present.
On a present-tensed reading of 'exists,' however, (P) collapses into a tautology:
P1) Nothing presently exists that is not present.
This trivial truth is not what the presentist intends. What he intends is a restriction of temporal things, things in time, to present things:
P2) Nothing exists in time that is not present.
I am assuming that there are timeless things, numbers for example. If there are no timeless things, and everything is in time, then (P2) reduces to
P2*) Nothing exists that is not present.
The trouble with (P2) and its starred cousin, however, is that they seem obviously false. Boston's Scollay Square no longer exists. That is: it did exist, but it does not now exist. Given that it did exist, it is a temporal item as opposed to an atemporal item such as a number. Now it it reasonable to think that its being past has consigned it to utter nonexistence? Arguably not. Here is a little argument.
a) What exists is actual.
b) What does not exist is either merely possible or impossible.
c) If a wholly past object such as SS does not exist, then it is either merely possible or impossible. From (b)
d) It is not the case that SS is either merely possible or impossible: what passes away does not become merely possible or impossible.
e) SS exists. From (c), (d), by modus tollens.
f) SS is not present. Datum.
g) Something exists in time that is not present. From (e), (f).
The intuition behind the argument is that actuality includes the past. An historian is neither a fiction writer nor a speculator about the merely possible. If it is true that Socrates drank hemlock, then there there was a time when Socrates drinks hemlock, Socrates himself, not his haecceity.
The foregoing is a version of the triviality objection to presentism. It has the form of a dilemma. (P) is trivally true if read as (P1) or trivially false if read as (P2), and these are the only two ways of reading (P). Either way it is trivial.
For a full-blown technical treatment, see Ulrich Meyer, The Triviality of Presentism.