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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic,comp.theory
Subject: Re: Minimal Logics in the 2020's: A Meteoric Rise --- Richard
 contradicts himself
Date: Mon, 8 Jul 2024 20:35:41 -0500
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On 7/8/2024 8:24 PM, Richard Damon wrote:
> On 7/8/24 8:56 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.
>>>
>>
>> *You already agreed that such things can never be known*
>>
>> The Goldbach conjecture is known to be true or false
>> yet not which one. Anything known to be true by an infinite
>> sequence of truth preserving operations contradicts the
>> fact that nothing can be known to be true by an infinite
>> sequence of truth preserving operations.
>>
> 
> Yes, if ALL we have is a statement that can only be shown by an infinite 
> series of steps, then we can not know that.
> 
> But many things that take an infinite number of steps in one system, 
> might have a finite proof in another system that can relate back to the 
> original one. KNOWLEDGE can cross system boundaries under the right 
> conditons, even if the proof doesn't transfer.
> 
> Just like Godel's G, that in F, needs an infinite number of tests to 
> prove in F, but by knowing from the meta-F of the implication of that 
> relationship, we can find the "shortcut" to proving it in a finite 
> number of steps.
> Goldbach's conjecture might be false, in which case that is provable by 
> just showing the even number that can't be the sum of two primes.
> 
> There might be a finite proof of it, either in the normal mathematics, 
> or in a meta-mathematics that allows us to transfer that knowledge back 
> to ordinary arithmetic.
> 
> Or, it might be that no such proof exists in any meta-mathematics, and 
> if so, it will just be unknown if it is true.
> 

Then why do you claiming that we can?

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