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 [email protected] 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
