On 6 March 2014 22:06, Bruno Marchal <marc...@ulb.ac.be> wrote: > > Liz, meanwhile you might try this one, which is a bit more easy than the > transitivity case: > > Show that (W,R) respects []A -> <>A if and only if R is ideal. > > (I remind you that R is ideal means that there is no cul-de-sac world at > all in (W,R)). >
OK, I consult my diary and... Ideal is as you say, yes! :-) So []A -> <>A means that A is some proposition universally true in an illuminated, accessible multiverse, and this implies that A is possible in that multiverse. Hang on I must be missing something. That seems trivially obvious! Maybe you could point out what I've misunderstood here... Let me try again. []p means that for any world alpha, p is true in all worlds accessible from alpha. (Doesn't it? Well if p is a proposition, which might be 'x is false' then that seems reasonable). And <>p means that, ah, ~[]~p iirc. Which is to say it isn't true that there is a world accessible from alpha in which ~p. But isn't that implied by []p? I must have a definition wrong somewhere. > > Do you see that (W, R) is reflexive entails that (W,R) is ideal? If all > worlds access to themselves, no world can be a cul-de-sac world, as a > cul-de-sac world don't access to any world, including themselves. > Reflexive is alpha R alpha for all alpha, so no cul de sac is possible. > > Bruno > > > > -- > 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. > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- > 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. > -- 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/d/optout.
