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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 18:47:19 -0400
Organization: i2pn2 (i2pn.org)
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In-Reply-To: <vsce69$2fv3s$1@dont-email.me>

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.
>>>>>>>>>>>
>>>>>>>>>>>> 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 
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