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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: Sun, 30 Mar 2025 16:47:52 -0500
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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.
>>>>>>>>>>
>>>>>>>>>> A list of sentences would not make for efficient processing.
>>>>>>>>>
>>>>>>>>> Unless you want to exclude uncertain facts the set of know 
>>>>>>>>> facts is
>>>>>>>>> small, probably empty. If you include many uncertain facts then
>>>>>>>>> almost certainly your True(X) is true for some false X.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Yes of course there are no known facts it might be the case
>>>>>>>> that feline kittens have always been 15 story office buildings
>>>>>>>> and we have been deluded into thinking differently.
>>>>>>>>
>>>>>>>>>> A knowledge ontology inheritance hierarchy is most efficient.
>>>>>>>>>>
>>>>>>>>>>> However, there could be no uncertain sentences as they are 
>>>>>>>>>>> not known
>>>>>>>>>>> (sensu Olcotti).
>>>>>>>>>>
>>>>>>>>>> Scientific theories would be uncertain truth.
>>>>>>>>>> It is a known fact that X evidence seems to make Y
>>>>>>>>>> a reasonably plausible possibility.
>>>>>>>>>
>>>>>>>>> A good example is Newtonial mchanics, which is known to be 
>>>>>>>>> wrong but is
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