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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 21:26:38 -0500
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On 4/1/2025 8:03 PM, Richard Damon wrote:
> On 4/1/25 7:09 PM, olcott wrote:
>> 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 
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