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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 22:06:22 -0500
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On 3/31/2025 8:23 PM, Richard Damon wrote:
> On 3/31/25 9:06 PM, olcott wrote:
>> On 3/31/2025 5:27 PM, Richard Damon wrote:
>>> On 3/31/25 2:36 PM, olcott wrote:
>>>> On 3/31/2025 5:59 AM, Richard Damon wrote:
>>>>> On 3/30/25 11:22 PM, olcott wrote:
>>>>>> 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.
>>>>>>>>>>>>>>>>>>>>>>>
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