“To physically play out this sequence would require many more pebbles than exist in the universe. Does it make sense to ask if the Goodstein sequence which starts with the length of this line of pebbles, “would halt”? Does it make sense to talk about the answer, in a case like this?
I’d say yes, personally.”
On the other hand you’re an infinite set atheist. How do you make a difference between those two cases ? In neither can it be said the process can exist in the physical universe, which is all there is.
Does it makes more sense just because “infinite” really seems too, too big, while the Goodstein sequence merely seems “big” ? None can exist in the physical universe, that is their similar property. Is that property, of physical implementation, and physical observation, not all that matters in the end ?
Same with the concept of a spaceship that’d disappear through the cosmological horizon of an expanding universe, can’t have any causal effect anymore, but still exists.
Can you explain, why, how, is it that you feel confident that those processes do in one case still make sense, yet not in the other ? In a technical way.