Re: [PO] Re: Can a regular Turing Machine provide Protected Memory?

From: Jym (moyen_at_loria.fr)
Date: 08/30/04 

Date: Mon, 30 Aug 2004 19:54:46 +0200

On Sun, 29 Aug 2004, Peter Olcott wrote:

>
> "Simon G Best" <s.g.best@btopenworld.com> wrote in message news:4131B073.8000909@btopenworld.com...
> > Here is the proof that you are a liar.
> >
> > But first, let's punish you some more anyway :-)
> >
> > Peter Olcott wrote:
> > > "Simon G Best" <s.g.best@btopenworld.com> wrote in message news:4130B2EA.5000909@btopenworld.com...
> > >
> > >>You obviously need some more punishment, so:
> > >>
> > >>String B: "String B will never be proven to constitute a true, valid
> > >>statement."
> > >>
> > >>String C: "String B will never be proven to constitute a true, valid
> > >>statement."
> > >>
> > >>String B will never be proven to constitute a true, valid statement.
> > >>
> > >>What about string C?
> > >
> > > String B is not a statement at all due to its infinitely recursive structure.
> > > String C would be a true statement.
> >
> > They're exactly the same string. Try again.
>
> They are not at all the same. The crucial difference is the reference.
> When you merely change the label of string "B" to string "C", then
> string "B" immediately loses its infinitely recursive structure and
> becomes a valid statement. String B has infinitely recursive self
> reference. String C does not have any sort of self-reference. That
> is the difference that causes the former to be invalid, and the latter
> to be valid. That is also why the Liar Paradox is not a paradox
> at all, but, merely an incorrectly formed statement.

Did you ever heard of Gödel's incompletness theorem ?
Did you ever realise that the proof of it merely consists in expressing
string B into arithmetic ?
Once you've given up Turing, do you intend to attack Gödel ?

> > > The kookiest thing that I heard was probably the guy that proved
> > > that no automobiles can ever possibly operate properly specifically
> > > because they can be made to not operate properly.
> >
> > Did he /really/ 'prove', or even claim to prove, any such thing?
> >
> > > All that I has
> > > to do was to substitute his reference to My Halt Analyzer with the
> > > term Automobile.
> >
> > No. As you clearly admit here, you had to change what he said to make
> > it seem that he was claiming something he simply wasn't claiming.
> >
> > You are clearly now a proven liar. This is proven by your own admission
> > to having changed what he actually claimed.
> >
> > Simon
> >
> I am not a liar. I merely used his own reasoning. I did not
> change the reasoning. I only changed the reference variable.
> His reasoning proves that automobiles can never run specifically
> because they can be caused to not run. His reasoning shows
> that X will not function properly because X can be made to
> not function properly. This is not at all any sort of lie.

You know what ? The sentence "every prime number greater than 3 cannot be
divided by 2" is actually true because prime number greater than 3 "are
made to not be divided by 2". Yet, if you change the "reference variable"
from "prime numbers" to, say, "even numbers" the whole sentence become
absolutly false. Incredible, changing terms in a sentence may actually
change its semantics !

Hypocoristiquement,
Jym.

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