[x, P, t] = [y, Q, t] just in case x = y, P = Q, and t = t.
The Identity Condition implies that if F and G are distinct properties and f and g are instances of F and G respectively, then f g. Given this, we can conclude from steps (1), (4), and (6) of the first argument that m p, and we can complete the argument:
(7) m p. [From (1), (4), and (6) by the Identity Condition.]
(8) p is not causally overdetermined by m and p. [From (4) by No Overdetermination.]
(9) m does not cause m. [From (5), (7), and (8) by Exclusion.]
With the introduction of the Identity Condition, however, the logical problem has been transformed into a dialectical problem for Kim.
6. The dialectictal prolem
The dialectical problem is that if Kim does include the Identity Condition among his assumptions, he can no longer claim to have shown that Causal Efficacy is inconsistent with nonreductive physicalism plus his metaphysical constraints. The Identity Condition implies that each event is an instance of exactly one property19—which is expressed using Kim’s notation as:
(F) If [x, F, t] = [y, G, t], then F = G.
Let us call any view of events that is committed to (F) fine-grained, and let us call any view of events committed to (F)’s denial coarse-grained. Let us now consider the question: What is nonreductive physicalism? According to one popular answer, nonreductive physicalism just is the conjunction of token physicalism with the denial of type physicalism.20 But to have a fine-grained conception of events is to assume that token physicalism implies type physicalism,21 which is—if you accept that popular answer—well nigh synonymous with the statement that nonreductive physicalism is false. On this conception of what nonreductive physicalism is, Kim’s supervenience argument, if it is to be viewed as an argument against nonreductive physicalism, reduces to the claim that the nonreductive physicalist gets the identity criteria of events wrong, and the various assumptions about causation and supervenience do no work at all.
This is not, of course, the only possible characterization of nonreductive physicalism,22 but it is certainly the classic one. Recall that token physicalism was an essential component of the positions defended in the two ur-documents of nonreductive physicalism—Davidson 1970 and Fodor 1974. Psychophysical supervenience played no role in their arguments, and it only became a physicalist staple due to Kim’s subsequent work. And although Kim regards psychophysical supervenience as a minimal requirement for any form of physicalism (Kim 1998, 15),23 at the same time he no longer regards it as a sufficiently robust relation on which to base a physicalist theory of mind, particularly since supervenience can be defined over “multiple domains” (Kim 1988), rendering it compatible with various forms of parallelism (including epiphenomenalism). Notice, however, that if psychophysical supervenience is defined over a single domain of events, it entails token physicalism, for every mental event will be a physical event. At any rate, token physicalism remains a highly plausible candidate for a “minimal” physicalist commitment, and it still enjoys wide acceptance as a position that purposively distinguishes itself from type physicalism. Consequently, to construct an argument against nonreductive physicalism, one of whose premises effectively says that token physicalism implies type physicalism, is to adopt a rather odd dialectical strategy.
We will consider in a moment the likely response that classic (token physicalist) versions of nonreductive physicalism lack the resources to account for mental causation (at least to the extent that they are silent about the causal role of properties), and so cannot be taken seriously as versions of nonreductive physicalism. But first there is a further problem with Kim’s argument that needs to be considered.
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