¹ For example, CMC may readily fail if there is selection bias. This is a particularly interesting case because defining selection bias in a usable way that does not presuppose knowledge of just those parts of the causal structure under investigation is tricky, perhaps even impossible.

² Steel would call this a ‘semantics’. Note that, from my pluralist point of view, this is a metaphysics for the particular causal relation under study, not for the causal relation wheresoever it appears.

³ This is much like the way the axioms of a physics theory implicitly define the theoretical concepts involved in them. In the case of causality and Bayes nets, the antecedently understood concepts are primarily probability concepts.

⁴ In the latter case one could either maintain that the connection is supported empirically or insist that only cases where the further manipulation conditions obtain are entitled to be called causal. I take it neither Steel nor I favour this last claim.

⁵ With respect to James Woodward's interpretation that Steel mentions, HC&UT does a similar thing: It provides a ‘representation theorem’ showing that Woodward's ‘level invariance’ interpretation is appropriate to causal laws systems where causation is asymmetric, irreflexive and all true functional relations derive from the basic causal laws.

⁶ Which Suppes would surely want to allow since for him probabilistic/deterministic are distinctions relative to a model.

⁷ The chapter on Hoover, reading directly from his own definitions, attributes to him a remarkable and original use-based theory of causality but one that is concomitantly not so responsive to standard methods for ascertaining causes. Hoover himself claims this is a mistaken understanding of what he intends. This is a topic for extended discussion, but not in this symposium.

⁸ Assuming independent evidence that the causes have a stable contribution to make in the first place.

⁹ I call this ‘underlying structure’ a ‘nomological machine’ (cf. my Nature's Capacities and their Measurement, 1989, OUP) because it gives rise to law-like regularities. Steel and others sometimes call it a ‘mechanism’. I avoid ‘mechanism’ because it has too many different meanings.

¹⁰ For more on this, see my APA Presidential address.

¹¹ As they can since they are variation free.

¹² What is it for a regression equation to be causally correct and what is it to pass the test for concomitant variation? I think answering either of these, as I do in HC&UT, makes a small contribution to getting our causal methodology straight.

¹³ In the chapter ‘Getting Causes from Probabilities: Cartwright on Simon on Causation’.

¹⁴ Note that I don't say, here or in the passage quoted from me, that the antecedent must be atomic. I apologize if what I wrote can be read that way.

¹⁵ As I characterize Hoover. See note 7.

¹⁶ For instance, following Pearl's suggestions in equations (1–4), in * substitute new values for p_t without changing θ. This is not what the government can actually do in the long run according to Lucas.

¹⁷ As must the information about how this contribution combines with contributions from other causes. Contributions in mechanics add vectorially, but not those in economics. HC&UT describes a number of different schemes from physics and from economics for combining contributions.

¹⁸ So long as the expression is well-formed.

¹⁹ Plus an assumption of an original causal ordering on the variables that we haven't discussed, and an assumption about the general functional form, also not discussed here.