Undermining and Admissibility

Abstract

Our best physical theories seem to tell us that the world is an objectively chancy place. Some possible futures have some chance of being actual, and this is the most that can be said. More knowledge about the way the world is now and what the laws are won't yield complete information about what will be. Of course, our best theories may be wrong, but they are not wrong merely because they advert to the notion of objective chance. Quantum mechanics may be incorrect because it postulates entities or properties that there aren't; it might even be wrong because it makes no sense; but it isn't wrong because the notion of chance it so freely makes use of makes no sense. Whether our best theories are to be believed or not, they force upon us the conceptual possibility of objectively chancy events. Given this, one might wonder whether the totality of facts about the world which aren't about chance determines the chances, whether matters of chance supervene on matters of non-chance. We do not learn about the chances directly, rather we make hypotheses about what the chances are based on information about relative frequencies. Induction justifies us in thinking that the relative frequencies we have observed will continue throughout world history. But if supervenience fails we have reason-in addition to general worries about i.nduction-to be sceptical concerning our knowledge of the chances. For if supervenience fails, the correctness of our views on what there is and how it behaves won't suffice to determine the chances. So one reason to hope for a successful reductive analysis of chance is that it would show that chance does supervene on matters of non-chance. One way that matters of chance might supervene on matters of non-chance is through Humean supervenience, the view that all supervenes on local matters of particular fact. David Lewis is the view's architect, but he has also given reason to think that chance cannot supervene in a Humean manner (Lewis 1994). He begins with a vague worry that does not itself force the Humean to give up hope. However, by adding an extremely plausible premise concerning the relationship between chance and credence, he turns the worry into a proper argument. It has gone unnoticed that the trouble Lewis raises is not restricted to Humean reductions of chance. The argument-if sound-destroys the hope of virtually any reductive analysis of chance. Indeed, the argument even raises difficulties for some views according to which chance is brute and unanalysable. The primary purposes of this paper are to show how broad the scope of the argument is, and then to offer a response.