Physical and Metaphysical Counterfactuals: Evaluating Disjunctive Actions

Abstract The structural interpretation of counterfactuals as formulated in Balke and Pearl (1994a,b) [1, 2] excludes disjunctive conditionals, such as “had X $X$ been x1 or x2 $x_1~\mbox{or}~x_2$,” as well as disjunctive actions such as do(X=x1 or X=x2) $do(X=x_1~\mbox{or}~X=x_2)$. In contrast, the closest-world interpretation of counterfactuals (e.g. Lewis (1973a) [3]) assigns truth values to all counterfactual sentences, regardless of the logical form of the antecedent. This paper leverages “imaging” – a process of “mass-shifting” among possible worlds, to define disjunction in structural counterfactuals. We show that every imaging operation can be given an interpretation in terms of a stochastic policy in which agents choose actions with certain probabilities. This mapping, from the metaphysical to the physical, allows us to assess whether metaphysically-inspired extensions of interventional theories are warranted in a given decision making situation.

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