Kazuo_Thow comments on Rationality quotes: May 2010 - Less Wrong

3 Post author: ata 01 May 2010 05:48AM

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Comment author: Kazuo_Thow 02 May 2010 06:47:05AM *  6 points [-]

[...] but we have no guarantee at all that our formal system contains the full empirical or quasi-empirical stuff in which we are really interested and with which we dealt in the informal theory. There is no formal criterion as to the correctness of formalization.

-- Imre Lakatos, "What Does a Mathematical Proof Prove?"

ETA: When I first read this remark, I couldn't decide whether it was terrifying, or just a very abstract specification of a deep technical problem. I currently think it's both of those things.

Comment author: gwern 02 May 2010 04:21:50PM *  4 points [-]

'102. One can't proceed from the informal to the formal by formal means.'

--Alan Perlis, Epigrams in Programming

Comment author: ciphergoth 02 May 2010 08:48:14PM 1 point [-]

Cox's theorem seems to reduce the gap between the formal and the informal, by deriving probability theory from axioms that seem easier to informally assess.

Comment author: gwern 03 May 2010 01:41:56PM 0 points [-]

Yes, and that is to me one of the main attractions of Bayesianism; but nevertheless, there is still a jump there between our informal considerations and formal means, and that ineradicable jump is what Perlis is talking about.

Comment author: RobinZ 04 May 2010 01:58:57PM 1 point [-]

Link appears to be broken.

Comment author: Kazuo_Thow 04 May 2010 04:47:19PM 0 points [-]

Fixed, thanks.

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