Re: Infinite proofs do not derive knowledge, but do define Truth!

On 7/11/24 10:57 AM, olcott wrote:

On 7/10/2024 8:41 PM, Richard Damon wrote:

On 7/10/24 9:26 PM, olcott wrote:

On 7/10/2024 8:13 PM, Richard Damon wrote:

On 7/10/24 8:53 PM, olcott wrote:

On 7/10/2024 7:33 PM, Richard Damon wrote:

On 7/10/24 8:17 PM, olcott wrote:

On 7/10/2024 7:13 PM, Richard Damon wrote:

On 7/10/24 8:09 PM, olcott wrote:

On 7/10/2024 7:01 PM, Richard Damon wrote:

On 7/10/24 9:58 AM, olcott wrote:

On 7/8/2024 7:37 PM, Richard Damon wrote:

On 7/8/24 8:28 PM, olcott wrote:

>
Every expression of language that cannot be proven
or refuted by any finite or infinite sequence of
truth preserving operations connecting it to its
meaning specified as a finite expression of language
is rejected.
>

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So?
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Tarski's x like Godel's G are know to be true by an infinite sequence of truth preserving operations.
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Every time that you affirm your above error you prove
yourself to be a liar.

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What error?
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We know, that in the system the statements are made, tehre is an infinite chain of truth preserving operationf from teh fundamental truths of the sytsems to the conclusion.
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We know that because in a meta-theory we can develop additional knowledge allowing us to see the infinite chain, with something like an induction property or something else that reduces the infinite to finite.
>

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On 7/8/2024 9:59 PM, Richard Damon wrote:
 > No, infinite "proofs" determine TRUTH, not knowledge.
>
You could just say, "I didn't say that correctly"
and we would be done.

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Right, an infinite "proof", in quotes because that is the term YOU use, even though there is no such thing, but in actuality it is an infinite chain of truth preserving operations  DO establish that something is True in the system, but by being infinite, we can never dirrectly follow that path to know it.

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That was your mistake. You said that we could know it.

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Because we can, by knowledge gained in the meta-system.
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Then it is no longer an infinite proof oh dim one.
It is a finite proof in another system.

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Right, ANOTHER SYSTEM. Godel's proof is that there is a statment that is true in the system it is in with no proof IN THAT SYSTEM.
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Incompleteness is about a SPECIFIC SYSTEM having true statements IN IT, what don't have proofs of them IN IT.
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That is the fatal flaw right there.
That I have food in my house does not mean
that you will not starve to death.
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So, you admit to not understand what is being talked about.
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I know what the common misconception is yet the
violates this truism:
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Every expression of language that is {true on the basis
of its meaning expressed using language} must have a
connection by truth preserving operations to its {meaning
expressed using language} is a tautology. The accurate
model of the actual world is expressed using formal language
and formalized natural language.

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NoThat is just "word Salad" that doesn't actually realte to the logic of the Formal systems, because you just don't understand what they are.
>

 A sequence of truth preserving operations in MM reaches g.
Not even an infinite sequence of truth preserving operations
in PA ever reaches g because there is a cycle in its directed
graph.

Your following the wrong graph, because you are doing it backwards, like everything you do. Since you don't understand what the statment G is, how can you show it has a loop?
Start at 0, and evaluate the relationship, and see that it fails.
Then go to 1, and evaluate the relationship, and see that it fails,
Then go to 2, and evaluate the relationship, and see that it fails.
keep on going for every n, all countable infinite number of them, and it turns out that they all will fail.
Thus, G, the statement that no natural number exists that satisfies that relationship is established, as we have checked EVERY number and see that it fails.
Thus, there IS an infinite sequence of truth preserving operations (counting 0, 1, 2, 3, ... through all the Natural Numbers) and for each one do the finite set of operations to see that it doesn't satisfy the relationship, that establishes that G is true.
The "Cycle" you see is from trying to move the interpretation that is shown in MM into PA, which isn't a legal operation
Again, your subject line (which I corrected) shows that basic error in your logic, no one says the infinite sequcence itself created knowledge, just the fact that G is true in PA. The finite proof in MM, with the transference property to PA gives us the knowledge, but not a proof in PA.

 Minimal Type Theory (MTT)
https://www.researchgate.net/publication/315367846_Minimal_Type_Theory_MTT