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g_pepper comments on Making Beliefs Pay Rent (in Anticipated Experiences) - Less Wrong

110 Post author: Eliezer_Yudkowsky 28 July 2007 10:59PM

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Comment author: g_pepper 22 February 2015 11:58:10PM *  0 points [-]

Unlike scientific knowledge or other beliefs about the material world, a mathematical fact (e.g. that z follows from X1, X2,..., Xn), once proven, is beyond dispute; there is no chance that such a fact will be contradicted by future observations. One is allowed to believe mathematical facts (once proven) because they are indisputably true; that these facts pay rent is supported by VKS's argument.

Comment author: TheAncientGeek 23 February 2015 11:02:44AM *  1 point [-]

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.

Comment author: RichardKennaway 23 February 2015 01:21:27PM 0 points [-]

Truths of pure maths don't pay rent in terms iof expected experience.

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 voilĂ !

Comment author: TheAncientGeek 23 February 2015 02:24:02PM 0 points [-]

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.

Comment author: RichardKennaway 23 February 2015 02:56:23PM *  1 point [-]

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.

Comment author: TheAncientGeek 23 February 2015 03:56:57PM 0 points [-]

Of course astrological claims pay rent.

Try telling Eliezer

Comment author: RichardKennaway 23 February 2015 04:41:40PM *  0 points [-]

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.

Comment author: polymathwannabe 23 February 2015 02:56:33PM -1 points [-]

From that belief, the expected experience should be Leo people being less fortunate during those days.

Comment author: TheAncientGeek 23 February 2015 03:50:16PM *  0 points [-]

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 ...

Comment author: RichardKennaway 23 February 2015 04:49:17PM 2 points [-]

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.

Comment author: TheAncientGeek 24 February 2015 10:37:47AM 0 points [-]

And a proof still isnt an .experience in the relevant sense. Its not like predicting an eclipse,

Comment author: g_pepper 24 February 2015 01:07:30AM *  1 point [-]

I think I see where you are going with this.

My initial interpretation of EY's original post is that he was explicating a scientific standard of belief that would make sense in many situations, including in reasoning about the physical world (EY's initial examples were physical phenomena - trees falling, bowling balls dropping, phlogiston, etc.). I did not really think he was proposing the only standard of belief. This is why I was baffled by your insistence that unless a mathematical fact had made successful predictions about physical, observable phenomena, it should be evicted.

However, later in the original post EY used an example out of literary criticism, and here he appears to be applying the standard to mathematics. So, you may be on to something - perhaps EY did intend the standard to be universally applied.

It seems to me that applying EY's standard too broadly is tantamount to scientism (which I suspect is more-less the point you were making).