> using this definition everything is Natural, including fore example Complex numbers, which is obviously incorrect

No, that's not "obviously incorrect", nor does it invalidate my argument: that is my exact argument. Complex numbers appear in electromagnetism, in exactly the same sense of "appear", as whole numbers appear in herds of sheep. Which is to say, it's the simplest and most useful model of the situation. And what's more natural than one of the four fundamental forces of nature? And the weak & strong nuclear forces have even more esoteric math structures appearing in their most parsimonious models as well.

> "No Foxes - All Clear" is not the same thing (the same level of abstraction) as 0.

In your model. In my model, it is the same thing. All models are wrong; some models are useful. Which one is more useful? Almost always, the one with 0 as a natural number. What about this:

    type PrairieDogFoxCount = NoFoxesAllClear | JustOneFox | ACoupleOfFoxes | SeveralFoxes 3..5 | ManyFoxes

I can make any model as complex as I want; that does not prove some other model wrong.

> using this definition everything is Natural, including fore example Complex numbers, which is obviously incorrect, and thus invalidates yr argument

Except you’re wrong here; should we thus call your argument “obviously incorrect”?

Complex numbers are natural; they’re fundamental in quantum mechanics. Ever since Schrödinger’s equation fundamentally required them for time evolution of states, physicists (and philosophers) wondered if they could be removed. Recent experiments say “no.” QED and QFTs are the most precise theories known in all of science.

https://physicsworld.com/a/complex-numbers-are-essential-in-...