Counterfactual theories of causation

• Were p to hold, q would hold (pÿ®q) is true provided that either:
• p holds at no world, or
• there is a world w where both p and q hold (“the witness to the conditional pÿ®q”) which is closer to the actual world than any world w* where both p and ~q hold. (Lewis)
• Simpler version (Stalnaker): pÿ®q is true provided at the closest world (to ours) at which p holds, q also holds.
• An actual event F causally depends on an actual event E provided that E and F happen, but were E not to have happened, F wouldn’t have happened. (Lewis, Hume₂)
• E causes F if and only if there is a sequence of events, starting with E and ending with F, where each item in the sequence, other than E itself, causally depends on the previous.
• Problems:
• Correlated epiphenomena
• Asymmetric overdetermination
• Version 1: x shoots z. y is standing by, and if x doesn’t press the trigger, y will. x’s pressing the trigger causes z to die, but were x not to have pressed the trigger, z would still have died.
• Answer: x’s pressing the trigger causes x’s bullet to enter z’s heart. Here we have causal dependence. And the bullet’s entry into z’s heart causes z’s death. Here we also have causal dependence.
• Version 2: z falls off a building. x shoots him dead while he flies past the window. At no point in the bullet’s activity can we say: were this not to have happened, z would not have died.
• Possible answer: There is a specific event of z’s dying in a particular way, and x causes that. Were x not to have shot z, z wouldn’t have died in that way.
• Problem: Suppose that to be the cause is to be the cause of such a finely delineated event. Suppose that x falls to his death, without being shot along the way, and some firemen set up a net to catch him. The net breaks—he is falling too fast. Then the firemen are causes of him having died in that way.
• Possible answer: We supplement Lewis’s story by adding that increasing the probability of an event is another way of causing the event, besides the causal dependence. x increased the probability of z’s death. But one can increase the probability of an event without causing the event. Consider a case where z is falling from a high building into a haystack. x shoots z along the way. y sees z falling, and y sweeps away the haystack. Then, y increased the probability of z’s death, but did not kill z, as he was dead before he hit the ground. Probability increase is neither necessary nor sufficient for causation.

Singularism

• B-type facts supervene on A-type facts iff any two worlds that are the same in respect of A, are the same in respect of B as well. (Perhaps moral facts supervene on non-moral ones.)
• There are three possible views of causation:
• Causal facts supervene on non-causal facts and causal laws.
• Causal relations presuppose causal laws but do not supervene on non-causal facts and causal laws. (Intermediate view)
• Causal relations can exist apart from causal laws. (Singularism.)

Arguments for singularism

1. (Premise) The following scenario is possible: “There are exactly two laws: (a) For any x, x’s having property P causally brings it about that x either has Q or has R. (b) For any x, x’s having S causally brings it about that x either has Q or has R. x has both P and S, and x gains Q and R.”
2. (Premise) No matter how many non-causal facts we add to the scenario, the scenario will be compatible with each of the following two hypotheses: (i) x’s having P caused x to have Q and x’s having S caused x to have R; (ii) x’s having P did not cause x to have Q (it caused x to have R) and x’s having S did not cause x to have R (it caused x to have Q).
3. There are two possible worlds which have the same non-causal facts and laws, and which satisfy the scenario in (1), but in one of them (i) holds, and in the other (ii) holds. (1 and 2)
4. (Premise) Two worlds that differ in whether (i) and (ii) hold differ in causal facts.
5. (Definition of supervenience) If two worlds differ in causal facts without differing in non-causal facts and laws, then causal relations do not supervene on non-causal facts and laws.
6. Therefore, causal relations do not supervene on non-causal facts and laws.

And the intermediate view is unduly complex.

Causation as a theoretical relation

If singularism holds, causation could be either:

• an observable relation (Anscombe), or
• an unobservable “theoretical” relation posited to explain data, much as we posit electrons.