24.221 Metaphysics Thursday, November 3, 2005 Causation as regularity. The short circuit A caused the fire P. Meaning what? Maybe this: Earlier event both necessary and sufficient for effect. But that can't be quite right. The short circuit isn'tnecessary – why not? It isn’t sufficient either – why not? OK, but something related seems true. The short circuit conjoined with certain other obtainingconditions is sufficient. And the short circuit is an indispensable part of the conjunction. Take it out and you no longer have sufficiency. It is necessary after all, not in the original sense but in the sense ofa necessary part of a sufficient condition. It’s for short an INUS condition: Insufficient but Necessarypart of a condition Unnecessary but Sufficient for the result. Say A is the inus condition. It together with B and C is sufficient. Also sufficient, let’s say, would beD, E, and F, G, H, and I, etc. So ABC ∨ DEF ∨ GHI ∨ ….. is necessary and sufficient. Now we simplify by abbreviating BC to X and DEF ∨ GHI ∨ ….. to Y; the result is AX ∨ Y. A is an INUS condition of a result P iff for some X and Y, (i) AX ∨ Y is necessary and sufficient for P, but (ii) A is not sufficient itself(insufficient necessary part) itself and (iii) neither is X (insufficient necessary part); also AX is notnecessary (….of an unnecessary sufficient condition). Here is the proposal: "A caused P" often means that (i) A is an INUS condition of P (ii) A was present on the occasion in question(iii) the X factors if any were present(iv) the Y disjuncts were absent (simplifying here) This misses something. See it best with general causation. What causes flu? This might mean: whatdistinguishes people in general who get it from those who don't. (They catch a bug.) Or it might mean:what distinguishes those exposed who get it from those who don't? (Weak immune system.) So causal attributions are relative to a “causal field”; people in general, or people exposed. Can see it in singular case too: what caused this student’s skin cancer? Could mean: why did shedevelop it now as opposed to earlier? (Radiation.) Or: why did she develop it while others equallyexposed to radiation did not? (Forgot to wear protective clothing.) Causal field in first case is stages ofthe student’s life, in second it's people exposed to radiation. Go back to fire example. Most natural interpretation is: why did it catch fire now as opposed to earlieror later? But could also mean: why this house in particular since short circuits are happening all thetime? Field is sometimes called contrast class. In place of (i) we need (ia) A is INUS in field F – meaning there is a condition AX ∨ Y such that (AX ∨ Y) is necessaryand sufficient looking just at cases of type F (so, (AX ∨ Y)&F  P&F Field often implicit or taken for granted; interesting exercise to work out what it is.General causal statements. "Lack of credit causes unemployment." "Eating sweets causes tooth decay."Analysis similar except that A, P etc. become types of event rather than tokens. This means we have to drop conditions like (ii) and (iii); A and X will be present sometimes and not other times. In a "developed economic theory," you'd have to state the field, and possibly also X and Y. At the other extreme you'd say some salient F, X, and Y, not sure which. Usually we're somewhere in between. "We do not know, indeed it is not true, that the eating of sweets by any such person is a sufficient conditionfor dental decay:" some people have peculiarly resistant teeth, some brush a lot…"All we know is thasweet-eating combined with a set of positive and negative factors we can specify only roughly andincompletely constitute a sufficient and unnecessary condition for dental decay." Next, what is meant by necessity and sufficiency in claims like ” S is a necessary condition of T.” If S and T are general, could mean all cases of T are cases of S. But not if they are singular. "All cases of this house's catching fire just now are cases of a short-circuit occurring here a moment before." Whycan’t that work? No, a particular token event S is necessary for a particular token event T iff T wouldnot have occurred if S hadn’t occurred. Notation for this is ~S → ~T. What about sufficiency?Mackie suggests a so-called semi-factual: "since a short-circuit occurred here, this house caught fire."Hard to explain semi-factuals the way we explain counterfactuals. True → True is always True on thestandard nearest-possible-world analysis. A word about causal priority since this is Lewis's reason for preferring counterfactual account. It mightseem that S is sufficient/necessary for T iff T is necessary/sufficient for S. But then S necessary andsufficient for T is equivalent to T necessary and sufficient for S. Given time-symmetry of laws, it seemslikely we can find a future AX ∨ Y that is necessary and sufficient for current P. E.g., putting a dollarin the coke machine (that’s P) is necessary and sufficient for the following disjunction: coke coming outand no money returned (that’s AX) ∨ no coke coming out and money returned (that’s Y). How to handle priority? Could stipulate that the event that happens first is the cause. Two problemswith this. One, couldn't there be backward or simultaneous causation? Maybe not, but it shouldn't bestipulated away; need an explanation of why not and this is prevented if temporal priority is written intothe definition. Two, there is a separate problem of explaining temporal priority, and some would wantto do it causally. Mackie gestures in the direction of an idea of Popper’s. Let A be necessary and sufficient for B; whichis prior? Imagine that A is simple (rock hitting pond) and B a complex coincidence (corks bobbing allover pond). Then other things equal we think that A causes B rather than other way around. You could formalize the idea like this. Suppose B is a complex event might up of B1…Bn. And supposethere are strong probabilistic correlation between B1……Bn: P(B /Bj)>>P(Bi). (It’s likelier that this corkiwill bob if that one does.) A is prior to B iff these correlations are “screened off” by A. P(B /Bj&A) isiNOT >> P(B /A). That the cork correlations are screened off by the rock hitting the water suggests thatiany information B1 is giving you about B2 is due to the fact that B1 and B2 are