From Newsgroup: comp.ai.philosophy

On 7/23/2024 11:26 AM, olcott wrote:

On 7/23/2024 9:51 AM, Wasell wrote:

On Mon, 22 Jul 2024 20:17:15 -0400, in article
<3fb77583036a3c8b0db4b77610fb4bf4214c9c23@i2pn2.org>, Richard Damon
wrote:

On 7/22/24 8:11 PM, olcott wrote:

[...]

*No stupid I have never been saying anything like that* If g and
~g is not provable in PA then g is not a truth-bearer in PA.

What makes it different fron Goldbach's conjecture?

I think a better example might be Goodstein's theorem [1].

* It is expressible in the same language as PA.

* It is neither provable, nor disprovable, in PA.

* We know that it is true in the standard model of arithmetic.

* We know that it is false in some (necessarily non-standard) models
   of arithmetic.

* It was discovered and proved long before it was shown to be
   undecidable in PA.

The only drawback is that the theorem is somewhat more complicated
than Goldbach's conjecture -- not a lot, but a bit.


[1] <https://en.wikipedia.org/wiki/Goodstein%27s_theorem>

I am establishing a new meaning for
{true on the basis of meaning expressed in language}
Formerly known as {analytic truth}.
This makes True(L,x) computable and definable.

L is the language of a formal mathematical system.
x is an expression of that language.

When we understand that True(L,x) means that there is a finite
sequence of truth preserving operations in L from the semantic
meaning of x to x in L, then mathematical incompleteness is abolished.

~True(L,x) ∧ ~True(L,~x)
means that x is not a truth-bearer in L.
It does not mean that L is incomplete

--
Copyright 2026 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable.

This required establishing a new foundation
for correct reasoning.
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