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Can You Prove Two Particles Are Identical?

Unless I'm totally confused, it seems like almost all the debate about this post is just about competing intuitions around the word "prove." If "prove" means "establish with probability exactly equal to 1," then Philosopher Bob is right for exactly the reasons he says he is: probabilities are never exactly 1, and you don't need to know the details of any specific theory to understand this. It's a fact of epistemology. If "prove" means "establish with the same level of credence we assign to things we generally take for granted" (like the sun rising tomorrow), then Bob is wrong, and he needs to take some QM classes. I think I hear a tree falling...