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From: Mikko <mikko.levanto@iki.fi>
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 09:58:39 +0200
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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.

-- 
Mikko