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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 --- eternal
 september failure
Date: Mon, 8 Jul 2024 19:00:37 -0500
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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

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).

The cycles in the following two cases never make any progress
towards any goal they are merely stuck in infinite loops.

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.

?- 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.


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