[msla]

> It is also related to Godel's incompleteness theorem. There are an infinite number of truths that cannot be derived from any finite axiomatic system. These truths are "beyond rational comprehension."

This isn't what it means. It simply means that all axiom systems of a certain form have that limit, not that human knowledge itself does.

> One obvious area this shows up in is the concept of infinity. There is no way to derive such a concept from any finite axiom.

Obviously false, given even Peano arithmetic.

> Every syllogism starts with premises, and at some point the premises have to be a fundamental given that cannot be further dissected. All of our fields of knowledge have this characteristic. They all have a set of foundational concepts.

Except we can interrogate reality and build from there. We're not reasoning in a vacuum.

[yters]

If human knowledge is bound in brains which run on the laws of physics, then axiomatic systems are all we can ever have.

That being said, I agree human knowledge is not limited by GIT. However, this is proof that the human mind transcends the finite physical realm.

Regarding infinity, check out the Wikipedia article on the axiom of infinity:

https://en.wikipedia.org/wiki/Axiom_of_infinity#Interpretati...

"However, the other axioms are insufficient to prove the existence of the set of all natural numbers. Therefore, its existence is taken as an axiom—the axiom of infinity."

[PixyMisa]

> That being said, I agree human knowledge is not limited by GIT.

That's like saying 2 + 2 is not limited by being 4. You can "know" that 2 + 2 is 5. You're just wrong.

[yters]

That doesn't follow.

The human mind could be meta-rational so it can generate new consistent axioms that cannot be derived from the existing known axioms. The history of mathematical progress seems to be pretty good evidence our minds can do this.