On 12 Feb 2009, at 22:12, russell standish wrote:

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> > On Thu, Feb 12, 2009 at 04:48:22PM +0100, Bruno Marchal wrote: >> >> Excellent post Johnatan. >> >> Of course those who know a bit of AUDA (which I have already >> explained >> on the list) know that from the third person self-reference views we >> have cul-de-sac everywhere ("we die all the times", cf the >> "Papaioannou multiverses"), and this is what forces us, when we >> want a >> theory of observation (which by UDA is a probability or credibilty >> calculus) to define the probabilities by imposing the absence of cul- >> de-sac. This is *the* motivation for the new box Bp & Dt. Dt, by >> Kripke semantics, is equivalent to imposing the absence of cul-de- >> sac. >> Yet, by incompleteness Dt is not provable by the machine, and after >> we >> make the addition of the "non-cul-de-sac" principle (Dt), we loose >> the >> Kripke semantics. But this is a good news, given that we will have to >> manage (plausibly) continua of "next observer momen or historiest". > > I'm a little confused. Did you mean Dp here? Dp = -B-p Fair question, given my sometimes poor random typo! In the so called "normal" modal logic, that is those system of modal logic containing the formula K B(p->q) -> (Bp -> Bq) and which are closed for both the modus ponens rule (from p and p->q you can deduce q) and the rule of necessitation (from p you can deduce Bp) , well, if you remind the definition of the Kripke semantics, you can see that Bp & Dp is equivalent with Bp & Dt Bp is true in the world alpha, means that p is true in all the worlds Beta accessible from Alpha. Dp is indeed equivalent to -B-p, it means that B-p is false, so it is false that in all the worlds Beta, accessible from Alpha, -p is true in them. So it means that there is world, accessible from Alpha, where -p is false, that means that there exists a world where p is true. Now if you have in a world, your world if you want, Bp & Dp, you have at least access to a world in which p is true, and thus you have access to a world where t is true, given that t is true in all worlds. So you have Bp & Dt. The inverse: now you have in a world Bp & Dt. Thus you have Bp and Dt, of course, and by Dt you have access to a world where t is true. But you have also Bp, so you know that in all the accessible world, from your world you have p, so you have Dp. A good and important exercise is to understand that with the Kripke semantics, ~Dt, that is B~t, that is Bf, that is "I prove 0=1", is automatically true in all cul-de-sac world. It is important because cul-de-sac worlds exists everywhere in the Kripke semantics of the self-reference logic G. If you interpret, if only for the fun, the worlds as state of life, then Bf is really "I am dead". Bruno > > >> >> Apology for those who have not follow the (many) old modal posts, but >> we will soon or later come back to this. Read Boolos book (and >> mathematical logic books). >> >> Bruno >> > > -- > > ---------------------------------------------------------------------------- > Prof Russell Standish Phone 0425 253119 (mobile) > Mathematics > UNSW SYDNEY 2052 hpco...@hpcoders.com.au > Australia http://www.hpcoders.com.au > ---------------------------------------------------------------------------- > > > http://iridia.ulb.ac.be/~marchal/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---