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IlyaShpitser comments on Causation, Probability and Objectivity - Less Wrong
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I said this once above, but it's worth repeating -- Pearl's view of causality has nothing to do with probabilities. It's a fully deterministic theory which can be augmented by modeling uncertainty via probability theory if you want.
A causal model uniquely specifies a bunch of conditional probabilities, right?
Only in a sense that a first order theory of natural numbers does. Really I think it is more accurate to view "a causal model" as a model in the mathematical logic sense -- an object about which logical assertions can be made. In the case of causal models, these assertions are modelling "interventions." Here's a paper on this:
http://www.jair.org/papers/paper648.html
This view appears in Pearl's chapter 7, as well.