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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 19:47:33 -0500
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On 3/21/2025 6:49 PM, Richard Damon wrote:
> On 3/21/25 8:49 AM, olcott wrote:
>> 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.
> 
> And thus your concept of truth breaks.
> 
> Truth, by its definition is an immutable thing, but you just defined it 
> to be mutable.
> 
> How often do we need to re-verify our truths?
> 
>>
>>>> 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.
>>
> 
> But you aren't begining with basic facts, but with what has been assumed 
> to be the basic facts. 

That is not what I stipulated.
When we begin with what actual are the set of basic
facts and are only allowed to apply truth preserving
operations to these basic facts then it is self-evident
that True(X) must always be correct.

> We don't actually KNOW the basics principles for 
> many things, but have been working to understand them.
Then these are not included in the set of knowledge.

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