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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: Thu, 27 Mar 2025 06:56:16 -0400
Organization: i2pn2 (i2pn.org)
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On 3/27/25 12:04 AM, olcott wrote:
> On 3/26/2025 10:29 PM, Richard Damon wrote:
>> On 3/26/25 10:58 PM, olcott wrote:
>>> On 3/26/2025 8:22 PM, Richard Damon wrote:
>>>> On 3/26/25 2:01 PM, olcott wrote:
>>>>> On 3/26/2025 3:36 AM, Mikko wrote:
>>>>>> On 2025-03-25 14:56:33 +0000, olcott said:
>>>>>>
>>>>>>> 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.
>>>>>>
>>>>>> What is presented as the body of human knowledge either is a very 
>>>>>> small
>>>>>> part of actual knowledge or contains false claims.
>>>>>>
>>>>>
>>>>> I am NOT referring to what is merely presented as the body
>>>>> of general knowledge, I am referring to the actual body of
>>>>> general knowledge. Within this hypothesis it is easy to see
>>>>> that True(X) would be infallible.
>>>>>
>>>>
>>>> So, How do we know what is in that?
>>>>
>>>
>>> It is the defined set such that every expression of
>>> language has the semantic property of true.
>>>
>>
>> So How?
>>
> 
> How many times do I have to repeat myself.
> Basic Facts stipulated to be true.
> Truth preserving operations applied to these basic facts.
> Boom, Done!!!  Now the 100% complete essence of my
> system is fully specified.

And Truth Perserving operations applied to those basic facts will create 
new TRUTHS that are not in your set that True sees, because some of them 
will not have been known before.

> 
>>>> How do you intend to construct this system?
>>>>
>>>
>>> This is 100% totally irrelevant until after the very
>>> simple idea that a True(X) predicate would necessarily
>>> exist for this set is totally accepted.
>>>
>>
>>
>> Nope, you are just falling into the trap of Naive Set Theory of not 
>> being able to define what you are talking about.
>>
> 
> By stipulating a set of basic facts
> and every expression that can be derived
> by applying truth preserving operations
> to these basic facts we now fully have
> the set of knowledge that can be expressed
> in language.

Except that we can, in the logic, apply an infinite set of those steps, 
creating a fact that can not be proven by a finite number of them.

> 
> In  such a system no counter example such
> that True(X) is incorrect can be provided.

Except that if you try to exclude that infinite chain creating truth, 
you can't have the properties of the Natural Numbers, so you system is 
insufficent to qualify for Tarski's claim.

> 
>> Membership in the original set of axioms for the system is NOT a Truth 
>> Predicate for any logic system which has the power to make inferences.
>>
> 
> Inferences that are not truth preserving are disallowed.
> Full semantics is always integrated into the language.

So, your "Truth Perserving Operations" can't be any of the normal logic 
rules, as those are syntactic, not semantic in operation, so you need to 
define what you actually mean to show you have them.

For instance, "Implication", that operation that says that if A -> B is 
a true statement, then if A is true, then B must be true doesn't exist 
in your system, as that in not semantic in operation as it applies to 
*ANY* term A and B, regardless of semantics.

Your problem is you just don't understand how "logic" works.

> 
>> You are just proving your stupidity and ignorance.
>>
> 
> Things that someone says when they don't understand
> the meaning of all of the big words that are  used.
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