From Dennis Lindley:
If your assumption, that controlling X at x is equivalent to removing the function for X and putting X=x elsewhere, is applicable, then it makes sense because, from my last paragraph, we need past information to select the correct function. What I do not understand at the moment is the relevance of this to decision trees. At a decision node, one conditions on the quantities known at the time of the decision. At a random node, one includes all relevant uncertain quantities under known conditions. Nothing more than the joint distributions (and utility considerations) are needed. For example, in the medical case, the confounding factor may either be known or not at the time the decision about treatment is made, and this determines the structure of the tree. Where causation may enter is when the data are used to assess the probabilities needed in the tree, and it is here that Novick and I used exchangeability. The Bayesian paradigm makes a sharp distinction between probability as belief and probability as frequency, calling the latter, chance. If I understand causation, it would be reasonable that our concept could conveniently be replaced by yours in this context.
From Dennis Lindley:
In the part of Chapter 1 that you kindly sent me, a functional, causal model is clearly defined by a set of equations in (1.40). The set provides a joint probability distribution of the variables using a specific order. That distribution may be manipulated to obtain an equivalent probability specification in any other order. I showed in my note that this probability structure could be described by a set of equations in an order different from that of (1.40). (That proof may be wrong, though on p. 31 you suggest the result was known in '93.) Consequently (1.40) can be replaced by a different set of equations. You tell us now to see what happens were a variable to be controlled; this in terms of the set, and I showed that different consequences flowed if different sets were used. How do I decide which set is correct?
From David Kenny (University of Connecticut)
Let me just say that it is very gratifying to see a philosopher give the problem of causality some serious attention. Moreover, you discuss the concept as it used in contemporary social sciences. I have bothered by the fact that all too many social scientist try to avoid saying "cause" when that is clearly what they mean to say. Thank you!
I have not finished your book, but I cannot resist making one point to you. In 5.4, you discuss the meaning of structural coefficients, but you spend a good deal of time discussing the meaning of epsilon or e. It seems to me that e has a very straight-forward meaning in SEM. If the true equation for y is
y = Bx + Cz + Dq + etc + r where is r is meant to allow for some truly random component, then e = Cz + Dq + etc + r or the sum of the omitted variables. The difficulty in SEM is that usually, though not always, for identification purposes it must be assumed that e and x have a zero correlation. Perhaps this is the standard "omitted variables" explanation of e that you allude to, but it does not seem at all mysterious, at least to me.
From David Bessler (Texas A&M University)
David Bessler pointed out that Bertrand Russell changed his views on causality relative the those he expressed in 1913 (see Epilogue, page 337). In his book Human Knowledge: Its Scope and Limits (Simon and Schuster, 1948) Russell states: "The power of science is its discovery of causal laws" (page 308).