DAN MCARTHUR

CONTRA CARTWRIGHT: STRUCTURAL REALISM, ONTOLOGICAL PLURALISM AND FUNDAMENTALISM ABOUT LAWS

ABSTRACT. In this paper I argue against Nancy Cartwright’s claim that we ought to abandon what she calls “fundamentalism” about the laws of nature and adopt instead her “dappled world” hypothesis. According to Cartwright we ought to abandon the notion that fundamental laws (even potentially) apply universally, instead we should consider the law-like statements of science to apply in highly qualified ways within narrow, non-overlapping and ontologically diverse domains, including the laws of fundamental physics. For Cartwright, “laws” are just locally applicable refinements of a more open-ended concept of capacities. By providing a critique of the dappled world approach’s central notion of open ended capacities and substituting this concept with an account of properties drawn from recent writing on the subject of structural realism I show that a form of fundamentalism is viable. I proceed from this conclusion to show that this form of fundamentalism provides a superior reading of case studies, such as the effective field theory program (EFT) in quantum field theory, than the “dappled world” view. The case study of the EFT program demonstrates that ontological variability between theoretical domains can be accounted for without altogether abandoning fundamentalism or adopting Cartwright’s more implausible theses.

1. INTRODUCTION

In this paper I argue against Nancy Cartwright’s claim that we ought to abandon what she calls “fundamentalism” about the laws of nature and adopt instead her “dappled world” hypothesis. According to Cartwright we ought to abandon the notion that fundamental laws (even potentially) apply universally. Instead we should consider the law-like statements of science to apply in highly qualified ways within narrow, non-overlapping and ontologically diverse domains. I do not, however, take issue with her emphasis on the differing ontologies associated with the domains of different scientific theories. Instead I will show that when the concept of a property possessed by constituent of a theory is considered closely it Synthese (2006) 151: 233–255 DOI 10.1007/s11229-004-5406-4

© Springer 2006

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becomes clear that properties confer dispositions for law-like regularities i.e., structural equations that can apply across instances of theory change and also different domains. I make it clear that this is in keeping with a structural realist account of properties and that such a view implies a version of fundamentalism about laws. In so doing, I show that Cartwright’s notion of capacity, which plays a large role in her anti-fundamentalism, breaks down into an account of properties defined as I suggest, and that her rejection of fundamentalism must then ultimately fail. Finally I consider a case study to illustrate my claims against Cartwright. I argue that when the structural realist account of properties that I provide is applied to the effective field theory program in quantum field theory, pluralism about ontology and a localist view of theories is well accounted for, but this pluralism nevertheless occurs within fundamentalist context. This conclusion fully undermines Cartwright’s case for anti-fundamentalism. For her, the adoption of her anti-fundamentalism is necessary to account for the ontologically pluralist and locally particular features of science. Indeed, it is the view’s ability to account for these features of science that, for Cartwright, make her view appealing.1 2. FUNDAMENTALISM AND THE “DAPPLED WORLD” HYPOTHESIS

Fundamentalism, for Cartwright, is the view that scientific laws apply universally and is closely related to the more familiar but currently unpopular doctrine of reductionism. Reductionists believe that explanations in higher level sciences, such as empirical psychology, can be ultimately reduced to explanations based on more fundamental phenomena, such as those provided by biology, which in turn can be reduced to still more fundamental explanations such as those provided by chemistry. This process of reduction can be carried out until the processes of the higher-level science can be completely understood in terms of fundamental physics. In practice, of course, reductions of this sort are impossible. Most philosophers and scientists hold out little hope for the sort of vertical reductions just described and would not describe themselves as reductionists. However, according to Cartwright, while not perhaps reductionists, most philosophers and scientists still adhere to the only slightly weaker position of fundamentalism. A fundamentalist might readily acknowledge that the sort of vertical explanatory reduction outlined above might be impossible in

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practice, she nevertheless holds that the reason for this is simply the practical fact that complex factors supervene, not that reductionism is incorrect in principle. In other words a fundamentalist still thinks that the general reductionist point that all phenomena ultimately result from the actions of basic processes described by fundamental physics is correct. This is so even if they are committed, for practical reasons, to more local and field specific explanations of phenomena. Cartwright opposes this position. Indeed, in her view, even if all the practical difficulties of explaining the phenomena of, say, empirical psychology could be eliminated somehow (perhaps through access to some Laplacian daemon that can keep track of every particle), reductions of the sort dreamed of by the fundamentalist would still be impossible. This is so because the laws of the various scientific disciplines (chemistry, biology and so on) apply only to their specific domains and not universally. This latter point is important, in addition to opposing any sort of vertical reduction to more fundamental sciences such as physics, her localist view also opposes horizontal reductions too. Because the fields of science are different for Cartwright, not only can they not be reduced to more fundamental sciences, but also the laws of one domain do not apply to other domains. Thus no scientific law is universal, even just in principle, and subsuming one branch of science into another (even if one is not more fundamental than the other) is something Cartwright resists (cf., 1999, 25). Cartwright illustrates her position through frequent references to the following example borrowed from Neurath (cf., 1999, e.g. 59–60, 65, 67, 71, 82). In some cases the physicist is a worse prophet than a [behaviourist psychologist] as when he is supposed to specify where in St. Stephen’s Square a thousand dollar bill swept away by the wind will land, whereas a [behaviourist] can specify the results of a conditioning experiment rather accurately (Cartwright, 1999, 27).

Neurath here is arguing against the practicability of straightforward reduction, and emphasising the practical and contextual aspect of applied science. Nevertheless, Cartwright proposes to apply a more robust interpretation than Neurath would likely sanction. Neurath would read the difficulty in predicting the bill’s motion as simply the result of the complexity of the task of specifying the total force acting on the bill. For Cartwright though, this begs the question in favour of fundamentalism (Cartwright 1999, 28). Something other than the sum total of forces on the bill might well form the causes

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of its motion. Thus, she resists not only the vertical reduction of the example to more fundamental physics but she also resists a horizontal reduction to physics that accounts for objects of the same scale as the bill. For her, in the absence of the possibility of constructing a model of forces that accurately accounts for the bill’s motion, no reason exists to assume any sort of fundamentalist position. Thus, in order to avoid question begging it is better to assume against fundamentalism (cf., 28, 32, 33). Neurath would no doubt have been sympathetic with the notion that to assume fundamentalism as an article of faith is to overstep the scope of philosophy into the realm of metaphysics. But, of course, Cartwright might well be accused of begging the question against fundamentalism in favour of her anti-fundamentalism since she offers no specific reason for it other than the point that fundamentalism ought not be assumed. Indeed, to jump from here to Cartwright’s dappled world hypothesis is, from Neurath’s point of view, to engage in exactly the same sort of illegitimate question begging as the fundamentalist. However, Cartwright nowhere considers this objection and takes Neurath’s example to stand both against fundamentalism and to argue in favour of her own view (all the while glossing over the nuances of Neurath’s version of logical empiricism). Be this as it may, in what remains of this paper I will not pursue this line of criticism. As I indicated in the introduction, my case against Cartwright will demonstrate that Cartwright’s account of laws presents us with a false distinction between a view of science that recognises an ontological pluralism with regards to differing theoretical domains and a view that takes a fundamentalist stance to laws. However, before I present this argument I will outline some of the details of Cartwright’s anti-fundamentalist position. In the absence of fundamentalism, what does her account say of the operation of the exact sciences?

3. CAPACITIES AND PROPERTIES

Clearly science makes extensive use of regularities that are observed in nature and expresses them in law-like statements. However, for Cartwright such regularities occur only locally, in the context of what she terms “nomological machines”. A nomological machine is just a “fixed (enough) arrangement of components, or factors, with stable (enough) capacities that in the right sort of . . . environment will. . . give rise to

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the kind of regular behaviour that we represent in our scientific laws” (Cartwright 1999, 50). Thus science does employ law-like regularities, but these never apply universally and in fact always are confined to the narrow domain of a nomological machine, thus her opposition to horizontal as well as vertical fundamentalism. For Cartwright what makes it possible for law-like regularities to be formulated in the context of a nomological machine are capacities. Capacities are a central scientific concept for Cartwright and indeed form the central theme of an earlier book and were defined there simply as “tendencies to cause or bring something about” (1989, 226). In The Dappled World, capacities function in an even more basic role than the law-like regularities formulated in nomological machines. In fact a nomological machine is simply that special sort of situation where sufficiently stable capacities exist for law-like regularities to plausibly apply (cf., 1999, 59 and cf. also 49 and 59). In other words, prior to the identification of law-like regularities what is basic to science is the recognition of stable tendencies that are possessed by the constituents of a particular science. From these, suitably limited and qualified law-like generalisations are made. For Cartwright, it is the capacities that are real and not necessarily the law-like generalisations based upon them since these are only approximate and apply only in a limited way anyway. In fact what is most important about capacities, for Cartwright, is their open-ended nature. They represent the ability and tendency to bring something about, and in the context of a nomological machine they do so regularly. They are not, however, guaranteed to do so. Thus, capacities are not equivalent to terms naming disposition properties. Cartwright claims that a familiar dispositional property such as solubility is typically tied one to one to a law-like regularity (cf., 59). For example, a soluble substance will, under specific and suitably qualified circumstances, always dissolve in water. A capacity however is different, the effect that the capacity can bring about is not guaranteed. As Cartwright notes, “objects with a given capacity can behave very differently in different circumstances” (1999, 59). The 1000-dollar bill example can serve as a paradigm case of what Cartwright has in mind. The bill has a capacity to flutter about, but will not always do so or it will do so in different and unpredictable ways depending of the vagaries of wind, weather and location. No law-like generalisation about how exactly the bill will flutter about can be forthcoming.

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It is clearly the case that the so-called open-ended and strictly local features of capacities are very important for Cartwright’s antifundamentalism. In her view the claim that something must always happen begs the question in favour of fundamentalism, and thus the open-ended status of capacities is mandated. However, there are some difficulties with the notion and with the distinction that Cartwright draws between capacities and disposition terms. The difference between dispositional properties and capacities is supposedly the open-endedness of capacities. In Cartwright’s view, being a capacity does not imply being regarded as a disposition. Nevertheless, the reverse must be true. After all, a disposition must imply a tendency to bring something about, and this is the definition of capacity. However, the open-ended nature of capacities does little to distinguish them from dispositions in the context of a nomological machine. It is the law-like regularities that operate in the domain of a nomological machine that make up the content of the exact sciences. So while Cartwright might want to suppose that open-ended capacities are real, to function in a nomological machine their operation must be regular enough to be quantified in at least probabilistic laws. Thus, in the context of a nomological machine, which for Cartwright exhausts the scope of the exact sciences, the distinction between dispositions and capacities accomplishes nothing. Indeed, although Cartwright sometimes, as we have seen, makes much of the distinction, she elsewhere admits that the distinction is probably dispensable (e.g., 73, this discrepancy has also been noticed by Teller, 1999, 721). Thus, in the context of the exact sciences, capacities must in the end amount to dispositional properties. That is, like dispositions, they are tied to law-like regularities. The much-vaunted open-ended nature of capacities comes to nothing. If something is sufficiently irregular in its occurrence to not permit any quantifiable understanding, no matter how limited or qualified, it cannot function in a nomological machine i.e. it cannot form part of the workings of science. Indeed, the idea of such a capacity makes no sense in the context of any form of empiricism. For something to be testable, if only in principle, it must be tied to a law-like regularity strong enough to generate some sort of a prediction. Be this as it may, Cartwright might point out that just because capacities and dispositional properties are the same in the context of a nomological machine, this does not make any trouble for her general anti-fundamentalism. While the capacities in play in a situation

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like the 1000-dollar bill example might not admit law-like formulation, that is exactly the point of her anti-fundamentalism. The 1000dollar bill example, in Cartwright’s picture, implies two conclusions. It implies not only the thesis that laws do not extend outside of their nomological machines, but also that not every case is entirely covered by a nomological machine, even by machines that are very, even uniquely, limited in scope. And, as we have seen, Cartwright stresses that to assume otherwise is to beg the question if favour of fundamentalism. However, a closer look at the 1000-dollar bill example will show that both of these claims are untenable and that a non question-begging case can be made for a fundamentalist reading of the example. That is, the fluttering of the bill can be reasonably understood in terms of more familiar law-like properties rather than in terms of Cartwright’s open ended capacities and that at least some of these laws are sufficiently universal to undermine Cartwright’s case.

4. THE CASE FOR ANTI-FUNDAMENTALISM

One of the key features of Cartwright’s reading of the bill example is its focus on the practical impossibility of predicting the behaviour of the fluttering bill. For Cartwright, to assume that this is only a practical difficulty in applying universal laws begs the question in favour of fundamentalism. The question, then, to ask is this: can an account of the laws that govern the bill’s behaviour be constructed that does not beg this question? When considering the problem of predicting the behaviour of a slip of paper fluttering in the wind, the first thing to do is to consider the specific explanation that a fundamentalist would give. As Cartwright notes, the fluttering of a bill across a windy square would be explained in terms of the balance of forces on the bill. In this example these are lift, created by air pressure differences above and below the bill, the force of gravity dragging the bill back to earth and, finally, the thrust created by the wind balanced by air resistance. The relatively low gravity and air resistance created by the bill’s small size and mass means that very slight and difficult to predict variations in the wind can cause the bill to flutter and move. Moreover the variations in lift and air resistance created by the complex shape of an irregularly folded bill preclude the exact prediction of the bill’s motion, even in a low wind. Here a fundamentalist is offering both horizontal and

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vertical reduction of the bill example, horizontal by importing the same laws used to explain the behaviour of airfoils, thrust, lift etc., from their quite different context. The reduction is in part vertical too because these laws are understood in this example in terms of more fundamental concepts such as air pressure. For Cartwright all of this begs the question because of the practical impossibility of accurate prediction. However, non-questionbegging elaboration of such a fundamentalist reading of the bill example is available. One very simple approach is to imagine how tests might be made of simple systems that model the forces said to be acting on the bill, perhaps in a small wind tunnel. For instance, the claim that the bill’s rising off of the ground is caused by lift created by differential air pressure is an easy thing to test by passing air over an object of the same mass and size as the bill and with a similar but more regular shape. That gravity counterbalances the bill’s lift in level flight is equally easy to test by passing air of a constant speed over heavier and heavier bill shaped objects. In this case, the point at which the “bill” no longer rises due its now too large mass can be exactly predicted. Likewise, changing (in measured amounts) wind-speed and direction and the relative position of the simplified bill can test predictions about variations in lift and drag. The irregular fluttering effect seen in the real situation could be predictably produced through the introduction of modulations in variables like wind-speed and direction, or through the introduction of ever more complex surface shapes that create turbulence and variable air pressure across the bill’s surface. In fact it is easy to see that all of the bill’s open-ended capacities that are putatively impossible to represent in a law-like way can be successfully and predictably modelled in this fashion. As the idealised models become more complex, exact predictions of behaviour become more and more difficult, true. However, the reverse is also true. The more closely the real situation in the windy square resembles the simplified models, for example in a period of steady unidirectional wind flowing over a crisp un-crumpled bill, the more accurately the bill’s behaviour could be predicted. Moreover, in the case of gravity, accurate predictions could always be made. Given the mass of the bill and its shape, good predictions could always be made to determine a minimum wind speed, beneath which the bill would always fall. St´ephanie Ruphy as also noticed this lawlike feature in the bill example. In the matter of gravity at least, the bill example is, contra Cartwright, a paradigm of a nomological

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machine (cf., Ruphy 2003, 59–61). Thus, in the case of gravity, a non-question begging case can certainly be made for a fundamentalist reading in the 1000-dollar bill example. Moreover, with regards to the other forces, the laboratory models also provide strong nonquestion-begging reasons to think that the bill’s other behaviours arise through the application of forces whose individual action can be modelled easily in the laboratory. Here we can see that the example of the bill does not support Cartwright’s claim against horizontal fundamentalism since universal laws governing gravity clearly apply, as do other laws that are imported from different nomological machines, such as those governing the behaviour of airfoils. The vertical reduction of the forces like lift and drag to still more fundamental laws such as those governing the properties of molecules can also be argued for in a non-question-begging way. For example, lift over a wing (or bent slip of paper) is caused by lower pressure regions created by airflow. Lower air pressure, of course, is a local reduction in the quantity of molecules in a given volume. This is easily demonstrated in a lab by simply measuring the masses of equal air volumes under different pressures. Thus, a molecular account of lift and drag on the bill is available as it is for airfoils. And again, idealised models yielding accurate predictions can be produced. Given all of this, it seems reasonable that a fundamentalist can take the predictive difficulties in the real situation to simply result from a paucity of information about the quantity and quality of deviation from the idealised models. A critic might object here that that this last point does not cause problems for Cartwright since the main target of the bill example is not this sort of vertical reduction. However, this matters little since a horizontally fundamentalist reading of the bill example is available. Moreover, although Cartwright’s main target is the more widely accepted horizontal fundamentalism, the more “vertical” points just noted still tell against Cartwright’s thesis. If you want to oppose horizontal fundamentalism, you can hardly accept that two different domains that you claim are unrelated can, even in principle, be understood in terms of the same fundamental physics, in this case a molecular account air pressure. Thus, to oppose horizontal fundamentalism entails strongly rejecting vertical fundamentalism too. And, the bill example makes a case neither against horizontal nor vertical fundamentalism. In fact, my reading of the bill example identifies an interesting feature of the distinction, to hold the distinction between the two sorts of fundamentalism requires

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that one be a fundamentalist already. This is so because in the dappled-world view different nomological machines are just different, no means exists to identify one as more fundamental than the other. Thus, any demonstration of the universal application of any law, or the general reduction of one sort of domain into another, whether typically viewed to be horizontally or vertically related, makes a case against Cartwright’s position. In the bill example, both sorts are available and both undermine Cartwright’s reading of that thought experiment. For Cartwright, the sort of “in-principle” reduction used to defend fundamentalism, horizontal or vertical, is exactly where the question is begged. However, given the amount of law-like behaviour in the bill situation that can be predictively modelled, to assume that the “open-endedness” of the bill’s behaviour results from hitherto unknown and purely local causes and capacities, instead of a paucity of information, begs the question the other way. This is especially so since it can be convincingly argued, and experimentally demonstrated, that known laws that cover forces such as gravity and lift are in play and that complete information on variables like wind-speed and direction is known to lacking. Thus, the fundamentalist can reasonably demand evidence for other causes of the bill’s unpredictability. Cartwright’s only evidence that any other causes are in play is her observation that the case for fundamentalism is not perfect. However, since my arguments above show that there is at the very least strong prima facie case of a fundamentalist reading of the example that is at least partially predictive, the burden of proof is here clearly with the anti-fundamentalist.

5. PROPERTIES AND STRUCTURAL REALISM

Cartwright, recall, is willing to concede that there is an overlap between dispositions or law-like properties and her concept of capacities. Additionally, since the fundamentalist analysis of Cartwright’s central 1000-dollar bill example leaves the utility of non-fundamentalist open-ended (i.e., impossible to predict) capacities in doubt, it is worthwhile to reconsider what the abandonment of Cartwright’s account of capacities has to say about the nature of properties. Minus fully open-ended capacities, what nomological machines are left with are regularities that admit law-like

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formulations. For Cartwright, of course, these do not apply outside of their respective nomological machine. However the re-assessment of Cartwright’s central 1000-dollar bill example calls this into question since it allows for the importation of laws from very different contexts. Nevertheless, we are left with a definition of property whereby the constituents of a theoretical domain, or nomological machine, are defined in terms of their properties, where these are expressed in terms of law-like statements about interactions. That is to say, properties are defined as conferring dispositions for lawlike regularities governing causal relations between the constituents of a theoretical domain. Recall that a nomological machine is just a situation where the capacities are stable enough to allow law-like formulation. Thus, rejecting fully open-ended capacities leaves us just with properties taken as dispositions for law-like relations. Seen this way, minus the main engine of anti-fundamentalism, fully openended unpredictable capacities, we are left with the view that science defines its objects of study in terms of their dispositions for causal regularities or the law-like relations that its objects of study obey. Such a picture of scientific properties has been well expressed recently by a much-discussed position, structural realism. Although structural realism is quite old and dates from Poincar´e (1905) and before, John Worrall (1989) has recently revived it, and it has since been much discussed by a number of other commentators (cf., e.g., Psillos 1995, 2001, Chakravartty 1998, 2002, McArthur 2003). This view essentially states that science provides knowledge of the structural relations that the constituents of scientific theories engage in, but does not necessarily tell us anything else of its objects of study. Although there are many formulations of structural realism one well known formulation that is particularly germane to the discussion of this paper has been provided by Chakravartty (1998, 2002). It is of particular interest here because his formulation specifically identifies “structural relations” with those law-like relations that an object’s properties confer a disposition to exhibit. To discuss all of Chakravartty’s arguments in detail would digress from the theme of this paper too much, as would a comprehensive discussion of the large body of current writing about structural realism.2 Thus, for the purposes of this discussion I will focus on Chakravartty’s definition of property and show how this view of properties taken within the general context of structural realism, as Chakravartty suggests, leads us to a fundamentalist view. At the same time I will make it clear that structural realism permits the sort

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of ontological pluralism that gives Cartwright’s view much of its appeal, making recourse to her view unnecessary. Chakravartty defines the properties of a theoretical entity as its dispositions for those law-like interactions that the entity engages in, and he contends that what can be known about a theoretical entity are the properties that are utilised in its detection. That is, science provides knowledge of those causal regularities (expressed in law-like terms, i.e., as equations) that are involved in experimental interaction with the entity. Thus, structural realists of Chakravartty’s sort think that the equations of old theories that survive theory change (that express these interaction properties) can be supposed to describe real relations that hold between whatever happens to exist. Or, at least approximately so, in situations where they are still utilised in the new theory. Since the constituents of theories are defined in terms of their properties, i.e., structurally, and some structure (i.e., interaction properties) survives theory change, some continuity exists between old and new theories. Nevertheless, no restriction is placed on a new theory adding new properties or recontextualising old properties along with sets of new ones. So, while supporting a continuity of at least some law-like statements between different domains, structural realists need not be reductionists. They can even accept two so-related theories referring to largely different ontologies since structural realism is only committed to the structural relations, expressed in well-confirmed equations that hold at least as limiting cases in either theory. Of course, since they are committed to the idea that well-confirmed equations do apply in new and potentially wider and wider contexts outside the confines of their originating nomological machine, possibly subsuming new and formerly unrelated ones (and possibly applying universally), this view is also a form of horizontal fundamentalism. Thus, a structural realist has no difficulty accounting for structural relations being recontexulaised in a new theory that subsumes formerly disparate domains that might in their new form be associated with a very different ontological features. A ready example is the use of Kepler’s laws of planetary motion in Newton’s much more general theory of gravitation replete with its reference to a non-mechanical universal gravitational force, absent in pre-Newtonian celestial mechanics. This particular case is, of course, a fairly classic example of the sort of theory change structural realism commonly tries to account for. But, it is also a clear case what Cartwright has in mind by horizontal fundamentalism

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since the new domain of application subsumes several formerly disparate nomological machines (specifically those machines covering celestial and terrestrial kinematics) along with new ontological conceptions of those domains. Thus, a structural realist of this sort can be a fundamentalist while still accepting some sort of ontological pluralism since the structural realist can be sanguine about the different domains interpreting the shared structure according to different ontological features. Seen this way, structural realism can be seen as an argument against the stronger claims of an account like Cartwright’s since it represents a more plausible way to consider the relation between newer and older theories and the horizontal subsumption of one domain into another by a new theory.

6. FUNDAMENTALISM AND THE EFFECTIVE FIELD THEORY PROGRAM

The re-reading of the 1000-dollar bill example and the fundamentalist casting of properties (and nomological machines) into a structural realist mould places Cartwright’s anti-fundamentalism in serious doubt. However, an anti-fundamentalist could try to find support for her view by finding cases that lend themselves to the “dappled world” interpretation rather than to fundamentalism. One case that might seem a natural choice is the effective field theory program (henceforth EFT) in quantum field theory (QFT). As commentators such as Cao and Schweber have noted the EFT program has caused “a localist view of physical theory to gain momentum” (Cao and Schweber 1993, 89). This is so because the EFT approach to QFT suggests limited domains within which a given field theory applies. In this section I will discuss the EFT program as informally as possible. I will show that while the EFTs are limited in scope, when they are re-considered in terms of the structural realist view of properties EFT can be more profitably read in fundamentalist terms. EFT has been gaining in popularity in recent years and stands in contrast with the better-known program to accommodate all of the QFTs within the scope of a final complete theory. This contrasting program is known as the grand unification (popularly GUT) program. Significantly, Cartwright takes GUT as the paradigm case of the bad effects of fundamentalism in physical theory (1999, 16). Rather than seeking one final renormalisable theory that accommodates all of the particles and interactions described by the

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various QFTs, EFT takes any given QFT to break down at some high energy (Cao and Schweber 1993, 90; Huggett and Weingard 1995, 186). QFTs, as is well known, generate infinite quantities in their equations and these are removed through the technique of renormalisation (cf., Teller 1989, 1990, Cao and Schweber 1993). However, for any given QFT, quantum electrodynamics for instance, non-renormalisable interactions appear at very high energies that delineate the domain of that QFT. However, the appearance of such interactions is not a problem for EFT, these interactions disappear because they are replaced by a “renormalisable QFT particle” in a new high-energy QFT (Huggett and Weingard 1995, 186). The usual example given to support the view is the relation between quantum electrodynamics and electroweak theory. In this example, quantum electrodynamics becomes a low energy approximation of a higher energy QFT, electro-weak theory (cf., Huggett and Weingard 1995, 187). The lower energy QFT models the results of the newer theory but only at energies where the higher energy or heavier particles need not be taken into account. Likewise, because non-renormalisable divergences are accommodated in new EFTs, earlier QFTs like Fermi’s theory, while not renormalisable, can be still be seen as EFTs of higher energy theories. Furthermore, just because non-renormalisable terms that appear in any given QFT can be accommodated as particles in a higher energy QFT, this does not mean that the new QFT is the fundamental theory. As Huggett and Weingard note, “it must be a possibility that as the energy increases, non-renormalisable interactions will appear, and our theory with the heavy particle will turn out to be an EFT of another theory with an even heavier particle. And mightn’t that turn out to be another EFT?” (156). An anti-fundamentalist might claim that the EFT program is fertile ground for the “dappled world” view and poses an insurmountable problem for fundamentalists. This is so because the EFT approach contends that the fundamentalist goal of reducing the whole of physics, and even science, to a fundamental theory must fail. Since any QFT turns out to be an EFT, no final theory exists to form the basis of the fundamentalist pyramid. Moreover, it can also imply that the constituents of an EFT are local since particles that exist in some EFTs do not exist in others. This implies that ontology ought to be taken to be local. In other words a supporter of Cartwright can try to use EFT as a strong case against both vertical and horizontal fundamentalism (the latter being her chief target).

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This is so because the EFTs represent a patchwork of theories that cover different local domains. Since (as we will discuss below) they can also have locally different ontologies, no one EFT is fundamental, nor are they individually more fundamental then one another, they simply account for different, and in one sense, parallel local domains. Indeed, some supporters of the EFT approach to fundamental physics do reason along lines that a first blush might seem to support such a view. As Cao and Schwiber note, the EFT approach “supports a localist view that characterises physical (or more generally scientific) theories as historically situated and context dependant. This view applies not only to phenomenological laws describing natural phenomena, but also to the fundamental laws that explain phenomena and give them meaning” (1993, 74).

For Cao and Schweber, EFT implies a localist view of scientific theories, ontologies and explanatory laws. Claims like Cao’s are not uncontroversial of course. First, the EFT approach to fundamental physics might not be the correct one. There might be a fundamental theory whose energies can be taken to infinity and remain renormalisable. The various GUT programs, quantum gravity and so on, aim to do just this. These projects enjoy lively support and are by no means dead. Moreover, the exact interpretation of EFT comes in two varieties. The first is an epistemological variety, call this epistemological EFT, it holds that to the best of our knowledge, any theory might turn out to be an EFT but that this is not entailed. The second is a metaphysical variety that states there really is only a tower of EFTs and that there is no final theory. Since existing science cannot establish the correctness of one over the other, a fundamentalist might try to find some minimal solace in epistemological EFT. However, for the purposes of my discussion here I will take the EFT approach to be broadly correct and even assume the defensibility of a metaphysical variant. I will proceed along these lines for several reasons. First, to determine the plausibility of the EFT approach relative to a given GUT approach to fundamental physics is to engage in a debate very far beyond the scope of this paper. Indeed, resolving this question involves a great deal of physics in addition to a great deal of philosophical controversy quite unrelated to the question of Cartwright’s anti-fundamentalism. Additionally, there are other reasons to take this approach, whatever the ultimate fate of the philosophy of QFT. EFT is well established and, at least

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superficially, it seems to avail itself nicely of an anti-fundamentalist stance. Thus, even if one is committed fundamentalist with GUT sympathies, one ought nevertheless to address an anti-fundamentalist recourse to EFT. Thus, as noted, I will assume the plausibility of the metaphysical variety of EFT and assess the degree to which it serves as a genuine counter example to a fundamentalist reading of theories. In the next section, then, I will examine EFT from the point of view of the fundamentalist reading of properties that the previous section wedded to the sort of structural realism I also discussed. When this is done, it becomes clear that the sort of ontological pluralism implied by EFT is compatible with a version of fundamentalism. This leads to two conclusions, first that ontological pluralism, while a perhaps a plausible reading of fundamental physics, is not incompatible with a fundamentalism of the sort I defend, and finally that Cartwright’s dappled world hypothesis is implausible and cannot be defended through appeal to anti-fundamentalist characteristics of fundamental physics.

7. EFT AND STRUCTURAL REALISM

The ontology in the different EFTs is local; this is so at least in terms of the particles that constitute the entities referred to by the various EFTs. For example in some QFTs the constituents are the commonly known nucleons such as protons and neutrons. In higher energy theories, such as quantum chromodynamics, the nucleons disappear and instead we have the various quarks and the force carrying gluons (c.f., Cao 2003b 27). But, of course, this sort of ontological variability between the various QFTs is not a complete or even quite correct picture of the ontological commitments in QFT. The notion of particle is not really a fundamental ontological component of any quantum field theory. This is so because particles, such as the familiar nucleons, are derived in QFT from the interactions and properties (defined in the structural realist sense outlined above) of fields. And, as Cao has also pointed out, the physical interactions accounted for by QFTs are not exhausted by the interaction properties of particles. A striking example of this is the Casimir effect where vacuum fluctuations create a measurable attraction between reflecting surfaces.3 Moreover, all the QFTs, and therefore all of the EFTs are identical in various basic aspects of their fundamental ontology, in spite of variations in many of their

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other theoretical constituents. All of them commit (within a fixed four dimensional Minkowski space-time manifold) to a “global substratum” which obeys quantum mechanical principles such as the uncertainty relations, is in a state of constant flux and which is locally excitable (cf., Cao 2003a, 5; 2003b, 25). In addition to sharing some unity of ontological commitment, the various EFTs also describe the properties of the field in their respective domains by means of common mathematical structure. As we saw above, the EFTs relate to each other by means of new renormalisable particles in higher energy scale EFTs. Thus, the various EFTs relate to each other through the equations of the so-called renormalisation-group where the divergent fluctuations in one EFT become renormalisable particles in another. However, because processes described in one EFT might have no effect on the objects of a different EFT applying to a different domain, no one EFT is more fundamental than all the others, as Cao points out, even though they are all related through the renormalisation group techniques. Consider again the case of the nucleons at one scale and quarks at another; it is not the case that the quark is more “fundamental”. At that scale there are no nucleons and the some of their properties are “decoupled” from events at the quark scale and vice versa. That is, their properties play no role in experimental interactions with quarks and gluons and vice versa (Cao 2003b, 27). In fact, it is exactly this decoupling of the constituents of the EFTs, which, for Cao and others, at least in part, localises their ontologies. Nevertheless, essentially the same mathematics applies at the different energy scales. While it may be that no one EFT derives the complete theoretical ontologies of all the others, this is so because the derivability (from renormalisation group techniques) is, in fact, mutual, low energy theory from a high energy theory and vice versa (c.f., Cao 2003b, 28). Thus, while unique and indeed decoupled theoretical constituents may well emerge in higher energy EFTs with no lower energy properties, stable properties do extend across the various EFTs, although they may be recontextualised at the new scale. This mathematical continuity that characterises the relationship between the EFTs lends itself to a structural realist reading. And, of course, Cao who is one of the strongest supporters of the EFT approach to QFT, and, as we have seen is an ontological pluralist who takes the EFTs to be horizontally not vertically (in Cartwright’s sense) related, has very prominently defended a

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structural realist reading of EFT. For Cao, we only come to know the unobservable entities named in the QFTs (quarks, fields etc.) through their “structural properties”, i.e., through their dispositions to exhibit “a set of empirically accessible relations describing structural features of the hypothetical entities” (2003b, 29). However, the QFTs, for Cao, provide more than knowledge of just empty structure and nothing of that which possesses that structure.4 This is so because “the structures here refer to stable physical relations. . . It is this set of physical relations that has provided a way to define a new type of natural kinds, thus we get the content in addition to the form of the world” (2003b, 30). Here we can see a structural realist reading of EFT that is quite in line with the structural realist account of properties that I proposed earlier specifically with regards to its account of properties. Cao here argues that the theoretical entities of the EFTs (e.g., particles and fields) are known through their structural properties, by which he means their dispositions for stable physical relations by which we interact with or construct the entities in the laboratory context. This is very close to what I proposed earlier, specifically that we understand the nature of an entity in terms of the structural laws it obeys that are involved in its laboratory interactions. Since the EFTs apply to specific domains and come with differing theoretical constituents and different theoretical domains, we have the horizontally related “localist” view of ontology described by Cao and other commentators on EFT. But as we saw above, this is not the whole story. The EFTs share some basic ontological commitments, for example, the fluctuating underlying vacuum field energy. And, of course, this particular commitment is not simply theoretical but cashes out in important interaction properties, such as those governing the Casimir effect. Moreover, as we have also seen, the EFTs approximate each other’s results at energies where divergences do not arise. In other words, stable structural (law-like) properties exist across the domains of the EFTs. And, as we have also seen, the EFTs are related to each other through the renormalisation group transformations and also in that they share a basic mathematical structure. So in spite of the localist view of ontology associated with the EFT program, we nevertheless observe stable law-like regularities that apply across laboratory contexts and, in Cartwright’s parlance, horizontally related theoretical domains (i.e., nomological machines). This situation is not merely an accident of the “open-ended-capacities” in play, the

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continuity of the stable properties is mandated by the basic mathematical and theoretical relation of the EFTs to one another thorough the renormalisation group and other shared features. Moreover, this structural realist reading, as was noted above, implies a fundamentalism of a sort. This is so because while the structural realist might not be a na¨ıve reductionist she is committed to the (potentially universal) application of law-like statements outside their originating domain (or, in Cartwright’s terms, their nomological machines). The key feature of the “dappled world” thesis is not simply that different scientific domains come with different ontological commitments and different laboratory practicalities and law-like regularities that render a na¨ıve (or vertical) reductionist program impracticable. Cartwright’s main thesis is that law-like regularities are specific to their nomological machines and that different theoretical domains are just different, unrelated and to be dealt with according to different science, laws from different contexts not applying. The EFT program does not fit this picture. In it we see stable properties (such as those relating to the vacuum energy) that apply universally across all the EFT domains. Also very prominent are intimate theoretical relationships connecting the various EFT domains with each other. While a simple reductionism is not in keeping with the spirit of EFT since no one EFT is more “fundamental” than the others, wider and wider domains of experimental interaction are subsumed under higher and higher energy EFTs. In other words, In the EFT picture one domain can at least in part be accounted for in terms of another. Several lessons can be learned from this approach to fundamental physical theory. Most important is that although EFT implies a localist view of theories, this turns out rest comfortably with the limited sort of fundamentalism that is implied by structural realism. Additionally, we see that a great deal of continuity of structure between the EFTs making structural realism a natural way to understand the relationships that prevail between the EFTs, rather that the dappled-world picture which provides no systematic account of the relations that exist between theoretical domains. In other words while EFT is difficult to reconcile with a na¨ıve reductionism (i.e., an overly simple vertical fundamentalism) it does exhibit a robust horizontal fundamentalism that is easily accommodated by a structural realist reading of properties. And of course this latter feature stands as a strong example against Cartwright’s main thesis.

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8. ONTOLOGICAL PLURALISM AND FUNDAMENTALISM ABOUT LAWS

As we have seen, neither the pluralist fundamentalism I advance in this paper nor the dappled-world approach rest well with a na¨ıve reductionism that seeks to account for all phenomena in terms of the ontology of just one fundamental theory. On the other hand, the view I defend view does not preclude subsuming one domain into another. However, because of its insistence on limiting law like statements to their originating domain, the dappled-world view can never really give a systematic account of relations between domains and Cartwright never systematically deals with this issue. And as we have seen, the form of structural realism I advance as an alternative to Cartwright’s view provides a natural explanation for this fairly common feature of science. Structural properties, especially those involved in experimental interaction, survive theory changes and apply in new and often much wider theoretical and experimental contexts well outside the scope of the originating nomological machine, even though much of the theoretical ontology might be greatly altered. Thus, laws from older and narrow theoretical contexts describe real “stable physical relations” (to borrow Cao’s phrase) and these still apply to newer theoretical formulations or in theories of a wider or even different scope, such as the higher energy EFTs. If, as the structural realists suggest, we take structural properties to be the rout to knowledge about the content of the world then it is natural to seek and expect structural connections between different theoretical domains, or older and newer theories, in the manor suggested by structural realism. In fact, as an alternative, Cartwright’s position might even have the effect of stifling progress in the sciences. A great deal of what would unequivocally count as progress in the natural sciences has come in the form of accommodating wider and disparate contexts under sets of more general laws. Newton’s laws, for example, unified the very different contexts of terrestrial kinematics and celestial mechanics. A great deal of progress in physics at the end of the 19th century was motivated by the goal of unifying Maxwell’s electromagnetic theory with classical mechanics. And, as the EFT example shows, the renormalisation group techniques so central to modern QFT are intimate with the structural connections connecting the domains of the various EFTs to each other. Cartwright’s focus on the uniqueness and separate nature of the domain of each nomological machine recommends against such generalising quests.

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Structural realism, with its attendant fundamentalism, nicely accommodates such practices. In Cartwright’s favour, there is of course much to be said for any position that emphasises the differences that attend the myriad of practical contexts that characterise the contemporary sciences and the role these differences have in theoretical ontology. There is no question that Cartwright is correct to draw attention this aspect of the scientific endeavour. However, is not the case that a plausibly localist view of ontology and the rejection of a na¨ıve reductionism precludes any sort horizontal fundamentalism about laws. The structural realist reading of properties that I advance in this paper presents itself as a good way to accommodate what is appealing about Cartwright’s view while avoiding its implausible implications. In closing, then, it is interesting to note that just as structural realism permits a modest realism while accounting for radical breaks in theoretical ontology, its also permits a modest fundamentalism about laws while at the same time providing a plausible accommodation for ontological pluralism. NOTES 1 One might object that this ontological emphasis misses Cartwright’s emphasis on simple law-locality. However, ontological pluralism follows from law-locality, different laws can imply different casual agents. I thank Sergio Sismondo for drawing my attention to this. I also thank Anjan Chakravartty and Idil Boran for their comments. 2 Some brief if incomplete look at the state of the literature is however warranted, if only to justify the focus on Chakravartty version of structural realism. In addition to its direct relevance to this paper Chakravartty’s formulation is a good place to begin for several other reasons. Worrall’s (1989) version of SR has been much criticised (e.g., by Psillos 1995, 2001; Ladyman 1998) because of its problematic distinction between structure and nature, the latter being undefinable. Chakravartty begins by accepting this criticism and avoids the difficulty by identifying the nature of an entity with its properties. Ladyman and French (Ladyman 1998; French and Ladyman 2003a, b) have proposed an alternative structural realism that denies the existence of anything other than structure, this thesis is stronger than Chakravartty’s who defines objects in terms of their properties, but does not deny that there are objects. As several commentators have noted Ladyman and French’s view leads to several problems that Chakravartty’s position avoids. For example, it must maintain the difficult concept of isomorphism divorced from the idea of paired groups of individuals (Psillos 2001). Moreover, since it denies the reality of anything other than structure it can stifle the search for anything new that might gives rise to the observed structure dealt with by current theory (Cao 2003a, b). And, it since it solves no

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problems that other recent formulations of SR do not, recourse to Ladyman and French’s view is unnecessary (McArthur 2003). 3 The Casimir effect is not simply an esoteric theoretical possibility. Its properties are involved in a variety of well-documented experimental interactions that confirm predictions with an extremely high degree of accuracy (Cf., e.g., Lamoreaux 1997). 4 As we saw in a previous note, a common and quite old criticism of SR is that its distinction between knowable structure and unknowable nature is problematic for a number of reasons, it renders the notion of nature obscure, or degenerates into an empty empiricism that is only vacuously true. Recent formulations such as Chakravartty or Cao’s avoid such accusations by identifying an entity’s nature with its properties. The classic example is given by Chakravartty (1998) where he points out that the transverse wave equations that describe the propagation of light in Fresnel’s and Maxwell’s theories amount to much of light’s nature. Although unlike Ladyman, Chakravartty allows that such nature defining properties might not exhaust an entity’s nature. As we will see Cao reads the nature of the entities of the EFTs in a fashion very similar to Chakravartty’s identification of nature with interaction properties.

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Psillos, S.: 1995, ‘Is Structural realism the Best of Both Worlds?’, Dialectica 49, 15–46. Psillos, S.: 2001, ‘Is Structural Realism Possible’, Philosophy of Science Association 68, S13–S24. Ruphy, S.: 2003, ‘Is The World Really ‘Dappled’ A Response to Cartwright’s Charge Against ‘Cross-Wise Reduction’, Philosophy of Science 70, 57–67. Teller, P.: 1988, ‘Three Problems of Renormalization’, in H. Brown and R. Harr´e (eds.), Philosophical Foundations of Quantum Field Theory. Clarendon Press, Oxford, 73–89. Teller, P.: 1989, ‘Infinite Renormalization’, Philosophy of Science 56, 238–257. Teller, P.: 2002, ‘Review of The Dappled World: A Study of the Boundaries of Science by Nancy Cartwright’, Cambridge University Press, Cambridge, Nous 36, 699–725. Worrall, J.: 1989, ‘Structural Realism: The Best of Both Worlds’, Dialectica 43, 99–124. Dept. of Philosophy, Queen’s University, Watson Hall Queen’s University, Kingston, ON, CANADA K7L 3N6