In an earlier post, I showed that presentists can count infinities—i.e., that presentists can give a paraphrase for sentences like "There have ever been aleph-0 horses." I did this by an ersatzist construction. I then left it open whether some such construction could work in general to give presentist paraphrase.
The problem is basically the problem of transtemporal quantification. If haecceitism is true, then it's easy. The presentist just replaces talk transtemporal talk of individuals with talk of haecceities. Likewise, if the presentist accepts the impossibility of exact intrinsic duplicates—for then one can replace talk of individuals with talk of individual-types. The interesting question is whether this can be done if you're a presentist who is not a haecceitist and who thinks there can be exact intrinsic duplicates.
I have a sentence that a non-haecceitist presentist who accepts intrinsic duplicates may have difficulty giving finite truth conditions for:
- Somebody will have infinitely many descendants.
I don't know if presentist truth conditions for (1) are possible.
If we allow infinite sentences, it can be done. But that's cheating. :-) Or is it?