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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: Wed, 26 Mar 2025 23:29:03 -0400
Organization: i2pn2 (i2pn.org)
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On 3/26/25 10:46 PM, olcott wrote:
> On 3/26/2025 9:32 PM, Richard Damon wrote:
>> On 3/26/25 9:27 PM, olcott wrote:
>>> On 3/26/2025 6:01 PM, Richard Damon wrote:
>>>> On 3/26/25 1:50 PM, olcott wrote:
>>>>> On 3/26/2025 6:12 AM, Richard Damon wrote:
>>>>>> On 3/25/25 10:15 PM, olcott wrote:
>>>>>>> On 3/25/2025 8:08 PM, Richard Damon wrote:
>>>>>>>> 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?
>>>>>>>>
>>>>>>>
>>>>>>> *This is a good first guess*
>>>>>>> The set of expressions of language that have the
>>>>>>> semantic property of true that are written down
>>>>>>> somewhere.
>>>>>>
>>>>>> SO that means that "Cats are Dogs" is part of Knowldedge?
>>>>>>
>>>>>
>>>>> Try re-reading what I said as many times as needed
>>>>> until you notice ALL of the words.
>>>>
>>>>
>>>> I have, and you can't explain the difference.
>>>>>
>>>>>>>
>>>>>>>> How do we know what we think to be True is actually True?
>>>>>>>>
>>>>>>>
>>>>>>> Stimulated relations between finite strings are necessarily
>>>>>>> true. "cats" <are> "animals"
>>>>>>
>>>>>> Only if "cats" and "animals" have the appropriate definitions.
>>>>>>
>>>>>
>>>>> Do think that anyone ever wrote these down?
>>>>> Then they exist in the body of general knowledge expressed in 
>>>>> language.
>>>>
>>>> So anything written down is true?
>>>>
>>>> Thus climare change must not be real, since THAT "fact" has been 
>>>> written down and accepted by a large number of peoplel
>>>>
>>>>>
>>>>>> The trator down the street that is a "cat" isn't an animal, but 
>>>>>> sometimes the person that operates it can be a bit of one.
>>>>>>
>>>>>
>>>>> General knowledge.
>>>>
>>>> But "cat" is a term for a type of tractor.
>>>>
>>>>>
>>>>>>>
>>>>>>>> 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). 
>>>>>>>
>>>>>>> Almost the same idea as basic facts.
>>>>>>
>>>>>> Yes, but more than basic facts. Note,
>>>>>>
>>>>>
>>>>> What formal system has an axiom that defines
>>>>> ice cream as a diary product?
>>>>
>>>> Many,
>>>>
>>>>>
>>>>>>>
>>>>>>>> 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.
>>>>>>>>
>>>>>>>
>>>>>>> Basic facts that cannot be derived from anything else.
>>>>>>
>>>>>> So what makes them true? 
>>>>>
>>>>> What makes a dairy cow not a kind of rattlesnake.
>>>>> Stipulated relations between finite strings that
>>>>> provides their semantic meaning.
>>>>
>>>> No, stipulated relationships between concepts.
>>>>
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