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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: Fri, 21 Mar 2025 07:49:06 -0500
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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.

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