All good questions about the cause/correlation issues… Do you have a classical example in mind as an answer to your last question?
Still, you can’t carefully address these questions without comparing your definition of causation to some *other* definition of causation. Even if you don’t want to bring in other causation accounts, where your definition yields conclusions that seem at odds with our common-sense notion of causation, you probably should address that mismatch. Certainly under Huw’s interventionist account you couldn’t claim that reflipping a fair coin is not a cause, and this account matches better with my common sense on this issue, at least.
And I think you’re always going to have some mismatch if your definition doesn’t delve in below the level of observable probabilities. Our causal instincts have to do with ontology, and if it’s possible that you’re working at an epistemic level, your definition won’t match common sense. Specifically, taking your coin example, I can’t imagine there are many people who would think the status of a “cause” could be dependent on what other external observers can *know*. (That said, I do think there is almost always going to be some subjective aspect to causation, but that should be the subjectivity of the agent doing the causing, not other external agents.)
Best, Ken
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