bryjnar comments on Godel's Completeness and Incompleteness Theorems - Less Wrong

34 Post author: Eliezer_Yudkowsky 25 December 2012 01:16AM

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Comment author: bryjnar 27 December 2012 02:34:59AM 1 point [-]

By semantics I mean your notion of what's true. All I'm saying is that if you think that you can prove everything that's true, you probably have a an overly weak notion of truth. This isn't necessarily a problem that needs to be "fixed" by being really smart.

Also, I'm not saying that our notion of proof is too weak! Looking back I can see how you might have got the impression that I thought we ought to switch to a system that allows infinite proofs, but I don't. For one thing, it wouldn't be much use, and secondly I'm not even sure if there even is such a proof system for SOL that is complete.