Deism for non-believers

[Angrboda]

Unlike many physicists before him, who insisted that great breakthroughs in physics be firmly grounded in experimental data, Dirac took the opposite strategy. To him pure mathematics, if it was beautiful enough, was the sure guide to great breakthroughs. He wrote, "It is more important to have beauty in one's equations than to have them fit experiments . . . It seems that if one is working from the point of view of getting beauty in one's equations, and if one has a really sound insight, one is on a sure line of progress."

— Physics Of The Impossible, Michio Kaku

I'm not of the opinion that there's anything ontologically distinctive about math and numbers, but then I wouldn't lean towards Quine's belief that mathematical concepts are derived empirically either. Philosophy of math gets into some serious shit, and like many of the purely theoretical sciences, there are more dead ends than hopeful avenues. Whatever, it's beyond me. I would lean toward a Kantian, underdetermined functionalism — numbers and math are abstractions built into our cognitions to allow us to map input behaviors to output behaviors in a probabilistic manner, without us having to figure out how the mathematical relationships between the environment and the life form actually work. In that sense, a number like '4' is a reference to a number of behavioral invariants, such that the invariants, like composition of functions, yields appropriate behaviors in response to contemplation of, and combination of, concepts.