Sujet : Re: Simple enough for every reader?
De : mikko.levanto (at) *nospam* iki.fi (Mikko)
Groupes : sci.logicDate : 27. May 2025, 13:01:16
Autres entêtes
Organisation : -
Message-ID : <10149ic$2jtva$1@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
User-Agent : Unison/2.2
On 2025-05-26 13:38:00 +0000, WM said:
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.
There is no mistake in that view. No alternative view is known to be better.
Without tools of the real world no mathematics is possible at all.
True, but there are many alternative tool sets we could use and as far as
we have seen the all tools tell about the same mathematics.
Therefore mathematics is limited by the power of these tools.
No, just our current knolwedge of mathematics. But mathematics is more
than what we already know about it.
But even pure mathematics proves that most natural numbers will never be definable:
{1} has infinitely many (ℵo) successors.
(2) there are infinitely many (ℵo) possible definitions.
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.
You can't formulate that as a logically or mathematically valid proof.
-- Mikko
Simple enough for every reader?
Re: Simple enough for every reader?
