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 14:39:30 -0500
Organization: A noiseless patient Spider
Lines: 287
Message-ID: <vsc6lj$27lbo$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>
 <vsb9d5$19ka5$1@dont-email.me>
 <04aa9edbe77f4e701297d873264511f820d85526@i2pn2.org>
 <vsbu9j$1vihj$1@dont-email.me>
 <215f3f8823df394f0cbd307af57a528cb3afc52f@i2pn2.org>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Sun, 30 Mar 2025 21:39:32 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="f2f9e78d7d6fc63266b591e45b410989";
	logging-data="2348408"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+GhrHc/1cv/qDshMfdqJ+G"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:f2NtSezxKs5plwe8jXdEaIPsWpA=
X-Antivirus: Norton (VPS 250329-4, 3/29/2025), Outbound message
In-Reply-To: <215f3f8823df394f0cbd307af57a528cb3afc52f@i2pn2.org>
Content-Language: en-US
X-Antivirus-Status: Clean
Bytes: 13727

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 wrong 
>>>>>>> but is
>>>>>>> useful and used for practical purposes. How should your True(X) 
>>>>>>> handle
>>>>>>> that?
>>>>>>>
>>>>>>>>>> The set of everything that anyone ever wrote
========== REMAINDER OF ARTICLE TRUNCATED ==========