From Newsgroup: comp.ai.philosophy

Le 22/01/2026 |a 04:54, olcott a |-crit :

On 1/21/2026 9:37 PM, Richard Damon wrote:

On 1/21/26 10:45 AM, olcott wrote:

On 1/21/2026 6:35 AM, Richard Damon wrote:

On 1/20/26 11:54 PM, olcott wrote:

On 1/20/2026 10:04 PM, Richard Damon wrote:

On 1/20/26 4:23 PM, olcott wrote:

On 1/19/2026 11:29 PM, Richard Damon wrote:

My system is not supposed to decide in advance whether
Goldbach is wellrCafounded. A formula becomes a truthrCabearer >>>>>>>>> only when PA can classify it in finitely many steps.
Goldbach may or may not be classifiable; thatrCOs an open
computational fact, not a semantic requirement. This has
no effect on G||del, because G||delrCOs sentence is structurally >>>>>>>>> nonrCatruthrCabearing, not merely unclassified.

Which shows that you don't understand what logic systems are.

The don't "Decide" on truths, they DETERMINE what is true.

Your problem is that either there is, or there isn't a finite >>>>>>>> length proof of the statement.

Semantics can't change in a formal system, or they aren't really >>>>>>>> semantics.

Your problem is you don't understand Godel statement, as it *IS* >>>>>>>> truth bearing as it is a simple statement with no middle ground, >>>>>>>> does a number exist that satisfies a given relationship. Either >>>>>>>> there is, or there isn't. No other possiblity.

You confuse yourself by forgetting that words have actual
meaning, and that meaning can depend on using the right context. >>>>>>>>
Godel's G is a statement in the system PA.

It is a statement about the non-existance of a natural number >>>>>>>> that satisfies a particular computable realtionship.

It is a statement defined purely by mathematics and thus doesn't >>>>>>>> "depend" on other meaning.

It is a mathematical FACT, that for this relationship, no matter >>>>>>>> what natural number we test, none will satisfy it, so its
assertation that no number satisfies it makes it true.

PA augmented with its own True(PA,x) and False(PA,x)
is a decider for Domain of every expression grounded
in the axioms of PA.

No, it becomes inconsistant.

A system at a higher level of inference than PA can
reject any expressions that define a cycle in the
directed graph of the evaluation sequence of PA
expressions. Then PA could test back chained inference
from expression x and ~x to the axioms of PA.

But there is no "cycle" in the statement of G. It is PURELY a
statement of the non-existance of a number that satisfies a purely >>>>>> mathematic relationship (which has no meaning by itself in PA).

Even the relationship cannot exist <in> PA.
Instead it is about PA in outside model theory

No, it doesn't mention PA, it is about the numbers that are IN PA.

Your problem is you forget to actually know what Godel's G is, a you
only read the Reader's Digest version of the proof, as that is all
you can understand.

That, or you are saying that mathematics itself isn't in PA, and that >>>> you proof-theoretic stuff isn't in PA either,

Sorry, you are just showing how ignorant you are.

G_F rao -4Prove_F(G||del_Number(G_F)) contains a semantic
dependency loop, because evaluating G_F requires
evaluating Prove_F on the G||del number of G_F, which
in turn requires evaluating G_F again;

But that isn't G_F

G_F is a statement that a particular relationship (lets call it R(x) )
will not be satisfied for any natural number x.

That relationship has never existed inside actual
arithmetic

It actually IS a relationship in the domain of PA. PUNTO.

It is what it is. Denial is hopeless.



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