Reply to Objections

1. The thesis that proportionality (in the sense of a specific degree of determination) can be used to single out higher-level causes has been questioned. Critics (Shapiro and Sober (2012), Franklin-Hall (2016)) point out that the “proportionality standard” possesses “no capacity to prefer high-level explanations over low-level ones (or the reverse)” (Franklin-Hall (2016: 564)) because “there will always be a low-level variable satisfying the letter of the proportionality standard” (Franklin-Hall (2016: 565)), as it has been expressed by Woodward (2010).

Franklin-Hall argues that there are, to take the case of the pigeon trained to peck at red targets, variables that are more determinate than variable Cx (as defined above), which are just as proportional (in Woodward’s sense) to the effect E (pecking) than Cx. One such variable (the example is not Franklin-Hall’s but it is in the same spirit as hers) would be C*, defined as having value c*+ iff the perceived color is that of monochromatic light with wavelength 550nm and c*- iff the perceived color is that of light with 300nm. Indeed, C* is a cause of E, and C* also satisfies the proportionality standard as it is spelled out by Woodward. Different values of C* are mapped on different values of E: c*+ is associated with pecking and c*- is associated with absence of pecking. However, C* seems intuitively to be too determinate to be the most relevant variable to choose for a causal explanation of E. This refutes Woodward’s claim that proportionality correctly characterizes the variable that is the most appropriate for a causal explanation of E.

However, variable C* is no counter-example against the construal of specificity developed above. C* is not specific for E in the sense of our definition (S-2) because C* fails to satisfy clause (2). C* is a variable representing a natural property (the wavelength of light to which a perceiving subject is exposed) that varies within a continuous spectrum. c* + corresponds to a part of the spectrum of wavelengths the light can take. However, the specification of c*- does not fit clause (2): c*- is not defined as corresponding to the complementary part of the spectrum with respect to c*+.

2. Franklin-Hall examines an analysis she calls “the spirit of proportionality” that results from combining the requirement of proportionality (in Woodward’s sense) with a requirement of “exhaustivity” according to which “the cause variable’s values collectively exhaust the causal possibility space” (Franklin-Hall (2016: 566)). This corresponds to our requirement in clause 2 of (S-2) that the values of the cause variable must together cover all possible values of the causally responsible property. However, she shows that her concept of the spirit of proportionality is not adequate to the purpose of justifying higher-level causation (in the sense of level of determination), because the variable that best fulfills the requirement corresponds to the disjunction of all possible causes of the property represented by the effect variable.

Let us go back once again to Yablo’s pigeon. Cx is the variable that is specific for E, representing pecking. However, Cx is not the variable that best fits the requirement of the spirit of proportionality. Franklin-Hall shows that there are variables that fulfill the requirement of exhaustivity better than Cx. As an example she offers the variable corresponding to the following disjunction: “the presentation of a red target or provision of food or tickling of the chin or electrical stimulation of the cerebellum (other value: none of the above)” (Franklin-Hall (2016: 566)). The variable, let us call it Cmax, which takes value cmax+ in case one of the conditions in this disjunction is fulfilled is indeed just as proportional to E in Woodward’s sense as Cx, but it fits the standard of the spirit of proportionality better than Cx because the value cmax+ covers a larger part of the possibility space that includes all possible causes of pecking.

However, Cmax is not specific for E in the sense of our (S-2) because it does not fit clause (2). Recall that we have raised the question of which variable best represents the property causally responsible for the effect E in the context in which the cause of the event of pecking is already known. Only variables that represent natural properties of that cause event are candidates for being specific for E. We already know that the cause event in terms of the transmission of conserved quantities is the light reaching the pigeon’s retina. The interventionist analysis is only used in a second step. Once the cause has been identified as an event, there remains the question as to which of the event’s natural properties is causally responsible for the property E of the effect event. The disjunctive predicate constructed by Franklin-Hall does not correspond to any natural property of the light reaching the pigeon’s retina.

With the distinction between causation and specific causation, it appears that Menzies and List’s claim that there can be “downward exclusion” is after all compatible with the fact that higher-level and downward causal influence are always accompanied by lower-level causal influence.

Downward exclusion in Menzies’ and List’s sense corresponds to situations in which there is 1) higher-level influence M^M2 that is specific for M2 but there are no lower-level variables N1 and N2 (in the supervenience bases of M1 and M2) for which it would be the case that N1^N2 is specific, or 2) situations in which there is 1) downward influence M1^N2 that is specific but there is no lower-level variables N1 (in the supervenience basis of M1) so that N1——N2 is specific.

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