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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: Tue, 1 Apr 2025 18:09:18 -0500
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On 4/1/2025 5:27 PM, Richard Damon wrote:
> On 4/1/25 1:51 PM, olcott wrote:
>> On 4/1/2025 5:31 AM, Richard Damon wrote:
>>> 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 
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