Can mathematics act causally?

[Chas]

I don't know whether mathematics can or cannot cause "things" (and note that in this case, causality and things are all mathematical objects). I'm not a fan of the mathematical universe hypothesis, but it seems to depend on a variant of the debate between Platonism and nominalism; is mathematics in any sense "real" or not. Most initial reactions to this question immediately assert "no," but I think the reasoning involved incorporates some question begging. I don't know what it would mean for the universe to be a mathematical structure, but our judgements about that cannot come from an assumption grounded in views that the universe is not a mathematical structure, ie. some form of realism. This is a form of question begging which I think is exemplified by Descartes in his cogito ergo sum argument: his conclusion rests on a premise which seems drawn from a realist assumption about the universe, namely that if there is an effect, then there must be a something which is its cause. For Descartes, the existence of a doubt implies the existence of a "something" which is responsible for this effect. That's a form of the Principle of Sufficient Reason, that effects must have causes, and it's drawn from an inductive observation of the universe under an assumption of realism. Similarly, when we say that mathematics doesn't cause anything, and therefore the universe can't be mathematical, then I think we're drawing that conclusion from a prior assumption of realism — but that is the very assumption which is at issue, so you can't draw your conclusion from there!

I don't think mathematics is "real" and so I don't think mathematics can have causality, but that belief is subject to many doubts, the likes of which are hard to resolve. The same doubts occur in arguments about the Platonic reality of math and logic, and also curiously, arguments about cosmological origins. The answer to the question of whether mathematics has causality seems to lie on the road ahead of us, not something that we've already figured out.

Wait a minute - there's a debate? Are there really any Platonists out there?

To the OP: No. Mathematics doesn't do anything. It is a way to model and describe, it is a tool invented by humans.