----- Original Message ----- From: Patrick Leahy <[EMAIL PROTECTED]> To: Alastair Malcolm <[EMAIL PROTECTED]> Cc: EverythingList <firstname.lastname@example.org> Sent: 24 May 2005 22:10 Subject: Re: White Rabbit vs. Tegmark . . > 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 seems to depend on whether one can find an intrinsic ordering (or something similar), such that relative frequency comes into play (so prime numbers *would* be less likely to be hit). As implied by my paper this would suggest a solution to the WR problem, but even if no ordering is possible or is irrelevant - the simple Cantorian situation - then there would be no WR problem anyway. (I have read hopefully the relevant passages in 'On the Plurality of Worlds' - I would think you are mainly referring to section 2.5; he doesn't actually mention either 'measure' or 'probability' here as far as I can see - more like 'outnumber', 'abundance' etc.) > 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. Lewis' approach to the inductive failure objection is slightly different, with the result that he can deploy a separate argument against it. Where he says "Why should the reason everyone has to distrust induction seem more formidable when the risk of error is understood my way: as the existence of other worlds wherein our counterparts are deceived? It should not." [p117] ... he is basically saying that from a deductive-logic point of view we have some degree of mistrust of induction anyway, and this will not be affected whether we consider the possible worlds (where induction fails) to be real or imaginary. However, it is the (for me) straightforward 'induction failure' objection - that the world should in all likelihood become unpredictable from the next moment on - that I address in my paper, (which in many ways more closely links to Lewis's 'rubbish universe' objection); my mentioning of 'rubbish' is in the different context of *invisible* universes, which is in the appendix argument concerning predomination of simpler universes. Alastair