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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Infinite proofs do not derive knowledge --- Olcott is proved
 wrong
Date: Mon, 15 Jul 2024 22:18:03 -0400
Organization: i2pn2 (i2pn.org)
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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:
>>
>>> On 7/11/2024 2:07 AM, Mikko wrote:
>>>> On 2024-07-10 13:58:42 +0000, olcott said:
>>>>
>>>>> 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.