The idea that the domain of science is restricted to falsifiable theories, and is therefore fundamentally empirical, dates only to the early part of the twentie

The idea that the domain of science is restricted to falsifiable theories, and is therefore fundamentally empirical, dates only to the early part of the twentieth century. Since the Enlightenment, and also in the much older Western classical tradition, the term science (and its closest translations in Greek, Latin, German, French, and many other languages) has referred much more broadly than that restriction permits, to all fields of knowledge established in a rigorous manner, whether deductive or inductive. It's in that sense that Gauss crowned mathematics the "Königin der Wissenschaften," the Queen of the Sciences. And indeed in German the term Wissenschaft in ordinary usage still includes mathematics, referring to all knowledge amenable to investigation (as opposed to received knoweldge) [0]. The terms for science in many other Western languages also retain this broader meaning to a greater extent that does contemporary English, and the same is true in many non-Western cultures as well. The problem here is mainly a terminological one: in English we've found it useful to have a word that refers specifically to the Popperian notion of what counts as science (mainly, I think, to gain the power easily to distinguish "scientific" ideas from "non-scientific" bunk), but we haven't come up with a new term for the older, broader meaning of science as rigorously establishable knoweldge. I should also point out that Popperian science involves plenty of deductive reasoning—we call it theory—so while it is true that Popper's notion of science requires empiricism, it is not correct to identify it with the distinction between empirical and deductive reasoning. At the same time, the practice of mathematics certainly does involve empirical reasoning, often resulting in a conjecture whose truth is subsequently subjected to rigorous deductive arguments. (There is a section in the English Wikipedia article on mathematics that discusses this a bit more [1].) 0. https://en.wikipedia.org/wiki/Wissenschaft https://en.wikipedia.org/wiki/Wissenschaft 1. https://en.wikipedia.org/wiki/Mathematics#Mathematics_as_science https://en.wikipedia.org/wiki/Mathematics#Mathematics_as_sci...