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> Obviously they're different, but they're equivalent for most purposes That is not even wrong. You are mixing up syntax and semantics, and that is because typ
by auggierose 1y ago
> Obviously they're different, but they're equivalent for most purposes
That is not even wrong. You are mixing up syntax and semantics, and that is because type theorists don't have a concept of semantics.
- lmm 1y ago> That is not even wrong. You are mixing up syntax and semantics, and that is because type theorists don't have a concept of semantics. Right back at you. I don't have to treat notation as something different from semantics, because I'm working in a theory that can handle both elegantly and consistently. Conventional mathematics struggles to describe mathematics as it is actually performed - working mathematicians rely extensively on "abuse of notation", but set-theoretic metamathematics pretends this is out of scope or safe to ignore.
- auggierose 1y agoIf you say that semantics and syntax are the same, then you don't have semantics. That is not elegant, just confused, and your statements in this thread here are a great example of that.