Except that mathematics mostly isn't a "casual model generating precise predictions", especially at the higher levels, famously so with the philosophical failures of Bertrand Russell.
No consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of natural numbers
Except that mathematics mostly isn't a "casual model generating precise predictions", especially at the higher levels, famously so with the philosophical failures of Bertrand Russell.
Gödel tapping the sign
:wojak-nooo: Kronecker and Wittgenstein crying: Noooo! you can't use a diagonalization argument to prove by contradiction.
Cantor, Gödel and Turing: haha, well look at that, the diagonal can't exist. QED
Whoops: Hilbert actually liked Cantor's proof.