3 ms·

I feel like a better, formal proof of this concept is Gödel Incompleteness, given this lemma, if true, would in turn invalidate itself.

adrianmonk 8y ago
Seems like a wash to me. It wouldn't invalidate itself any more than it would invalidate other alternatives to it.
jerf 8y ago
The problem with using math to address this is that it very subtly ends up begging the question. Math has an answer to the trilemma: Math is based on axioms. The question of whether math corresponds to anything in the real world is a separate question from the mathematics itself. Godel's theorem is thus based on mathematical axioms, but the trilemma questions the axioms themselves. No structure built on the axioms can prove the axiomatic formulation is correct. Godel's incompleteness is an important part of math history about how that was finally proved so hard that modern mathematics now deeply accepts that non-uniqueness of axioms, but again, this is all happening at a level too high to help us with the trilemma. So no, the trilemma can not be solved or even particularly refined by feeding it to mathematics. "From whence mathematics?", it asks. If you are going to play philosophical games with the trilemma, a better approach is simply to feed it to itself. If the trilemma is true, then we can't be confident that we've properly read it, because it cuts away the foundation we are using to communicate. If any of us have successfully extracted even a portion of understanding about the trilemma from the reading of this text, we must be sharing a certain very basic amount of rationality to get that far, even if we can't nail down where that rationality came from exactly. You could then proceed to say that this basic shared rationality is de facto usable as a foundation. But that still doesn't answer the question of where it comes from.

3 ms·

I feel like a better, formal proof of this concept is Gödel Incompleteness, given this lemma, if true, would in turn invalidate itself.

by subroutine 8y ago

adrianmonk 8y ago
Seems like a wash to me. It wouldn't invalidate itself any more than it would invalidate other alternatives to it.
jerf 8y ago
The problem with using math to address this is that it very subtly ends up begging the question. Math has an answer to the trilemma: Math is based on axioms. The question of whether math corresponds to anything in the real world is a separate question from the mathematics itself. Godel's theorem is thus based on mathematical axioms, but the trilemma questions the axioms themselves. No structure built on the axioms can prove the axiomatic formulation is correct. Godel's incompleteness is an important part of math history about how that was finally proved so hard that modern mathematics now deeply accepts that non-uniqueness of axioms, but again, this is all happening at a level too high to help us with the trilemma. So no, the trilemma can not be solved or even particularly refined by feeding it to mathematics. "From whence mathematics?", it asks. If you are going to play philosophical games with the trilemma, a better approach is simply to feed it to itself. If the trilemma is true, then we can't be confident that we've properly read it, because it cuts away the foundation we are using to communicate. If any of us have successfully extracted even a portion of understanding about the trilemma from the reading of this text, we must be sharing a certain very basic amount of rationality to get that far, even if we can't nail down where that rationality came from exactly. You could then proceed to say that this basic shared rationality is de facto usable as a foundation. But that still doesn't answer the question of where it comes from.