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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: Tue, 1 Apr 2025 06:31:13 -0400
Organization: i2pn2 (i2pn.org)
Message-ID: <6edcdf0fa4f6ec503240b27a5801f93c470ed7d6@i2pn2.org>
References: <vrfvbd$256og$2@dont-email.me> <vs63o2$2nal3$1@dont-email.me>
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On 3/31/25 11:06 PM, olcott wrote:
> 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.
>>>>>>>>>>>>>>>>>>>>>>>>>>
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