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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: Thu, 3 Apr 2025 10:09:43 +0300
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On 2025-04-03 02:51:32 +0000, olcott said:

> On 4/2/2025 8:56 PM, Richard Damon wrote:
>> On 4/2/25 9:30 PM, olcott wrote:
>>> On 4/2/2025 5:05 PM, Richard Damon wrote:
>>>> 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.
>>>> 
>>> 
>>> It never has been that natural numbers have
>>> ever actually had any inconsistency themselves
>>> they are essentially nothing more than an ordered
>>> set of finite strings of digits.
>> 
>> No, but any logic system that can support them
> 
> Can be defined in screwy that has undecidability
> or not defined in this screwy way.

And you can't define it otherwise.

-- 
Mikko