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: Thu, 3 Apr 2025 14:21:14 -0500
Organization: A noiseless patient Spider
Lines: 77
Message-ID: <vsmn3a$1bbrc$2@dont-email.me>
References: <vrfvbd$256og$2@dont-email.me>
 <215f3f8823df394f0cbd307af57a528cb3afc52f@i2pn2.org>
 <vsc6lj$27lbo$1@dont-email.me>
 <ba194532a2343e7068ed57b756a99f48241a94fb@i2pn2.org>
 <vsce69$2fv3s$1@dont-email.me>
 <7e0f966861ff1efd916d8d9c32cc9309fd92fe82@i2pn2.org>
 <vsckdc$2l3cb$1@dont-email.me>
 <cd467496ff18486f746047b3b1affc4927981c0c@i2pn2.org>
 <vsct12$2ub5m$1@dont-email.me>
 <3ab00594a6cdaa3ca8aa32da86b865f3a56d5159@i2pn2.org>
 <vsd1p9$379dn$3@dont-email.me>
 <45167877871179050e15837d637c4c8a22e661fd@i2pn2.org>
 <vsenb0$th5g$7@dont-email.me>
 <4c1393a97bc073e455df99e0a2d3a47bfc71d940@i2pn2.org>
 <vsfe66$1m8qr$4@dont-email.me>
 <7286761fb720294d7a87d883fc82c8f8cf95a460@i2pn2.org>
 <vsfl7f$1s8b0$3@dont-email.me>
 <6edcdf0fa4f6ec503240b27a5801f93c470ed7d6@i2pn2.org>
 <vsh931$3mdkb$1@dont-email.me> <vsivgk$1fjla$1@dont-email.me>
 <vsjmtj$26s7s$2@dont-email.me>
 <a4fce1db1fdba9c5eba3e64dc7dba83caff192cf@i2pn2.org>
 <vskobk$378kj$4@dont-email.me> <vslc4t$26a4$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Thu, 03 Apr 2025 21:21:15 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="6f7c1ef7ed393c1fe15fc2cd7d6d1f22";
	logging-data="1421164"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18qS70flZ3MKM5trAXtXVdX"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:3biyRNu/IqcAahk1avblcC1iEqI=
X-Antivirus: Norton (VPS 250403-8, 4/3/2025), Outbound message
Content-Language: en-US
X-Antivirus-Status: Clean
In-Reply-To: <vslc4t$26a4$1@dont-email.me>

On 4/3/2025 2:08 AM, Mikko wrote:
> On 2025-04-03 01:30:28 +0000, olcott said:
> 
>> 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
> 
> That is generally believed but not actually proven.
> 
>> they are essentially nothing more than an ordered
>> set of finite strings of digits.
> 
> The "nothing more" part cannot be proven. 

It is a stipulated basic fact.
There is no way that elements of the set of natural
is anything more or less then an ordered set of
concepts that can be expressed in some way such as a
string of digits.

When we ADD the notion of arithmetic this notion
is added on top of the notion of an ordered set
of concepts.

> In first order logic one cannot

We are still adding notions on top of the notion
of an ordered set of concepts.

> even say that those strings must be finite. 

It would seem to be a stipulated aspect of the
definition of natural number: ∀n ∈ ℕ (n ≠ ∞)

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