This talk explores an apparent tension between two widely held views about logic: that logic is normative and that there are multiple equally legitimate logics. The tension is this. If logic is normative, it tells us something about how we ought to reason. If, as the pluralist would have it, there are several correct logics, those logics make incompatible recommendations as to how we ought to reason. But then which of these logics should we look to for normative guidance? I argue that inasmuch as pluralism draws its motivation from its ability to defuse logical disputes---that is, disputes between advocates of rival logics---it is unable to provide an answer: pluralism collapses into monism with respect to either the strongest or the weakest admissible logic.
See the seminar webpage http://users.ox.ac.uk/~philmath/pomseminar.html for titles and abstracts of other speakers when available.
Philosophy of Mathematics Seminar Convenors: Daniel Isaacson and Volker Halbach