On Mon, May 28, 2012 at 10:37:53AM +0200, Bruno Marchal wrote: > > On 28 May 2012, at 04:00, Russell Standish wrote: > > >On Sun, May 27, 2012 at 06:20:29PM +0200, Bruno Marchal wrote: > >> > >>On 27 May 2012, at 12:15, Russell Standish wrote: > >>>I still don't follow. If I have proved a is true in some world, why > >>>should I infer that it is true in all worlds? What am I missing? > >> > >>I realize my previous answer might be too long and miss your > >>question. Apology if it is the case. > >> > >>Here is a shorter answer. The idea of proving, is that what is > >>proved in true in all possible world. If not, a world would exist as > >>a counter-example, invalidating the argument. > > > >I certainly missed that. Is that given as an axiom? > > That would be a meta-axiom in a theory defining what is logic. But > that does not exist. It is just part of what logic intuitively > consists in.
Well, I can tell you, it is not intuitive! Perhaps there is some background understanding that is missing. > Logicians are not interested of truth or interpretation of > statements. They are interested in validity. What sentences follow > from what sentences, independently of interpretations, and thus true > in all possible worlds. > > > > >It seems like that > >would be written p -> []p. > > This means that if p then p is provable. "p -> Bp", if B = provable, []p means (primarily) true in all worlds. In Kripke semantics, it is relativised to mean true in all accessible worlds. The meaning of provability is a different interpretation. > > > > > >When I say p is true in a world, I can only prove that p is true in > >that world. > > I don't think so. If p is true, that does not mean you can prove it, > neither in your world, nor in some other world. p may be true, but if I don't know it (or can't prove it), I shouldn't be asserting it :). > > > >I am mute on the subject of whether p is true in any other > >world (unless I can use an axiom like the above). > > By the logicians notion of proof, if you prove a proposition, it is > true in all worlds/model/interpretation. > Even if the proof relied upon some facet that may or may not be true in all worlds? > > > > >In what class of logics would such an axiom be taken to be true. > > All. > > -- ---------------------------------------------------------------------------- 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 post to this group, send email to everything-list@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.
