On the Definition of Actual Cause

1 Background This note proposes a formal explication of the notion of \actual cause" as in, for example, \Socrates drinking hemlock was the actual cause of Socrates death." The philosophical literature has been struggling with this notion at least since Mackie (1965) put forward his famous INUS condition and, as we shall outline shortly, no satisfactory solution has emerged from either the logical, probabilistic, or counterfactual approaches to causality Sosa and Tooley, 1993]. My interest in this topic has been kindled by a recent paper of Michie (1998) where Good's probabilistic measures of causal tendency (Good, 1961{62) are extended to individual events. Michie argues persuasively that in many legal settings, what need be established (for determining responsibility) is not a counterfactual kind of causation, but \cause in fact." A typical example (introduced by Wright (1988)) considers two res advancing toward a house. If re A burned the house before re B, we (and many juries nationwide) would consider re A \the actual cause" for the damage, even supposing the house would have deenitely burned down by re B, if it were not for A. The fact that the standard counterfactual test fails in such examples has prompted me to seek an explication for \actual cause" using the Structural Logic (SL) described in Galles and Pearl (1997, 1998) and Halpern (1988) which is also known as Modiiable Structural Equation Model. This logic has been very successful in explicating a number of causal concepts, for example , unit-potential-response Rubin, 1974; Robins, 1986], truth and probabilities of coun-terfactuals, eeect of action, direct and indirect eeects, confounding Greenland et al., 1998], exogeneity, causal relevance, and instrumental variables. (The reader is referred to Pearl (1995) and Galles and Pearl (1997, 1998) for explication of these concepts.) SL was proposed as a general language for causal reasoning, capable of representing any concept connected with causation. The notion of \actual cause" has somehow escaped the attention of our 1