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CronoDAS comments on Rationality Quotes - September 2009 - Less Wrong
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Consistency checking is NP-complete... "Compartmentalization" may be a rationalist sin, but you can't learn anything efficiently if you have to keep checking every fact against every other fact.
That's a pretty strong claim. Is there a proof? Or did you just mean that consistency checking is in NP?
It's worse than that, consistency checking is undecidable. This is implied by Gödel's second incompleteness theorem.
Well, 3-SAT is NP-complete, anyway. If consistency checking in mere propositional logic is already NP-complete, then it can't be any easier to do consistency checking to real-world arguments that require predicate logic or other, even more complicated systems to express.
Godel Escher Bach has a section that talks about this.