that’s a really good way of putting it yeah, thanks.
and then, there’s also something in here about how in practice we can approximate the evolution of our universe with our own abstract predicctions well enough to understand the process by which the physical substrate which is getting tripped up by a self-reference paradox, is getting tripped up. which is the explanation for why we can “see through” such paradoxes.
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?
that’s a really good way of putting it yeah, thanks.
and then, there’s also something in here about how in practice we can approximate the evolution of our universe with our own abstract predicctions well enough to understand the process by which the physical substrate which is getting tripped up by a self-reference paradox, is getting tripped up. which is the explanation for why we can “see through” such paradoxes.
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?