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]]] . . .
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.