**From:** H C (*lphege@hotmail.com*)

**Date:** Fri Feb 17 2006 - 16:12:58 MST

**Next message:**Tyler Emerson: "Reminder: SIAI Challenge expires this Sunday | SIAI February news"**Previous message:**Woody Long: "RE: Commercials Re: Psychopathic Uploads and other SIs"**In reply to:**Marc Geddes: "Fundamental problems"**Next in thread:**Marc Geddes: "RE: Fundamental problems"**Reply:**Marc Geddes: "RE: Fundamental problems"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Hi,

'Probability Theory : The Logic of Science' by E. T. Jaynes

http://www.amazon.com/gp/product/0521592712/102-0054744-3138528?n=283155

Sincerely,

hegem0n

*>From: Marc Geddes <m_j_geddes@yahoo.com.au>
*

*>Reply-To: sl4@sl4.org
*

*>To: sl4@sl4.org
*

*>Subject: Fundamental problems
*

*>Date: Fri, 17 Feb 2006 18:04:00 +1100 (EST)
*

*>
*

*> >Eliezer has posted a job notice at the SIAI website,
*

*> >looking for research partners to tackle the problem
*

*> >of rigorously ensuring AI goal stability under
*

*>self->enhancement transformations.
*

*> >I would like to see this problem (or perhaps a more
*

*> >refined one) stated in the rigorous terms of
*

*> >theoretical computer science; and
*

*> >I'd like to see this list try to generate such a
*

*> >formulation.
*

*>
*

*>Fascinating, fascinating.
*

*>
*

*>I thought as a final post I'd better try to say
*

*>something actually intelligable, so I shall take one
*

*>crack at actually pointing to a solution :D
*

*>
*

*>O.K...
*

*>
*

*>Is there such a thing as
*

*>'a probability of a probability' ?
*

*>
*

*>See a new paper by Robin Hanson arguing for a new
*

*>Bayesian framework wherein probabilities can be
*

*>assigned to priors:
*

*>http://hanson.gmu.edu/prior.pdf
*

*>
*

*>
*

*>Also see blog entry by Ben Goertzel:
*

*>
*

*>*The management of uncertainty in the human brain: new
*

*>experimental insights*
*

*>
*

*>"In other words, some of us maverick AI theorists have
*

*>been saying for a while that using just ONE number
*

*>(typically probability) to measure uncertainty is not
*

*>enough. Two numbers -- e.g. a probability and another
*

*>number measuring the "weight of evidence" in favor of
*

*>this probability (or to put it differently, the
*

*>"confidence" one has in the probability) -- are needed
*

*>to make a cognitively meaningful algebra of
*

*>uncertainty."
*

*>
*

*>Link:
*

*>http://www.post-interesting.com/
*

*>
*

*>
*

*>I assume Bayesian probability theory could be
*

*>reformulated in terms of some kind of fuzzy set
*

*>theory. Then the notion of 'a probability of a
*

*>probability' would be referring to fuzzy sets
*

*>containing other fuzzy sets. The problem of sets
*

*>containing other sets has never been fully solved.
*

*>According to Roger Penrose:
*

*>
*

*>'In fact, the way that mathematicians have come to
*

*>terms with this apparently paradoxical situation is to
*

*>imagine that some kind of distinction has been made
*

*>between 'sets' and 'classes'...Roughly speaking, any
*

*>collection of sets whatever could be allowed to be
*

*>considered as a whole, and such a collection would be
*

*>called a *class*. Some classes are respectable enough
*

*>to be considered as sets themselves, but other classes
*

*>would be considered to be 'too big' or 'too untidy' to
*

*>be counted as sets. We are not neccessarily allowed
*

*>to collect *classes* together, on the other hand, to
*

*>form larger entities. Thus 'the set of all sets' is
*

*>not allowed...but the 'class of all sets' is
*

*>considered to be legitimate...
*

*>
*

*>There is something unsatisfactory about all
*

*>this...This procedure might be reasponable if there
*

*>were a clear-cut criterion telling us when a class
*

*>actually qualifies as being a set. However the
*

*>'distinction' appears often to be made in a very
*

*>circular way."
*

*>
*

*>-Roger Penrose. 'The Road To Reality' , Page 373
*

*>(Hard-back version)
*

*>
*

*>Paper on possible extensions to set theory:
*

*>http://web.mit.edu/dmytro/www/NewSetTheory.htm
*

*>
*

*>"Abstract: We discuss the problems of incompleteness
*

*>and inexpressibility. We introduce almost
*

*>self-referential formulas, use them to extend set
*

*>theory, and relate their expressive power to that of
*

*>infinitary logic. We discuss the nature of proper
*

*>classes. Finally, we introduce and axiomatize a
*

*>powerful extension to set theory."
*

*>
*

*>O.K, so... did I solve it? Are any of these ideas of
*

*>relevence?
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>"Till shade is gone, till water is gone, into the shadow with teeth bared,
*

*>screaming defiance with the last breath, to spit in Sightblinder’s eye on
*

*>the last day”
*

*>
*

*>
*

*>
*

*>____________________________________________________
*

*>Do you Yahoo!?
*

*>The New Yahoo! Movies: Check out the Latest Trailers, Premiere Photos and
*

*>full Actor Database.
*

*>http://au.movies.yahoo.com
*

**Next message:**Tyler Emerson: "Reminder: SIAI Challenge expires this Sunday | SIAI February news"**Previous message:**Woody Long: "RE: Commercials Re: Psychopathic Uploads and other SIs"**In reply to:**Marc Geddes: "Fundamental problems"**Next in thread:**Marc Geddes: "RE: Fundamental problems"**Reply:**Marc Geddes: "RE: Fundamental problems"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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