## Invariant Generalizations and Causal Explanation

February 20, 2010

I am re-reading the chapters devoted to causal explanation of Woodward’s Making Things Happen: A theory of causal explanation.  The book is very interesting and ambitious and probably Woodward is offering there one of the most complete and attractive theories of causal explanation available today.  I am sympathetic to some of the main ideas.  The purpose of this note is to indicate some potential problems with the general account defended by Woodward.

Some background first.  Woodward proposes necessary and sufficient conditions for a generalization to represent a causal or explanatory relationship.  The idea is that the generalization should be invariant under some testing interventions on variables occurring in the relationship (page 253).  This simple formulation presupposes a lot.  For example, it presupposes that the generalization is expressible in a functional form $Y = f(X)$. The technical term “testing intervention” needs to be explained as well. Consider an intervention (meeting the conditions specified by Woodward in chapter 3 of his book) that changes the value of $X$, say $x_{0}$, that presently holds to some other value $x_{1}$, where $x_{1}$ is claimed by the generalization to be associated with a value of $Y$ that is different from the value associated with $x_{0}$. So, if $G$ abbreviates our generalization we have that $x_{0}$ is different from $x_{1}$ and $G(x_{0}) = y_{0}$ is also different from  $G(x_{1}) = y_{1}$. Such interventions are called “testing interventions.”