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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: How a True(X) predicate can be defined for the set of analytic
 knowledge
Date: Fri, 28 Mar 2025 09:46:04 -0400
Organization: i2pn2 (i2pn.org)
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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.