[Avodah] [Areivim] Godel's incompleteness theorems -- Proof of G-d'sexistence

[Micha Berger]

On Tue, Nov 16, 2010 at 03:03:51PM -0500, Hankman wrote:
: As "Chosomo shel HKB'H emes," I presume that implies that the statement
: "I am false" wrt to HKB'H, cholila, would be inadmissable (and certainly
: untrue). What would that mean in our context wrt Godel?

The statement "I am false" is made WRT the statement "I am false".
It's self referential. The "I" is the sentence itself, not its
speaker.

Normal statements that refer to things other than statements, such as
those about HQBH or what He isn't, are not part of Goedel's proof.

Goedel proved that a formal system of a certain complexity can't be
both complete and consistent. (Although it's usually phrased that it
can't be complete, with the possibility of an inconsistent system --
one in which both X and not X can be proven -- ruled out prema facae.)
He did so by showing that the assumption that it is possible would lead
to paradox. But the only incompleteness he proved MUST exist in such
systems are self-referential ones, statements that refer to themselves,
directly or not.

Second, this is a formal system. Meaning, a bunch of rigorously defined
rules and an algorithm. Who said the human mind and its proofs can be
reduced to a formal system? Perhaps artificial intelligence is impossible
simply because the mind does things digital computers, meaning "formal
system engines" can't? (Turing proved that two technical terms that
roughly are the same as "digital computer" and "formal system engine"
are identical.) And what if theological argument is within that domain
of things we do in ways that are beyong computing?

Tir'u baTov!
-Micha

-- 
Micha Berger             Spirituality is like a bird: if you tighten
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