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Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic,comp.theory
Subject: Infinite proofs do not derive knowledge
Date: Wed, 10 Jul 2024 19:17:13 -0500
Organization: A noiseless patient Spider
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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.
>>>
>>>>
>>>> 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.
> 
> 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.

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

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