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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: Wed, 2 Apr 2025 18:05:29 -0400
Organization: i2pn2 (i2pn.org)
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On 4/2/25 11:59 AM, olcott wrote:
> 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 you can't do that unless you limit the system to only have a finite 
number of statements expressible in it, and thus it can't handle most 
real problems

> 
> A system entirely comprised of Basic Facts and Semantic logical 
> entailment cannot possibly be inconsistent.
> 

Sure it can.

The problem is you need to be very careful about what you allow as your 
"Basic Facts", and if you allow the system to create the concept of the 
Natural Numbers, you can't verify that you don't actually have a 
contradition in it.

Your problem is you can't process what that means, because your mind 
seems to obly understand the so basic logic system that actually can't 
be inconsistant, but it also isn't actually useful for anything.

All you are doing is showing how ignorant you are of what you are 
talking about.