The Incompleteness Theorem

"It's like, uh, the whole 'I have a question, but I forget what it is' thing,"

"— Gödel's Ghost, 1931"

Paradoxical Logic | Unsolved Problems

Imagine, if you will, a machine that spits out answers to every question you could ever possibly ask. Sounds like a dream, right?

But what if the machine is incomplete? What if it can't possibly answer every single one of them? That's basically what Gödel showed us with the Incompleteness Theorem: that any system of axioms and rules can't be both complete and consistent.

So, what's the point of it all? Is it like, just a bunch of fancy math? Or is it, like, the whole 'limits of human knowledge' thing? Maybe it's like... actually, I'm not really sure.

But hey, at least it's not like, you know, the halting problem or something.

More on Paradoxical Logic