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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: Tue, 25 Mar 2025 09:56:33 -0500
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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.

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