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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: Mon, 31 Mar 2025 13:34:15 -0500
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On 3/31/2025 4:10 AM, Mikko wrote:
> On 2025-03-31 03:22:17 +0000, olcott said:
> 
>> On 3/30/2025 9:31 PM, Richard Damon wrote:
>>> On 3/30/25 10:01 PM, olcott wrote:
>>>> On 3/30/2025 7:25 PM, Richard Damon wrote:
>>>>> On 3/30/25 7:34 PM, olcott wrote:
>>>>>> On 3/30/2025 5:47 PM, Richard Damon wrote:
>>>>>>> On 3/30/25 5:47 PM, olcott wrote:
>>>>>>>> On 3/30/2025 3:59 PM, Richard Damon wrote:
>>>>>>>>> On 3/30/25 3:39 PM, olcott wrote:
>>>>>>>>>> On 3/30/2025 1:53 PM, Richard Damon wrote:
>>>>>>>>>>> On 3/30/25 1:16 PM, olcott wrote:
>>>>>>>>>>>> On 3/30/2025 6:24 AM, Richard Damon wrote:
>>>>>>>>>>>>> On 3/30/25 7:20 AM, olcott wrote:
>>>>>>>>>>>>>> On 3/30/2025 4:57 AM, Mikko wrote:
>>>>>>>>>>>>>>> On 2025-03-29 14:06:17 +0000, olcott said:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> On 3/29/2025 5:20 AM, Mikko wrote:
>>>>>>>>>>>>>>>>> On 2025-03-28 19:59:16 +0000, olcott said:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> On 3/28/2025 7:12 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>> On 2025-03-28 01:04:45 +0000, olcott said:
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> 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.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> First one should define what the elements of that set 
>>>>>>>>>>>>>>>>>>> could be.
>>>>>>>>>>>>>>>>>>> If sentences, and there are not too many of them, a 
>>>>>>>>>>>>>>>>>>> set of knowledge
>>>>>>>>>>>>>>>>>>> could be presented as a book that contains those 
>>>>>>>>>>>>>>>>>>> sentences and nothing
>>>>>>>>>>>>>>>>>>> else.
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