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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: Sat, 5 Apr 2025 16:01:14 -0500
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On 4/5/2025 3:03 PM, Richard Damon wrote:
> On 4/5/25 1:51 PM, olcott wrote:
>> 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.
>>
> 
> Your problem is you are making the error of assuming the concluion.
> 
> You can't tell that you axioms ARE consistant excpet by proving that the 
> system itself is consistant, 

Counter-factual. A system with a consistent set of basic
facts can possibly have inference rules that derive
inconsistency because these rules are less than perfectly
truth preserving.

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