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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, 28 Mar 2025 15:07:22 -0500
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On 3/28/2025 8:46 AM, Richard Damon wrote:
> On 3/27/25 10:18 PM, olcott wrote:
>> On 3/27/2025 8:54 PM, Richard Damon wrote:
>>> On 3/27/25 9:04 PM, olcott wrote:
>>>> On 3/27/2025 5:48 AM, Mikko wrote:
>>>>> On 2025-03-26 17:58:10 +0000, olcott said:
>>>>>
>>>>>> On 3/26/2025 3:39 AM, Mikko wrote:
>>>>>>> On 2025-03-26 02:15:26 +0000, olcott said:
>>>>>>>
>>>>>>>> On 3/25/2025 8:08 PM, Richard Damon wrote:
>>>>>>>>> On 3/25/25 10:56 AM, olcott wrote:
>>>>>>>>>> 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.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> How do you DEFINE what is actually knowledge?
>>>>>>>>>
>>>>>>>>
>>>>>>>> *This is a good first guess*
>>>>>>>> The set of expressions of language that have the
>>>>>>>> semantic property of true that are written down
>>>>>>>> somewhere.
>>>>>>>
>>>>>>> We already know that many expressions of language that have the 
>>>>>>> semantic
>>>>>>> proerty of true are not written down anywhere.
>>>>>>
>>>>>> Only general knowledge
>>>>>
>>>>> What is "general" intended to mean here? In absense of any definition
>>>>> it is too vague to really mean anything.
>>>>>
>>>>
>>>> Reverse-engineer how you could define a set of
>>>> knowledge that is finite rather than infinite.
>>>
>>> In other words, you don't understand the question.
>>>
>>>>
>>>> The set of everything that anyone ever wrote
>>>> down would be finite. Most of this would be
>>>> specific knowledge Pete's dog was named Bella.
>>>> Some is general dogs are animals.
>>>
>>> So, what is the DEFINITION of "General Knowledge"?
>>>
>>
>> Knowledge that lacks specific details of specific situations.
>> A set of knowledge that can be algorithmically compressed
>> as a finite set of finite strings.
>>
> 
> Ok, so therefore it includes all the "laws of mathematics" and the 
> "rules of inference" and thus, the system is capable of creating the 
> rules and properties of the Natural Numbers, so it supports the proofs 
> of Godel and Tarski, and thus there are statements in that sytstem that 
> are True but unprovable and no definition of the Truth Predicate can 
> handle those,
> 
> Sorry, you are just showing you don't understand what you are talking 
> about.

Yes it will showed the formal system can be defined
that have all kinds of issues because they were defined
incoherently.

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