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- Robert Northcott (2009). On Lewis, Schaffer and the Non-Reductive Evaluation of Counterfactuals. Theoria 75 (4):336-343.Jonathan Schaffer (2004 ) proposes an ingenious amendment to David Lewis's semantics for counterfactuals. This amendment explicitly invokes the notion of causal independence, thus giving up Lewis's ambitions for a reductive counterfactual account of causation. But in return, it rescues Lewis's semantics from extant counterexamples. I present a new counterexample that defeats even Schaffer's amendment. Further, I argue that a better approach would be to follow the causal modelling literature and evaluate counterfactuals via an explicit postulated causal structure. This alternative approach easily resolves the new counterexample, as well as all the previous ones. Up to now, its perceived drawback relative to Lewis's scheme has been its non-reductiveness. But since the same drawback applies equally to Schaffer's amended scheme, this becomes no longer a point of comparative disadvantage.
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One criticism of David Lewis''s account of counterfactuals is that it sometimes assigns the wrong truth-value to a counterfactual when both antecedent and consequent happen to be true. Lewis has suggested a possible remedy to this situation, but commentators have found this to be unsatisfactory. I suggest an alternative solution which involves a modification of Lewis''s truth conditions, but which confines itself to the resources already present in his account. This modification involves the device of embedding one counterfactual within another. On the revised set of truth conditions, counterfactuals with true components are sometimes true and sometimes false, in a way that is more in keeping with our intuitive judgments about such statements.
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In “Backward Causation and the Stalnaker–Lewis Approach to Counterfactuals,” Analysis 62:191–7, (2002), Michael Tooley argues that if a certain kind of backward causation is possible, then a Stalnaker–Lewis comparative world similarity account of the truth conditions of counterfactuals cannot be sound. In “Tooley on Backward Causation,” Analysis 63:157–62, (2003), Paul Noordhof argues that Tooley’s example can be reconciled with a Stalnaker–Lewis account of counterfactuals if the comparative world similarity relation on which the Stalnaker–Lewis account relies is allowed to be antecedent-relative. In this paper I show that taking comparative world similarity to be antecedent-relative results in a formal semantics which is a comparative world similarity semantics in name only.
In the artificial intelligence literature a promising approach to counterfactual reasoning is to interpret counterfactual conditionals based on causal models. Different logics of such causal counterfactuals have been developed with respect to different classes of causal models. In this paper I characterize the class of causal models that are Lewisian in the sense that they validate the principles in Lewis’s well-known logic of counterfactuals. I then develop a system sound and complete with respect to this class. The resulting logic is the weakest logic of causal counterfactuals that respects Lewis’s principles, sits in between the logic developed by Galles and Pearl and the logic developed by Halpern, and stands to Galles and Pearl’s logic in the same fashion as Lewis’s stands to Stalnaker’s.
In assessing counterfactuals, should we consider circumstances which match the actual circumstances in all probablistically independent fact or all causally independent fact? Jonathan Schaffer argues the latter and claims that the former approach, advanced by me, cannot deal with the case of Morgenbesser’s coin. More generally, he argues that, where there is a difference between the two, his account yields our intuitive verdicts about the truth of counterfactuals where mine does not (Schaffer 2004: 307, n. 16). In this brief note, I explain how my approach deals with the case of Morgenbesser’s coin and argue that the situation is, in fact, the reverse. To keep things brief, I rely upon Schaffer’s paper for general explanation of the context of our debate.
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