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Physical and Metaphysical Counterfactuals: Evaluating Disjunctive Actions

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  • Pearl Judea

    (Computer Science Department, University of California, Los Angeles, Los Angeles, CA 90095-1596, USA)

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.

Suggested Citation

  • Pearl Judea, 2017. "Physical and Metaphysical Counterfactuals: Evaluating Disjunctive Actions," Journal of Causal Inference, De Gruyter, vol. 5(2), pages 1-10, September.
    • Handle: RePEc:bpj:causin:v:5:y:2017:i:2:p:10:n:8
    DOI: 10.1515/jci-2017-0018
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    References listed on IDEAS

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    1. Peter Spirtes & Clark Glymour & Richard Scheines, 2001. "Causation, Prediction, and Search, 2nd Edition," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262194406, December.
    2. Hendry,David F. & Morgan,Mary S., 1997. "The Foundations of Econometric Analysis," Cambridge Books, Cambridge University Press, number 9780521588706, May.
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