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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 20:27:20 -0500
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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
finite strings, the ultimate formalism.

>>
>>> Note, EVERYTHING we know about the real world starts with 
>>> observations, and observations are always only approximate.
>>>
>>
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