Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
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 06:20:05 -0500
Organization: A noiseless patient Spider
Lines: 203
Message-ID: <vsb9d5$19ka5$1@dont-email.me>
References: <vrfvbd$256og$2@dont-email.me> <vrh432$39r47$1@dont-email.me>
 <vrhami$3fbja$2@dont-email.me> <vrj9lu$1791p$1@dont-email.me>
 <vrjn82$1ilbe$2@dont-email.me> <vrmpc1$bnp3$1@dont-email.me>
 <vrmteo$cvat$6@dont-email.me> <vru000$33rof$1@dont-email.me>
 <vrug71$3gia2$6@dont-email.me>
 <0306c3c2d4a6d05a8bb7441c0b23d325aeac3d7b@i2pn2.org>
 <vrvnvv$ke3p$1@dont-email.me> <vs0egm$1cl6q$1@dont-email.me>
 <vs1f7j$296sp$2@dont-email.me> <vs3ad6$2o1a$1@dont-email.me>
 <vs4sjd$1c1ja$8@dont-email.me> <vs63o2$2nal3$1@dont-email.me>
 <vs6v2l$39556$17@dont-email.me> <vs8hia$13iam$1@dont-email.me>
 <vs8uoq$1fccq$2@dont-email.me> <vsb4in$14lqk$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Sun, 30 Mar 2025 13:20:06 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="4510a7740351c2a9dd78cd9cd81f9c96";
	logging-data="1364293"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19TbU63Q9weli2Uxl/TKhYI"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:nqDuU1QUFsUrmQ5v+0bUQGuGM7U=
X-Antivirus: Norton (VPS 250329-4, 3/29/2025), Outbound message
X-Antivirus-Status: Clean
Content-Language: en-US
In-Reply-To: <vsb4in$14lqk$1@dont-email.me>
Bytes: 9906

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.
>>>>>>
>>>>>>>>> Ae also know that many expressions of language that are written 
>>>>>>>>> down
>>>>>>>>> somewhere lack the semantic property of true.
>>>>>>>>
>>>>>>>> False statements do not count as knowledge.
>>>>>>>
>>>>>>> No, but your "the set of expressions of language that have the 
========== REMAINDER OF ARTICLE TRUNCATED ==========