Re: Infinite proofs do not derive knowledge --- Olcott is proved wrong

On 7/15/24 10:06 AM, olcott wrote:

On 7/15/2024 3:48 AM, Mikko wrote:

On 2024-07-11 13:51:47 +0000, olcott said:
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On 7/11/2024 2:07 AM, Mikko wrote:

On 2024-07-10 13:58:42 +0000, olcott said:
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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.

>
It is quite obvious that you are the liar. You have not shown any error
above.
>

>
Richard said the infinite proofs derive knowledge
and that infinite proofs never derive knowledge.

>
That is included in my "not shown above", in particular the word "proofs".
>

 On 7/8/2024 7:37 PM, Richard Damon wrote:
 >
 > Tarski's x like Godel's G are know to be true by an
 > infinite sequence of truth preserving operations.
 >
 We cannot know that anything is true by an infinite
sequence of truth preserving operations as Richard
falsely claims above.

You are just mixing up your words because you don't understd that wrores. amnd just making yourself into a LIAR.
Our KNOWLEDGE that the statement is true, comes from a finite proof in the meta system. BECAUSE we know the statment is true, we know that there exists an infinite chain of logic in the system that makes it true.

 This was eventually resolved by Richard acknowledging
that he never meant what he said.

No, you still don't understand what i have been say, that or you are just being your pathological liar again.

 What he meant was that when an infinite sequence of truth
preserving operations are transformed into a finite proof
then we can know what the result of an infinite sequence
of truth preserving operations would be.

And that transformation is done in a META system. Something you seem to be incapable of understanding as you seem incapable of understand what the FORMAL part means in Formal Logic.

 His claim is that an infinite sequence of truth preserving
operations derives g in PA. This is known by a finite proof
in meta-math.
 I disagree.

And you are wrong.

 ...We are therefore confronted with a proposition which
asserts its own unprovability. 15 ... (Gödel 1931:40-41)

So? That is a statement in MM, not PA.

 Not even an infinite sequence of truth preserving operations
can show that a self-contradictory expression is true in PA.
When examined in meta-math the expression ceases to be
self-contradictory making it provable.

But asserting your own unprovablity ISN'T "Self-Contradictory" unless you are in a primitive system that specifies that truth must be provable.

 More generically every expression that is neither provable
nor refutable is any formal system F is not a proposition of F.
>

Nope. Where are you getting THAT from?
I guess you are saying that the great problems of mathematics like the twin primes conjecture might not be propositions in mathematics.
I.E. You are just showing you don't know what you are talking about.
Having a truth value, whether known or even knowable make a statment a proposition in the system.
By your logic, we can't talk about a proposition to ask if it is true, until we first prove or refute it, and thus, can't work on the proof or refutation in the system.
That makes you system pretty worthless, it knows what it started with, and only what you stumbles upon.