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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Infinite proofs do not derive knowledge --- Richard is proved
 wrong
Date: Mon, 15 Jul 2024 09:06:49 -0500
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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.

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

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.

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.

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

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.

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



-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer