Possibilism

In the opening chapter, I characterised chance as the degree of belief recommended by the best identifiable advice function, given the available evidence. In the following chapters, I have sketched the sort of conceptual tools used by physicists to obtain probabilities in classical statistical mechanics: a measure over phase space. So a naive response to this presentation is to think that classical statistical mechanics actually tells us what makes a fact of chance. It is a measure over a space of possibilities. The space of possibilities contains the states the system might be in, given the available evidence. Given the right measure – something that we have confirmed by experience – chances are just facts about the relative measures of different macro-conditions. Call this the modal volume theory of chance. In order to assess this idea adequately, we first need to unpack it.

Chances are ratios of volumes

Given I toss a coin, what is the chance that it will land heads? The answer has something to do with two sets of possibilities: that in which I toss a coin, and that in which I toss a coin and it lands heads.