On Wed, Sep 25, 2013 at 4:52 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:
>
> On 25 Sep 2013, at 15:50, Telmo Menezes wrote:
>
>> On Mon, Sep 23, 2013 at 7:49 PM, Bruno Marchal <marc...@ulb.ac.be> 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 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/groups/opt_out.

Reply via email to