If presentism holds, it makes perfect sense to talk of what Alexander and Bucephalus did, of the properties they had, of the relations they stood in, and so on, and for none of this do we need Alexander and Bucephalus to exist. After all, Bucephalus doesn't exist any more. Alexander does exist (in heaven, purgatory or hell), but his present existence has nothing to do with the truth of propositions such as that Alexander conquered much of the world and rode Bucephalus. Bucephalus led a full horsey life, as descriptively rich as the life of any presently existing horse. Truths about the past are just as true as truths about the present, and according to the presentist, we do not surrender realism in the case of truths about the past.
But if we can make sense of talk about the past without positing past substances, why can't we equally make sense of talk of the present without positing present substances? If one can be a realist and yet say that dinosaurs once walked the earth without quantifying over dinosaurs, why can't we equally well be realists and yet say that horses now walk the earth without quantifying over horses?
There is a hole in this argument. Perhaps on Cartesian grounds it is undeniable that I now exist, and hence that there is at least one presently existing substance—I. But it is unclear that the Cartesian argument establishes my present existence. I think to myself: "I think, therefore I am." What gives evidence for the "I think" is already in the past by the time I get to the "I am". So, rather, I should say: "I think, therefore I was." At least, I can say this: any certainty that I have about the "I am" is a certainty that I also have about the "I was". Anyway, this seems beside the point. For the same strategy that the presentist uses to explain the truth of "Bucephalus was" without presupposing Bucephalus can surely be used to explain the truth of "Alexander Pruss is" without presupposing Alexander Pruss.
I am not satisfied with this argument. I feel that a sophistry is in the air, or else that I am unfair to presentists. But I suspect the following is true: The presentist who accepts a tenseless quantifier, a tenseless "exists", which I'll indicate as "exists*", and who then says that only presently existing things exist*, will probably be subject to this worry. On the other hand, the presentist who doesn't accept a tenseless quantifier may have some difficulty in explaining presentism: it is a triviality that only presently existing things presently exist.