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 23:27:10 -0500
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On 4/2/2025 10:09 PM, Richard Damon wrote:
> On 4/2/25 10:51 PM, olcott wrote:
>> 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].
>>
> 
> Wrong, Godel shows that having the properties of the Natural numbers is 
> enough.
> 

They are merely an ordered set of finite strings of digits.

> Show what property he uses that you can withhold and still have a 
> reasonably usable mathematics.
> 
> Your problem is you don't understand the power that basic logic gets 
> from the basic nature of the Natural Numbers.


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