Supervenience Argument

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4.2. Kim’s second argument

Let us now turn to the second version of Kim’s argument. What follows is more paraphrase than reconstruction. Our lines (1) and (3)-(6) come from Kim more or less verbatim except for a change in the numbering, and as noted in note 7 above; the remaining lines are close paraphrases of lines in Kim’s argument. Lines (1)-(3) are what Kim calls “Stage 1”, and lines (4)-(7) he calls “Completion 2”. These taken together comprise Kim’s second argument. As before, we make for a reductio the assumption that there is a case of mental-to-mental causation:

(1) M causes M'.
Again we know by Supervenience that:
(2) There is a P' such that P' is a supervenience base of M'.
From (1) and (2) it follows by SC I that:
(1) M causes P'.
By Closure, (3) implies that:
(4) P' has a physical cause—call it P—occurring at the time M occurs.
But Irreducibility tells us that:
(5) PM.
Next Kim asserts a line without justification [he introduces it only with “hence” (p. 44)]:
(6) P' is not overdetermined by P and M.
Now, from (4), (5), (6) and Exclusion it follows that:
(7) M does not cause P'.
(7) contradicts (3), and once again we must conclude that M did not cause M'. As M and M' were arbitrary mental properties, the conclusion must be that no mental-to-mental causation occurs ever, and the conclusion that no mental-to-physical causation occurs either follows as in the second variant of the first argument.

In addition to the large problem shared by both versions of Kim’s argument discussed in the next two sections, there are two minor problems specific to the second version, as presented by Kim.

The first problem is that not only is line (6) not justified, but it can’t be justified from assumptions explicitly made by Kim, his “substantive premises”. This is why we attributed Closure-Overdetermination to Kim. It would enable him to complete the argument as follows.16

(4) P has a physical cause—call it P—occurring at the time M occurs—and P is not overdetermined by P and M. [From (3) by Closure-Overdetermination.]

(5) PM. [From Irreducibility.]
(7) M does not cause P. [From (4) and (5) by Exclusion.]
The second problem is not so easy to solve on Kim’s behalf. It is that Kim says that in his second argument “Supervenience is not needed as a premise” (p. 44), but this is not so: the second argument shares what Kim calls “Stage 1” with the first argument, and Supervenience is needed in Stage 1. Without Supervenience, we cannot conclude that M has a physical supervenience base P. According to our reconstruction, the difference between the two arguments is different from what Kim asserts: they differ with respect to two premises: the first argument makes use of SC II and No Overdetermination whereas the second does not; the second argument makes use of Closure-Overdetermination whereas the first one does not. It is, of course, entirely possible that our reconstruction does not capture Kim’s intentions (see note 15), but our goal has been to produce a reconstruction that is as close to the letter of Kim’s exposition as possible.

5. The main logical problem

Here is the most serious problem with Kim’s arguments. That the arguments appear to have a valid form is only an artifact of the abbreviating convention used by Kim—unabbreviated, the arguments are either invalid or enthymematic; we suppose the latter. We followed Kim in using the same variables for both properties and events, but now we will adopt a more explicit nomenclature, with uppercase letters (“M” and “P”, possibly supplemented with primes) for properties and lowercase letters for their instances (“m” and “p”, possibly supplemented with primes). Using this convention and adding material presumably elided by Kim, the steps of our first reconstruction are as follows, where the added material is in boldface.

(1) An instance m of M causes an instance m of M [Assumption].

(2) There is an instance p of a physical property P such that p is a supervenience base of m. [From (1) by Supervenience.]

(3) m causes p. [From (1) and (2) by SC I.]

(4) There is an instance p of a physical property P such that p is a supervenience base of m. [From (1) by Supervenience.]

(5) p causes p. [From (3) and (4) by SC II.]

(6) MP. [By Irreducibility.]

(7) p is not causally overdetermined by m and p. [From (4) by No Overdetermination.]

(8) m does not cause p. [From (5), (6), and (7) by Exclusion.]

It is clear that (8) cannot be derived from (5), (6), and (7) by Exclusion: for (8) to be so derivable, (6) would have to say “mp ”, not “MP ”. Nor does (8) follow from previous steps by any of the other assumptions that we have made explicit so far. However, one interesting conclusion does follow, namely:
(8) m = p.
The argument is straightforward: since m and p are simultaneous causes of p [by (3) and (4)], and m and p do not jointly overdetermine p [by (7)], it follows by Exclusion that m = p.

Since we assumed nothing about m except that it is a cause of some other mental event, what we have here is a proof that any mental event that causes another mental event is identical to a physical event. If we assume, instead of (1) that m causes a physical event, we can show that any mental event that causes a physical event must also be identical to a physical event. So we have shown that any mental event that causes any other event—mental or physical17—must be identical to a physical event. We have, in other words, a new argument for the token identity theory (or token physicalism) first proposed in Davidson 1970. Unlike Davidson’s argument for the theory, however, this one does not assume what Davidson called the “nomological character of causality”—that causes and effects must be related by deterministic laws—which many philosophers now find implausible, so perhaps this argument is more compelling than Davidson’s.

But clearly Kim does not think he is giving us an argument for the token identity theory. He thinks he is showing the inconsistency of Causal Efficacy with the assumptions he attributes to the nonreductive physicalist and certain “general metaphysical constraints”. So what has gone wrong? It would be most implausible to suggest that Kim has simply confused properties with their instances because of his abbreviating convention. Rather, we suggest that Kim is making use of an unstated premise which he likely thinks of as yet another “general metaphysical constraint”. It’s not difficult to see what this hidden premise might be, as Kim makes it explicit in his earlier work on events. It is an assumption about the identity conditions of events. To express this assumption we must first introduce a bit of notation from Kim 1976: let
[x, F, t]
denote the event (if any) in which object x possesses property F at time t.18 Using this notation, Kim (1976, 35) states what he calls the “identity condition”:

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