Re: Analytic Truth-makers

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 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer