““Scientists, famously, use a lot of mathematics, at least in many disciplines (including both cognitive science and economics). Much of this is simply statistics, and derives from the importance of exact measurement. But that is not the whole story. Natural languages and the distinctions they draw are evolutionary products shaped by the interaction of cultural and genetic selection. They therefore encode, in deeply embedded and mutually reinforcing levels, distinctions important to folk theories—that is, the nonscientific social-cognitive structures that organize relationships important to special human purposes. Mathematical language is quite different, and this reflects differences between the nature of mathematical and of practical reasoning. Mathematical reasoning begins from sets of rigorously fixed procedural concepts, and these fixed points then have absolute authority, relative to special purposes in application, over what can and cannot be stated in the language. If we suspect there may be some particular structural fact but cannot figure out how to express it mathematically, this does not show that there is no such fact; but it implies that we must do some more work, either logical or empirical or both, before we can say that we are quite sure just what the putative structural fact is that we are trying to claim.””
