#### Flagpoles, Anyone? Independence, Invariance and the Direction of Causation

This talk will explore some recent ideas concerning the directional features of explanation (or causation). Woodward begins by describing an ideal of explanation, loosely motivated by some remarks in Wigner’s Symmetries and Reflections. It turns out that broadly similar ideas are used in recent work from the machine learning literature to infer causal direction (Janzig et al. 2102).

One such strategy for inferring causal direction makes use of what Woodward calls variable independence. This exploits the idea that in systems which have two or more cause variables, we should, ceteris paribus, expect these to be independent in the sense of statistical independence or something like it. (This is a version of Wigner’s ideas about independence or randomness of initial conditions.) Roughly speaking, if a relationship involves 3 (or more) measured variables X, Y, and Z, or two variables X and Y and an unmeasured noise term U and two of these are independent but no other pairs are independent, then it is often reasonable to infer that the correct causal or explanatory direction is from the independent pair to the third variable.

A second strategy, which makes use of what Woodward calls, value/ relationship independence, exploits the idea that we expect that the causal or explanatory relationship between two variables (Xa Y, where X may be a vector) will be “independent” of the value (s) of the variables that figure in the X or cause position of the relationship Xa Y. Here the relevant notion of independence is linked to notions of invariance in a sense described in Woodward (2003). According to this strategy, if X --> Y is independent of (or invariant under) changes in X and the X—Y relationship in the opposite direction (Y—>X) is not invariant under changes in Y, we should infer that the causal direction runs from X to Y rather than from Y to X.

Both of these strategies have a natural justification in terms of the interventionist account of causation described in Woodward, 2003. As an empirical matter, both strategies “work” in the sense of being fairly reliable in reaching the correct conclusion about causal direction when this is independently known. These ideas also lead to a satisfying solution to Hempel’s famous flagpole problem which asks why we think that the length of a flagpole can be used to explain its shadow but not conversely.