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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic,comp.theory
Subject: Re: Minimal Logics in the 2020's: A Meteoric Rise --- Olcott caught
 in inescapable contradiction
Date: Mon, 8 Jul 2024 22:59:02 -0400
Organization: i2pn2 (i2pn.org)
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On 7/8/24 10:31 PM, olcott wrote:
> On 7/8/2024 9:11 PM, Richard Damon wrote:
>> On 7/8/24 10:04 PM, olcott wrote:
>>> On 7/8/2024 7:37 PM, Richard Damon wrote:
>>>> On 7/8/24 8:28 PM, olcott wrote:
>>>>> On 7/8/2024 7:07 PM, Richard Damon wrote:
>>>>>> On 7/8/24 8:00 PM, olcott wrote:
>>>>>>> On 7/7/2024 10:09 PM, olcott wrote:
>>>>>>>> On 7/7/2024 10:02 PM, olcott wrote:
>>>>>>>>>
>>>>>>>>> Formal logic is a subset of this.
>>>>>>>>> Not-a-logic-sentence(PA,g) ≡ (~True(PA,g) ∧ ~True(PA,~g))
>>>>>>>>> There are no truth preserving operations in PA to g or to ~g
>>>>>>>>>
>>>>>>>>
>>>>>>>> https://liarparadox.org/Tarski_275_276.pdf
>>>>>>>>
>>>>>>>> Within my analytical framework this Tarski sentence is merely
>>>>>>>> self-contradictory
>>>>>>>>
>>>>>>>> (3) x ∉ Provable if and only if x ∈ True. // (1) and (2) combined
>>>>>>>>
>>>>>>>> There are no truth preserving operations in Tarski's
>>>>>>>> theory to x if and only if There are truth preserving
>>>>>>>> operations in Tarski's theory to x
>>>>>>>>
>>>>>>>
>>>>>>> There cannot possibly be an infinite proof that proves
>>>>>>> that there is no finite proof of Tarski x in Tarski's theory
>>>>>>
>>>>>> Who says there needs to be a infinite proof, since there is no 
>>>>>> such thing.
>>>>>>
>>>>>> As I said, one example of such an x is Godel's G.
>>>>>>
>>>>>>>
>>>>>>> The infinite proof of the Goldbach conjecture
>>>>>>> (if it is true) continues to find more true
>>>>>>> cases than it had before, thus makes progress
>>>>>>> towards its never ending goal (if its true).
>>>>>>
>>>>>> or, it continue to show that there is no counter examples.
>>>>>>
>>>>>> "Progress" on an infinite path isn't really measurable.
>>>>>>
>>>>>>>
>>>>>>> The cycles in the following two cases never make any progress
>>>>>>> towards any goal they are merely stuck in infinite loops.
>>>>>>
>>>>>> Which just means you are on the wrong path. One wrong path doesn't 
>>>>>> me that there is no path.
>>>>>>
>>>>>>>
>>>>>>> The Prolog unify_with_occurs_check test means that
>>>>>>> LP is stuck in an infinite loop that makes no progress
>>>>>>> towards resolution. I invented Minimal Type Theory to
>>>>>>> see this, then I noticed that Prolog does the same thing.
>>>>>>
>>>>>> Which is irrelevent, since Prolog can't handle the basics of the 
>>>>>> field that Traski assumes.
>>>>>>
>>>>>>>
>>>>>>> ?- LP = not(true(LP)).
>>>>>>> LP = not(true(LP)).
>>>>>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>>>>>> false.
>>>>>>>
>>>>>>> LP := ~(L ⊢ LP)
>>>>>>> 00 ~ 01
>>>>>>> 01 ⊢ 01, 00
>>>>>>> 02 L
>>>>>>>
>>>>>>> The cycle in the direct graph of LP is
>>>>>>> an infinite loop that make no progress
>>>>>>> towards the goal of evaluating LP as
>>>>>>> true or false.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> So?
>>>>>>
>>>>>> Failure to prove by example doesn't show something isn't true.
>>>>>>
>>>>>> You are just proving you are stupid and don't know what you are 
>>>>>> talking about.
>>>>>
>>>>> 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.
>>>>
>>>
>>> Liar?
>>>
>>
>> What lie?
>>
>> I guess you have confused yourself and lost your train of thought 
>> (which I think is just N gauge)
> 
> Maybe the actual problem is that your ADD is much worse than I thought.
> 
> You know that infinite proofs never determine knowledge AND claim
> that infinite proofs determine knowledge.
> 
> 

No, infinite "proofs" determine TRUTH, not knowledge.

That is part of you problem you think truth and knowledge are the same 
thing, but they are not.