It’s not about those specific proofs. You’re claiming, that every possible proof stated in lean will always halt. Lean tries to evade the halting problem best as possible, by requiring functions to terminate before it runs a proof. But it’s not able to determine for every lean program it halts or not. That would solve the halting problem. Furthermore, the kernel still relies on CPU, memory and OS behavior to be bug free. Can you be sure enough in practice, yeah probably. But you’re claiming absolute metaphysical certainty that abolishes the need for philosophy and sorry, but no software will ever achieve that.
It certainly is about those specific proofs and anything that has been rigorously proven in Lean. We’re discussing techniques that show something is correct forever, and those proofs show that something is correct forever. Philosophical arguments don’t even show that something is correct today. This is why the examples I gave earlier are now not explained by philosophy but by other systems. Once the tooling exists to lift a discussion out of philosophy, that is the end of philosophical debate for that topic.
Furthermore, the kernel still relies on CPU, memory and OS behavior to be bug free.
Only to a point, just like human language proofs require the reviewers brains to be bug free to a point. The repeated verification makes proofs as correct as anything can get.
It’s not about those specific proofs. You’re claiming, that every possible proof stated in lean will always halt. Lean tries to evade the halting problem best as possible, by requiring functions to terminate before it runs a proof. But it’s not able to determine for every lean program it halts or not. That would solve the halting problem. Furthermore, the kernel still relies on CPU, memory and OS behavior to be bug free. Can you be sure enough in practice, yeah probably. But you’re claiming absolute metaphysical certainty that abolishes the need for philosophy and sorry, but no software will ever achieve that.
It certainly is about those specific proofs and anything that has been rigorously proven in Lean. We’re discussing techniques that show something is correct forever, and those proofs show that something is correct forever. Philosophical arguments don’t even show that something is correct today. This is why the examples I gave earlier are now not explained by philosophy but by other systems. Once the tooling exists to lift a discussion out of philosophy, that is the end of philosophical debate for that topic.
Only to a point, just like human language proofs require the reviewers brains to be bug free to a point. The repeated verification makes proofs as correct as anything can get.