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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: How a True(X) predicate can be defined for the set of analytic
 knowledge ---ZFC
Date: Wed, 26 Mar 2025 17:04:14 -0500
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In-Reply-To: <vs0c3f$1aje5$1@dont-email.me>

On 3/26/2025 2:58 AM, Mikko wrote:
> On 2025-03-25 14:28:49 +0000, olcott said:
> 
>> On 3/25/2025 4:50 AM, Mikko wrote:
>>> On 2025-03-23 04:24:51 +0000, olcott said:
>>>
>>>> On 3/22/2025 9:53 PM, Richard Damon wrote:
>>>>> On 3/22/25 2:33 PM, olcott wrote:
>>>>>> On 3/22/2025 12:34 PM, Richard Damon wrote:
>>>>>>> On 3/22/25 11:13 AM, olcott wrote:
>>>>>>>> On 3/22/2025 5:11 AM, joes wrote:
>>>>>>>>> Am Fri, 21 Mar 2025 22:03:39 -0500 schrieb olcott:
>>>>>>>>>> On 3/21/2025 9:31 PM, Richard Damon wrote:
>>>>>>>>>>> On 3/21/25 9:24 PM, olcott wrote:
>>>>>>>>>>>> On 3/21/2025 7:50 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 3/21/25 8:40 PM, olcott wrote:
>>>>>>>>>>>>>> On 3/21/2025 6:49 PM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 3/21/25 8:43 AM, olcott wrote:
>>>>>>>>>>>>>>>> On 3/21/2025 3:41 AM, Mikko wrote:
>>>>>>>>>>>>>>>>> On 2025-03-20 14:57:16 +0000, olcott said:
>>>>>>>>>>>>>>>>>> On 3/20/2025 6:00 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>> On 3/19/25 10:42 PM, olcott wrote:
>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> 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.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Which just means that you have stipulated yourself 
>>>>>>>>>>>>>>>>>>> out of all
>>>>>>>>>>>>>>>>>>> classical logic, since Truth is different than 
>>>>>>>>>>>>>>>>>>> Knowledge. In a
>>>>>>>>>>>>>>>>>>> good logic system, Knowledge will be a subset of 
>>>>>>>>>>>>>>>>>>> Truth, but you
>>>>>>>>>>>>>>>>>>> have defined that in your system, Truth is a subset of
>>>>>>>>>>>>>>>>>>> Knowledge, so you have it backwards.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> True(X) always returns TRUE for every element in the 
>>>>>>>>>>>>>>>>>> set of
>>>>>>>>>>>>>>>>>> general knowledge that can be expressed using language.
>>>>>>>>>>>>>>>>>> It never gets confused by paradoxes.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Not useful unless it returns TRUE for no X that 
>>>>>>>>>>>>>>>>> contradicts
>>>>>>>>>>>>>>>>> anything that can be inferred from the set of general 
>>>>>>>>>>>>>>>>> knowledge.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> I can't parse that.
>>>>>>>>>>>>>>>>   > (a) Not useful unless (b) it returns TRUE for (c) no 
>>>>>>>>>>>>>>>> X that
>>>>>>>>>>>>>>>>   > contradicts anything (d) that can be inferred from 
>>>>>>>>>>>>>>>> the set of
>>>>>>>>>>>>>>>>   > general knowledge.
>>>>>>>>>>>>>>>>   >
>>>>>>>>>>>>>>>> Because my system begins with basic facts and actual 
>>>>>>>>>>>>>>>> facts can't
>>>>>>>>>>>>>>>> contradict each other and no contradiction can be formed by
>>>>>>>>>>>>>>>> applying only truth preserving operations to these basic 
>>>>>>>>>>>>>>>> facts
>>>>>>>>>>>>>>>> there are no contradictions in the system.
>>>>>>>>> The liar sentence is contradictory.
>>>>>>>>>
>>>>>>>>>>>>>>> No, you system doesn't because you don't actually 
>>>>>>>>>>>>>>> understand what
>>>>>>>>>>>>>>> you are trying to define.
>>>>>>>>>>>>>>> "Human Knowledge" is full of contradictions and incorrect
>>>>>>>>>>>>>>> statements.
>>>>>>>>>>>>>>> Adittedly, most of them can be resolved by properly 
>>>>>>>>>>>>>>> putting the
>>>>>>>>>>>>>>> statements into context, but the problem is that for some
>>>>>>>>>>>>>>> statement, the context isn't precisely known or the 
>>>>>>>>>>>>>>> statement is
>>>>>>>>>>>>>>> known to be an approximation of unknown accuracy, so doesn't
>>>>>>>>>>>>>>> actually specify a "fact".
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> It is self evidence that for every element of the set of 
>>>>>>>>>>>>>> human
>>>>>>>>>>>>>> knowledge that can be expressed using language that 
>>>>>>>>>>>>>> undecidability
>>>>>>>>>>>>>> cannot possibly exist.
>>>>>>>>> Not self-evident was Gödel's disproof of that.
>>>>>>>>>
>>>>>>>>>>>>> SO, you admit you don't know what it means to prove something.
>>>>>>>>>>>>>
>>>>>>>>>>>> When the proof is only syntactic then it isn't directly 
>>>>>>>>>>>> connected to
>>>>>>>>>>>> any meaning.
>>>>>>>>>>>
>>>>>>>>>>> But Formal Logic proofs ARE just "syntactic"
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>>>> When the body of human general knowledge has all of its 
>>>>>>>>>>>> semantics
>>>>>>>>>>>> encoded syntactically AKA Montague Grammar of Semantics then 
>>>>>>>>>>>> a proof
>>>>>>>>>>>> means validation of truth.
>>>>>>>>>>> Yes, proof is a validatation of truth, but truth does not 
>>>>>>>>>>> need to be
>>>>>>>>>>> able to be validated.
>>>>>>>>>> True(X) ONLY validates that X is true and does nothing else.
>>>>>>>>> Not if X is unknown (but still true).
>>>>>>>>>
>>>>>>>>
>>>>>>>> You must pay complete attention to ALL of my words
>>>>>>>> or you get the meaning that I specify incorrectly.
>>>>>>>>
>>>>>>>
>>>>>>> The problem is that statement, you don't get to change the 
>>>>>>> meaning of the core terms and stay in the system, so you are just 
>>>>>>> admitting that all your work is based on strawmen, and thus frauds.
>>>>>>>
>>>>>>
>>>>>> <sarcasm>
>>>>>>    In the exact same way that ZFC totally screwed up
>>>>>>    and never resolved Russell's Paradox because they
>>>>>>    were forbidden to limit how sets are defined.
>>>>>>
>>>>>>    When the definition of a set allowed pathological
>>>>>>    self-reference they should have construed this
>>>>>>    as infallible and immutable.
>>>>>> </sarcasm>
>>>>>>
>>>>>
>>>>> IN other words, you admit that you can't refute what I said, so you 
>>>>> just go off beat.
>>>>>
>>>>
>>>> By the freaking concrete example that I provided
>>>> YES YOU DO GET TO CHANGE THE MEANING OF THE TERMS.
>>>
>>> No, you can't. The nearest you can is to create a new term that
>>> is homonymous to an old one. But you can't use two homonymous
>>> terms in the same opus.
>>
>> Original set theory became "naive set theory".
>> ZFC set theory corrected its shortcomings.
> 
> The original one is Cantor's. But that his presentation was too informal
> to determine whether Russell's set is expressible. But he did show that
> one can construct from nothing enough sets for natural number arithmetic.
> Russell's set cannot be constructed.
> 

My whole point is that a broken system was fixed by redefining it.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer