Can other "sciences" (it's in quotation marks, because the definition for a science is not necessarily exact) be applications of mathematics?
If other sciences, be it philosophy or economics or linguistics or philology, deal with concepts such as:
- Set theoretic notions (belongs to a set, does not belong to a set, ...)
And if these are defined "in the most pure way" in foundations of mathematics (logic etc.), then can this motivate the idea that all other sciences are applications of mathematics, even when they're not called mathematics proper?
I don't mean to ask, whether other sciences reduce to math, because that's unreasonable. Mathematics only doesn't allow one to do physics or economics or so, but my question is more about whether e.g. the notions on truth in mathematics extend to other sciences? Which I think is true?