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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 12:50:12 -0500
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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.

>>
>>> 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.

> 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.

>>
>>> 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?

>>
>>> 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.

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

So the integer 5 is in the fake world?

>>
>>> Thus we hit the problem that Philosophers debate about how can we 
>>> know what we know?
>>>
>>
>> Epistemology is my favorite subject.
> 
> Then why are you so ignorant of it?
> 
>>
>>> 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.
>>>
>>
>> There is no real world problem with the actual set of knowledge
>> that can be expressed using language.
> 
> So, you admit that you system won't be able to rebute the climate 
> deniers, as that problem can't be expressed?
> 

The set of general knowledge expressed in language
already proves the truth of climate change.

An easier case to understand is that there never has been
any actual evidence of election fraud that could have
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