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The argument discussed here was first published by Lucas in 1961 ("Minds, Machines and Goedel"). What seems to me a conclusive refutation of it was published by
by gjm11 5y ago
The argument discussed here was first published by Lucas in 1961 ("Minds, Machines and Goedel"). What seems to me a conclusive refutation of it was published by Hilary Putnam in 1960 ("Minds and Machines"). Putnam's point is much the same as simonh's in a comment here: the Lucas(/Penrose) argument makes assumptions about human mathematicians that do not in fact apply to human mathematicians.
[EDITED to add:] Contra simonh, though, one can refute the argument without going so far as to say that human mathematicians are definitely inconsistent. (Maybe a sufficiently careful human mathematician is consistent.) All that's required is that we not be able to prove that we are consistent, and I think it is extremely clear that we can't.
In other words, the Lucas(/Penrose) argument was refuted before it was ever published.
(Penrose's version isn't really any improvement on Lucas's.)
Note: The video is 2 hours long and highly technical. I haven't watched anything like all of it. The speaker is _not_ endorsing Lucas's or Penrose's conclusion that Goedel's theorem shows that minds cannot be mechanized; he makes observations similar to Putnam's, simonh's, and mine, but clearly makes them with more subtlety and intricacy :-).
- simonh 5y agoThanks so much for the reference, it's great to see someone expressed this much more rigorously.
- raoof 5y agoI have to say I'm just an amateur programmer but if there are absolute undecidable statements then what is the point of thinking? and if we are inconsistent what is the point of science? why not call it religion?
- simonh 5y agoScience isn't about formal and absolutely certain proofs. That's why we have things like the 5 Sigma standard for evidence in physics. We come up with a plausible theory, then look for evidence that it makes useful predictions. No experimental verification can be truly absolute though. Also consider the fact that Newtonian mechanics was superseded by Relativity, and that even though relativity and Quantum Mechanics are thoroughly verified across many domains they are also inconsistent with each other in some ways. We don't have absolute knowledge in Physics, or science generally in the strict sense that this video and philosophers of logic discuss. We only have useful theories that describe the world very closely to reality across most situations. We also very importantly get to conclusively rule out an awful lot of ideas and theories. That's very important work. It is all about levels of confidence though. If you think about it, you probably already knew all this, you just hadn't considered the consequences yet. We're all in that boat about a lot of things. I'm afraid in the grand scheme of things, despite all out truly incredible accomplishments, it's also true that we're stuck with fairly limited mental faculties. As to why? Well, we need to feed and clothe our children somehow. That means figuring out how to get stuff done. Working out explanations of the world that verifiably work, more or less, has turned out pretty well for us.
- deleted 5y ago[deleted]
- raoof 5y agoif I am inconsistent how can I trust the conclusion that I am a machine considering that my desire is to not to be?
- simonh 5y agoI don't think you can. We don't have enough information to be certain yet, we can just try to estimate the least inconsistent hypothesis.
- raoof 5y agoI don't understand your philosophical position. mind body problem is not about the data it's about explanation, how much data do you need? we are bombarded with data every second of our lives.
- simonh 5y agoWe don't have a sufficiently robust explanation, backed up by evidence for it's accuracy.