Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Simple enough for every reader?
Date: Mon, 26 May 2025 15:38:00 +0200
Organization: A noiseless patient Spider
Lines: 53
Message-ID: <1011qrn$20v83$1@dont-email.me>
References: <100a8ah$ekoh$1@dont-email.me> <100ccrl$upk6$1@dont-email.me>
 <100cjat$vtec$1@dont-email.me> <100fdbr$1laaq$1@dont-email.me>
 <100funo$1ous9$1@dont-email.me> <100haco$24mti$1@dont-email.me>
 <100hocb$2768i$1@dont-email.me> <100mpm7$3csuv$1@dont-email.me>
 <100much$3drk8$1@dont-email.me> <100p8v7$k2$1@dont-email.me>
 <100pbot$dmi$1@dont-email.me> <100rv2t$jpca$1@dont-email.me>
 <100sajh$lkp7$2@dont-email.me> <100us6p$1b4q2$1@dont-email.me>
 <100uvfe$1b4dh$3@dont-email.me> <1011fkf$1v4kb$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Mon, 26 May 2025 15:37:59 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="ded62fba97cd51fa961522ddeb9d1c91";
	logging-data="2129155"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18bpkXV8M4OxS7MYlS3iTTBEo6Kuz5UneM="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:8loHkPANzCobWLD4HO7NHp6j8RI=
Content-Language: en-US
In-Reply-To: <1011fkf$1v4kb$1@dont-email.me>
Bytes: 3448

On 26.05.2025 12:26, Mikko wrote:
> On 2025-05-25 11:38:23 +0000, WM said:
> 
>> On 25.05.2025 12:42, Mikko wrote:
>>> On 2025-05-24 11:29:53 +0000, WM said:
>>>
>>>> On 24.05.2025 10:13, Mikko wrote:
>>>>> On 2025-05-23 08:31:27 +0000, WM said:
>>>>>
>>>>>> On 23.05.2025 09:43, Mikko wrote:
>>>>>>> Do you mean that every natural number is dark until
>>>>>>> someone mentions it but no longer?
>>>>>>>
>>>>>> Every natural number is dark in a system that cannot represent it 
>>>>>> in any form like writing, thinking or whatever. The pocket 
>>>>>> calculator is limited to decimal representations below 10^100, the 
>>>>>> universe is limited to more or less sophisticated formulas 
>>>>>> requiring less than 10^80 bit.
>>>>>>
>>>>>> In every system almost all natural numbers are and remain dark - 
>>>>>> if an actual infinity of them exists.
>>>>>
>>>>> That is not a useful concept as it is not possible to know wich 
>>>>> numbers are
>>>>> presentable in future sysems and which will be actually presented.
>>>>
>>>> But it is fact.
>>>
>>> But not a mathematical fact.
>>
>> That depends on the definition of mathematics.
> 
> An exact definition of mathematics is not needed except by some 
> philosophers.
> Even whithout a definition there understood meaning of the word varies only
> a little. By the usual understand ot the word of a fact about people or 
> other
> real world beings is not a mathematical fact.

That is the common but mistaken view. Without tools of the real world no 
mathematics is possible at all. Therefore mathematics is limited by the 
power of these tools.

But even pure mathematics proves that most natural numbers will never be 
definable:

{1} has infinitely many (ℵo) successors.
If {1, 2, 3, ..., n} has infinitely many (ℵo) successors, then {1, 2, 3, 
...., n, n+1} has infinitely many (ℵo) successors, for every n that can 
be defined.

Regards, WM