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Decius comments on Godel's Completeness and Incompleteness Theorems - Less Wrong
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Comments (85)
Why is the mystical ability to see implications that machines can't mutually exclusive with the ability to fail at basic logic?
It's not logically exclusive. It's just that the only evidence for the existence of this ability comes from logical reasoning done by people. Which contains failures at basic logic.
I didn't evaluate the strongest arguments for the human-superior crowd, because I find the question irrelevant. If some evidence comes from arguments which have not been shown to be flawed, then there is reason to believe that some humans are better at Godelian reasoning than machines can be.
The response wasn't "All of the evidence is logically flawed". The response was
(emphasis added)
I disagree with EY. I think all of them, while making this claim, fail at basic logic, although their failures come in several kinds.
This is based on arguments I have seen (all flawed) and my inability to come up myself with a non-flawed argument for that position. So if you think I am wrong, please point to evidence for human-only mystical powers, which is not logically flawed.
Suppose that humans had the ability to correctly intuit things in the presence of inadequate or misleading evidence. That ability would require that humans not follow first-order logic in drawing all of their conclusions. Therefore, if did not follow perfect logic it would be (very weak) evidence that they have superior ability to draw correct conclusions from inadequate or misleading evidence.
Humans do not always follow perfect logic.
I don't have good evidence, but I haven't searched the available space yet.
This is negligibly weak evidence, not even strong enough to raise the hypothesis to the level of conscious consideration. (Good evidence would be e.g. humans being actually observed to deduce things better than the evidence available to them would seem to allow.)
Consider that there are much much better reasons for humans not to follow logic perfectly. The stronger these are, the less evidence your approach generates, because the fact humans are not logical does not require additional explanation.
Logic is hard (and unlikely to be perfect when evolving an existing complex brain). Logic is expensive (in time taken to think, calories used, maybe brain size, etc.) Existing human adaptations interfere with logic (e.g. use of opinions as signalling; the difficulty of lying without coming to believe the lie; various biases). Existing human adaptations which are less good than perfect logic would be, but are good enough to make the development of perfect logic a bad value proposition. There are others.
Ever known someone to jump to the correct conclusion? Ever tried to determine how likely it is, given that someone is jumping to a conclusion with the available evidence, that the conclusion that they reach is correct?
Consider that several people have asserted, basically, that they have done the math, and more people than expected do better than expected at reaching correct conclusions with inadequate information. I haven't gathered empirical data, so I neither support nor refute their empirical claim about the world; do your empirical data agree, or disagree?
In my personal experience I can't think offhand of people who guessed a correct answer when a random guess, given available evidence, would have been very unlikely to be correct.
Sometimes people do guess correctly; far more often they guess wrong, and I expect the two to be balanced appropriately, but I haven't done studies to check this.
Can you please point me to these people who have done the math?
I played the Calibration Game for a while and I got right more than 60% of the questions to which I had guessed with “50%”. It kind-of freaked me out. (I put that down to having heard about one of the things in the question but not consciously remembering it, and subconsciously picking it, and since the bigger something is the more likely I am to have heard about it... or something like that.)
I have like 53% - 55% in the 50% category. 60% seems high. Since I have some knowledge of the questions I would expect to answer above above 50% correctly.
The human-superiorists make the claim that they have done the math; I haven't checked their work, because I find the question of whether humans can be better than a machine can be are irrelevant; the relevant fact is whether a given human us better than a given machine is, and the answer there is relatively easy to find and very hard to generalize.
So, can you point me to some specific claims made by these human-superiorists? I know of several, but not any that claim to back up their claims with data or evidence.