Re: Simple enough for every reader?

On 27.05.2025 14:01, Mikko wrote:

On 2025-05-26 13:38:00 +0000, WM said:
 No alternative view is known to be better.

That does not make this view good.

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.

No. All natural numbers can be manipulated collectively, for instance subtracted: ℕ \ {1, 2, 3, ...} = { }. Here all have disappeared.
Could all natural numbers be distinguished by individually defining each one, then this subtraction could also happen but, caused by the well-order, a last number would disappear.

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.
 

It is a valid proof by induction. Claim it for all natural numbers. Get a contradiction. But perhaps you prefer geometry?
The set of finite initial segments of natural numbers is potentially infinite but not actually infinite. (Actual infinity is a fixed number greater than all natural numbers.) The height of the figure
{1}
{1, 2}
{1, 2, 3}
...
cannot be greater than its width which by definition is not greater than all natural numbers.
Regards, WM