On Tue, May 24, 2005 at 10:10:19PM +0100, Patrick Leahy wrote: > > This is very reminiscent of Lewis' argument. Have you read his book? IIRC > he claims that you can't actually put a measure (he probably said: you > can't define probabilities) on a countably infinite set, precisely because > of Cantor's pairing arguments. Which seems plausible to me.

It makes a very big difference whether he said probability or measure. One can easily attach a measure to a countable set. Give each element the same value (eg 1). That is a positive measure. However, it is not a probability, as it cannot be normalised. One can also sample from a measure without mean - however the rules for computing expected outcomes differs somewhat from just taking the mean as the expectation. For example with a uniform measure, the expected outcome is any point in the set. Assume some property is distributed over those points - for example the property is identical (the delta distribution). The the expected value of that property is the constant value. and so on. > > Lewis also distinguishes between inductive failure and rubbish universes > as two different objections to his model. I notice that in your articles > both you and Russell Standish more or less run these together. > I'm interested in this. Could you elaborate please? I haven't had the advantage of reading Lewis. If what you mean by by the first is why rubbish universes are not selected for, it is because properties of the selected universe follow a distribution with well defined probability, the universal prior like measure. This is dealt in section 2 of my paper. If you mean by failure of induction, why an observer (under TIME) continues to experience non-rubbish, then that is the white rabbit problem I deal with in section 3. It comes down to a "robustness" property of an observer, which is hypothesised for evolutionary reasons (it is not, evolutionarily speaking, a good idea to be confused by hunters wearing camouflage!) In that case, how am I conflating the two issues? If I'm barking up the wrong tree, I'd like to know. Cheers -- *PS: A number of people ask me about the attachment to my email, which is of type "application/pgp-signature". Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics 0425 253119 (") UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 ----------------------------------------------------------------------------

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