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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 caught
 in contradiction
Date: Mon, 8 Jul 2024 21:02:41 -0500
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On 7/8/2024 8:55 PM, Richard Damon wrote:
> On 7/8/24 9:35 PM, olcott wrote:
>> 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?
>>
> 
> I don't, we know 

Then why keep claiming it?

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