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RichardKennaway comments on Making Beliefs Pay Rent (in Anticipated Experiences) - Less Wrong
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Truths of pure maths don't pay rent in terms iof expected experience. EY has put forward a criterion of truth, correspondence, and a criterion of believability, expected experience , and pure maths fits neither. He didn't want that to happen, and the problem remains, here and elsewhere, of how to include abstract maths and still exclude the things you don't like. This is old ground, that the logical postivists went over in the mid 20th century.
Here is a truth of pure mathematics: every positive integer can be expressed as a sum of four squares.
Expected experiences: there will be proofs of this theorem, proofs that I can follow through myself to check their correctness.
Et voilà!
Truth of astrology: mars in conjunction with Jupiter is dangerous for Leos
Expected experience: there will be astrology articles saying Leo's are in danger when mars is in conjunction with Jupiter.
Of course astrological claims pay rent. The problem with astrology is not that it's meaningless but that it's false, and the problem with astrologers is that they don't pay the epistemological rent.
Also, a proof is a different thing from a mathematician saying so. The rent that is being paid there is not merely that the theorem will be asserted but that there will be a proof.
Try telling Eliezer
The original post does not mention astrology. If you want to spy out some place where Eliezer has said that astrological claims are meaningless, go right ahead. I am not particularly concerned with whether he has or not.
Here and now, you are talking to me, and as I pointed out, the belief can pay rent, but astrologers are not making it do so. Those who have seriously looked for evidence, have, so I understand, generally found the beliefs false.
From that belief, the expected experience should be Leo people being less fortunate during those days.
That was the point. Its a cheat to expect astrology truths to product experiences of reading written materials about astrology, so it's a cheat expect to pure maths truths ...
Let me complete the ellipsis with what I actually said. A mathematical assertion leads me to expect a proof. Not merely experiences of reading written materials repeating the assertion.
And a proof still isnt an .experience in the relevant sense. Its not like predicting an eclipse,