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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: How a True(X) predicate can be defined for the set of analytic
 knowledge (GKEUL)
Date: Sat, 22 Mar 2025 12:49:01 -0500
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On 3/22/2025 11:38 AM, Mikko wrote:
> On 2025-03-22 03:03:39 +0000, olcott said:
> 
>> On 3/21/2025 9:31 PM, Richard Damon wrote:
>>> On 3/21/25 9:24 PM, olcott wrote:
>>>> On 3/21/2025 7:50 PM, Richard Damon wrote:
>>>>> On 3/21/25 8:40 PM, olcott wrote:
>>>>>> On 3/21/2025 6:49 PM, Richard Damon wrote:
>>>>>>> On 3/21/25 8:43 AM, olcott wrote:
>>>>>>>> On 3/21/2025 3:41 AM, Mikko wrote:
>>>>>>>>> On 2025-03-20 14:57:16 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> On 3/20/2025 6:00 AM, Richard Damon wrote:
>>>>>>>>>>> On 3/19/25 10:42 PM, olcott wrote:
>>>>>>>>>>>> It is stipulated that analytic knowledge is limited to the
>>>>>>>>>>>> set of knowledge that can be expressed using language or
>>>>>>>>>>>> derived by applying truth preserving operations to elements
>>>>>>>>>>>> of this set.
>>>>>>>>>>>
>>>>>>>>>>> Which just means that you have stipulated yourself out of all 
>>>>>>>>>>> classical logic, since Truth is different than Knowledge. In 
>>>>>>>>>>> a good logic system, Knowledge will be a subset of Truth, but 
>>>>>>>>>>> you have defined that in your system, Truth is a subset of 
>>>>>>>>>>> Knowledge, so you have it backwards.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> True(X) always returns TRUE for every element in the set
>>>>>>>>>> of general knowledge that can be expressed using language.
>>>>>>>>>> It never gets confused by paradoxes.
>>>>>>>>>
>>>>>>>>> Not useful unless it returns TRUE for no X that contradicts 
>>>>>>>>> anything
>>>>>>>>> that can be inferred from the set of general knowledge.
>>>>>>>>>
>>>>>>>>
>>>>>>>> I can't parse that.
>>>>>>>>  > (a) Not useful unless
>>>>>>>>  > (b) it returns TRUE for
>>>>>>>>  > (c) no X that contradicts anything
>>>>>>>>  > (d) that can be inferred from the set of general knowledge.
>>>>>>>>  >
>>>>>>>> Because my system begins with basic facts and actual facts
>>>>>>>> can't contradict each other and no contradiction can be
>>>>>>>> formed by applying only truth preserving operations to these
>>>>>>>> basic facts there are no contradictions in the system.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> No, you system doesn't because you don't actually understand what 
>>>>>>> you are trying to define.
>>>>>>>
>>>>>>> "Human Knowledge" is full of contradictions and incorrect 
>>>>>>> statements.
>>>>>>>
>>>>>>> Adittedly, most of them can be resolved by properly putting the 
>>>>>>> statements into context, but the problem is that for some 
>>>>>>> statement, the context isn't precisely known or the statement is 
>>>>>>> known to be an approximation of unknown accuracy, so doesn't 
>>>>>>> actually specify a "fact".
>>>>>>
>>>>>> It is self evidence that for every element of the set of human
>>>>>> knowledge that can be expressed using language that undecidability
>>>>>> cannot possibly exist.
>>>>>>
>>>>>>
>>>>>
>>>>> SO, you admit you don't know what it means to prove something.
>>>>>
>>>>
>>>> When the proof is only syntactic then it isn't directly
>>>> connected to any meaning.
>>>
>>> But Formal Logic proofs ARE just "syntactic"
>>>
>>>>
>>>> When the body of human general knowledge has all of its
>>>> semantics encoded syntactically AKA Montague Grammar of
>>>> Semantics then a proof means validation of truth.
>>>
>>> Yes, proof is a validatation of truth, but truth does not need to be 
>>> able to be validated.
>>>
>>
>> True(X) ONLY validates that X is true and does nothing else.
> 
> We can believe the "nothing else" part. The rest would require a proof.
> 

True(X) is a predicate implementing a membership algorithm
for the body of general knowledge that can be expressed
using language.

Infinite proofs cannot be provided. Find a counter-example
where an element of the set of general knowledge that can
be expressed using language(GKEUL) would fool a True(X)
predicate into providing the wrong answer.

"This sentence is not true" cannot be derived by applying
truth preserving operations to basic facts thus is rejected
as not a member of (GKEUL).

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer