In his recent book, Causation: A Realistic Approach,’ Michael Tooley discusses the following thesis, which he calls the ‘thesis of the Humean Supervenience of Causal Relations’:

(T) represents one version of the ‘Humean’ idea that there is no more factual content to the claim that two particular events are causally connected than that they occur, instantiate some law or regularity, and perhaps bear some appropriate non-causal (e.g. spatio-temporal) to each other. This is an idea that is tacitly or explicitly assumed in most familiar accounts of singular causal statements. For example (T) is assumed by many probabilistic theories of singular causal statements, by theories which attempt to analyse singular causal statements in terms of necessary and sufficient conditions, and, as I shall argue below, by David Lewis’ counterfactual theory.

As Tooley recognizes, (T) should be distinguished from another central assumption to which Humean theories of causation are committed : that laws of nature are susceptible of some sort of regularity analysis which does not rely on unreduced notions of physical possibility and necessity. Whether or not a regularity analysis of natural laws is correct, it appears to be a distinct question whether (T) is true. (T) should also be distinguished from another claim that is frequently made about the connection between singular causal statements and causal laws: that every true singular causal claim entails the existence of some associated causal law. Here too, this last claim might be true, even though (T) is mistaken.