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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 right here
Date: Mon, 8 Jul 2024 22:32:30 -0500
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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.
> 

"are *know to be true* by an infinite sequence"
"are *know to be true* by an infinite sequence"
"are *know to be true* by an infinite sequence"
"are *know to be true* by an infinite sequence"
"are *know to be true* by an infinite sequence"

On 7/8/2024 9:59 PM, Richard Damon wrote:
 > No, infinite "proofs" determine TRUTH, not knowledge.

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