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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: How a True(X) predicate can be defined for the set of analytic
 knowledge
Date: Tue, 25 Mar 2025 21:08:18 -0400
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On 3/25/25 10:56 AM, olcott wrote:
> On 3/25/2025 5:19 AM, Mikko wrote:
>> On 2025-03-22 17:53:28 +0000, olcott said:
>>
>>> On 3/22/2025 11:43 AM, Mikko wrote:
>>>> On 2025-03-21 12:49:06 +0000, olcott said:
>>>>
>>>>> On 3/21/2025 3:57 AM, Mikko wrote:
>>>>>> On 2025-03-20 15:02:42 +0000, olcott said:
>>>>>>
>>>>>>> On 3/20/2025 8:09 AM, Mikko wrote:
>>>>>>>> On 2025-03-20 02:42:53 +0000, olcott said:
>>>>>>>>
>>>>>>>>> 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.
>>>>>>>>
>>>>>>>> A simple example is the first order group theory.
>>>>>>>>
>>>>>>>>> When we begin with a set of basic facts and all inference
>>>>>>>>> is limited to applying truth preserving operations to
>>>>>>>>> elements of this set then a True(X) predicate cannot possibly
>>>>>>>>> be thwarted.
>>>>>>>>
>>>>>>>> There is no computable predicate that tells whether a sentence
>>>>>>>> of the first order group theory can be proven.
>>>>>>>>
>>>>>>>
>>>>>>> Likewise there currently does not exist any finite
>>>>>>> proof that the Goldbach Conjecture is true or false
>>>>>>> thus True(GC) is a type mismatch error.
>>>>>>
>>>>>> However, it is possible that someone finds a proof of the conjecture
>>>>>> or its negation. Then the predicate True is no longer complete.
>>>>>>
>>>>>
>>>>> The set of all human general knowledge that can
>>>>> be expressed using language gets updated.
>>>>>
>>>>>>> When we redefine logic systems such that they begin
>>>>>>> with set of basic facts and are only allowed to
>>>>>>> apply truth preserving operations to these basic
>>>>>>> facts then every element of the system is provable
>>>>>>> on the basis of these truth preserving operations.
>>>>>>
>>>>>> However, it is possible (and, for sufficiently powerful sysems, 
>>>>>> certain)
>>>>>> that the provability is not computable.
>>>>>>
>>>>>
>>>>> When we begin with basic facts and only apply truth preserving
>>>>> to the giant semantic tautology of the set of human knowledge
>>>>> that can be expressed using language then every element in this
>>>>> set is reachable by these same truth preserving operations.
>>>>
>>>> The set of human knowledge that can be expressed using language
>>>> is not a tautology.
>>>>
>>>
>>> tautology, in logic, a statement so framed that
>>> it cannot be denied without inconsistency.
>>
>> And human knowledge is not.
>>
> 
> What is taken to be knowledge might possibly be false.
> What actually <is> knowledge is impossibly false by
> definition.
> 

How do you DEFINE what is actually knowledge?

How do we know what we think to be True is actually True?

In FORMAL systems we can rigorously define what is true in that system, 
as we start with a defined set of given facts (which is why you can't 
change the definitions and stay in the system, as those definitions are 
what made the system). When you talk about "Human Knowledge" for the 
"Real World" you run into the problem that we don't have a listing of 
the fundamental facts that define the system, but are trying to discover 
our best explainations by observation.

Thus we hit the problem that Philosophers debate about how can we know 
what we know?

This is, as I just explained, only a problem in the "real world", as in 
a Formal System, Truth has a precise definition, as does Knowledge.

Your problem is your "True" predicate detects the later, not actually 
Truth, and thus calling it True is just a lie.