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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 23:04:15 -0500
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On 3/26/2025 10:29 PM, Richard Damon wrote:
> On 3/26/25 10:58 PM, olcott wrote:
>> On 3/26/2025 8:22 PM, Richard Damon wrote:
>>> On 3/26/25 2:01 PM, olcott wrote:
>>>> On 3/26/2025 3:36 AM, Mikko wrote:
>>>>> On 2025-03-25 14:56:33 +0000, olcott said:
>>>>>
>>>>>> 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.
>>>>>
>>>>> What is presented as the body of human knowledge either is a very 
>>>>> small
>>>>> part of actual knowledge or contains false claims.
>>>>>
>>>>
>>>> I am NOT referring to what is merely presented as the body
>>>> of general knowledge, I am referring to the actual body of
>>>> general knowledge. Within this hypothesis it is easy to see
>>>> that True(X) would be infallible.
>>>>
>>>
>>> So, How do we know what is in that?
>>>
>>
>> It is the defined set such that every expression of
>> language has the semantic property of true.
>>
> 
> So How?
> 

How many times do I have to repeat myself.
Basic Facts stipulated to be true.
Truth preserving operations applied to these basic facts.
Boom, Done!!!  Now the 100% complete essence of my
system is fully specified.

>>> How do you intend to construct this system?
>>>
>>
>> This is 100% totally irrelevant until after the very
>> simple idea that a True(X) predicate would necessarily
>> exist for this set is totally accepted.
>>
> 
> 
> Nope, you are just falling into the trap of Naive Set Theory of not 
> being able to define what you are talking about.
> 

By stipulating a set of basic facts
and every expression that can be derived
by applying truth preserving operations
to these basic facts we now fully have
the set of knowledge that can be expressed
in language.

In  such a system no counter example such
that True(X) is incorrect can be provided.

> Membership in the original set of axioms for the system is NOT a Truth 
> Predicate for any logic system which has the power to make inferences.
> 

Inferences that are not truth preserving are disallowed.
Full semantics is always integrated into the language.

> You are just proving your stupidity and ignorance.
> 

Things that someone says when they don't understand
the meaning of all of the big words that are  used.

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