Do Numbers Exist?

[bennyboy]

Of these three, I'd say that fictionalism is clearly bullshit, nominalism is insufficient, and Platonic numbers don't meet the definition of "exist" that we normally use. Frankly, though, I prefer the Platonic view, when taken abstractly rather than literally.

I think a kind of numerical realism should be considered: that rather than numbers being representative of things, all things are a representation of an underlying mathematical reality. For example, if you were to calculate a wave, you'd find no such thing really exists: there are the lateral motions of large numbers of discrete objects, from which we infer a "best fit," i.e. a mathematical function. If you "zoom" in on a flat surface, you'll see no such surface actually exists: what exists are a bunch of atoms, or a bunch of wave functions if you zoom in even further.

So which is more "real," the physical particles whose positions roughly approximate the mathematical perfection of a wave function, or the wave function itself? I'd argue that the math is more real, and that physical objects are expressions of the math, rather than vice versa.