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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: Thu, 20 Mar 2025 10:02:42 -0500
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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.

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.

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