Counterlegal dependence and causation’s arrows: causal models for backtrackers and counterlegals
A counterlegal is a counterfactual conditional containing an antecedent that is inconsistent with some set of laws. A backtracker is a counterfactual that tells us how things would be at a time earlier than that of its antecedent, were the antecedent to obtain. Typically, theories that evaluate counterlegals appropriately don’t evaluate backtrackers properly, and vice versa. Two cases in point: Lewis’ (Noûs 13:455–476, 1979a) ordering semantics handles counterlegals well but not backtrackers. Hiddleston’s (Noûs 39(4):632–657, 2005) causal-model semantics nicely handles backtrackers but not counterlegals. Taking Hiddleston’s account as a starting point, I offer steps toward a theory capable of handling both counterlegals and backtrackers. The core contribution of this paper is a means for evaluating counterlegals relative to minimally-illegal models.
KeywordsCounterfactuals Causal models Backtracking counterfactuals Counterlegal conditionals Conditionals
- Fisher, T. (2016). Causal counterfactuals are not interventionist counterfactuals. Synthese. doi:10.1007/s11229-016-1183-0.
- Glymour, C. (2001). The Mind’s arrows: Bayes nets and graphical causal models in psychology. Cambridge, MA: MIT Press.Google Scholar
- Halpern, J. Y. (2000). Axiomatizing causal reasoning. Journal of Artificial Intelligence Research, 12, 317–337.Google Scholar
- Lewis, D. (1973). Counterfactuals. Blackwell Publishing. First published in 1973.Google Scholar
- Pearl, J. (2000). Causality: Models, reasoning, and inferences (1st ed.). Cambridge: Cambridge University Press.Google Scholar
- Spirtes, P., Glymour, C. N., & Scheines, R. (2000). Causation, prediction, and search (2nd ed.). Cambridge, MA: MIT Press.Google Scholar
- Woodward, J. (2003). Making things happen: A theory of causal explanation. Oxford: Oxford University Press.Google Scholar