Scott
Posts:
66
Registered:
2/2/07
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Re: New essay on Goedel's Incompleteness Theorem
Posted:
Oct 1, 2009 7:17 AM
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I have already warned the one-starrer that I have been retching in
anguish for three years and that I have *deliberately avoided suicide*
to study Goedel's Incompleteness Theorem. He does not seem to realize
or care about the danger of his actions. If he continues to hide and
one-stars this post, we will take it as further evidence of his lack
of empathy and his willingness to 'cross a line' with someone on the
brink of suicide. This, in turn, will reflect on the moral character
of the entire country.
Remember, one-starrer: I wrote this essay for *you*.
On Sep 30, 11:12 pm, Tim Little <t...@little-possums.net> wrote:
> On 2009-09-30, Scott H <zinites_p...@yahoo.com> wrote:
>
> > At any rate, I have proposed that G refers to its 'reflection' or
> > Goedel code, which I have called G' instead of t.
>
> Yes, statement G refers to the number G'. G' does not literally refer
> to anything, as it is not a statement. If it is interpreted as a
> statement via the decoding, that statement is G and refers to G'.
> There is no G'', and no endless reference.
I've deliberately left it an open question whether G, G', G'', ... are
the same statement. Calling the referent of G' G'' does not mean that
G' and G'' are not equal.
It is important to consider Goedel's theorem from the perspective of
endless reference because a self-referential statement and its
analogous endlessly referential statement may have different
properties. For instance, "This statement is false," we think as
paradoxical, as opposed to
The following is false: The following is false: The following is
false: ...
which may have a truth value of T or F, as actual self-reference is
avoided. Knowing this, how would you prove that G, G', G'' ... were
really the same?
Come to think of it, this is what sci.math may be looking for: an
equivalent of
~Pr S[~Pr S x]
~Pr [~Pr S[~Pr S x]]
~Pr [~Pr [~Pr S[~Pr S x]]]
. . .
written as
G_0
G_1 --> G'_0
G_2 --> G'_1 --> G''_0
. . .
I have chosen to write G -> G' -> G'' -> ... because G_0, G_1,
G_2, ... are all equivalent. I think this will simplify the essay;
however, as always, I'm open to constructive feedback.
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