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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: Sun, 30 Mar 2025 14:53:04 -0400
Organization: i2pn2 (i2pn.org)
Message-ID: <215f3f8823df394f0cbd307af57a528cb3afc52f@i2pn2.org>
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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
>>>>>> 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.
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