Not long after the last post, I ran across this one:
http://www.michaelnielsen.org/ddi/if-correlation-doesnt-imply-causation-then-what-does/
in which Michael Nielsen grapples with something called the “causal calculus”. At the risk of massively oversimplifying, the key idea seems to be to construct a causal model for some system, and then to introduce a more refined type of conditional probability. The new type of conditional probability involves the probability of X given do(Y), where do(Y) implies that not only are we interested in instances of X occurring given that Y occurred, but rather, we are interested in instances of X occurring when we *make* Y occur. What this means is that we imagine that we can manipulate the causal structure of our model so that occurrences of Y are externally controlled and disconnected from the “endogenous” factors that influence it in the model.
Frontier Scientist 