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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: How a True(X) predicate can be defined for the set of analytic knowledge
Date: Sun, 6 Apr 2025 14:03:04 +0300
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On 2025-04-05 17:51:03 +0000, olcott said:

> On 4/5/2025 2:30 AM, Mikko wrote:
>> On 2025-04-03 18:59:15 +0000, olcott said:
>> 
>>> 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.
>> 
>> For that sort of system paraconsistency is possible, depending on
>> what else there is in the system.
> 
> https://en.wikipedia.org/wiki/Paraconsistent_logic
> Starting with a consistent set of basic facts (AKA axioms)
> while only allowing semantic logical entailment thus
> truth preserving operations does not seem to allow
> any contradictions, thus paraconsistency.
> Try to provide a concrete counter-example.

Obviously, as any inconsistency is an indication that the set of basic
facts is not consistent under the chosen inference rules (in this case
semantic logical entailment). But the question of paraconsistency is
not very interesting unless the set of basic facts is inconsistent.

-- 
Mikko