Identity is a modeling choice.  There's no such thing in physics, as far as anyone can tell.  All models are wrong, some models are useful.  Continuity of identity is very useful for a whole lot of behavioral and social choices, and I'd recommend using it almost always.

As a thought experiment in favor of presentism being conceivable and logically consistent with everything you know, see Boltzmann brain - Wikipedia .

I think that counter-argument is pretty weak.  It seems to rely on "exist" being something different than we normally mean, and tries to mix up tenses in a confusing way.

• (1) If a proposition is true, then it exists.

Ehn, ok, but for a pretty liberal and useless use of the word "exists".  If presentism is true, then "exists" could easily mean "exists in memory, there may be no reality behind it".

• (2) <Socrates was wise> is true.

Debatable, and not today's argument, but you'd have to show WHY it's true, which might include questions of what other currently-nonexistent things can be said to be "was wise".  

• (3) <Socrates was wise> exists. (1, 2)

The proposition exists, yes.

• (4) If a proposition exists and has constituents, then its constituents exist.
• (5) Socrates is a constituent of <Socrates was wise>.
• (6) Socrates exists. (3, 4, 5)

Bait and switch.  The constituent of <Socrates was wise> is either <Socrates>, the thing that can be part of a proposition, or "Socrates was", the existence of memory of Socrates.

• (7) If Socrates exists, then presentism is false.

Complete non-sequitur.  Both the proposition-referent or the memory of Socrates can exist in presentism.

• (8) Presentism is false. (6, 7)

Nope.

The Stanford Enyclopedia thing is a language game. Trying to make deductions in natural language about unrelated statements is not the kind of thing that can tell you what time is, one way or another. It can only tell you something about how we use language.

But also, why do we need an argument against presentism? Presentism seems a priori quite implausible; seems a lot simpler for the universe to be an unchanging 4d block than a 3d block that "changes over time", which introduces a new ontological primitive that can't be formalized. I've never seen a mathematical object that changes over time, I've only seen mathematical objects that have internal axes.

"If we also consider only the present moment is real, then past X and future X don't exist. Since it is impossible that the same person exists and does not exist, we conclude present X and past X are different persons."

I cannot agree with your logic here, you have stated past X does not exist, then in the next sentence you say it is a different person than present X (implying that it does exist and can be compared and contrasted). I don't belive that there is a meaningful conclusion to be had by comparing something real (present X) to something nonexistent (past X) in any case.

This is my first time reading the Stanford's argument against presentism, and possibly I am not understanding this fully but point (6) "Socrates exists", is either obviously true (Socrates was a man, man exists, so Socrates exists) or obviously false (he is long dead, so he does not exist). Maybe this is because the logic mixes up past and present. If we logically arrive at "(6) Socrates exists", then we should be able to use present tense and have the same logical validity, point (2) becoming "Socrates IS wise", which is false, as a dead person cannot be wise.

I am unsure on whether or not presentism is true or not (personally I do not care, I don't see how it would make a difference to me either way). Possibly time exists and we can navigate through it (either by the "regular" passage of time, maybe time travel is possible in the forward or backward direction), or time exists "all at once", and we living human beings are somehow limited to only experience it instant by instant. Or else time does not exist at all or is essentially meaningless (or is a human construct, in the same way that numbers and math are).