Abstract
Instances of many supervenient properties have physical effects. In particular, instances of mental properties have physical effects if non-reductive physicalism is true. This follows by a straightforward argument that assumes a counterfactual criterion for causation. The paper presents that argument and discusses several issues that arise from it. In particular, the paper addresses the worry that the argument shows too many supervenient property-instances to have physical effects. The argument is also compared to a similar argument that has been suggested by Lei Zhong and is shown to be superior to the latter.
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Notes
Here and throughout, ‘necessarily’ expresses metaphysical necessity. The notion of supervenience defined here is standardly called strong supervenience when contrasted with other stripes of supervenience (none of which is relevant for our purposes). More precisely, my formulation of the definition follows what McLaughlin calls “Modal-Operator Strong Supervenience” (1995, p. 95). For further discussion, see Kim (1984) and McLaughlin (1995).
Sometimes the counterfactual dependence of e on c is taken to involve not just that e wouldn’t have occurred if c hadn’t occurred, but also that e would have occurred if c had occurred. Given Lewis’s truth-conditions, the second counterfactual is redundant given that (i) c and e actually occur and that (ii) the actual world is closer to itself than any other worlds are. The account of mental causation developed in List and Menzies (2009) rejects claim (ii).
The inference from (1) and (2) to (3) is valid not only given Lewis’s truth-conditions for counterfactuals, but in any logic for counterfactuals that creates non-hyperintensional contexts in Williamson’s (2006, p. 312) sense. The inferences between counterfactuals that will be made in Sect. 4.2, however, are not valid in all logics that merely satisfy this minimal requirement.
For further discussion of how counterfactual theories of causation might apply to such cases, see Fenton-Glynn and Kroedel (forthcoming).
This suggestion can be finessed in different ways. Lewis (1979) claims that the combination of his truth-conditions for counterfactuals with a similarity ordering of worlds that features big and small violations of (actual) laws of nature and match of particular fact with the actual world rules out ‘backtracking’ evaluations of counterfactuals whose antecedents talk about specific events. It is somewhat controversial whether Lewis’s strategy succeeds (see Kment 2010, p. 84). Alternatives that could be built upon for our purposes that don’t involve commitment to Lewis’s similarity ordering include the accounts of Maudlin (2007) and Paul and Hall (2013, pp. 47–48).
A related worry is about omissions. Lots of events counterfactually depend on omissions, but one might not want to accept that they are caused by those omissions. That omissions can’t be causes is more controversial than that properties like S+ can’t be causes. If one wants to rule out omissions as causes, one could pursue a similar strategy, however: restrict our sufficient condition for causation to instances of ‘positive’ properties and disallow instances of ‘negative’ properties. For further discussion, see Lewis (1986b, pp. 189–193).
The example is a variation of an example from Lewis (1986b, p. 184).
For a recent elaboration of this approach, see Swanson (2010).
The example is due to Jackson and Pettit (1990), who use it in a different context.
If artefacts such as ladders have their origin essentially, as Kripke (1980) holds, the ladder could not have been made of a different material from the one it is actually made of. If that is the case, the problem can be reformulated by taking the relevant events to be instances of the property of containing a ladder that is made of such-and-such a material by the spatial region that is occupied by the ladder.
Which is not to say that (6-O) follows logically from \(\sim \) \(\varvec{\cup }\mathbf{P}_{C}\,\square \) \(\rightarrow \) \(\sim \)E, for it doesn’t (see Lewis 1973b, p. 31).
At least in our case. In general, properties that feature in the description of an event don’t have to be essential to that event, however. See Lewis (1986a, pp. 247–254) for discussion.
Friends of false counterpossibles, that is, false counterfactuals with impossible antecedents, will disagree. For a given (allegedly) false counterpossible, they cannot accept that it is logically implied by the corresponding strict conditional, which is trivially true owing to the impossible antecedent. But friends of false counterpossibles can still accept the weaker claim that strict conditionals with possible antecedents logically imply the corresponding counterfactuals. This weaker claim is all that is needed for the present derivation.
The inference has the form of an inference from \(\upphi \,\square \) \(\rightarrow \) \(\upchi ,\, \upchi \,\square \) \(\rightarrow \) \(\upphi ,\) and \(\sim \)[\(\upchi \,\square \) \(\rightarrow \) \(\uppsi ]\) to \(\sim \)[\(\upphi \,\square \) \(\rightarrow \) \(\uppsi ],\) which is valid if and only if the inference from \(\upphi \,\square \) \(\rightarrow \) \(\upchi ,\,\upchi \,\square \) \(\rightarrow \) \(\upphi ,\) and \(\upphi \,\square \) \(\rightarrow \) \(\uppsi \) to \(\upchi \,\square \) \(\rightarrow \) \(\uppsi \) is, which in turn is valid according to Lewis (1973b, p. 33).
Difference-making is supposed to captured by counterfactuals that are non-vacuously true. The fact that, say, ‘\( Phys = 0\, \& \,{Con}= 0\,\square \) \(\rightarrow \) \({El} =0\)’ is vacuously true while ‘\(Phys =0\,\square \) \(\rightarrow \) \({El} = 0\)’ is false isn’t a reason for including Con in the equation for El.
If that assumption seems implausible, we could still justify the inclusion of Con in the equation for Phys, and hence the arrow from Con to Phys in the causal graph, from the truth of the counterfactual ‘\({Con} = 0\,\square \) \(\rightarrow \) \({Phys} = 2\,\vee \,{Phys} = 3\)’.
Strictly speaking, there are paths from Con to El that include Op, e.g., the sequence \({Con} \rightarrow {Phys} \rightarrow {Op} \rightarrow {Phys} \rightarrow {El}.\) Thus, we should understand a path as a non-cyclic sequence here, that is, a sequence that doesn’t include any variable more than once.
While the antecedent is merely supposed to be sufficient, not necessary, for causation, its falsity might sometimes be taken to be a defeasible reason for denying, or at least doubting, the existence of a causal relation. This might explain why some doubt that an overdetermining event causes the overdetermined event: an overdetermining event makes no difference to the occurrence of the overdetermined event if we hold the occurrence of the other overdetermining event, which is off-path, fixed.
Similarly for a model that includes Con in addition to Op and El, but doesn’t contain Phys. In that model, the value of Op makes a difference to the value of El, but this difference is nothing over and above the difference made by the value of Con. So Con is on the path from Op to El, and again it is trivially true that the value of Op makes a difference with respect to the value of El if all off-path variables are held fixed at their actual values.
Fig. 2 
The graph of a simple causal model for the electrocution case
See Halpern and Hitchcock (2010) for discussion of the notion of an appropriate causal model.
For a defence of these unorthodoxies for the purposes of modelling mental causation, see Kroedel (ms).
It might seem promising to apply Swanson’s (2010) account of the context-sensitivity of causal talk to our case. Unfortunately, there are some prima facie difficulties with this application. Swanson appeals to the principle that when ascribing causal responsibility for a given effect to a causal path, one should use good representatives of that path (see ibid., p. 225). One can’t use this principle to show that the conductivity-instance is a better representative of a path that contains both the conductivity-instance and the opacity-instance than the opacity-instance is, for both by Swanson’s definition and by the causal modelling definition the two property-instances are on different paths. (They are also in different causal clusters in Swanson’s (ibid., p. 237) sense, because they have different effects; for instance, the opacity-instance causes the ladder to cast a shadow, but the conductivity-instance doesn’t.) Perhaps it could be shown that the opacity-instance is a poor representative of a path that contains it but doesn’t contain the conductivity-instance. But showing that wouldn’t be straightforward either, since one of Swanson’s principal criteria for an event’s being a good representative, the effect’s counterfactually depending on the representative, does apply to the opacity-instance and the electrocution.
This valid inference should not be confused with the similar but invalid inference that was discussed in Sect. 4.1.
Proponents of the so-called autonomy approach such as Gibbons (2006) accept mental-to-mental causation while denying mental-to-physical causation.
Zhong addresses the objection by Christensen and Kallestrup in Zhong (forthcoming).
See Kroedel (forthcoming).
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Acknowledgments
For helpful comments and suggestions, I would like to thank Sebastian Bender, Catharine Diehl, Luke Fenton-Glynn, Jan Gertken, Franz Huber, Beate Krickel, Rory Madden, Beau Madison Mount, Christian Nimtz, Tobias Rosefeldt, Thomas Sattig, Peter Schulte, Moritz Schulz, Wolfgang Schwarz, Barbara Vetter, Timothy Williamson, audiences in Aarhus, Berlin, Bielefeld, and Dubrovnik, and two anonymous referees.
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Kroedel, T. A simple argument for downward causation. Synthese 192, 841–858 (2015). https://doi.org/10.1007/s11229-014-0600-5
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DOI: https://doi.org/10.1007/s11229-014-0600-5