On 24 February 2014 07:57, Bruno Marchal <[email protected]> wrote: > About [](A -> B) -> ([]A -> []B), let me ask you a more precise exercise. > > >> Convince yourself that this formula is true in all worlds, of all Kripke >> multiverses, with any illumination. >> Hint: you might try a reductio ad absurdum. try to build a multiverse in >> which that law would be violated. >> > > [](A -> B) -> ([]A -> []B) > > OK. For a disconnected universe this is t -> (t -> t) or t -> t which is > true. > > And for a Leibniz universe, I'm fairly sure this is also true. > > So that leaves {alpha R alpha} and {alpha R beta} and .... so on, for any > number of universes + relations. > > Maybe I can come back on this one. > > > Sure. Me too. (I will myself be plausibly slowed down, as I have two weeks > of teaching, take your time, just try to not forget what you learn, by > having good summary, that you can read from time to time). >
Well, does an illuminated Kripke universe effectively act as a Leibniz universe? If so this is definitely true (OK I try to jump in quickly here...) > > You do good work, but I am not sure if you have good notes. That is not > grave, but not helpful to you. > Yes, I know - about the notes, I mean. (Maybe I just need to search the list for []p to find some...) > Never hesitate to ask for any definition or recall. > > Thank you, don't worry I will :) > The modal logic part is not the real thing. The "real thing" will be the > interview of universal and Löbian machines, and some modal logics will just > sum up infinite conversations we can have with them, notably on predictions > and physics. > > Yes, that is where it all happens! But I feel like I am quite a way from that. -- 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.
