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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
Date: Sat, 22 Mar 2025 11:22:46 -0500
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On 3/22/2025 8:37 AM, Richard Damon wrote:
> On 3/21/25 11:03 PM, olcott wrote:
>> 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.
>>
> 
> But can't do that, as Tarski shows, as it creates contradictions when 
> the system is able to generate unprovable truths.
> 

Unless we do what ZFC did to redefine the foundations
of set theory and redefine the notion of a formal system.

If a formal system only contains a finite set of basic
facts and facts are only derived by applying truth
preserving operations to elements of this set then
True(X) has already been implicitly defined for every
element of this set.


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