125 7 The Metaphysics of Mind and the Multiple Sources of Multiple Realizability Gualtiero Piccinini and Corey J. Maley Different structures can have the same function. The wings and feet of insects, birds and bats have different structural properties, yet they perform the same functions. Many important concepts and explana- tions in the special sciences depend on the idea that the same func- tion can be performed by different structures. For instance, in biology, although both homologous and analogous structures of a given type have the same function, only homologous structures of that type have a common evolutionary history. These observations undergird the concepts of homologous and analogous structures and the distinc- tion between them: we cannot make sense of this important biological distinction in any other way. Similar considerations seem to be true of psychology. Different structures might well have the same psychological function, particularly across species. The eye of an octopus might be quite different from the eye of a human being, although both have the same function. Making sense of these phenomena is central to the discussion of Multiple Realizability (MR). Originally, philosophical attention to MR was focused on issues in the philosophy of mind; more recently, philos- ophers have realized that MR is an important issue in the metaphysics of science, particularly in the special sciences. To a first approximation, a property P is multiply realizable if and only if there are multiple properties P 1 , ... , P n , each one of which can realize P, and where P, P 1 , P 2 , ... , P n are all distinct from one another. The idea that mental properties are multiply realizable was introduced in the philos- ophy of mind in the early functionalist writings of Putnam and Fodor (Fodor 1968; Putnam 1960, 1967a). Since then, MR has been an impor- tant consideration in favour of antireductionism in psychology and other special sciences (e.g., Fodor 1974, 1997). Initially, the reductionist 9781137286710_08_ch07.indd 125 9781137286710_08_ch07.indd 125 1/27/2014 10:48:41 AM 1/27/2014 10:48:41 AM PROOF 126 Gualtiero Piccinini and Corey J. Maley resistance accepted MR, limiting itself to searching for ways to maintain reductionism in the face of MR (e.g., Kim 1992). More recently, the tide has turned. Critics pointed out that MR had neither been clearly analysed nor cogently defended. It became fashionable to deny MR, either about mental properties or about any properties at all (Bechtel and Mundale 1999; Bickle 2003; Couch 2005; Keeley 2000; Klein 2008, 2013; Shagrir 1998; Shapiro 2000, 2004; Polger 2009; Zangwill 1992). But this recoil is no more warranted than was the original intuitive appeal to MR. One goal of this paper is to examine MR carefully enough to determine which, if any, versions of MR occur. Clarifying MR has several benefits. It contributes to the philosophy of science and metaphysics in its own right. It sheds light on one of the central issues in the philosophy of the special sciences. Finally, it helps clarify one of the central issues of the mind-body problem. In this essay, we analyse MR in terms of different mechanisms for the same capacity, explore two different sources of MR and how they can be combined, and conclude that both traditional reductionism and traditional antireductionism should be abandoned in favour of an inte- grationist perspective. 1 Troubles with multiple realizability Discussions of MR are usually centred on intuitions about certain cases. The prototypical example is the same software running on different types of hardware (Putnam 1960). Another prominent class of examples includes mental states, such as pain, which are supposed to be either real- ized or realizable in very different types of creature, such as non-human animals, Martians, robots and even angels (Putnam 1967a, 1967b). 1 A third class of examples includes artefacts such as engines and clocks, which are supposed to be realizable by different mechanisms (Fodor 1968). A fourth class of examples includes biological traits, which may be thought to be realized in different ways in different species (Block and Fodor 1972). A final class of examples includes certain physical prop- erties, such as being a metal, which are allegedly realized by different physical substances (Lycan 1981). On a first pass, it may seem that in all these examples the same high- level property (being a certain piece of software, being a pain, etc.) is realized by different lower-level properties (running on different types of hardware, having different physiological states, etc.). For these intui- tions to prove correct, at least two conditions must be satisfied. First, 9781137286710_08_ch07.indd 126 9781137286710_08_ch07.indd 126 1/27/2014 10:48:41 AM 1/27/2014 10:48:41 AM PROOF The Metaphysics of Mind 127 the property that is putatively realized by the realizers must be the same property, or else there wouldn’t be any one property that is multiply realized. Second, the putative realizers must be relevantly different from one another, or else they wouldn’t constitute multiple realizations of the same property. Unfortunately, there is little consensus on what counts as realizing the same property or what counts as being relevantly different realizers of that same property (cf. Sullivan 2008; Weiskopf 2011, among others). To make matters worse, supporters of MR often talk about MR of func- tional properties without clarifying which notion of function is in play and whether the many disparate examples of putative MR are instances of the same phenomenon or different phenomena. Thus, the notion of function is often vague, and there is a tacit assumption that there is one variety of MR. As a consequence, critics of MR have put pressure on the canonical examples of MR and the intuitions behind them. Three observations will help motivate our account. First, the proper- ties (causal powers) of objects can be described with higher or lower resolution – in other words, properties can be described in more specific or more general ways (cf. Bechtel and Mundale 1999). When using a higher-level description with high enough resolution, the set of causal powers picked out by that description may be so specific that it has only one lower-level realizer, so it may not be multiply realizable. When using a higher-level description with lower resolution, the set of causal powers picked out by that description might have many lower-level real- izers but perhaps only trivially so; its multiple realizability might be an artefact of a higher-level description construed so broadly that it has no useful role to play in scientific taxonomy or explanation. Consider keeping time. What counts as a clock? By what mechanism does it keep time? How precise does it have to be? If we answer these questions liberally enough, almost anything counts as a clock. The ‘property’ of keeping time might be multiply realizable but trivially so. If we answer these questions more restrictively, however, the property we pick out might be realized by only a specific kind of clock or perhaps only one particular clock. Then, the property of keeping time would not be multiply realizable. Can properties be specified so that they turn out to be multiply realizable in a non-trivial way? A second important observation is that things are similar and different in many ways, not all of which are relevant to MR. For two things to realize the same property in different ways, it is not enough that they are different in just some respect or other. The way they are different might be irrelevant: they might realize the same high-level property 9781137286710_08_ch07.indd 127 9781137286710_08_ch07.indd 127 1/27/2014 10:48:41 AM 1/27/2014 10:48:41 AM PROOF 128 Gualtiero Piccinini and Corey J. Maley by possessing the same relevant lower-level properties while possessing different lower-level properties that contribute nothing to the high-level property (cf. Shapiro 2000). This is especially evident in the case of prop- erties realized by entities made of different kinds of material. Two other- wise identical chairs may be made of different metals, woods or plastics. Yet these two chairs may be instances of the same realizer of the chair type, because the different materials may contribute the same relevant properties (such as rigidity) to realization. The same point applies to the property of being a metal. There are many kinds of metal, and this has suggested to some that the property of being a metal is multiply realiz- able. But this is so only if the property of being a metal is realized in relevantly different ways. If it turns out that all metals are such in virtue of the same realizing properties, then despite appearances, the property of being a metal is not multiply realizable after all. A similar case is differently coloured objects: two hammers made of the same material in the same organization but differing only in their colour do not count as different realizations of a hammer. More generally, given two things A and B, which are different in some respects but realize the same property P, it does not follow that A and B are different realizations of P and that P is therefore multiply realizable. A third observation is that the realization relation may be stricter or looser. A heavily discussed example is that of computer programs. If all it takes to realize a computer program is some mapping from the states of the program while it runs once to the states of a putative realizer, then most programs are realized by most systems (Putnam 1988). This result is stronger than MR: it entails MR at the cost of trivializing it, because MR is now a consequence of an intuitively unattractive result. Is there a way of constraining the realization relation so that MR comes out true and non-trivial? Is it desirable to find one? 2 The easy way out of this conundrum is to deny MR. For example, Shapiro (2000) argues that the notion of MR is so confused that nothing can be said to be multiply realizable in any meaningful sense. For Shapiro, a high-level property can be related to its realizers in one of two ways. On the one hand, a property can be realized by entities with the same relevant properties, as in chairs made of different metals. But these do not count as multiple realizations of the property, because the differ- ences between the realizers are irrelevant (as Shapiro puts it, the rele- vant high-level law can be reduced to a lower-level law). On the other hand, a high-level property can be realized by entities with different relevant lower-level properties, as in corkscrews that operate by different causal mechanisms. But then, Shapiro contends, the different causal 9781137286710_08_ch07.indd 128 9781137286710_08_ch07.indd 128 1/27/2014 10:48:41 AM 1/27/2014 10:48:41 AM PROOF The Metaphysics of Mind 129 mechanisms are the genuine kinds, whereas the putative property that they realize needs to be eliminated in favour of those different kinds. For example, one should eliminate the general kind corkscrew in favour of, say, the more specific kinds winged corkscrew and waiter’s corkscrew 2 Multiple realizability regained Rejecting MR is tempting but premature: a satisfactory account of MR would be useful both in metaphysics and in the philosophy of the special sciences (more on this below). We must specify three things: the proper- ties to be realized, the properties to serve as realizers and the realization relation. Furthermore, this must all be done in a way that allows proper- ties to be multiply realizable without begging any questions. We start with a minimal notion of a functional property as a capacity or disposition or set of causal powers; this is to be explained by a minimal notion of mechanistic explanation as explanation in terms of compo- nents, their capacities and their organization. 3 Notice that, unlike others (e.g., Shoemaker 2007), we are not merely saying that properties are individuated by causal powers or that properties ‘bestow’ causal powers; for present purposes, we identify properties with sets of causal powers. 4 A property to be realized is generally a functional property; that is, a capacity or disposition or set of causal powers. Something’s causal powers may be specified more finely or more coarsely. At one extreme, where objects are described in a maximally specific way, no two things are functionally equivalent; at the other extreme, where objects are described in a maximally general way, everything is functionally equiva- lent to everything else. Special sciences tend to find some useful middle ground, where capacities and functional organizations are specified in such a way that some things (but not all) count as functionally equiva- lent in the sense of having the same capacity or the same. The grain that is most relevant to a certain level of organization appears to be the grain that picks out sets of causal powers that suffice to produce the relevant phenomena (e.g., how much blood pumping is enough to keep an organism alive under normal conditions, as opposed to the exact amount of pumping that is performed by a given heart). We assume that this practice is warranted and take it for granted. A system’s functional properties are explained mechanistically in terms of the system’s components, their functional properties and their organization. The explaining mechanism is the set of components, capacities and their organization that produce the capacity (disposition, AQ: This sentence reads incom- plete. Could you please check? 9781137286710_08_ch07.indd 129 9781137286710_08_ch07.indd 129 1/27/2014 10:48:41 AM 1/27/2014 10:48:41 AM PROOF 130 Gualtiero Piccinini and Corey J. Maley set of causal powers) in question. The same explanatory strategy iterates for the functional properties of the components. Claims of realization, multiple or not, presuppose an appropriate spec- ification of the property to be realized and a mechanism for that prop- erty. If the kind corkscrew is defined as a device with a part that screws into corks and pulls them out, then winged corkscrews and waiter’s corkscrews count as different realizations (because they employ different lifting mechanisms). If it is defined more generally as something with a part that only pulls corks out of bottles, then two-pronged ‘corkscrews’ (which have no screw at all but instead have two blades that slide on opposite sides of the cork) also count as another realizer of the kind. If it is defined even more generally as something that simply takes corks out of bottles, then air pump ‘corkscrews’ count as yet another realizer of the kind. Whether something counts as a realization of a property depends in part on whether the property is defined more generally or more specifically. Someone might object that this seems to introduce a bothersome element of observer relativity to functional descriptions. By contrast, the objector says, the identification ‘water = H 2 O’ does not seem to have the same kind of observer relativity. But this is a confusion. Functional descriptions are neither more nor less observer-dependent than descrip- tions of substances. Whether more fine- or coarse-grained, if they are true, they are objectively true. It is both true of (some) corkscrews that they pull corks out of bottles and that they pull corks out of bottles by having one of their parts screwed into the cork: there is no observer relativity to either of these facts. In fact, non-functional descriptions can also be specified with higher or lower resolution. You can give more or fewer decimals in a measurement, or you can get more or less specific about the impurities present in a substance such as water. None of this impugns the observer independence of the descriptions. Multiple realization depends on mechanisms. If the same capacity of two systems is explained by two relevantly different mechanisms, the two systems count as different realizations. Shapiro (2000, 647) objects that if there are different causal mechanisms, then the different proper- ties of those causal mechanisms and not the putatively realized property are the only real properties at work. A similar objection is voiced by Kim (1992) and Heil (2003), who ask, what more is there to an object’s possessing a given higher-level property beyond the object’s possessing its lower-level realizing property? 5 Our answer is that there is something less , not more, to an object’s possessing a higher-level property. The worry that higher-level properties 9781137286710_08_ch07.indd 130 9781137286710_08_ch07.indd 130 1/27/2014 10:48:41 AM 1/27/2014 10:48:41 AM PROOF The Metaphysics of Mind 131 are redundant disappears when we realize that higher-level properties are subtractions of being, as opposed to additions to being, from lower- level properties. Multiple realizability is simply the relation that obtains when there are relevantly different kinds of lower-level properties that realize the same higher-level property. Lower-level properties may realize a lot of higher-level ones, none of which are identical to any lower-level property. And different lower-level properties may realize the same higher-level property without being identical to it. For instance, storing a ‘1’ (as opposed to a ‘0’) within a computer circuit is a high-level property of a memory cell that may be realized by a large number of voltages (all of which must fall within a narrow range; e.g., 4 ± 0.1 volts). Each particular voltage, in turn, may be realized by an enormous variety of charge distributions within a capac- itor. Each particular distribution of charges that corresponds to a ‘1’ is a very specific property: we obtain a particular voltage by abstracting away from the details of the charge distribution, and we obtain a ‘1’ by abstracting away from the particular value of the voltage. Thus, a higher-level property is a (partial) aspect of a lower-level property. That’s not to say that different charge distributions amount to multiple realizations of a given voltage (in the present sense) or that different volt- ages within the relevant range amount to multiple realizations of a ‘1’. On the contrary, these are cases of differences in the realizers of a property that do not amount to multiple realizations of that property but merely variant realizers of that property. Many lower-level differences are irrel- evant to whether a higher-level property is multiply realized. Multiple realization is more than mere differences at the lower level. As we soon argue, multiple realization of a property requires relevant differences in causal mechanisms for that property. The objection, à la Shapiro (2000), that the realizing properties, rather than the realized properties, are doing all the work depends on a hierar- chical ontology in which parts are prior to (i.e., more fundamental than) wholes and therefore the properties of parts are prior to the properties of wholes. This hierarchy may be reversed in favour of the view that wholes are prior to parts (e.g., Schaffer 2010) and therefore the properties of wholes are prior to the properties of parts. We reject both kinds of hierarchical ontologies in favour of a neglected third option: an egalitarian ontology. According to our egalitarian assumption, neither parts nor wholes are prior to one another, and therefore neither the properties of parts nor the prop- erties of wholes are more fundamental than one another. 6 Our egalitarian assumption allows us to cut through the debate about realization. According to the flat view (Polger 2007; Polger and Shapiro 9781137286710_08_ch07.indd 131 9781137286710_08_ch07.indd 131 1/27/2014 10:48:41 AM 1/27/2014 10:48:41 AM PROOF 132 Gualtiero Piccinini and Corey J. Maley 2008; Shoemaker 2007, 12), realization is a relation between two different properties of a whole in which a subset of the realizing properties of that whole constitute the causal powers individuative of the realized prop- erty. By contrast, according to the dimensioned view (Gillett 2003, 594), realization is a relation between a property of a whole and a distinct set of properties/relations possessed (either by the whole or) by its parts, such that the causal powers individuative of the realized property are possessed by the whole ‘in virtue of’ (either it or) its parts possessing the causal powers individuative of the realizing properties/relations. There is something appealing about both the flat and the dimensioned views of realization. The flat view makes multiple realization non-trivial and provides a clear explanation of the relation between the realized and realizing properties (the former’s powers are a subset of the latter). This accounts for the intuitive idea that realizations of, say, corkscrews are themselves corkscrews, even though corkscrews have properties irrel- evant to their being corkscrews (e.g., their mass, colour or temperature). At the same time, the dimensioned view connects different mechanistic levels and thus fits well with multilevel mechanistic explanation, the prevailing view of explanation about the things that motivated talk of realization and MR in the first place. The firing of a single neuron is real- ized (in part) by ions flowing through ion channels; clearly, the proper- ties of the ions and the channels they move through are not properties of the whole neuron, although they are constitutive of a property of the whole neuron. There is also something unattractive about both the flat and the dimensioned views. The flat view makes it sound like realized proper- ties are superfluous, since the realizing properties are enough to do all the causal work. We might as well eliminate the realized property. On the other hand, the dimensioned view is somewhat murky on how the realized property relates to its realizers and suggests that (almost) any difference in the realizers of a property is a case of multiple realization. For example, as Gillett (2003, 600) argues, the dimensioned view entails that two corkscrews whose only difference is being made of aluminum versus steel count as different realizations, even though, as Shapiro (2000) notes, the aluminum and the steel make the same causal contri- bution to lifting corks out of bottles. Shapiro is right that if the differ- ences between putative realizations of a property make no difference to the ways in which they realize that property, then this is not MR. Thus, the dimensioned view makes it too easy to find cases of multiple realization. But if there are different causal mechanisms that realize a property in different ways, then this is indeed genuine MR. On both 9781137286710_08_ch07.indd 132 9781137286710_08_ch07.indd 132 1/27/2014 10:48:41 AM 1/27/2014 10:48:41 AM PROOF The Metaphysics of Mind 133 views, there are worries about causal or explanatory exclusion, whereby causes or explanations at a lower level render causes or explanations at a higher level superfluous (Kim 1998). On the flat view, what is left to cause or explain if realizing properties provide causal explanations of interest? And on the dimensioned view, what could the properties of wholes cause or explain if the realizing properties of their parts consti- tute the mechanism of interest? Our egalitarian ontology allows us to accommodate what is appealing about both the flat and dimensioned views without inheriting their unattractive features: Property P of object O is realized by properties and relations Q + R if and only if Q + R belong to O’s components and P is a proper subset of the causal powers of Q + R According to our egalitarian account of realization, realization is a rela- tion between a property (i.e., a set of causal powers) of a whole and the properties and relations (i.e., a set of causal powers) of its component parts (per dimensioned view). The relations between the components are what give them organization; hence, realization is a relation between a property of a whole and the properties of its component parts in an organization . The realized property is nothing but a proper subset of the causal powers possessed by the organized parts (per flat view, modulo the appeal to parts and their organization). The relation between realized property and realizing properties is clear: it’s the proper subset relation (as per the flat view). The account fits like a glove with the kind of mechanistic explanation that motivated this dialectic in the first place (as per the dimensioned view). Whether there is multiple realization remains a non-trivial matter, because it depends on whether different mechanisms generate the relevant proper subsets of their causal powers in relevantly different ways (more on this below). And yet realized properties are not superfluous, because they are not posterior to (nor are they prior to) the properties of their parts. They are simply proper subsets of them. There may appear to be a problem in the way we combine the subset relation between different levels and an egalitarian ontology. 7 Given that, on the subset account, lower-level properties can do everything that higher-level properties can do but not vice versa, it seems that they aren’t on equal footing at all. The lower-level properties are more powerful, as it were, than the higher-level ones. Hence, the lower-level properties appear to be more fundamental. But consisting of fewer powers does 9781137286710_08_ch07.indd 133 9781137286710_08_ch07.indd 133 1/27/2014 10:48:42 AM 1/27/2014 10:48:42 AM PROOF 134 Gualtiero Piccinini and Corey J. Maley not entail being ontologically less fundamental. Higher-level properties are just (proper) subsets of lower-level properties. A (proper) subset is neither more nor less fundamental than its superset. It’s just a partial aspect of its superset, as it were. A proponent of the dimensioned view of realization might object to the subset relation between realizing and realized property. According to this objection, entities at different levels of organization are qualitatively distinct because they have different kinds of properties and relations that contribute different powers to them (Gillett 2002, 2010). Carbon atoms do not scratch glass, though diamonds do; corkscrew handles do not lift corks, though whole corkscrews do; and so on. If the lower-level mechanisms are different from the higher-level ones, then the powers are different; so we do not have a subset relation between powers but qualitatively different powers at the different levels of organization. This objection is a non sequitur. Sure, an individual carbon atom taken in isolation cannot scratch. Nor can a bunch of individual carbon atoms taken separately from one another. But large enough arrays of carbon atoms held together by appropriate covalent bonds into an appropriate crystalline structure do scratch: on our view, under appropriate condi- tions, a (proper) subset of the properties of such an organized structure of carbon atoms just is the scratching power of a diamond. This organ- ized collection of atoms does many other things besides scratching – including, say, maintaining the bonds between the individual atoms, having a certain mass, reflecting and refracting electromagnetic radia- tion and so on. By the same token, a single corkscrew lever, taken in isolation, cannot lift corks. But corkscrew levers that are attached to other corkscrew components in an appropriately organized structure, in cooperation with those other components, do lift corks: under appro- priate conditions, a (proper) subset of the properties of that organized structure just is the property of lifting corks out of bottles. A whole’s parts and their properties, when appropriately organized, do what the whole and its properties do, and they do much more besides. Hence, what the whole and its properties do is a (proper) subset of what the parts and their properties do (when appropriately organized and taken together). Here our hypothetical proponent of the dimensioned view might reply that we make it sound like there are (i) parts with their properties, (ii) wholes with their properties and then (iii) a further object/property hybrid, parts in an organization. But why believe in (iii)? An ontology that includes (iii) is clearly profligate and therefore should be rejected (cf. Gillett 2010). 9781137286710_08_ch07.indd 134 9781137286710_08_ch07.indd 134 1/27/2014 10:48:42 AM 1/27/2014 10:48:42 AM PROOF The Metaphysics of Mind 135 This objection leads us squarely into the metaphysics of composition. We have room only for a brief sketch. A whole can be considered in two ways: as consisting of all its parts organized together or in abstraction from its organized parts. Of course, the parts of a whole may change over time. Nevertheless, when a whole is considered as consisting of all of its parts organized together, at any time instant the whole is identical to its organized parts. Hence, at any time instant, the organized parts are nothing over and above the whole, and the whole is nothing over and above the organized parts. The organized parts are no addition of being over the whole (and vice versa). Since the whole and its organized parts are the same thing, an ontology that includes organized parts is no more profligate than an ontology that includes wholes. But a whole can also be considered in abstraction from its organized parts, such that the whole remains ‘the same’ through the addition, subtraction and substitution of its parts. When a whole is considered in abstraction from its organized parts, the whole is an invariant over loss, addition or substitution of its (organized) parts. That is, a whole is that aspect of its organized parts that remains constant when a part is lost, added or replaced with another part (within limits). Thus, even when a whole is considered in abstraction from its organized parts, a whole is nothing over and above its organized parts. Rather, a whole is one aspect of its organized parts – a subtraction of being from its organized parts. Since wholes considered in abstraction from their organized parts are less than their organized parts, positing wholes as well as organized parts is not profligate. 8 Take the example of a winged corkscrew. The property of lifting corks out of bottles is a property of the whole object, and it is realized by the parts (the worm, the lever arms, rack, pinions, etc.) in a particular organ- ization (the rack connected to the worm, the pinions connected to the lever arms, etc.). Those parts in that organization lift corks out of bottles , and because lifting corks out of bottles is not, in any sense, a property over and above what those parts in that organization do, we can also say that those parts in that organization are a realization of a corkscrew. In our egalitarian account, the existence of higher-level properties does not entail that they are properties over and above their realizers. They are aspects of their realizers – that is, (proper) subsets of the causal powers of their realizers – that are worth singling out and focusing on. This notion of a higher-level property, as well as the related notion of MR, is useful for several reasons. First, higher-level properties allow us to individuate a phenomenon of interest , such as removing corks from bottles, which might be difficult or 9781137286710_08_ch07.indd 135 9781137286710_08_ch07.indd 135 1/27/2014 10:48:42 AM 1/27/2014 10:48:42 AM PROOF 136 Gualtiero Piccinini and Corey J. Maley impossible to individuate on the basis of lower-level properties of cork- screws. Shapiro points out that in the case of corkscrews made of different metals, rigidity screens off composition (Shapiro 2000). True enough. And for something to be a functional corkscrew, it’s not enough that it be rigid. It must be hard enough to penetrate cork but not so brittle that it will break when the cork is lifted. Many different substances can be used to build corkscrews, but their only insightful, predictive, explana- tory, non-wildly-disjunctive specification is that they must lift corks out of bottles (or do so in such-and-such a way). Second, this notion of a higher-level property allows for the explanation of the phenomenon in question in terms of a relevant property ; for example, we explain the removal of corks from bottles in terms of corkscrews’ power to remove corks from bottles rather than any of the other proper- ties of corkscrews. And they explain what systems with that property can do when organized with other systems (i.e., in a higher-level func- tional context). Higher-level properties have non-trivial consequences – for example, about what a system can and cannot do. To take just one example, results from computability theory specify precise limits about what can and cannot be computed by those things that realize various kinds of automata (and Turing’s original universality and uncomput- ability results themselves were the foundations of the field). Two things that realize the same finite state automaton – even if they realize that automaton in very different ways – will have the same computational limits in virtue of their sharing that higher-level property. Third, this notion of a higher-level property supports an informa- tive taxonomy of systems that differ in their lower-level properties. What these systems have in common, which is not revealed by listing their lower-level properties, is a higher-level property. In other words, although the lower-level properties that realize the higher-level prop- erty in these different systems are different, they also have something in common, and what they have in common is the aspect of the lower- level properties that we call the higher-level property. In other words, different lower-level properties realize the same higher-level property when the different sets of causal powers that make them up have a common subset of causal powers. The same subset (higher-level prop- erty) may be embedded in different supersets (lower-level properties), as illustrated in Figure 7.1. Finally, a higher-level property calls for its explanation to be provided in terms of appropriate combinations of lower-level properties (i.e., by mechanistic explanation). The dual role of higher-level properties as 9781137286710_08_ch07.indd 136 9781137286710_08_ch07.indd 136 1/27/2014 10:48:42 AM 1/27/2014 10:48:42 AM PROOF The Metaphysics of Mind 137 Q (M) Q (N) T Figure 7.1 A property T is multiply realized when different supersets of causal powers Q (M) and Q (N) (lower-level properties) share the same subset (higher-level property) explanantia of higher-level phenomena as well as explananda in terms of lower-level properties adds to our understanding of a system. 3 Sources of multiple realizability MR has at least two sources. Each source is sufficient to give rise to MR, but the two sources may also be combined to form a composite form of MR. 3.1 Multiple realizability 1 : multiple organizations The first kind of MR results when the same components exhibit the same capacities but the organization of those components differs. Suppose that a certain set of components, S 1 , when organized in a certain way, O 1 , form a whole that exhibits a certain capacity. It may be that those same components (S 1 ) can be organized in different ways (O 2 , O 3 , ... ) and still form wholes that exhibit the same capacity. If so, then the property is multiply realizable. A simple example is what you can do with a round tabletop and three straight bars of equal length. If the three bars are arranged so as to support the tabletop in three different spots far enough from the table- top’s centre, the result is a table – that is, something with the properties of a table. Alternatively, two of the legs may be arranged to form a cross, 9781137286710_08_ch07.indd 137 9781137286710_08_ch07.indd 137 1/27/2014 10:48:42 AM 1/27/2014 10:48:42 AM PROOF 138 Gualtiero Piccinini and Corey J. Maley and the remaining leg may be used to connect the centre of the cross to the centre of the tabletop. The result of this different organization is still a table. For this proposal to have bite, we need to say something about when two organizations of the same components are different. Relevant differences include spatial, temporal, operational and causal differ- ences. Spatial differences are differences in the way the components are spatially arranged. Temporal differences are differences in the way the components’ operations are sequenced. Operational differences are differences in the operations needed to exhibit a capacity. Finally, causal differences are differences in the components’ causal powers that contribute to the capacity and the way such causal powers affect one another. Two organizations are relevantly different just in case they include some combination of the following: components spatially arranged in different ways, performing different operations or the same operations in different orders, such that the way the causal powers that contribute to the capacity or the way the causal powers affect one another are different. MR 1 is ubiquitous in computer science. Consider two programs (running on the same computer) for multiplying very large integers, stored as arrays of bits. The first program uses a simple algorithm, such as what children learn in school, and the second uses a more sophisti- cated (and faster) algorithm, such as the Fast Fourier Transform. These programs compute the same function (i.e., they multiply two integers) using the same hardware components (memory registers, processor, etc.). But the temporal organization of the components mandated by the two programs differs considerably: many children could understand the first, but understanding the second requires non-trivial mathemat- ical training. Thus, the processes generated by the two programs count as two different realizations of the operation of multiplication. The notion of MR 1 allows us to make one of Shapiro’s conclusions more precise. Shapiro (2000) is right that components made of different materials (e.g., aluminum vs steel) need not count as different realiza- tions of the same property (e.g., lifting corks out of bottles) because they contribute the same property (e.g., rigidity) that effectively screens off the difference in materials. But this is true only if the different sets of components are organized in the same way. It is important to realize that if two sets of components that are made of different materials (or even the same material) give rise to the same functional property by contributing the same properties through different functional organiza- tions, those are multiple realizations of the same property. 9781137286710_08_ch07.indd 138 9781137286710_08_ch07.indd 138 1/27/2014 10:48:42 AM 1/27/2014 10:48:42 AM PROOF The Metaphysics of Mind 139 3.2 Multiple realizability 2 : multiple component types The second kind of MR results when sets of different component types are organized in the same way to exhibit the same capacity. By different components, we mean components with different capacities or func- tional properties (i.e., components of different kinds). Again, suppose that a certain set of components, S 1 , when organized in a certain way, O 1 , form a whole that exhibits a certain property. It may be that a set of different components, S 2 , can be organized in the same way O 1 and yet still form a whole that exhibits the same property. As in the case of different organizations mentioned above, we need to say something about when two components belong to different kinds. Two components are different in kind just in case they contribute different causal powers to the performance of their capacity. Here is a simple test for when two components contribute the same or different causal powers: to a first approximation, if two components of similar size can be subst