I think it’s more the latter, although I’m not terribly convinced myself that you’re wrong. But the arguments you may or may not have missed are in the middle of OP’s section 1, with paragraphs starting “The causal way,” “The acausal way,” and “Perhaps you say.”
Personally, I am more open than most rationalists to the idea that there may be a way to escape heat death without actually violating Liouville’s theorem or other justifications for the Second Law. If so, that would make the set of future temporal locations infinite. Even if the amount of energy in the accessible universe is finite, and even if that implies the state-space of the universe is finite, and so its state trajectory must either terminate or repeat itself, maybe it would then repeat itself for 𝜔 many cycles, and so the question of which cycle of state space is entered first matters infinitely much.
I think it’s more the latter, although I’m not terribly convinced myself that you’re wrong. But the arguments you may or may not have missed are in the middle of OP’s section 1, with paragraphs starting “The causal way,” “The acausal way,” and “Perhaps you say.”
Personally, I am more open than most rationalists to the idea that there may be a way to escape heat death without actually violating Liouville’s theorem or other justifications for the Second Law. If so, that would make the set of future temporal locations infinite. Even if the amount of energy in the accessible universe is finite, and even if that implies the state-space of the universe is finite, and so its state trajectory must either terminate or repeat itself, maybe it would then repeat itself for 𝜔 many cycles, and so the question of which cycle of state space is entered first matters infinitely much.