Re: Infinite proofs do not derive knowledge

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.
>

>
So?
>
Tarski's x like Godel's G are know to be true by an infinite sequence of truth preserving operations.
>

>
Every time that you affirm your above error you prove
yourself to be a liar.

>
What error?
>
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.
>
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.

>
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.

>
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.
>

 Then it is no longer an infinite proof oh dim one.
It is a finite proof in another system.

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.
Incompleteness is about a SPECIFIC SYSTEM having true statements IN IT, what don't have proofs of them IN IT.
You don't seem to understand that difference.
Likely because you just don't understand what formal system are.

 I am going to rename this post so that we don't Hijack
Mild Shock's post.