On 6 March 2014 22:06, Bruno Marchal <[email protected]> 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 [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. > > > 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 [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. > -- 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/d/optout.
