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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: Thu, 3 Apr 2025 13:59:15 -0500
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On 4/3/2025 2:03 AM, Mikko wrote:
> On 2025-04-02 15:59:47 +0000, olcott said:
> 
>> On 4/2/2025 4:20 AM, Mikko wrote:
>>> On 2025-04-01 17:51:29 +0000, olcott said:
>>>
>>>>
>>>> All we have to do is make a C program that does this
>>>> with pairs of finite strings then it becomes self-evidently
>>>> correct needing no proof.
>>>
>>> There already are programs that check proofs. But you can make your own
>>> if you think the logic used by the existing ones is not correct.
>>>
>>> If the your logic system is sufficiently weak there may also be a way to
>>> make a C program that can construct the proof or determine that there is
>>> none.
>>
>> When we define a system that cannot possibly be inconsistent
>> then a proof of consistency not needed.
> 
> But a proof of paraconsistency is required.
> 

When it is stipulated that {cats} <are> {Animals}
When it is stipulated that {Animals} <are> {Living Things}
Then the complete proof of those is their stipulation.
AND {Cats} <are> {Living Things} is semantically entailed.

>> A system entirely comprised of Basic Facts and Semantic logical 
>> entailment cannot possibly be inconsistent.
> 
> It can if the set of basic facts is inconsistent or if the logical
> entailment sematics is not sufficiently weak. Inconsistencies are
> avoided if your system has no way to express logical negations
> (which incudes negative quantification).
> 

Stipulated basic facts + semantic logical entailment
guarantees True(X). When the basic facts do not contradict
each other then undecidability is impossible.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer