Interactionism and Physicality

Eugene Mills

Substance-dualist interactionism faces two sorts of challenge. One is empirical, involving the alleged incompatibility between interactionism and the supposed closure of the physical world. Although widely considered successful, this challenge gives no reason for preferring materialism to dualism. The other sort of challenge holds that interactionism is conceptually impossible. The historically influential version of the conceptual challenge is now discredited, but recent discussions by Chomsky and by Crane and Mellor suggest a new version. In brief, the argument is that anything that interacts causally with physical things would have to be sanctioned by physics, and anything sanctioned by physics is ipso facto (as a matter of conceptual necessity) physical. I focus on the second premise. I show that plausible arguments for it are in fact fallacious and that counterexamples undermine it. Thus the argument fails: substance-dualist interactionism cannot be ruled out on conceptual grounds alone.

quoted from: Ratio (new series) 10 (2), (2 September 1997)  pp.169-183.

 1. Introduction

Two sorts of objections, one empirical and one conceptual, have long challenged substance-dualism (hereafter, 'dualism').1 The empirical challenge is widely seen as successful, while the conceptual challenge has largely faded from discussion. I will begin by sketching some reasons for thinking that the empirical challenge gives no reason to prefer materialism to dualism, though establishing this is not my main concern here. If I am right, dualism is due for a revival, given its admitted wide pre-theoretical appeal. A new version of the conceptual challenge, however, lies implicit in some recent discussions of physicalism. This conceptual objection threatens to block dualism's revival. My aim here is to articulate and rebut it.

Dualism has languished, despite its admitted wide pre-theoretical appeal, because it has seemed to most philosophers to preclude a wanted reconciliation between science and common sense. Common sense insists that the mind matters to what we do: our experiences, beliefs and wants cause us to act and our bodies to move. Our 'scientific world-view' commits us, many philosophers think, to the contingent but (allegedly) empirically well-established view that the physical world is causally closed: every physical event which has any (sufficient) cause has a physical one. Hence, the argument goes, there is no room for non-physical causation of physical events. If we would reconcile common sense with science, we seem driven to monism, of which only a materialist version seems plausible.

This argument from physical causal closure has close cousins, if not fraternal twins, that threaten to render the mental features of physical events, no less than non-physical mental events, causally irrelevant to physical events.2 Much ink has been spilled over the last couple of decades in debating the merits of these arguments. What has generally gone unrecognized, though, is that all the standard strategies for defeating them have exact analogues applying to the argument against dualist interaction-ism (hereafter just 'interactionism'). Some (e.g. Kim 1993) think that mental causation can be saved only by the nomological reducibility of mentality to a non-mental base; a dualist, however, can perfectly well accept such nomological reducibility, for alone it brings no ontological reduction. Others (e.g. Yablo 1992) hold that mental causes overdetermine events for which there are also physical sufficient causes; this claim is no more and no less plausible for event-causation than for property-causation, so dualists can avail themselves of it. Others (e.g. LePore and Loewer 1987) refocus mentality's causal relevance on things which lack purely physical sufficient causes (e.g. not a physical event's occurrence but its having such-and-such properties), and claim this is enough for common sense; dualists can likewise restrict the causal relevance of non-physical mental events.

For present purposes, I need not take a stand on which if any of these responses — or the direct approach of denying physicalcausal closure - succeeds.3 In saying that the rejection of dualism fails to yield the wanted reconciliation between science and common sense, I do not claim that such a reconciliation is unattainable. I claim rather that its attainability is independent of the truth of dualism: if a material mind can matter, so can an immaterial one.

To convince interactionism's foes would, of course, take much more argument. And even if they are persuaded that dualism can fend off the objection from the causal closure of the physical world, they might still appeal to Occam's razor: if dualism and materialism fare equally well with psychophysical causation, we should opt for materialism on grounds of ontological parsimony. This response would be correct if the only basis for admitting non-physical mental events stemmed from their role in explaining purely physical events. Standard arguments for dualism do not, however, proceed by such inference to the best explanation. They rest instead on claims of modal independence (see, for example, Kripke 1980, pp. 146-7). These arguments are contestable, of course, but respectable. It is one aim of this essay to refocus attention on them: enemies of dualism must show that they fail, not appeal blithely to ontological parsimony.

Suppose I am right that the empirical objection to interactionism fails. There remains another traditional objection to which its foes might turn. This holds that interactionism is not just empirically but conceptually impossible.

The historically important version of the conceptual objection is that the distinct mental and physical things dualism endorses are so radically unlike that we have no clear notion of how one could exercise causal influence on the other.4 Expressed thus crudely, this criticism nowadays holds only antiquarian interest. For one need not accept Hume's positive view of causation to have learned his negative lesson: if apprehension of some necessary connection is needed for understanding causality, mental causation poses no special problem, for it is at least no worse off than purely physical causation in this regard (see Crane and Mellor 1990, p. 192). The argument I will shortly consider, however, develops the spirit of the historical objection into onewhich, although it should ultimately be rejected, must be taken seriously - especially since, as the failure of physical causal closure to rule out dualism grows more apparent, this objection is likely to come to the fore.

The conceptual threat to interactionism could take one of three forms. Note that dualism entails the denial of a basic 'ontological physicalism' which holds that everything is physical (or physically composed: I will henceforth leave this qualification tacit).5 One could, then, argue against dualism by either elevating or eviscerating ontological physicalism. First, one could maintain that physicalism is conceptually necessary and dualism, therefore, impossible. Second, one could argue that the notion of physicality apparently common to both dualism and ontological physicalism is confused, so that the distinction between the two collapses. The third sort of conceptual threat to interactionism, like the traditional version, challenges the possibility not of dualism but of interactionism, by challenging the compossibility of dualism with the thesis that non-physical events cause physical events.

Recent arguments by Chomsky (1995) and Crane and Mellor (1990) appear to pose a threat of the second sort, and seem clearly so intended by their authors. It turns out, I will argue, that the considerations they cite fail to support this interpretation. These considerations could be interpreted as arguing for the necessary truth of physicalism; but they are best interpreted, I will show, as a threat of the third sort, challenging the compossibility of dualism with psychophysical causation.

Although this threat receives little explicit support beyond the authors just mentioned, it commands wide casual allegiance and exerts significant sub rosa influence. Thus Fodor, for example, says without argument that 'Whatever has causal powers is ipso facto material' (Fodor 1987, p. x); Dennett claims, also without argument, that 'Anything that can move a physical thing is itself a physical thing' (Dennett 1991, p. 35). This is the threat that concerns me. I will show that it is empty.

II. An attack on physicalism

Crane and Mellor argue that 'physicalism lacks a clear and credible definition, and that in no non-vacuous interpretation is it true' (1990, p. 185). If they are right, then dualism will also lack a clear and credible definition. So it is worth seeing whether they are right.

Crane and Mellor consider several formulations of physicalism. Of these, only one poses a serious threat to the conceptual coherence of interactionism. It suggests that physics is the arbiter of claims to physicality and that physicalism should be understood as the claim that all ontologically acceptable sciences are reducible in principle to physics (Crane & Mellor 1990, p. 188).

Crane and Mellor argue that if this be physicalism, then physicalism is false. For if current physics is the arbiter of physicality, then physicalism's prospects are as embarrassingly low as those for current physics. We must leave open the possibility that contemporary physics is mistaken or at least incomplete. If to be physical is to be sanctioned by current physics, then any new entities introduced by future physics cannot be physical, and this is plainly absurd.

If not current physics, what? Two possibilities suggest themselves. One is an analysis of physicality. But  we have no such analysis in hand, and as old versions of materialism show, any such analysis is wont to be overrun by the advance of physics. The other possible arbiter is some sort of ideal version of physics. But, as Crane and Mellor point out (1990, p. 188), there is no saying in advance what this will look like. If it turns out that mental events are nothing remotely like what is recognizably 'physical' by intuitive standards but do nevertheless have causal influence on what is paradigmatically physical, then - the argument goes -such things would have to be sanctioned by physics and so would qualify as 'physical'. But to render physicality thus open-ended is to render it vacuous.

Recent remarks by Chomsky (1995, pp. 3-5) tend in the same direction. He points out that Newton's introduction of gravitational force was roundly criticized by his contemporaries as a retreat in the direction of mystery and immateriality, opposed to sound mechanistic principles. Recent discussions of physicalism, says Chomsky, assume,  contrary to Newton  and his  contemporaries,  that Newton remained within 'the materialist world picture'; thatwould be true only if we understand 'the materialist world picture' to be whatever science constructs, however it departs from 'mechanical causes'. To put it differently, the discussions presuppose some antecedent understanding of what is physical or material, what are the physical entities. These terms had some sense within the mechanical philosophy, but what do they mean in a world based on Newton's 'mysterious force', or still more mysterious notions of fields of force, curved space, infinite one-dimensional strings in ten-dimensional space, or whatever science concocts tomorrow? Lacking a concept of 'matter' or 'body' or 'the physical', we have no coherent way to formulate issues related to the 'mind-body problem'.

Two points need remarking. First, it plainly overstates the case to say that construing Newton as a materialist requires the materialist picture to be whatever science constructs; it would be enough to understand it as whatever physics constructs. After all, it is at least not obviously impossible that, for example, mental events interact causally with one another in lawful, scientifically describable ways while having no such interaction with the things studied by physics. To hold this would go far beyond embracing Newton's 'mysterious forces' — which are not mental, for all their mystery — and would allow a useful distinction between materialism and dualism which puts Newton on the materialist side.

Second, Chomsky's suggestion that he is putting one point in two different ways here is misleading. It is one thing to say that 'physical' just means sanctioned by physics, another to say that it means nothing at all. Chomsky seems to intend the latter: we are, he says, 'Lacking a concept of... "the physical"'.

Suppose we read Chomsky as holding that there is no concept attached to 'physical'. (I'm sure Chomsky would agree that 'physical' expresses a concept in some contexts, as when we say 'They play a physical game of basketball'. This is irrelevant, though. The claim under discussion is that it expresses no concept in contexts in which the physical is supposed to contrast ontologically with the non-physical, as in debates over physicalism and dualism.) What is the argument for this claim? It seems to be simply that all sorts of things that far outstrip Lockean primary qualities and the ontology of mechanism — fields of force, curved space and the rest — would not have been regarded as physical by Newton's predecessors, but are sanctioned by our best currentphysics. (One cannot consistently add, 'and so are physical'.) But this is no argument at all: one might as well say that since viruses would not have been regarded as living by our biologist-ancestors but are sanctioned by our best current biology, there is no concept of living being.

Someone might wonder whether ancestral biologists would have rejected viruses as non-living, especially if they were given a full understanding of their function and of the biological theory requisite for such understanding. Two points are in order. The first is that similar remarks apply in the physical case. It may perhaps have been rational to dismiss gravity as a mysterious, non-physical force if it were described merely as an attractive force introduced for ad hoc reasons; it less obviously rational to dismiss it in the context of a full understanding of a highly unified and successful physical theory. But this is a murky matter on which we need not decide. The second point is gratifyingly clear. Whether or not the viral analogy is apt, the logical point is simply that there is no license for the claim that a term is senseless in the mere variability of its application over time, place and person.

In any case, the claim that there is no concept of physicality (in the sense in which physicality is supposed by dualists to contrast with mentality) is implausible in the extreme. As Crane and Mellor point out, physicalism's insistence on physicality is supposed to oppose immaterial mental entities, not immaterial entities of all sorts: physicalists need not be nominalists, and can accept the existence of abstract, non-physical sets, numbers, propositions and the like. But if there is sense to be made of the claim that numbers (for example) are non-physical — whether or not this claim is true — then there is sense to be made of 'physical'.

So despite remarks which suggest otherwise, it would be uncharitable to interpret Chomsky or Crane and Mellor as arguing that 'physical' (and, by extension, 'dualism') is nonsensical.6 A better interpretation is that the concept physical just is, or at least is equivalent to, the concept sanctioned by physics. The considerations they cite are best understood as providing empirical support for a certain linguistic hypothesis: we see that we, and especially the scientists among us whom we take as authorities,consistently apply the term 'physical' to all and only those things sanctioned by physics. Furthermore, history suggests that our counterfactual judgments follow suit. We see that, over and over, things pre-theoretically believed to fall outside the extension of 'physical' have come to be accepted as falling within it when they have come to be accepted by physics. This seems to suggest that if an ideal physics were to need some utterly odd entity, we would come to count it as physical, whether or not we so regard it now. If all this is right, it lends strong support to the empirical hypothesis that what we mean by 'physical' and by 'sanctioned by physics' are identical or equivalent. To get from this to the relevant conceptual equivalence is a matter of tying mention to use: add that what we mean by 'physical' is physical and what we mean by 'sanctioned by physics' is sanctioned by physics.

I will argue that it is a mistake to equate the concept physical with the concept sanctioned by physics. First, though, I want to set aside two bad reasons for rejecting such an identification.

It might be objected, for starters, that (for example) we all allow that chairs and rocks are physical objects, but physics makes no mention of them; hence 'physical' cannot mean 'sanctioned by physics'.

This objection fails, but does show that the notion of being sanctioned by physics needs clarification. First, it is plausible to maintain that physics (construed as a set of theoretical assertions) does not entail the existence of any physical thing. What the theoretical assertions of physics explicitly invoke are properties or types: the property of being a quark figures in physical theory, but the existence of particular quarks does not. Thus talk of rocks being sanctioned by physics is really about rockhood being sanctioned by physics. This point leads to the second: being sanctioned by physics and being explicitly invoked by physics are not the same. In saying that chairhood and rockhood are sanctioned by physics, we do not mean that they are explicitly invoked by physical theory. We mean, I think, that the instantiation of these properties is consistent with the truth of physics.7

On this understanding of 'sanctioned by physics', the initial objection against the identification of the concept physical with the concept sanctioned by physics collapses.

A second objection might be that there is something circular here, since we understand physics only as the study of the physical. I think there is a way of blocking the charge of circularity, but I need not state it. For even if the charge is true, it is not fatal. Circularity would vitiate the claim that physicality is defined in terms of what's sanctioned by physics. No such claim is at issue, however. The relevant claim is simply one of conceptual identity (or, perhaps, mere equivalence). Such a claim need not be touted as a definition.

We should take seriously, then, the suggestion that the concept physical is just (equivalent to) the concept sanctioned by physics. It is easy to see why Chomsky, Crane and Mellor would think, on this interpretation of their claims, that a dispute between dualist and physicalist advocates of psychophysical causation would be vacuous. For suppose that mental events cause physical ones. Physics aims at a comprehensive account of the behaviour of physical entities and of the causes of physical events; so if mental events were to act on physical ones, they would have to be sanctioned by physics. But to be an event of a sort sanctioned by physics just is to be physical. So if mental events cause physical ones, they must be physical.

Descartes could have been right, according to this argument, only if he were wrong: if motions of paradigmatically physical objects (pineal ones, for example) could be explained only by invoking mental events as their causes, then an ideal physics would have to bring such causes within its scope and thus render them physicalistically acceptable.

It might be thought that this argument poses the first sort of conceptual threat to interactionism, one aimed at rendering physicalism conceptually necessary (and so dualism conceptually impossible). This interpretation is consistent with Crane and Mellor's suggestion that physicalism is true only on a vacuous interpretation. For one sort of vacuity is trivial necessity, and the argument under discussion might be thought to make everything trivially physical. It does not, however, for it applies only to those things that cause physical events. Dualist epiphenomenalism, for example, escapes it unscathed. It aims not at dualism, as Chomsky's remarks suggest, but at interactionism.

The real threat, then, is of my third sort: a contemporary analogue of old conceptual worries about inter-substance causation. The argument is as follows:

(1)  necessarily, anything of a type sanctioned by ideal physics is physical;

(2)  necessarily,   anything which  exerts  causal  influence  on physical events (states, objects, facts, properties) will be of a type sanctioned by ideal physics;8 therefore

(3)  necessarily,  anything which  exerts  causal  influence  on physical events (states, objects, facts) is physical.

If this argument is sound, then interactionism is necessarily false. (The necessity invoked should be understood throughout as conceptual necessity, for those who would distinguish this from metaphysical.)

III. The flaw in the argument

It is worth noticing that premise (2) is far from obvious: it should be enough for ideal physics to invoke everything necessary to explain the physical, and - given the possibility of causal overdetermination - this could well fall short of everything that actually exerts causal influence on it.9 For now, though, I will grant (2) for the sake of argument.

My focus is premise (1): it is mistaken. Given that entities of a certain type are sanctioned or even explicitly invoked by physics -ideal or otherwise - it does not follow that entities of that type are physical. Although it seems doubtful given our evidence, it could turn out that a story like Descartes' is correct. If it were, then an ideal physics would have to appeal to Cartesian egos. But it is a mistake to infer from this, I shall argue, that Cartesian egos would then be physical things. Contrary to the argument set out above, our counterfactual judgments do not follow the pattern suggested by the usual historical examples, and the empirical evidence does not support the view that 'physical' just means 'sanctioned by physics'. Thus the argument given above for the identity of the concept physical with that of the concept sanctioned by physics fails.

Premise (1) presupposes that anything which must be invoked to explain physical phenomena must itself be physical. But analogues of this presupposition in sciences other than physics are transparently false. It would be bizarre to maintain that any entity invoked by biology, for example, is a biological entity. Some biological event - a bit of organismic behaviour - may be explicable only by mercury poisoning; a comprehensive science of biology must then recognize the existence of mercury. But this recognition does not convert the element mercury into a biological entity: not every biologically relevant thing is itself biological. An ideal science of chemistry, meteorology, or psychology will have to make room in its ontology for things that are not chemical, meteorological or psychological. Similarly, an ideal physics could turn out to invoke non-physical things to explain the behaviour of physical ones. Cartesian egos, whether or not they exist, provide one example. God, whether or not he exists, provides another: the mere intelligibility of the claim that God exerts causal influence on the physical world does not require that the truth of this claim would render God physical.

In fact, as already mentioned, abstract entities seem to provide a clear example of non-physical entities invoked by physics. Even if it is possible to do science without numbers (as Field [1980] suggests), those who think otherwise surely do not think that numbers become physical just because they are indispensable for physics.

For charity's sake, set aside God and abstract entities, even if doing so seems ad hoc. It might then be replied that ideal physics determines what is physical, even though ideal biology, chemistry, economics, and so on do not determine what is biological (and so on), because biological and all other facts supervene globally and conceptually on the facts recognized by physics.10 Since these latter facts typically concern microphysical particles, fields, and so on, we may phrase the claim of supervenience compactly in the language of possible worlds by saying that any conceptually possible world which differs from the actual world biologically (chemically, economically) must also differ from it microphysically. A 'higher-level' science may have to incorporate the ontology of 'lower-level' sciences, but never the reverse. Since physicsis the most fundamental science, on which all others supervene, it could never need to invoke anything outside itself. Thus, the argument goes, anything it invokes is, necessarily, physical.

However, it is hard to see any motivation for maintaining such supervenience. Even those who balk at the intelligibility of disembodied existence typically nod at the mere conceptual possibility of a world which duplicates the actual world physically but which is devoid of mentality. And even if this is rejected, there is to my knowledge no argument whatsoever against the claim that some pairs of possible worlds are physical but not mental duplicates.11 But once this is granted, the game is up, for this entails the falsity of conceptual psycho-physical supervenience.

Hence even if physics is 'fundamental' in the sense that all facts supervene nomically on the facts it describes, it has this fundamental status only contingently; it is not conceptually fundamental. Since mental facts (unlike biological facts) do not supervene conceptually on physical ones, there is no license along the lines suggested for the claim that, necessarily, anything invoked by ideal physics is physical. I know of no other even remotely plausible argument for this claim.

IV. Physics and physicality

I have rebutted the conceptual argument against interactionism. I offer now a diagnosis of its appeal, a diagnosis which serves as well to rebut some objections that might be raised to my account. The notion that ideal physics is the ultimate arbiter of physicality may be explained by, though it does not follow from, the Chomskian observation that many things sanctioned by current physics are accepted as physical despite being disqualified by older, quainter criteria of physicality. Fields, strings, neutrinos, and so on don't fit classical notions of materiality. If we cannot give a satisfactory analysis of physicality — and the prospects for this are dim — then, it might seem, we must have some other criterion of it, and there is nowhere to turn but to the science of physical things. Hence if the notion of physicality is to be respectable at all, the argument goes, it must be underwritten by a criterion of applicability derived from physics.

This argument suffers from a false dilemma: it presupposes, wrongly, that the intelligibility of a notion must be underwritten either by analysis or by scientific sanction. If this were so, we would have to give up on most quotidian notions, and this is plainly absurd. Claims to 'chairhood' or 'gamehood', for example, are unsupported either by analysis or by sciences of furniture or gaming, but this does not threaten their intelligibility. Physicality needs an arbiter no more than gamehood, and claims to physicality are likewise independent of analysis and physics. Contrary to Chomsky's suggestion, this independence provides no reason for thinking that we lack a concept of the physical.

I have admitted that the notion that materiality is analyzable in terms of primary qualities has been overthrown by the advance of physics. But if physics does not provide a criterion of physicality, it might be objected, this fact would be inexplicable. Our only reason for thinking that a physical thing may lack mass (for example) comes from our embrace of massless neutrinos and their ilk; but our only reason for thinking that neutrinos are physical at all stems from their role in physical theory.

I answer that there are at least two other ways to account for the role of physics in shaping our judgments of physicality, neither of which has the consequence that (necessarily) anything invoked by physics is physical. I do not know whether both are true, but each is at least as plausible in its own right as the view that physics provides a criterion of physicality, and their disjunction is much more plausible.

One explanation is that physics has served heuristically as a source of independently recognizable counter-examples to classical analyses of materiality. Our reasons for thinking that neutrinos (fields, strings and the like) exist, if we do think this, may be derived from the success of physics — perhaps via inference to the best explanation. Indeed, it is quite plausible that one cannot understand what a neutrino is ('grasp the concept of neutrino-hood') without at least some grasp of the physicist's art. But it follows from neither of these admissions that our reasons for thinking neutrinos are physical must be derived from their role in physics. I offer no competing account of why we think that neutrinos are physical — perhaps an illuminating account can be given, perhaps not. But the point is that we can see how physics can play a role in shaping our judgments about the adequacy of a proposed analysis of physicality without thereby providing a criterion of physicality.

The other explanation is more concessive. It may be that any entity which is invoked by physics and which meets some further (non-trivial) independent condition is necessarily physical. Since I don't know whether there is any such condition, I cannot say how it should be put. What matters is that while it may be that having a certain sort of role in physical theory confers physicality if some further, non-trivial, independent condition is met, it does not follow that having such a role confers physicality tout court.12

V. Conclusion

The sort of argument offered by Chomsky and by Crane and Mellor suggests a resurrection of the traditional conceptual objection to interactionism. As we have seen, putting the objection in fancy modern dress does not improve its standing. Absent some other, more compelling, argument, we should conclude that interactionism faces no serious conceptual threat: it could, at least, be true. Whether the evidence supports it, or the causal closure of the physical world precludes it, are matters for another.


Virginia Commonwealth University Richmond, Virginia 23284-2025 USA



1 By 'dualism' I mean the thesis that mental states and events such as sensings, believings, wantings, rememberings and so on are non-physical, while bodily states are physical. Dualism is thus neutral with respect to Humean reductionism about people.

2 See, for example, Honderich (1988); Kim (1993); Lewis (1983); and Sosa (1984). The literature on these topics is too vast to survey. For a good sampling of recent discussion, see Heil and Mele (1993).

3  I show in Mills (1996) that overdeterministic interactionism is wholly defensible. Thus I show that interactionists need not deny the causal closure of the physical, as most do - see, for example, John Foster (1990) and EJ. Lowe (1993).

4  See, for example, Gassendi's criticism of Cartesian interaction (Cottingham et. al. 1984, pp. 236 ff).

5 Crane (1993) seems to maintain that the mere assertion that everything is physical is too weak to count as robust physicalism, since it does no more than rule out dualism: it does not give physics pride of place among the sciences. It is worth recognizing, though, that a physicalism which consists merely in the assertion of (say) the nomic reducibility of all sciences to physics, or their global supervenience upon it, does not even rule out dualism.

6 Crane and Mellor insist that their 'arguments entail that there is no divide between the mental and the non-mental sufficient even to set physicalism up as a serious question, let alone as a serious answer to it' (1990, p. 206). In a later article, however, Crane (1993) admits that this is a mistake; see note 12 below.

7 Without going into its motivation, I offer the following more precise recursive definition of 'sanctioned by physics':

(a) A type is sanctioned by physics if is explicitly invoked by physics;

(b) A type is sanctioned by physics if (i) it is instantiable, and (ii) all its tokens are (and would be) wholly composed of things which are themselves tokens of types sanctioned by physics; and

(c)  Only types satisfying (a) or (b) are sanctioned by physics.

8 Nothing rides here on exactly what sorts of things - events, properties, or whatever -the causation-relation relates.

9 See my 1996.

10 Note, however, that mathematics supervenes globally on physics, and everything else, this way too: since no two

11 Horgan (1987) comes closest, arguing for what he calls 'strict' psycho-physical supervenience at least where qualia are concerned, but this falls well short of global conceptual (or metaphysical) supervenience.

12 Crane, responding to Philip Petit (1993), admits as much (Crane 1993, p. 224). This admission conflicts with his and Mellor's earlier explicit statement (see note 6 above).

13  Work on this paper was doubly supported by the National Endowment for the Humanities. I began considering the issues it concerns while attending a 1993 NEH Institute on 'The Nature of Meaning', and I am grateful to the Institute's leaders -Jerry Fodor and Ernie LePore - and participants for stimulating discussion. A subsequent NEH Summer Stipend supported the writing of the paper. An ancestral paper received helpful discussion at a colloquium at the University of Virginia. Special thanks to James Cargile, Tony Ellis, Trenton Merricks, Peter Vallentyne, and the editor of this journal for helpful comments and suggestions.



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