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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic,comp.theory
Subject: Re: Infinite proofs do not derive knowledge
Date: Wed, 10 Jul 2024 21:41:13 -0400
Organization: i2pn2 (i2pn.org)
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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.

It CAN'T be correct, as Formal Logic systems do not need to actually 
relate to the "actual world" but create their own "world" by their 
definitions and fundamental assumptions.

> 
> There is no such connection from g in PA

Yes there is, it is just infinite, so it is not a proof.

> there is such a connection from g in MM.

In MM, we just have a way to make it finite.

> 
> You even mistook a finite proof for an infinite one.
> That is as bad as mistaking a turd for a hamburger.
> 

But you are the one who is working on POOP.

What finite proof did I mistake for an infinite one?

You do understand that a proof is defined in a specific system, and can 
only be moved to another if all the premises and operations it uses are 
equivalently satisfied there. Thus a proof in MM that uses information 
from MM can't be moved into PA, but if the final premise doesn't use any 
of the thngs in MM, then the knowledge of the results do, and imply a 
proof (in MM) that an infinite chain of operations exist in PA to 
establish the statement, but not prove it in PA.