2 ms·
They didn't claim that. They claimed that any (sound and consistent) finitely axiomatizable theory (basically, any recursively enumerable set of theorems) can o
by tromp 1y ago
They didn't claim that. They claimed that any (sound and consistent) finitely axiomatizable theory (basically, any recursively enumerable set of theorems) can only prove finitely many theorems of the form BB(n) = N.
- Kranar 1y agoI quoted the specific statement that I refuted.
- IsTom 1y agoOnly if your goalpost of what "mathematics" is endlessly shifting. To prove values of BB(50000) you're probably going to need some pretty wacky axioms in your system. With BB(any large number) that's just going to be unfeasible to justify that the system isn't tailored to prove that fact, just short of adding axiom of "BB(x) = y".