Where would we be without counterfactuals?

Huw Price gives his inaugural lecture as Bertrand Russell Professor of Philosophy. Bertrand Russell’s celebrated essay “On the Notion of Cause” was first delivered to the Aristotelian Society on 4 November 1912, as Russell’s Presidential Address. The piece is best known for a passage in which its author deftly positions himself between the traditional metaphysics of causation and the British crown, firing broadsides in both directions: “The law of causality”, Russell declares, “Like much that passes muster in philosophy, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm.” To mark the lecture’s centenary, we offer a contemporary view of the issues Russell here puts on the table, and of the health or otherwise, at the end of the essay’s first century, of his notorious conclusion

The “world's simplest axiom of choice” fails

We use topos-theoretic methods to show that intuitionistic set theory with countable or dependent choice does not imply that every family, all of whose elements are doubletons and which has at most one element, has a choice function.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46645/1/229_2005_Article_BF01170929.pd