## Singular causation and model reduction

In my previous post I tried to get clear about when variables could be safely removed from a causal model without affecting what the model is capable of telling us about singular causal relations. There, I endorsed two principles stating when causal models may be reduced by excising variables in a particular way. If we endorse these principles, and we want to give a theory of singular causation formulated in terms of correct causal models, then we should want that theory to give the very same verdicts before and after model reduction. The point of today’s post is that there is a wide family of theories of causation which run afoul of this constraint. Those theories will say that two variable values are causally related in one model, but reverse this judgment when the model is reduced.

## When can variables be safely removed from a causal model?

Much of our causal talk consists of sentences of the form “c caused e”, where both c and e are token, non-repeatable events or facts or what-have-you (there will be disagreement about what kinds of things ‘c’ and ‘e’ denote, but for now, I’ll just call them ‘events’). Let’s call the kinds of causal relations we’re talking about with sentences like those ‘singular causal relations’. The topic of causation is not exhausted by singular causal relations.

## When do Variables Overlap?

I spent the past two days preparing comments on a very interesting paper by Vera Hoffmann-Kolss for the upcoming Society for the Metaphysics of Science meeting. Thinking through the paper got me freshly confused about some matters that I had thought settled, and so I thought I’d write up a blog post on those confusions in an attempt to sort them out.

It’s tempting to think that counterfactual dependence suffices for causation. But this can’t be quite right. I both played cards and played poker. Had I not played cards, I wouldn’t have played poker. So there is counterfactual dependence between my playing poker and my playing cards. But my playing cards didn’t cause me to play poker. The relationship between my playing cards and my playing poker is constitutive, not causal.

Sophisticated counterfactual theories of causation, therefore, do not say that counterfactual dependence suffices for causation. Rather, what they say is that counterfactual dependence between distinct events suffices for causation. By ‘distinct’, we mean a bit more than ‘non-identical’. The event of my playing poker is not identical to the event of my playing cards. (If you doubt this, note that they differ causally. I played poker because I didn’t have a pinochle deck—I usually play pinochle. But I certainly didn’t play cards because I didn’t have a pinochle deck.) Rather, ‘distinct’ in this context means something more like ‘not logically related’. If two events are not distinct, then let’s say that they overlap.

Worries about overlap plague other theories of causation, too. My playing poker is a minimally sufficient condition for my playing cards, so—unless overlapping conditions are specifically excluded—Mackie’s account of causation will deem them causally related.

Today, I’ll be exploring this problem as it plays out for those who, like myself, think that the causal relata are variable values. For such theorists, the problem is to say when variables are distinct, and when they overlap.