Re: practical application of Godel's Incompleteness Theorem

MoeBlee wrote:
On Feb 7, 11:11 am, Nam Nguyen <namducngu...@xxxxxxx> wrote:
Jesse F. Hughes wrote:
Nam Nguyen <namducngu...@xxxxxxx> writes:
Whatever. The fact remains Godel's work assumes we knew what we meant by
"the standard [arithmetic] model", which we actually don't. (E.g. Is GC
true in that model?)
Right. For exactly the same reason, I don't know what is meant by
"Barack Obama" (e.g., is the statement "Obama has an ingrown toenail"
true?)
Would "Obama has an ingrown toenail"'s being true or false have
anything to do with truth or falsehood of "The US economy is very
bad"? Unless one works for a tabloid, the answer would be a "No".

Your analogy is incorrect in that GC and G(PA) [or CON(PA)] are bound
tightly together in truth/falsehood, in computability, in the rules
of inference, in definition of models, ... (to name a few), while
the statements about Obama's toenail and US economy aren't bound by
any reasoning framework, and one is free to assign any truth value
to them all, at will! [It might be of your interest to note that
in his "Gödel Theorem" TF spent some effort defining "Goldbach-like"
statements, in conjunction the Incompleteness!].

Jesse's just saying that we don't have to know every attribute of an
object just to identity the object.

Say, you've identified a 50-mile radius meteor hurling toward the Sun,
by its *precise* brightness and location on the sky-map. Don't you think
you'd like to know if it would slam into the Earth within 6 months?

We can identify the standard model
of PA while not knowing whether it has the attribute of GC being true
in it.

So, let me ask you this question: would both GC and cGC be "absolute
undecidable" formulas?

--
"To discover the proper approach to mathematical logic,
we must therefore examine the methods of the mathematician."
(Shoenfield, "Mathematical Logic")
.

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