On Wed, Sep 25, 2013 at 4:52 PM, Bruno Marchal <[email protected]> wrote: > > On 25 Sep 2013, at 15:50, Telmo Menezes wrote: > >> On Mon, Sep 23, 2013 at 7:49 PM, Bruno Marchal <[email protected]> wrote: >>> >>> >>> On 23 Sep 2013, at 12:41, Telmo Menezes wrote: >>> >>> <snip> >>> >>> >>> >>> Thus your interest in near-death experiences? >>> >>> >>> >>> Yes. And in all "extreme" altered state of consciousness. Those extreme >>> cases provide key information. >> >> >> Can this information be recovered? > > > A part of it, but it is experiential and not really communicable or > rationally justifiable. The wise searcher will remain mute on this, or be > precise that it gives only a report of an experience, or perhaps suggests a > (meta) theory in which such experience exists and are not communicable.
Ok. > > > >> For example, is a NDE that did not result in death, was it really a >> cul-de-sac? > > > > I would say no. But this is complex question, and the salvia experience > confused me on this topic. > In the NDE, people come back, but with salvia, locally, people does not come > back, only an approximative copy. I read several reports on this sensation of having been copied. It's very intriguing. > That's why i say that salvia is not an NDE, but a DE. That is why it can be > quite literally "life changing", and why I would not recommend it to > anybody. > > For the feeler or observer there is no cul-de-sac (thanks to the "& Dt" > added to the Bp, by Gödel's completeness theorem (not incompleteness!). > > But the scientist part of him has cul-de-sac, perhaps the publish or perish, > that is the fact that proofs must be finite, before publication. > > But it is hard to interpret all this literally. Caution. Sure. > > > > > > > >> >>> >>> >>> >>> We should *try* to avoid it, but we can't avoid it without loosing our >>> >>> universality. >>> >>> >>> The consistent machines face the dilemma between security and lack of >>> >>> freedom-universality. With <>p = ~[] ~p, here are equivalent way to >>> write >>> >>> it: >>> >>> >>> <>t -> ~[]<>t >>> >>> <>t -> <> [] f >>> >>> []<>t -> [] f >>> >>> >>> I don't understand how you arrive at this equivalence. >>> >>> >>> I use only the fact that (p -> q) is equivalent with (~q -> ~p) (the >>> contraposition rule, which is valid in classical propositional logic), >>> and >>> the definition of <> p = ~[] ~p. I use also that ~~p is equivalent with >>> p. >>> >>> Note that []p = ~~[]~~p = ~<> ~p. And, >>> >>> ~[]p = <> ~p >>> and >>> ~<>p = [] ~p >>> >>> Like with the quantifier, a not (~) jumping above a modal sign makes it >>> into >>> a diamond, if it was a bo, and a box, if it was a diamond. >>> >>> >>> Starting from <>t -> ~[]<>t. >> >> >> But where does <>t -> ~[]<>t come from? > > > <>t -> ~[] <> t > > is the same as > > ~[] f -> ~[] (~[] f) > > OK? Ok. > And that is .... the modal writing of Gödel's second incompleteness theorem: > if the false is not provable, then that fact (that the false is not > provable) is itself not provable. Nice, that is very satisfying. > Keep in mind that <>t (which I write also Dt) is the same as —[] f, which > is equivalent with "I am consistent", and Gödel's second theorem asserts: If > I am consistent then I cannot prove that I am consistent. Note that the "I" > is a third person I. (The first person "I" considers his/her consistency > trivial). > > > > > > >> >>> Contraposition gives ~~[]<>t -> ~<>t, and this >>> gives by above, []<>t -> []~t, which gives >>> []<>t -> []f (as ~t = f, and ~f = t). >>> >>> OK? >> >> >> Ok! >> >>> For the third one, starting from the first one again: <>t -> ~[]<>t, By >>> contraposition []<>t -> ~<>t , but ~<>t = []~t = [] f. >>> >>> OK? >> >> >> Ok! Thanks Bruno. My only problem now is the above. > > > Tell me if you see that it was the modal version of Gödel's second > incompleteness theorem. > > You might as an exercise show that it follows from Löb's theorem: > > [] ([] p -> p) -> [] p > > Two hints: 1) "~p" is the same as "p -> f", 2) replace p by f. > > OK? > > Löb's formula *is* the main axiom of the modal logic G. Alright, it's simple with the hints: [] ([] p -> p) -> [] p repalce p by f: [] ([] f -> f) -> [] f []f -> f = ~[]f: [](~[]f) -> []f contraposition: ~[]f -> ~(~[]f) Thanks! Telmo. > > Bruno > > > > 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/groups/opt_out.
