Re: Analytic Truth-makers

On 7/24/24 10:20 AM, olcott wrote:

On 7/24/2024 6:28 AM, Richard Damon wrote:

On 7/24/24 12:09 AM, olcott wrote:

On 7/23/2024 10:27 PM, Richard Damon wrote:

On 7/23/24 11:17 PM, olcott wrote:

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.

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In other words, NOTHING you are talking about apply to the logic that anyone else is using.
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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

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You ONLY construe it to be true in PA because that is
the answer that you memorized.

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No, it is True in PA, because it is LITERALLY True by the words it uses.
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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.

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But they DO exist in PA, I guess you just don't understand how math works.
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The sequence of steps is:
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Check the number 0 to see if it satisfies the PRR. Answer = No.
Check the number 1 to see if it satisfies the PRR. Answer = No.
Check the number 2 to see if it satisfies the PRR. Answer = No.
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keep repeating counting up through all the Natural Numbers.
 From the trick in MM, we can see that the math in PA will say no to all of them.
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Thus, after an infinite number of steps of truth preserving operations, we reach the conclusion that NO natural numbers actually exist that meet that PRR, just like G claimed, so it is correct.
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The lack of a proof means untruth.

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Nope, lack of a proof means unknown, as you have agreed.

 If an infinite number of steps fail to show that G is
provable in PA then G is untrue in PA.

But the infinte number of steps DO show that G is true in PA, because is shows that EVERY Natural Number fails to meet the requirment.
YOu don't seem to be understanding the English, I think your brainwashed filter is just clogged.

 

After all, you admitted that if the Goldbach conjecture would be an Analytic TRUTH if it was only established by an infinite sequence of truth preserving operations.
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 If an infinite number of steps do show that Goldbach is
provable in PA then Goldbach is true in PA.

Right, Just like they showed that G is true.

 

Since you don't know the meaning of the words, you just prove yourself unqualified to talk about such things.
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 Any proof requiring an infinite number of steps never resolved
to a truth value thus its truth value remains unknown.

No, "Proofs" can not have an infinite number of steps, proofs are ALWAYS finite in conventional logic.

 An alternative finite proof in MM only shows that the expression
is true in MM.

Nope, since the rules of math are the same, it must also be true in PA.
I guess you think that just because 2+3 = 5 in one system with normal mathematics, in another system with the exact same rules for mathematics then 2 + 3 might be 6.

 Truthmakers cannot cross system boundaries. --
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
 

But the base truthmakers for G in MM and PA are the same items, there is just a short cut in MM to let us colapse the infinte chain to a finite chain.
Those based truthmakers are that when we access every number, none of them will satisfy the PRR. It is just that in MM, we know something new about those models.