Abstract
It is widely held that, as Morgenbesser’s case is usually taken to show, considerations of causal or probabilistic dependence should enter into the evaluation of counterfactuals. This paper challenges that idea. I present a modified version of Morgenbesser’s case and show how probabilistic approaches to counterfactuals are in serious trouble. Specifically, I show how probabilistic approaches run into a dilemma in characterizing probabilistic independence. The modified case also illustrates a difficulty in defining causal independence. I close with a suggestion for a strategy to handle this difficulty.
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Notes
The counterfactual (C1) is not the one that was actually discussed in Slote (1978), though the case of Bet and Toss is essentially the same as Morgenbesser's original case as cited there. (C1) is rather an instance of what I will call Tichý-counterfactuals, in which, unlike Morgenbesser-counterfactuals, the antecedent has some causal bearing on its consequent. Tichý (1976) uses such counterfactuals to criticize the Lewis-Stalnaker semantics.
One might argue that if we truly assume indeterminism, (C2) is in fact false. See, for instance, Phillips (2007). I proceed on the standard assumption that it is indeed true.
See Jackson (1977) for an earlier proposal that stresses the role of causal notions in semantics for counterfactuals.
Kvart’s theory is based on causal notions, but they are ultimately analyzed in probabilistic terms. I interpreted his view in terms of similarity weighting, though he doesn’t adopt the possible worlds framework.
From this observation, Schaffer concludes that where causal and probabilistic independence diverge, our intuitions track causal independence (Schaffer 2004, p. 307f).
Noordhof’s (2004, p. 193) definition is actually a bit more complicated to accommodate Lewis’s point that there is no precise chance of B’s occurring because it may fluctuate. The simplification I made does not affect my argument.
In fact, what I said is stronger than what probabilistic theorists actually need. All that is needed, for example, concerning (C2) is that in considering the circumstances where Lucky does not bet tails, we should not assume that he bets heads; he might not have bet at all. This way the probabilistic theorists can have weak centering. They could hold that the closest worlds where Lucky does not bet tails are of two sorts: the worlds where he does not bet at all and the worlds, to which the actual world belongs, where he bets heads. Indeed, Noordhof claims, “Schaffer assumes that if Lucky had not bet tails he would have bet heads rather than not betting at all. Since not betting at all is one way that Lucky may not bet heads, it is not true that [the chance of Lucky’s losing the bet given his not betting tails] would generally have the value 0.5” (Noordhof 2005, p. 261). The argument that follows applies to this sort of move as well mutatis mutandis.
See Edgington (2004) for more examples favorable to causal approaches.
References
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Acknowledgments
I would like to thank Sungho Choi, Jamie Dreier, Doug Kutach, Paul Noordhof and an anonymous referee for helpful comments.
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Won, C. Morgenbesser’s Coin, Counterfactuals, and Causal Versus Probabilistic Independence. Erkenn 71, 345–354 (2009). https://doi.org/10.1007/s10670-009-9189-3
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DOI: https://doi.org/10.1007/s10670-009-9189-3