A Chancy 'Magic Trick'

Various philosophers are skeptical about modalities such as laws of nature, counterfactuals, dispositions, and so on. Chance is in a way the black sheep of the modal family: not only is it a modality, but it is one that comes in degrees. One might as a result be skeptical about it twice over: as modal witchcraft with spurious numbers attached! In this chapter, it is argued that the numbers provide no extra reason for skepticism. A whole range of chance values, of arbitrary precision, can be derived from very basic and intuitive comparative assumptions. In fact, for a wide range of systems these assumptions seem hard to deny. The centrepiece of the argument is a ‘magic trick’. Give me any object, any number between 0 and 1 inclusive, and a specified accuracy, and I will use the object to generate an event whose chance is the number given to the accuracy specified.