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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: Wed, 26 Mar 2025 12:58:10 -0500
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On 3/26/2025 3:39 AM, Mikko wrote:
> On 2025-03-26 02:15:26 +0000, olcott said:
> 
>> On 3/25/2025 8:08 PM, Richard Damon wrote:
>>> On 3/25/25 10:56 AM, olcott wrote:
>>>> On 3/25/2025 5:19 AM, Mikko wrote:
>>>>> On 2025-03-22 17:53:28 +0000, olcott said:
>>>>>
>>>>>> On 3/22/2025 11:43 AM, Mikko wrote:
>>>>>>> On 2025-03-21 12:49:06 +0000, olcott said:
>>>>>>>
>>>>>>>> On 3/21/2025 3:57 AM, Mikko wrote:
>>>>>>>>> On 2025-03-20 15:02:42 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> On 3/20/2025 8:09 AM, Mikko wrote:
>>>>>>>>>>> On 2025-03-20 02:42:53 +0000, olcott said:
>>>>>>>>>>>
>>>>>>>>>>>> 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.
>>>>>>>>>>>
>>>>>>>>>>> A simple example is the first order group theory.
>>>>>>>>>>>
>>>>>>>>>>>> When we begin with a set of basic facts and all inference
>>>>>>>>>>>> is limited to applying truth preserving operations to
>>>>>>>>>>>> elements of this set then a True(X) predicate cannot possibly
>>>>>>>>>>>> be thwarted.
>>>>>>>>>>>
>>>>>>>>>>> There is no computable predicate that tells whether a sentence
>>>>>>>>>>> of the first order group theory can be proven.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Likewise there currently does not exist any finite
>>>>>>>>>> proof that the Goldbach Conjecture is true or false
>>>>>>>>>> thus True(GC) is a type mismatch error.
>>>>>>>>>
>>>>>>>>> However, it is possible that someone finds a proof of the 
>>>>>>>>> conjecture
>>>>>>>>> or its negation. Then the predicate True is no longer complete.
>>>>>>>>>
>>>>>>>>
>>>>>>>> The set of all human general knowledge that can
>>>>>>>> be expressed using language gets updated.
>>>>>>>>
>>>>>>>>>> When we redefine logic systems such that they begin
>>>>>>>>>> with set of basic facts and are only allowed to
>>>>>>>>>> apply truth preserving operations to these basic
>>>>>>>>>> facts then every element of the system is provable
>>>>>>>>>> on the basis of these truth preserving operations.
>>>>>>>>>
>>>>>>>>> However, it is possible (and, for sufficiently powerful sysems, 
>>>>>>>>> certain)
>>>>>>>>> that the provability is not computable.
>>>>>>>>>
>>>>>>>>
>>>>>>>> When we begin with basic facts and only apply truth preserving
>>>>>>>> to the giant semantic tautology of the set of human knowledge
>>>>>>>> that can be expressed using language then every element in this
>>>>>>>> set is reachable by these same truth preserving operations.
>>>>>>>
>>>>>>> The set of human knowledge that can be expressed using language
>>>>>>> is not a tautology.
>>>>>>>
>>>>>>
>>>>>> tautology, in logic, a statement so framed that
>>>>>> it cannot be denied without inconsistency.
>>>>>
>>>>> And human knowledge is not.
>>>>>
>>>>
>>>> What is taken to be knowledge might possibly be false.
>>>> What actually <is> knowledge is impossibly false by
>>>> definition.
>>>>
>>>
>>> How do you DEFINE what is actually knowledge?
>>>
>>
>> *This is a good first guess*
>> The set of expressions of language that have the
>> semantic property of true that are written down
>> somewhere.
> 
> We already know that many expressions of language that have the semantic
> proerty of true are not written down anywhere.

Only general knowledge

> Ae also know that many expressions of language that are written down
> somewhere lack the semantic property of true.
> 

False statements do not count as knowledge.

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