On Wed, Feb 05, 2014 at 02:57:15PM +0100, Bruno Marchal wrote: > > On 05 Feb 2014, at 02:37, Russell Standish wrote: > > > > >I understand that Bp&Dt gives one of von Neumann's quantum logics, but > >it still seems an enormous jump from there to the FPI, > > It will be the other way round. By UDA we have the FPI. To translate > that FPI we need to define "probability or measure on consistent > extensions" in arithmetic. By the FPI, to say that I will necessary > drink coffee after the WM-duplication, means that I will get coffee > in all consistent extensions (here W and M). >
I don't see how a probability=1 concept helps with the FPI, which requires probability < 1 (p=0.5 at a minimum, for two equally probable possibilities). > The []p will ensure that p is true in all accessible worlds. > > But unfortunately, []p is true for all p in the cul-de-sac world (a > future exercise for Liz!), which shows that provability is not a > probability, nor a measure of certainty. To get the certainty, we > have to explicitly assume at least one accessible world, and this is > done by imposing "<>t", which imposes one accessible world, and > makes disappear the cul-de-sac possible situation. > I appreciate the no cul-de-sac result in the []p&<>p hypostase, but does that really mean much when Kripke frames are lost? I guess you replace Kripke by Scott-Montegue, is that right? > > > > > >or to call the > >Deontic relation a Schroedinger equation, even a little abstract one. > > The deontic relation is []p -> <>p. > > The "little schroedinger equation" will be > > p -> []<>p (together with []p -> p), > Ah - it was 15 years ago when I read your (Lille) thesis cover-to-cover. My confusion no doubt comes from you introducing both concepts on the one page. I still slightly get the french words "encore" and "deja" confused, because they were introduced on the same page in my French text book. > It is the one bringing back the symmetry, and leading to the quantum > logic, and the proximity spaces (where the measure will live), > thanks to Goldblatt results. I'd be interested in the "proximity spaces". Is this a new result, or just some speculation? -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
