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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 20:25:56 -0400
Organization: i2pn2 (i2pn.org)
Message-ID: <cd467496ff18486f746047b3b1affc4927981c0c@i2pn2.org>
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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 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.
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