Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
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 (GKEUL)
Date: Wed, 26 Mar 2025 10:07:49 +0200
Organization: -
Lines: 113
Message-ID: <vs0ckl$1b340$1@dont-email.me>
References: <vrfvbd$256og$2@dont-email.me> <3cf0a34d9382774fd8275a118d1af8b0841c8eb1@i2pn2.org> <vrhacd$3fbja$1@dont-email.me> <vrj8nr$16c78$1@dont-email.me> <vrjmtr$1ilbe$1@dont-email.me> <7d0164a6001fc519a244b7ed4930d757b9bd7ac1@i2pn2.org> <vrl0tr$2na3e$1@dont-email.me> <cc75e1bdfa918eedc80a9230b0484acda284dc56@i2pn2.org> <vrl3fn$2nttr$3@dont-email.me> <8c4ea7f74348f8becac017bb33d6cab1b30f5e01@i2pn2.org> <vrl9ab$2t44r$3@dont-email.me> <vrmp2s$bc8p$2@dont-email.me> <vrmt6e$cvat$5@dont-email.me> <vrtv1n$333lh$1@dont-email.me> <vruepv$3gia2$2@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Wed, 26 Mar 2025 09:07:50 +0100 (CET)
Injection-Info: dont-email.me; posting-host="f5d176a35312dcf4617a2b35e821f8a8";
	logging-data="1412224"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18YWSP1rTqaqcsblRR98QsJ"
User-Agent: Unison/2.2
Cancel-Lock: sha1:svbPdHUom46Rut4dNYBXvj+9zZc=
Bytes: 6178

On 2025-03-25 14:32:31 +0000, olcott said:

> On 3/25/2025 5:03 AM, Mikko wrote:
>> On 2025-03-22 17:49:01 +0000, olcott said:
>> 
>>> On 3/22/2025 11:38 AM, Mikko wrote:
>>>> On 2025-03-22 03:03:39 +0000, olcott said:
>>>> 
>>>>> 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.
>>>>>>>>>>> 
>>>>>>>>>>> 
>>>>>>>>>> 
>>>>>>>>>> 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.
>>>>>>>>> 
>>>>>>>>> 
>>>>>>>> 
>>>>>>>> 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.
>>>> 
>>>> We can believe the "nothing else" part. The rest would require a proof.
>>>> 
>>> 
>>> True(X) is a predicate implementing a membership algorithm
>>> for the body of general knowledge that can be expressed
>>> using language.
>>> 
>>> Infinite proofs cannot be provided. Find a counter-example
>>> where an element of the set of general knowledge that can
>>> be expressed using language(GKEUL) would fool a True(X)
>>> predicate into providing the wrong answer.
>>> 
>>> "This sentence is not true" cannot be derived by applying
>>> truth preserving operations to basic facts thus is rejected
>>> as not a member of (GKEUL).
>> 
>> What does your True(X) say when X means that there is no method to
>> determine whether a sentence of the first order group theory can
>> be proven.
> 
> That is either in the body of knowledge or not.

It is.

-- 
Mikko