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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
Date: Sat, 22 Mar 2025 18:39:50 +0200
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On 2025-03-22 10:11:34 +0000, joes said:

> 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).

And it shouldn't if X is unknown but false.

-- 
Mikko