Lewis Causation is a Special Case of Spohn Causation
Franz Huber · The British Journal for the Philosophy of Science · 2010
Lewis ([1973a]) famously defined event c to be causally relevant to event e in world w just in case Oc ðÞand Oe ðÞas well as:OðÞ c!:OðÞare e true in w, where Oc ðÞand Oe ðÞsay that c occurs and that e occurs, respectively. For him, this implied that Oc ðÞ! Oe ðÞis true, because he was assuming the underlying logic to be VC, which validates ð ^ Þ ð! Þ. If one works with the weaker system V, the causal relevance of event c to event e has to be defined as follows: (1) both c and e occur in w; i.e. Oc ðÞand Oe ðÞare true in w; (2) if c had not occurred, e would not have occurred either in w; i.e.:OðÞ c!:OðÞis e true in w; (3) if c had occurred, e would have occurred as well in w; i.e. Oc ðÞ! Oe ðÞis true in w; A typical semantics for counterfactual conditionals says that ‘if A were the case, C would be the case’, ! , is true if and only if C is true in all the closest A-worlds (Stalnaker [1968]; Lewis [1973b]). Closeness or distance is spelt out in terms of a relation between possible worlds. In another paper