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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Analytic Truth-makers
Date: Tue, 23 Jul 2024 11:26:08 -0500
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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