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I think the reasoning presented in this article generalizes pretty well to a refutation of most arguments involving proving the impossibility of some complex, i

I think the reasoning presented in this article generalizes pretty well to a refutation of most arguments involving proving the impossibility of some complex, ill-defined, "I'll know it when I see it" kind of phenomenon via a tidy, small logical proof. There's a lot of ways that those kinds of complex phenomenon can be functionally equivalent to human observers, but can have different underlying mechanisms. These tidy logical proofs only ever cut off one extremely specific incarnation of that complex phenomenon rather than the entire equivalence class.

gwern 6y ago
Yep. Even assuming the proof is formally valid, often, what an impossibility or no-go result means is just that one of the premises is wrong. (In this case, I think all the premises are wrong in any fixed-up formalized version of the argument from computational complexity, but it's usually not that bad.) Similarly, all of the Godelian or Penrose-style uncomputability arguments tend to rely on some premise like "humans never make mistakes" or "humans never contradict themselves" or "humans can prove any theorem" (or inverse computer versions thereof), which is the sort of premise which once you highlight it and make it explicit, you instantly lose all faith in any conclusion which supposedly follows from it. The relevant saying there is "one man's modus ponens is another man's modus tollens". I have another page on that particular interpretation or argument pattern: https://www.gwern.net/Modus https://www.gwern.net/Modus