Single case probabilities

The history of probability can be thought of as a history of frustrated causality. Humans have always wanted to answer 'why' questions, but since the advent of modern science this desire has taken the form of a quest for law-like explanation - a desire to demonstrate what it is that determines something should happen under particular circumstances. That is, an instance of a phenomenon X should be explained by a civering law appropriate to an explanation of all instances of the x kind. This chapter claims to offer a limited easement of that frustration by beginning from a different place, both in causal and problematic thinking. It is an argument for causal explanation, but one based on the measurable probabilities of the single case. This, we maintain, can provide explanations of underlying structures, rather than leading to causal laws.