Okay, I read to the end and I’m a little skeptical that you properly understand the incompleteness theorem. Are you aware, for instance, that the incompleteness theorem prohibits us from even proving all first-order statement the natural numbers using any consistent mathematical framework (regardless of how powerful it is)? And that it was later shown that no consistent mathematical framework can even prove the existence/non-existence of solutions to diophantine equations? The reason I ask is that you brought up the necessity of abstract categories and I’m not really sure what you meant by that. It also seemed that you might be unaware that no mathematical framework can resolve the halting problem for any Turing complete system (this is essentially a tautology). Am I misunderstanding what you meant?
Okay, I read to the end and I’m a little skeptical that you properly understand the incompleteness theorem. Are you aware, for instance, that the incompleteness theorem prohibits us from even proving all first-order statement the natural numbers using any consistent mathematical framework (regardless of how powerful it is)? And that it was later shown that no consistent mathematical framework can even prove the existence/non-existence of solutions to diophantine equations? The reason I ask is that you brought up the necessity of abstract categories and I’m not really sure what you meant by that. It also seemed that you might be unaware that no mathematical framework can resolve the halting problem for any Turing complete system (this is essentially a tautology). Am I misunderstanding what you meant?