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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 13:29:32 -0500
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On 3/31/2025 4:04 AM, Mikko wrote:
> On 2025-03-30 11:20:05 +0000, olcott said:
> 
>> 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
>>>>> useful and used for practical purposes. How should your True(X) handle
>>>>> that?
>>>>>
>>>>>>>> The set of everything that anyone ever wrote
>>>>>>>> down would be finite.
>>>>>>>
>>>>>>> But not knowable.
>>>>>>>
>>>>>>>> Most of this would be
>>>>>>>> specific knowledge Pete's dog was named Bella.
>>>>>>>> Some is general dogs are animals.
>>>>>>>>
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