Re: Analytic Truth-makers

On 7/23/2024 10:03 PM, Richard Damon wrote:

On 7/23/24 10:45 PM, olcott wrote:

On 7/23/2024 9:15 PM, Richard Damon wrote:

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>

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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.

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You may say that, but you then refuse to do the work to actually do that.
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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.
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L is the language of a formal mathematical system.
x is an expression of that language.
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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.

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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,

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I redefined analytic truth to account for that. Things
like the Goldbach conjecture are in the different class
of currently unknowable.

 In other words, NOTHING you are talking about apply to the logic that anyone else is using.
 Note, Godel's G can't be put into that category, as it is KNOWN to be true in PA, because of a proof in MM

You ONLY construe it to be true in PA because that is
the answer that you memorized.
When you understand that true requires a sequence of
truth preserving operations and they do not exist in
PA then it is not true in PA.
Memorizing a view and insisting that this view must
be correct because that is what you memorized is what
mindless robots would do.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer