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.
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.
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.
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.
Bruno
--
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.
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/d/optout.
