[wruza]

Interestingly, this argument was weak before we ended up with truly elementary particles. Cause there’s no such thing as three apples or three people. They are unique objects with similarities defined by an observer, and then you go deeper and note that “object” is also a purely synthetic delineation. 3 is a model, not an element of reality. Even advanced maths define it as a set which contains nothing, 1 and 2 (which contains nothing and 1, which contains nothing and is preceded by nothing). Counting and measuring is equivalent to drawing lines — adding something that wasn’t there before.

The fact that particles have identity is also vague, afaiu, so existence of numbers or their non-biological origin is not as easy to prove by example as it seems.

[timschmidt]

> [sic]Cause there’s no such thing as three apples or three people.

I understand what you're saying. Occurrences like https://en.wikipedia.org/wiki/Ring_species demonstrate that the idea of "species" isn't firm and that what truly matters is each individual and their unique circumstances. But this seems to me to be more a limitation of language and philosophy than a repudiation of math.

As you pointed out, it's all equivalent to drawing tally lines, counting pebbles, sliding counters on an abacus, or counting fingers and toes. Despite the fractal nature of coastlines and the constant exchange of matter and energy between adjacent parts of the universe, it is possible to agree upon useful delineations. And there is not any alternative maths which happens to describe practical observations in a way which does not reduce to the maths with which we are familiar.

[lazide]

I’d argue that is because the maths we are familiar with are familiar exactly because they are useful, and repeatedly so.

But that is a philosophical oroboros.

[timschmidt]

They are useful repeatedly because they derive from fundamental properties of the observable universe. We can imagine other sorts of universes - one with hyperbolic geometry as opposed to flat, for instance ( https://en.wikipedia.org/wiki/Shape_of_the_universe ). Parts of geometry would work differently there, and laws of motion as well. But interestingly, many fundamental rules of math would still apply. Just with different outcomes which are less useful for predicting results here.

[throwway120385]

Kind of like trying to prove Euclid's Fifth Postulate, which we know now is truly a postulate and not an axiom.