Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
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: Wed, 2 Apr 2025 21:51:32 -0500
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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.

Basic facts and expressions semantically entailed
by the basic facts cannot have undecidability[math].

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