Greg Restall on Nostr: nprofile1q…z8k6c Thanks! (The typo is fixed.) I’m not sure whether I am in a ...
nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqymhcc5hsmqa74q7agz6yp8wvm0rfg7ej8q8t0ms7kvqa52nycexszz8k6c (nprofile…8k6c) Thanks! (The typo is fixed.)
I’m not sure whether I am in a position to speak for the realist or not, but I think they can respond in a number of different ways.
For one, though, I’d ask whether adding “actually” (or “really” or whatever) into the statement of (CH ∨ ¬CH) clarifies anything. The issue is whether (CH ∨ ¬CH) is true and what it means to say that it’s true. The proponent of ZFC (whether realist or not) is committed to (CH ∨ ¬CH), because it’s undeniable, in the strong sense that denying (CH∨¬CH) is inconsistent.
Now, what it means to be committed to a disjunction without being committed to either disjunct is another matter, but presumably that’s something that we’re all familiar with from other cases where our evidence is incomplete. Exactly what could count as evidence when it comes to sets and reasoning about them, is something that can be cashed out in various ways, some more amenable to realists than others, I suppose…
I’m not sure whether I am in a position to speak for the realist or not, but I think they can respond in a number of different ways.
For one, though, I’d ask whether adding “actually” (or “really” or whatever) into the statement of (CH ∨ ¬CH) clarifies anything. The issue is whether (CH ∨ ¬CH) is true and what it means to say that it’s true. The proponent of ZFC (whether realist or not) is committed to (CH ∨ ¬CH), because it’s undeniable, in the strong sense that denying (CH∨¬CH) is inconsistent.
Now, what it means to be committed to a disjunction without being committed to either disjunct is another matter, but presumably that’s something that we’re all familiar with from other cases where our evidence is incomplete. Exactly what could count as evidence when it comes to sets and reasoning about them, is something that can be cashed out in various ways, some more amenable to realists than others, I suppose…