  Timothy Williamson has recently argued that the applicability of classical
mathematics in the natural and social sciences raises a problem for the
endorsement, in non-mathematical domains, of a wide range of non-classical
logics. We first reconstruct his argument and present its restriction to the
case of quantum logic (QL). Then we show that there is no problematic tension
between the applicability of classical mathematical models to quantum phenomena
and the endorsement of QL in the reasoning about the latter. Once we identify
the premise in Williamson's argument that turns out to be false when restricted
to QL, we argue that the same premise fails for a wider variety of
non-classical logics. In the end, we use our discussion to draw some general
lessons concerning the relationship between applied logic and applied
mathematics.
