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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: How a True(X) predicate can be defined for the set of analytic
 knowledge
Date: Wed, 26 Mar 2025 21:46:57 -0500
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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.
>>>
>>
>> OK, I will give you that and qualify my original statement.
>> Stipulated relations between concepts that are labeled by
>> finite strings, thus ultimately stipulated relations between
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