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
Date: Tue, 25 Mar 2025 11:54:15 +0200
Organization: -
Lines: 96
Message-ID: <vrtug7$32lmi$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> <62c876a60bf34cc552df0add63825957ba24d9c3@i2pn2.org> <vrmo4m$5bpl$8@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 25 Mar 2025 10:54:15 +0100 (CET)
Injection-Info: dont-email.me; posting-host="2f0cf999c00fadfadc7508b49d8fc2da";
	logging-data="3233490"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18TW7O++/Dwa3SJdRbrjiGW"
User-Agent: Unison/2.2
Cancel-Lock: sha1:ry79DeiZazf8azhTkF8VFbLSnnY=
Bytes: 5411

On 2025-03-22 16:22:46 +0000, olcott said:

> On 3/22/2025 8:37 AM, Richard Damon wrote:
>> On 3/21/25 11:03 PM, olcott wrote:
>>> 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.
>>> 
>> 
>> But can't do that, as Tarski shows, as it creates contradictions when 
>> the system is able to generate unprovable truths.
> 
> Unless we do what ZFC did to redefine the foundations
> of set theory and redefine the notion of a formal system.

The notion of a formal system is sufficiently generic that there is no
need to redefine it. If you want something else then call it something
else.

-- 
Mikko