Re: Analytic Truth-makers

On 7/23/24 12:26 PM, 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:

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

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[...]
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*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.

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What makes it different fron Goldbach's conjecture?

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I think a better example might be Goodstein's theorem [1].
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* It is expressible in the same language as PA.
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* It is neither provable, nor disprovable, in PA.
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* We know that it is true in the standard model of arithmetic.
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* We know that it is false in some (necessarily non-standard) models
   of arithmetic.
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* It was discovered and proved long before it was shown to be
   undecidable in PA.
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The only drawback is that the theorem is somewhat more complicated
than Goldbach's conjecture -- not a lot, but a bit.
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[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.

You may say that, but you then refuse to do the work to actually do that.
The problem is that if you try to redefine the foundation, you need to build the whole building all over again, but you just don't understand what you need to do that.

 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.

Except you just defined that this isn't true, as you admit that the Goldbach conjecgture COULD be an analytic truth even if it doesn't have a finte sequence of truth perserving operations, but only an infinite sequence. But a Analytic Truth MUST be a "truth-bearer", so you just blew up your whole logic system with your lies.

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