When false dichotomies are neither false, nor dichotomous
When you prove, say, the Pythagorean theorem, you don't go around measuring a bunch of triangles, you begin with certain axioms and background conditions (e.g., declaring that you are working within Euclidean geometry), and then logically deduce the theorem. What's empiricism got to do with it?
Here Quine, to put it boldly, just cheated his way out of the problem. He began by saying that math was really a type of science, after which he argued that he was primarily concerned with applied math, which clearly makes contact with science and the empirical world. Yes, but most math is not applied, and even the part that is, isn't derived from science, it applies to science. Then he argued that math as a whole is justified by the fact that a part of it makes contact with the empirical world. That would surprise the hell out of mathematicians and philosophers of mathematics, and frankly, amounts to a lot of handwaving to save an extreme form of holism about knowledge that is ultimately untenable. Mathematics remains a very good example of analytic truth, pace Quine. And so does logic, by the way.