Inference to the best explanation is a time honored strategy for convincing scientific naturalists to be mathematical realists. But the best known abductive argument for realism (Quine's) has recently been criticized by Penelope Maddy for not taking a truly naturalistic approach to mathematical practice, and in particular to higher set theory. Drawing on work in the structuralist tradition (by Michael Resnik, Stewart Shapiro and others), I will begin with a review of Maddy's criticisms, and then sketch an abductive argument for realism which seeks to avoid and build upon them.

I argue that the way Lewis employs natural properties in the BSA account of laws undermines the connection between the BSA and scientific practice and overburdens the notion of natural property with work it cannot perform. I sketch a version of the BSA that doesn't depend on Lewis' account of natural properties. The significant difference between my account and Lewis' is that where he invokes naturalness as a metaphysical primitive and explains laws partly in terms of it, my account involves a genuine "package deal" that characterizes laws and scientifically fundamental properties together.

Donald Davidson and Carl Hempel disagree about the role of the state of being rational in the explanation of action. Hempel thinks that being rational plays a crucial explanatory role in addition to the roles played by desire and belief. Davidson disagrees. He thinks that since desire and belief attribution require that a desirer and believer be rational, the explanatory role of being rational is already absorbed into the explanatory roles of desire and belief. Davidson's critique of Hempel has been influential, but the influence has been very much for the worse. I explain both why Hempel was right and the important implications this has for the way in which we think think about action explanation and psychological attribution.

A number of philosophers (who I will call 'Cancellers') have postulated a 'speech act' of denial and have argued that we can sometimes deny a proposition whose negation we cannot assert. It is widely known that anyone who is inclined to be a canceller must face an argument that Frege launchedÑone that Geach refined and Searle and Dummett employedÑwhich is sometimes called 'the Frege Point'. While I take the Frege Point to be serious, I believe that there are other independent arguments that also undermine the cancellers' position. In this talk, I will introduce and motivate the canceller view, briefly explain Frege's point, and then turn to some new reasons for worrying about that view. In addition, I will sketch what I take to be a better answer to the problem that the cancellers are trying to resolve.