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buybuydandavis comments on Mathematics as a lossy compression algorithm gone wild - Less Wrong
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I believe I'm in basic agreement. Definitely in the nominalist camp.
Math is an evolved conceptual structure. Why does the math we use work? About the same reason the hammers we use work. Things that work, get used. We make changes, see which ones work better, and use those.
How is it that math can work? Well, how is it that the conceptual structures we use work? We try to use the ones that do, and move on from those that don't. Nothing to see here folks, move along.
There's an infinite space of conceptual structures. Most of them suck. Some don't. Math doesn't suck. Huckleberry Finn doesn't either. Were both "discovered" out of that infinite space of structures? I guess you could say so, but that seems quite a peculiar way of looking at it.
Doesn't seem that way to me. The moon is not a conceptual structure.
Work at what? For whom? Mathematicians are happy with maths that is of no use to physicists.
And that's fine. In fact, that's great. If people want to enjoy the aesthetics of conceptual structure, I hope they call me over for the fun.
But the "what" in the "work at what" I was speaking, is "predicting other data points, not yet observed", per the OP.
Not actually the job of maths..."this hammer doesn't work, you can't drive in screws with it"
Math doesn't have a "job". It's use by people to fulfill their ends. For most people, those ends are prediction.
Grab an arbitrary piece of maths and it won't predict anything. There is a technique and speciality and skill of finding the right pieceof maths to match the territory, and that is called physics.
Meanwhile...no professional mathematician gets sacked for failing to predict or otherwise being empirically correct. It's not their job.
Actually, I am not a nominalist, I only adopted a somewhat-nominalist position for this post to express what I think about math. In actuality I slide all the way down the slippery slope and consider the term "exist" meaningless except in the original sense of "perceived". But that would be a subject for a different post.
Not even "potentially receivable"?