[Moderator's note: Followups, if any, should contain enough astronomy
content. -P.H.]

On 1/19/18 1/19/18 1:19 AM, Richard D. Saam wrote:
On 1/10/18 3:15 PM, Jonathan Thornburg [remove -animal to reply] wrote:
[...]
All of the above logic must consider Goedel's incompleteness theorem

Not really (see below).

First Incompleteness Theorem from Wiki: "Any consistent formal system F
within which a certain amount of elementary arithmetic can be carried out is
incomplete; i.e., there are statements of the language of F which can neither
be proved nor disproved in F." (Raatikainen 2015)

Yes. That simply does not apply to what JT wrote. (And it misses some important
conditions of the actual theorem.)

or perhaps another statement: all hypotheses cannot be considered true or
untrue within any axiomatic structure defining the hypotheses.

This is NOWHERE CLOSE to Goedel's incompleteness theorems. Moreover, it is
FALSE, at least in general.

Perhaps you are thinking of Tarski's undefinability theorem --
I believe it is closer to what you seem to be trying to say. But
it, too, does not apply to using math for physical models (where
validity is not "true or false", but rather agreement with
experiment).

So, it is impossible to prove or disprove the complete universe structure
based on any axiomatic structure

You need to learn basic logic, as yours here is fatally flawed.

You also need to learn the different between mathematics (incl. logic) and
physics. No axiomatic structure has anything to do with the "structure of the
universe". But, of course, axiomatic structures in the form of mathematics
figure prominently in our MODELS of the universe. That the math is necessarily
incomplete does not affect its applicability for constructing physical models.

Tom Roberts