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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, 3 Apr 2025 18:34:04 -0400
Organization: i2pn2 (i2pn.org)
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In-Reply-To: <vsmlq3$1bbrc$1@dont-email.me>

On 4/3/25 2:59 PM, olcott wrote:
> 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.

Which doesn't prove what was asked for.

You are just proving the fact that you don't understand what you are 
talking about.


> 
>>> 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.
> 

Nope. Tarski proved otherwise.

The problem is that your "assumption" that a True(x) exist creates an 
inconsistant set of "basic facts" when combined with the other basic 
facts that allow us to do arithmatic.