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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 20:07:43 -0400
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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.