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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic,comp.theory
Subject: Re: Infinite proofs do not derive knowledge
Date: Thu, 11 Jul 2024 09:57:33 -0500
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On 7/10/2024 8:41 PM, Richard Damon wrote:
> On 7/10/24 9:26 PM, olcott wrote:
>> On 7/10/2024 8:13 PM, Richard Damon wrote:
>>> On 7/10/24 8:53 PM, olcott wrote:
>>>> On 7/10/2024 7:33 PM, Richard Damon wrote:
>>>>> 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.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> 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.
>>>>>
>>>>> 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.
>>>>>
>>>>
>>>> That is the fatal flaw right there.
>>>> That I have food in my house does not mean
>>>> that you will not starve to death.
>>>>
>>>
>>> So, you admit to not understand what is being talked about.
>>>
>>
>> I know what the common misconception is yet the
>> violates this truism:
>>
>> Every expression of language that is {true on the basis
>> of its meaning expressed using language} must have a
>> connection by truth preserving operations to its {meaning
>> expressed using language} is a tautology. The accurate
>> model of the actual world is expressed using formal language
>> and formalized natural language.
> 
> NoThat is just "word Salad" that doesn't actually realte to the logic of 
> the Formal systems, because you just don't understand what they are.
> 

A sequence of truth preserving operations in MM reaches g.
Not even an infinite sequence of truth preserving operations
in PA ever reaches g because there is a cycle in its directed
graph.

Minimal Type Theory (MTT)
https://www.researchgate.net/publication/315367846_Minimal_Type_Theory_MTT


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