Thanks so much for this—it was just the answer I was looking for!
I was able to follow the logic you presented, and in particular, I understand that {3}⇝{2,3} and {2,3}⇝{2} but not {3}⇝{2} in the example given.
So, I was correct in my original example of c->d->e that
(1) if c were to not happen, d would not happen
(2) if d were to not happen, e would not happen
BUT it was incorrect to then derive that if c were to not happen, e would not happen? Have I understood you correctly?
I’m still a bit fuzzy on the informal counterexample you presented, possibly because of the introduction of probability. For example, I don’t understand how not winning big entails not winning something because winning nothing is more likely than winning small. If you did not win big, you might still have won small (even if it’s unlikely); I don’t understand how the likelihood comes into account.
I wish I had an intuitive example of a c and e where c is a cause of e without e causally depending on c, but I’m struggling to imagine one.
If I understand the example and the commentary from SEP correctly, doesn’t this example illustrate a problem with Lewis’ definition of causation? I agree that commonsense dictates that Alice throwing the rock caused the window to smash, but I think the problem is that you cannot construct a sequence of stepwise dependences from cause to effect:
Lewis’s theory cannot explain the judgement that Suzy’s throw caused the shattering of the bottle. For there is no causal dependence between Suzy’s throw and the shattering, since even if Suzy had not thrown her rock, the bottle would have shattered due to Billy’s throw. Nor is there a chain of stepwise dependences running cause to effect, because there is no event intermediate between Suzy’s throw and the shattering that links them up into a chain of dependences. Take, for instance, Suzy’s rock in mid-trajectory. This event depends on Suzy’s initial throw, but the problem is that the shattering of the bottle does not depend on it, because even without it the bottle would still have shattered because of Billy’s throw.
Is the example of the two hitmen given in the SEP article (where B does not fire if A does) an instance of causation without causal dependence?
Thanks so much for this—it was just the answer I was looking for!
I was able to follow the logic you presented, and in particular, I understand that {3}⇝{2,3} and {2,3}⇝{2} but not {3}⇝{2} in the example given.
So, I was correct in my original example of c->d->e that
(1) if c were to not happen, d would not happen
(2) if d were to not happen, e would not happen
BUT it was incorrect to then derive that if c were to not happen, e would not happen? Have I understood you correctly?
I’m still a bit fuzzy on the informal counterexample you presented, possibly because of the introduction of probability. For example, I don’t understand how not winning big entails not winning something because winning nothing is more likely than winning small. If you did not win big, you might still have won small (even if it’s unlikely); I don’t understand how the likelihood comes into account.
I wish I had an intuitive example of a c and e where c is a cause of e without e causally depending on c, but I’m struggling to imagine one.
Suppose Alice and Bob throw a rock at a fragile window, Alice’s rock hits the window first, smashing it.
Then the following seems reasonable:
Alice throwing the rock caused the window to smash. True.
Were Alice ot throw the rock, then the window would’ve smashed. True.
Were Alice not to throw the rock, then the window would’ve not smashed. False.
By (3), the window smashing does not causally depend on Alice throwing the rock.
If I understand the example and the commentary from SEP correctly, doesn’t this example illustrate a problem with Lewis’ definition of causation? I agree that commonsense dictates that Alice throwing the rock caused the window to smash, but I think the problem is that you cannot construct a sequence of stepwise dependences from cause to effect:
Is the example of the two hitmen given in the SEP article (where B does not fire if A does) an instance of causation without causal dependence?
tbh, Lewis’s account of counterfactual is a bit defective, compared with (e.g.) Pearl’s