Are you intending to raise the traditional question of whether verificationism is itself verifiable?
I’m just trying to understand the statement Eliezer is making in this post.
What would you expect to experience differently if the axiom of choice were true or false?
I don’t think the axiom of choice is a first-order tautology so you wouldn’t call it true or false. It could be inconsistent within certain popular theories in which case for each inconsistent theory I would expect the the negation of the conjunction of the axiom of choice and the theory to eventually appear in an enumeration of first order validities.
I’m just trying to understand the statement Eliezer is making in this post.
I don’t think the axiom of choice is a first-order tautology so you wouldn’t call it true or false. It could be inconsistent within certain popular theories in which case for each inconsistent theory I would expect the the negation of the conjunction of the axiom of choice and the theory to eventually appear in an enumeration of first order validities.