Suppose Colin and Frank are both in their offices. Colin flipped a fair coin and it landed heads. Frank didn't scratch his nose. Assuming their offices are causally isolated, the following counterfactual seems true:
(1) Had Frank scratched his nose, Colin's coin still would have landed heads.
The intuition that (1) and counterfactuals like it are true motivates a general principle:
Causal Independence Principle (CIP): If A and C are true, and the mechanisms settling whether A and whether C are causally independent, then: if A had been false, C would still have been true.
I find CIP extremely plausible. Unfortunately, I'll argue it's false. I'll first rehearse an old argument against CIP, and then outline a better one, both based on considerations about chance. While this argument assumes the controversial principle 'Duality', I'll argue that views rejecting Duality fare even worse if CIP is assumed true. After briefly arguing against other views on which CIP fails, I’ll offer my own account: CIP seems true because counterfactual truth depends on which facts context tells us to hold fixed. While Context often requires keeping facts causally independent from the antecedent fixed, it need not.
