On Fri, Oct 17, 2014 at 5:06 PM, Bruno Marchal <[email protected]> wrote:
> > On 16 Oct 2014, at 16:39, Platonist Guitar Cowboy wrote: > > > > On Thu, Oct 16, 2014 at 8:44 AM, LizR <[email protected]> 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 -- 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.
