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 -- 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 email@example.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.