On Fri, Oct 17, 2014 at 5:06 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:

>
> On 16 Oct 2014, at 16:39, Platonist Guitar Cowboy wrote:
>
>
>
> On Thu, Oct 16, 2014 at 8:44 AM, LizR <lizj...@gmail.com> wrote:
>
>> Sounds like doublethink to me....which was of course a virtue and a
>> necessity if you lived on Airstrip One.
>>
>
> Right. If I remember correctly, peculiar machine is inaccurate but not
> necessarily inconsistent.
>
>
> Smullyan introduced that term in "Forever Undecided" (the little bible!)
>  with a slight different meaning. A reasoner (machine or not) is peculiar
> with respect to a proposition p, if he believes p, but also believes that
> he does not believe p. A reasoner is peculiar if there is a proposition p
> to which he is peculiar about.
>
> Such entities will be inaccurate, but not necessarily inconsistent. So you
> are right. The reverse does not follow, note.
>
> Exercise: find or build a peculiar entity.
> Solution: just that follish thing that Smullyan dares to do, and fake that
> you believe that G* is not talking about some machine or on G, but that G*
> talk about itself.
>

That was the funky move I forgot, which places this in good perspective.


>
> G* typically proves <>t   (correct intepretation: the machine I talk about
> is consistent)
> G* proves also, like G, the incompleteness theorem: <>t -> ~[]<>t, and G*
> is closed fro the modus ponens, so, G* prove ~[]<>t.
> So G* proves both <>t and  ~[]<>t, making G* peculiar on <>t. And G* is
> consistent, it does not prove the false.
>
> Of course G* is *not* peculiar on <>t. G* is peculiar on <>t only if
> *you* interpret (wrongly) the box of G* as being the provability by G. Of
> course the box of G* is the provability by G, or by any correct Löbian
> entity.
>
> This shows that any machine confusing science and truth (the box at the G
> level and the box at the *-level) will be peculiar on her consistency.
>

Somehow, I feel a bit more sorted now. I'll be able to sleep better tonight
;-)


>
> I think that we become peculiar if we identify consciousness and
> self-consistency, that might be true, but is at the star level. May be
> Dennett, the Churchland are peculiar, or a negative version of it.
>
> Interesting. I am so busy on clarifying the []p and []p & p confusion,
> that I forget the quite important G/G* confusion, which leads to the queer
> reasoner, as Smullyan called them also.
>

That's a lot of confusion on your shoulders.


>
>
> So you have to doublethink in consistent ways, to not generate suspicion.
>
> And they're also not conceited ( Believing for all p: Bp -> p, or there
> doesn't exist p such that: ~p & Bp ), thus believing in their
> infallibility. PGC
>
>
>
> Of course, with that same "queer" interpretation of the box (the
> provability by G* itself on itself), G* is conceited, as he believes in []p
> -> p for all p.
>

That's "of course" to you and "huh? Ah, nice!" again to me. PGC

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