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 t

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