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hairyfigment comments on A quick sketch on how the Curry-Howard Isomorphism kinda appears to connect Algorithmic Information Theory with ordinal logics - Less Wrong
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Comments (27)
I think the grandparent silently assumes we've solved logical uncertainty, and can use this to decide an axiom does not produce a contradiction by observing the lack of explosion. Though "routing through logic" seems like an incredibly bad way to say that.
Wouldn't that imply having solved undecidability?
I spoke imprecisely, or at least the OP argues that I did. It assumes we have a progressive solution to undecidability/ logical uncertainty that can take us pretty far, eventually, but does not allow self-knowledge at any time.
No. We don't decide an axiom does not produce a contradiction by observing the lack of explosion. We just raise the probability of noncontradiction by observing the lack of explosion.
EDIT: Axiom, not acronym. Holy God I need more sleep.
-_-. The post itself was a sketch, not a finished, formalized publication. Please refrain from being anal about phrasings or imagining that I've done far more math than I really have. If I want to be precise, I'll just use symbols -- that's what they're for.