Here is a puzzle for a presentist. There seems to be a determinate answer to the question "How many zebras lived (at least in part) in the 19th century?" or at least it is quite possible there is a determinate answer.[note 1] But can the presentist make any sense of the question?
This puzzle is somewhat different from the general puzzle about truths about the past. I am willing to grant for the sake of argument that the presentist can make sense of questions like: "Did Napoleon win at Waterloo?" For the presentist can take the proposition p that Napoleon wins at Waterloo, and say that p was false at the relevant time, and hence the answer is negative.
But the question how many zebras lived in the 19th century is much tougher. Given any time t in the 19th century, the presentist can make sense of the question how many zebras there were alive at t.[note 2] That question is the question of what number z(t) is such that it was true at t that there are z(t) zebras. But the answer to the question of how many zebras lived in the 19th century does not supervene on the values of z(t) as t ranges over the 19th century.
If the presentist has haecceities in her ontology, she can probably make sense of the question. For then the question is: "How many haecceities h are there such that h is a haecceity of a zebra, and h was instantiated in the 19th century?" So the haecceitist presentist seems to be out of trouble.
Can a non-haecceitist presentist do the job? Yes, if she is a closed-future presentist. (A closed-future presentist accepts bivalence for claims about the future.) But it is surprisingly tricky (at least if we want to take into account the possibility that a zebra might have a temporally gappy existence). Here is the simplest way I have. Let T be the set of times in the 19th century. Let S be a non-empty subset of T. Let z(S) be defined as follows. Choose any t in S. Let z(S) be the unique number n such that it was true at t that there exist exactly n zebras z such that PS(z). Here, PS(z) is the claim that for every time t' in S, z exists, existed or will exist at t', and for no time t' in T−S is it the case that z exists, existed or will exist at t'. (A−B is the set of all members of A that are not members of B.) (This a definition apparently compatible with presentism, but since PS(z) partly concerns the then-future, only a closed-future presentist will have no qualms about it.) Then the number of zebras that lived in the 19th century is equal to the sum of z(S) as S ranges over all non-empty subsets of T.
Maybe there is a simpler way of counting 19th century zebras on presentism. But I can't think of one. More obvious solutions fail (thus one might keep track of when zebras come into existence, and count the comings into existence, but this doesn't work very well on presentist grounds for zebras that come into existence on an interval of times open at the bottom end).
There may be a clever way to do this within the confines of open-future presentism. But it's going to be tricky and messy. If it can't be done, then we have an argument why an open-future presentist should be a haecceitist.
I wonder if how complicated the answer to the question is does not give an argument against presentism. For, intuitively, the claim that there were exactly n1 zebras at noon on January 18, 1855 should be made true similarly to the way the claim that there were n2 zebras in the 19th cenutry is made true. But the non-haecceitist presentist will have to use very different counting methods for the two cases.