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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 --- eternal
 september failure
Date: Mon, 8 Jul 2024 20:37:23 -0400
Organization: i2pn2 (i2pn.org)
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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.

Godel's G is clear since we know the struture of the statement.

I would need to study Tarski's work a bit more to see if the proof gives 
us an idea to bring that sequence down to baby steps you would understand.

We know it is true, as a result of the work that proved statements (1) 
and (2), so there IS an infinite set of steps to it, we just might not 
know what they are.

The fact you can't understand their existance, doesn't mean it isn't 
there, just that you are too stupid to understand it.