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?
If haecceitism is true, then it's easy. The presentist just replaces talk transtemporal talk of individuals with talk of haecceities.
ReplyDeleteWhat about: "someone will have infinitely many descendants, who will be non-identical with their infinitely many haecceities"?
How about a meta-linguistic move?
ReplyDeleteFirst, define a predicate D_n(x) which says that x has at least n descendants. It's messy, but can be done. E.g., assuming that at some point the parent is contemporaneous with the child (not exactly true, but I think one can just add the necessary complications), D_1(x) says that there is a time t such that at t there was, is or will be a y and x existed, exists or will exist at t, and at t x is a parent of y. D_2(x) says that there is a time t such that at t there was, is or will be a y and x existed, exists or will exist at t, and at t both x was, is or will be a parent of y and D_1(y). And so on.
Now, our truth conditions for (1) are: "There is an x that satisfies every predicate D_n."
It's odd that one needs to go metalinguistic, though.
Next question: Can we form a presentist-friendly sentence that says that x has uncountably infinitely many descendants?