Unorthodox Humeanism 9783110323986, 9783110323740

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Georg Sparber Unorthodox Humeanism

LOGOS Studien zur Logik, Sprachphilosophie und Metaphysik

Herausgegeben von / Edited by Volker Halbach • Alexander Hieke Hannes Leitgeb • Holger Sturm Band 14 / Volume 14

Georg Sparber

Unorthodox Humeanism

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Table of contents The nature of fundamental properties . . . . . . . . . . . . . . . . . . .

7

Orthodox Humeanism on laws of nature and causation . . . . . . . 1.1 The ontology . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Humean laws of nature . . . . . . . . . . . . . . . . . . . . . 1.3 Humean laws of nature at work . . . . . . . . . . . . . . . . . 1.4 Humean causation . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 The regularity theory . . . . . . . . . . . . . . . . . . 1.4.2 Counterfactual theories of causation . . . . . . . . . . 1.4.3 Counterfactual theories of causation amended . . . . . 1.4.3.1 Preemption and causation as influence . . . 1.4.3.2 The non-sufficiency challenge: causation by omissions . . . . . . . . . . . . . . . . . . 1.4.3.3 The non-necessity challenge: no alterations available . . . . . . . . . . . . . . . . . . . 1.4.4 Regular causation vs. counterfactual causation . . . . 1.4.5 Humean causation in the mental domain . . . . . . . .

15 16 20 23 31 32 34 41 41

Orthodox dispositionalism on laws of nature and causation . . . . 2.1 The ontology . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Metaphysical necessity . . . . . . . . . . . . . . . . 2.1.2 Defining dispositionalism and categorialism . . . . . 2.1.3 The intrinsity of dispositions . . . . . . . . . . . . . 2.1.4 Variations of dispositionalism . . . . . . . . . . . . 2.1.5 The prima facie plausibility of dispositionalism . . . 2.2 The conceptual level of dispositional predicates . . . . . . . 2.2.1 Semantic reductionism of dispositional predicates . . 2.2.1.1 Finkish dispositions . . . . . . . . . . . . 2.2.1.2 A counterfactual analysis for all predicates 2.2.1.3 Ontological elimination of dispositions . .

67 67 68 70 74 78 82 85 85 87 93 95

1

2

. . . . . . . . . . . .

48 50 53 60

Contents

2.2.2 Counterfactuals for dispositionalists . . . . . . . . . . Dispositionalist laws of nature . . . . . . . . . . . . . . . . . 2.3.1 Strict laws of nature and ceteris paribus laws of nature 2.3.2 Probabilistic laws of nature . . . . . . . . . . . . . . . 2.3.3 Truthmakers of uninstantiated laws of nature . . . . .

96 100 100 104 108

Humeanism vs. dispositionalism . . . . . . . . . . . . . . . . . . . 3.1 Advantages of Humeanism . . . . . . . . . . . . . . . . . . . 3.2 Challenges for Humeanism . . . . . . . . . . . . . . . . . . . 3.2.1 Pre-philosophical intuitions against Humeanism . . . . 3.2.1.1 The status of Humean regularities . . . . . . 3.2.1.2 Humeanism and the dynamic world . . . . . 3.2.2 Epistemological challenges . . . . . . . . . . . . . . . 3.2.2.1 Explanation of regularities and property instances . . . . . . . . . . . . . . . . . . . . 3.2.2.2 Conservative reductionism . . . . . . . . . 3.2.2.3 The ungrounded argument . . . . . . . . . . 3.2.2.4 The argument from humility . . . . . . . . . 3.2.2.5 The argument from quidditism . . . . . . .

113 113 116 117 117 121 123

Unorthodox Humeanism . . . . . . . . . . . . . . . . . . . . . . . 4.1 The unorthodox turn . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Physical reasons in favour of an unorthodox ontology . 4.1.2 The metaphysical principles of an unorthodox ontology 4.2 Humean and dispositionalist structural realism . . . . . . . . . 4.3 Unorthodox Humean metaphysics of causation . . . . . . . . 4.3.1 Regularities and laws of nature in unorthodox Humeanism . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Counterfactual accounts on causation in unorthodox Humeanism . . . . . . . . . . . . . . . . . . . . . . . 4.4 The arguments against Humeanism in a new light . . . . . . . 4.4.1 Quidditism . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Humility . . . . . . . . . . . . . . . . . . . . . . . . 4.5 A new challenge for Humeanism: anti-realism . . . . . . . . .

151 153 155 162 169 174

2.3

3

4

Humean metaphysics of causation as informed of contemporary science

124 128 137 141 144

175 179 185 186 190 193 211

Contents

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

Acknowledgements I would like to thank Michael Esfeld for the support, criticism and friendship he has generously offered me in the last four years. He has provided the perfect conditions under which this thesis was written. Helen Beebee and Max Kistler have given their valuable expertise. My friends Christian Bach, Jens Harbecke, Vincent Lam, Christian Sachse and Patrice Soom have all contributed to the development of my opinions and have helped to improve parts of this work. I am grateful for the year I could spend at Rutgers University, in particular to Barry Loewer for his supervision and to the Janggen-P¨ohn Foundation (St. Gallen, Switzerland) for the research grant making my stay possible. Rafael H¨untelmann and the Ontos-Verlag made the publication of this manuscript possible. My family, Dominique, Judith and Peter, as well as my friends in Lausanne and abroad never doubted that something valuable will emerge from the philosophical business I was engaged in. Thanks, in particular, to Martin for everything. Most importantly, Yvonne, I truly believe none of this could have happened without you.

University of Lausanne, November 2008

Georg Sparber

The nature of fundamental properties From many perspectives the world is a weird place. There are countless systematical descriptions of the world that try to capture its characteristics. Systematical means that these descriptions are not simple listings or strings of individual descriptions like in dictionaries. They comprise some, however weak, deductive organisation that permits to distinguish and to deduce less general from more general descriptions. In this sense, the conspiracy theorist, the religious fundamentalist and the scientist all assume principles (or hypotheses, as I will call them from now on) in the form of general descriptions from which they deduce the world’s particular characteristics. Their descriptions (subsequently called theories) share the intention to explain the world as it actually is: they claim to be true. Not all of them attain the same level of success. The conspiracy theorist endorses a relatively large set of hypotheses to explain a relatively small set of phenomena. The religious fundamentalist accepts a minimal set of hypotheses (usually just one) to explain a maximal set of phenomena. Scientists find themselves in the middle. They distinguish themselves from the conspiracy theorist in that they look for explanations for a maximal set of phenomena and from the religious fundamentalist in that their theories are informative and thus open to revision and amendment. In sum, scientists search for a theory with a better balance of simplicity, informativity and completeness. Only if a theory-builder’s primary intention consists in optimising this balance can the theory be considered scientific. In this case does the theory not only claim to be true, but can be said to aspire at truth. The quest for simplicity, informativity and completeness testifies to the fundamental interest of science in truth. I leave it to the reader how theories that lack this fundamental interest in truth should be qualified (a suggestion is given in Frankfurt 2005). The commitment to universality and empirical strength has guided scientific investigation throughout human history to the discovery of previously unknown mechanisms that explain the behaviour of the world at a more fundamental level than before. These mechanisms can be spelled out in terms of objects and their properties. Thus, over the centuries scientists have come to the conclu-

8

The nature of fundamental properties

sion that atoms (in spite of their names) are not the simple and fundamental constituents of the world, but are themselves composed by more fundamental objects. The behaviour of atoms can, for example, be identified with and explained by the behaviour of electrons, protons and the like and their interactions with one another. Scientific investigation is the only theory-building enterprise within which the aspiration at truth is corroborated by the continuous enlargement of its scope into the smallest interstices of nature. For the enterprise of a metaphysics of nature – to which this work commits itself – there is no firmer guide to the nature of fundamental objects and properties of the world than contemporary fundamental physical science. In the ideal case, where human cognitive limitations are removed and we can know everything about every property of every fundamental object in the world, we therefore assume throughout this work that the theory organising this knowledge would be a physical theory talking about physical objects and properties. Or in other words, if God were to explain to us the behaviour of the world, he would talk physics. Of course, we are – and may stay – far away from such an ideal theory. But the unprecedented empirical success and degree of confirmation of our actual fundamental physical theories (the theories of general relativity and quantum mechanics) are good reasons to believe that even if these theories are going to be replaced one day by a more fundamental world-description some of their findings are going to be preserved. That is, we have reason to believe that our actual fundamental theories are good candidates to be once in the future revealed as being of the same kind as the then fundamental theory. From this kind of optimism – that is assumed here and not justified – it follows that contemporary fundamental physics delivers us good candidates for the fundamental properties and objects of nature and for the fundamental laws of nature and causal relations that hold between them. It is a contingent, empirical truth that the behaviour of fundamental objects happens to be fairly regular and constant such that the world is, after all, not such a weird place from the perspective of fundamental physics. Fundamental physics disposes us with an inventory of what there is at the fundamental level of complexity or composition. This inventory is the proper object of the metaphysics of nature. It is the aim of metaphysics to develop a coherent account of the nature of the fundamental properties and objects as identified by science. This is a delicate task. Metaphysics suffers in princi-

The nature of fundamental properties

9

ple from double underdetermination. Already one arrangement of fundamental properties is compatible with infinitely many true and complete descriptions of it. If we are justified in our optimism, however, we can hope for a single robustly best description in the end. But, in addition, the set of fundamental properties and objects as identified by a robustly best theory is compatible with infinitely many coherent metaphysical interpretations of this theory and the natures of the fundamental properties and objects. The compliance with three methodological recommendations is necessary to prevent metaphysical exuberance: (1) The development of a problem-oriented argumentation (2) The adoption of the principles that make natural science the most serious candidate to attain objectivity: theoretical economy, conceptual clarity and transparence of justification (3) The respect of the intuitions of contemporary science about fundamental properties and about the macroscopic world These are the principles of analytic metaphysics. They set the mandatory methodological standards for this work. On this background one can legitimately ask what it means to determine the true “nature” of fundamental properties. Successful science identifies the kinds of natural properties that are instantiated in the world (think of the properties of being charged, of having a mass and so on). Moreover, it establishes laws of nature that hold between these properties (for example, Coulomb’s law or the laws of gravitation) as well as causal dependencies between individual property instances (the specific deviation of particle A’s trajectory by the presence of particle B). Intuitively, we think of all of these property dependencies as necessary. It seems to be part of the meaning of being a law of nature or of being related as cause and effect to be in some sense necessary. Science itself is silent about the relevant interpretation of the concept of necessity involved in the formulation of its principles. It is hence a metaphysical task to settle the question. Two possibilities are at hand: either the necessity that causal and nomological claims allude to is only apparent and there is no such thing as necessity in the world, or causal and nomological claims really refer to an objective modal feature in the world. This entire work is dedicated to the explicitation of both

10

The nature of fundamental properties

positions as they appear in the literature, their evaluation and the proposition of a new, alternative account on how to conceive an encompassing metaphysics of nature. The first part consists in an introduction to the standard or orthodox position that denies the existence of any natural necessity in the world (chapter 1). It is commonly labeled as Humeanism (after the main representative of the Scottish Enlightenment David Hume). Standard Humeanism is mainly promoted by the american philosopher David Lewis (1941 – 2001). Not only does he formulate the ontology, but he also presents a reductive ontological and epistemological programme that intends to analyse the notions of laws of nature and causation in such a way that they do not refer to the any natural modality in the world. He thus succeeds in being both realist about laws of nature and causation without being committed to natural modality. After the presentation of the general ontology (chapter 1.1) Lewis’s account on laws of nature as the theorems of our best theory describing the world is introduced (chapter 1.2). A metaphysical account on laws of nature has to display a number of characteristics. A discussion of these follows accordingly (chapter 1.3). On the basis of a valid account on laws of nature the Humean has several possibilities to analyse the notion of causation (chapter 1.4) the most promising of which – the counterfactual analysis of causation – is discussed in most detail (chapter 1.4.2). There are a number of objections to the standard analysis which will prove not to be essential. Therefore, the standard account has the potential to be amended (chapter 1.4.3). A discussion on the application of a Humean account on causation in the field of philosophy of mind and agency concludes the considerations on orthodox Humeanism (chapter 1.4.5). After all Lewis’s Humean reductionism turns out to be a competitive position in what regards its metaphysical potential to meet the specific challenges for his accounts on causation and laws of nature. The second part presents the rival metaphysical position to Humeanism called dispositionalism (chapter 2). The name reflects the fact that this metaphysical position (unlike Humeanism) postulates the existence of natural modality in the form of irreducible and hence fundamental dispositional properties that manifest themselves necessarily as characteristic effects. As before, the ontology is specified (chapter 2.1). Dispositions incorporate metaphysical necessity in the sense that the causal role they play is essential and definitional to

The nature of fundamental properties

11

them (chapter 2.1.1). The way properties play their causal roles – either essentially or contingently – permits to draw a fundamental distinction between dispositionalist and non-dispositionalist (so-called categorialist) ontologies (chapter 2.1.2). Any Humean ontology falls, of course, in the second domain. Both orthodox Humeanism and orthodox dispositionalism subscribe to an atomistic world-view. They both postulate the intrinsity of fundamental properties (i.e. the independence of individual property instances from other objects and their properties). For the dispositionalist, however, the fundamental properties ought to be considered as non-intrinsic (i.e. extrinsic) in order to avoid unwelcome metaphysical consequences (chapter 2.1.3). In any case, dispositionalism and its different formulations in the literature (chapter 2.1.4) are prima facie coherent metaphysical accounts that represent a serious challenge for the orthodox Humean (chapter 2.1.5). With this metaphysical background being set there are a number of philosophical questions on the conceptual level of dispositional predicate ascriptions (like the ascription of < being fragile >) that have to be addressed (chapter 2.2). It will be discussed whether dispositional predicates can be analysed in terms of counterfactual statements. Even though the majority of dispositionalists is hostile to a semantic reductionism (chapter 2.2.1), our evaluation pleads in favour of such a move (chapter 2.2.2). It argues that a semantic reduction of dispositional predicates does not decide the metaphysical debate between dispositionalists and Humeans and can therefore be safely applied by the dispositionalist. Finally, the dispositionalist conception of laws of nature is presented (chapter 2.3), in particular, the conceptions of strict and ceteris paribus (chapter 2.3.1), probabilistic (chapter 2.3.2) and empty laws of nature (chapter 2.3.3). These considerations complete the presentation of orthodox dispositionalism. The third part consists in the metaphysical evaluation of the debate between orthodox Humeanism and orthodox dispositionalism (chapter 3). In spite of the appeal of a Humean position, due to its clarity and simplicity, as well as the success of the reductive programme coming along with it (chapter 3.1), there is a vast set of metaphysical challenges for Humeanism to be found in the contemporary literature (chapter 3.2). Some philosophers hold that Humeanism clashes with important pre-philosophical intuitions that we have about the world we inhabit (chapter 3.2.1). The argumentation will show that these objections are unjustified, as Humeanism proves to be a metaphysical position

12

The nature of fundamental properties

that is compatible with important intuitions like, for example, that the course of the world is fairly regular or that it displays a fundamentally dynamic behaviour (as described by physics). The epistemological objections against orthodox Humeanism are more serious (chapter 3.2.2). It is, however, not the case that orthodox dispositionalism has a general explanatory advantage over the Humean (chapter 3.2.2.1). Nor is the Humean committed to a specifically austere and model of reductionism (chapter 3.2.2.2). It is further not true that our guide to the nature of fundamental properties – contemporary physics – excludes the possibility of fundamental non-dispositional properties on conceptual grounds (chapter 3.2.2.3). But an important problem arises for the orthodox Humean, because the nature (or essence) of the fundamental properties she postulates are in principle inaccessible to us (chapter 3.2.2.4). The underlying metaphysical reason is that for the orthodox Humean fundamental properties have primitive identities that escape our perceptual grasp (chapter 3.2.2.5). It is a bad metaphysical consequence that we are in principle never in a position to know what kinds of properties are instantiated in our world. As orthodox dispositionalism remains unaffected by these problems it has a decisive advantage over orthodox Humeanism. Even though both of these orthodox metaphysical positions are coherent and appealing (dispositionalism slightly more that Humeanism) they share a major drawback when it comes to the compatibility with contemporary fundamental physics. Both make the assumption that our world is atomistic, an assumption that proves to be unjustified in the light of the scientific discoveries of the last century. The fourth part of this work hence consists in the development of an unorthodox, holistic version of Humeanism and the evaluation of its potential to catch up with the disadvantages its orthodox version has compared to the dispositionalist (chapter 4). First, the physical reasons for the unorthodox turn and the metaphysical principles of an unorthodox metaphysics are presented (chapter 4.1). The resulting ontologies are called structural realist, because they postulate fundamental relational properties that constitute fundamental physical structures. Second, it is shown that structural realism can come in a Humean or a dispositionalist flavour, according to the metaphysics of causation that one likes to adopt (chapter 4.2). Third, the Humean metaphysics of causation is adapted to the new, unorthodox framework (chapter 4.3). This brings us in a position to reconsider the arguments from the previous chapter

The nature of fundamental properties

13

that plead in favour of dispositionalism and against Humeanism (chapter 4.4). The unorthodox version of Humeanism turns out not to fall short of the problem of primitive identities of fundamental properties (chapter 4.4.1) or of the problem of principled ignorance about fundamental properties (chapter 4.4.2). There arises, however, a new and more general worry about the capacity of the Humean to know theoretical entities. Unorthodox Humeanism might, after all, be committed to anti-realism about these entities (chapter 4.5). The discussion of this last anti-Humean challenge concludes our task. Orthodox Humeanism has come under serious attack in the last two decades with the result that it is about to be replaced as the predominant metaphysical position in the metaphysics of nature. It is the aim of the following discussion to show that an unorthodox turn can preserve the appeal of Humeanism as both informed by contemporary scientific knowledge and as a competitive metaphysical candidate in the race for the best all-embracing explanatory system for our world.

Chapter 1

Orthodox Humeanism on laws of nature and causation Humean metaphysics is the view that the world consists only of contingencies. Contingencies are entities (like things, objects and whatnot) that are strictly independent of the existence of other entities. Contingent entities could have been different (or even absent) regardless of how other entities are or whether these other entities exist at all. Whatever these entities might be they do not ground the existence of other entities, or produce them, or bring them about. Humean metaphysics is independent of the ontological accounts one favours with respect to the further specification of the nature and quantity of entities. In particular, it is consistent with the adoption of a one-category ontology, like pure event-ontologies (where everything that exists is an event), or twocategory ontologies that distinguish between objects and their properties, or substances and their modes. Humean metaphysics is the deliberate affirmation that, as a matter of fact, our world is such that it instantiates no necessary connections between its entities. Nothing follows in a metaphysical sense from something else. There is only contingent co-existence. This is the simple and explicit framework of Humean ontologies. The whole but only the distribution of fundamental contingent entities in the world is to be taken as a primitive ontological given. According to the Humean, this distribution is enough to determine all the other features of our world. There could not be a difference in the world without a difference in the distribution of fundamental contingent properties. In other words, this distribution is the basis on which everything there is in the world supervenes. In denying fundamental necessity the Humean is particularly interested in relations that seem to include the idea of necessity, like nomological (that is law-like) or causal relations between entities. Humean metaphysics implies that such relations, if they exist, supervene on the distribution of fundamental contingencies. Therefore, they do not have to be regarded as primitive,

16

The ontology

but as explainable and determined by arrangements of fundamental contingent entities.

1.1

The ontology

On a physicalist view of the world there may not be any difference in the world without a difference in the underlying physical base properties. More precisely, it is commonly accepted that all and only those theories about our world are physicalistic that imply the principle that any minimal physical copy of the actual world is a copy simpliciter (see Jackson 1998, 12). Thus, a Humean view of the world combined with a physicalistic attitude amounts to the acceptance of the following claim: all there is in the world supervenes on a contingent arrangement of fundamental physical properties. In other words, there cannot be a difference in the world without a difference in the underlying contingent arrangement of physical base properties. All the features of the world supervene at least globally on the whole arrangement of physical properties. The most famous ontology combining the Humean intuition and a physicalistic vision about our world is presented by David Lewis (1986b, ix-x), when he introduces the concept of Humean supervenience: “Humean Supervenience is named in honor of the greater denier of necessary connections. It is the doctrine that all there is to the world is a vast mosaic of local matters of particular fact, just one little thing and then another. [...] We have geometry: a system of external relations of spatio-temporal distance between points. [...] And at those points we have local qualities: perfectly natural intrinsic properties, which need nothing bigger than a point at which to be instantiated. For short: we have an arrangement of qualities. And that is all. There is no difference without difference in the arrangement of qualities. All else supervenes on that.” (Lewis 1986b, ix - x)

According to Lewis our world consists of the following features only: – space-time points that are contiguously arranged according to a space-time metric that defines the geometric relations between them – contingent intrinsic and perfectly natural properties (qualities) that only need a space-time point (or a point-sized object) to be instantiated From contingency it follows that the world is a set of independently arranged, pointlike quality instances. Each point-quality instance is independent of any other point-quality instance. The set of all point-qualities in the whole of space-

Orthodox Humeanism on laws of nature and causation

17

time forms the set of primitives for this particular Humean ontology. There are no fundamental relations over and above this arrangement of intrinsic properties. However, there are internal relations between individual quality instances. A relation R is internal if and only if R supervenes only on the intrinsic properties of its relata. An internal relation is thus completely determined by the intrinsic properties of its relata (independently of the relations between them). The most fundamental internal relation between two Humean qualities is their co-instantiation. Any two distinct point-qualities instantiated at spacetime points are co-instantiated. In order to discriminate between those coinstantiations in an informative way we need another internal relation S between point-qualities. This relation is such that it objectively determines values of similarity for every couple of point-qualities. It assigns maximal value to certain couples and intermediate or minimal value to other couples. Relation S is another primitive element of Humean ontology although it does not introduce new entities. Often it is referred to as primitive similarity between point-qualities. Together with the fundamental arrangement of point-qualities relation S allows for the definition of perfectly natural kinds of properties as sets of perfectly similar property instances (Lewis 1983a calls them universals for they regroup fundamental and perfectly similar quality tokens in an objective way, even across possible worlds. However, he does not subscribe to a realist theory of universals as, for example, the one of Armstrong 1978). Note that the introduction of primitive similarity does not depend on the specific account of property-theory that one adopts, for example, a trope- or a universalist theory of properties. Although David Armstrong takes it to be an advantage of a realist theory of universals that it can dispose of primitive similarity in the benefit of primitive identity, it can be doubted that this works for any similarity relation. As John Heil (2003, 157-158) argues Armstrong’s pretended advantage is only real if imperfect similarity among simple property instances is impossible. It is an intuitive possibility that fundamental pointqualities show a positive but not maximal degree of similarity and do not belong to the same natural kind, because they occupy different causal and nomological roles. Think of examples like two different, simple, quantitatively distinct instances of charge, α-charge and β-charge, both being of a fundamental physical property kind. They are similar in that they are both charges, but they are not

18

The ontology

perfectly similar in that they are not only distinguishable by the position of the points that instantiate them, but also by the charge-value they instantiate. This need not be an actual situation. To the extent that a universalist claims to defend a metaphysically necessary property theory the mere possibility of α-charges and β-charges is sufficient to have primitive similarity in her account as well. A realist about universals therefore faces the same problem in some cases as the trope-theorist who only accepts particulars in her basic ontology. She cannot analyse the notion of similarity in general by means of the notion of identity. The presence of primitive similarity relations S in Lewis’s Humean ontology does not constitute a disadvantage, because it is doubtful that considerations about primitive similarity provide sufficient reason to opt for either universalist or tropist theories of properties. Primitive similarity relations between simple point-qualities determine derived similarity relations between property complexes. Similarity among properties makes for similarity among their bearers. At the lowest degree of complexity similarity obtains between couples of contiguous simple point-qualities or the space-time points (or point-sized objects) instantiating them. As a special case perfect similarity between both members of the point-quality sequences makes for perfect similarity of the sequences. These features of contingent point-quality sequences permit to discriminate between different contiguous co-instantiations. There are dissimilar contiguous co-instantiations and there are similar or perfectly similar contiguous co-instantiations, where the latter are commonly referred to as fundamental regularities. Via similarity relations Humean metaphysics includes regularities of all degrees, having as parts point-quality instances or whatever complex thereof. In Humean metaphysics all fundamental entities (the base properties and the internal relations that they instantiate) are given from the beginning (in a logical sense). After adopting the thesis of Humean supervenience as a metaphysical principle it has to be explained how familiar characteristics of our world supervene on the set of ontological primitives. The most important scientific concepts that have to be made explicit are the laws of nature and causation. Thus, the Humean owes the reader an account of how and in virtue of what features of the world laws of nature and causation supervene on an exclusively contingent arrangement of point-qualities. The philosophical accounts that are presented by Lewis and others in the spirit of serving the cause of Humean

Orthodox Humeanism on laws of nature and causation

19

supervenience are under examination in this chapter. Its aim is to reveal the strengths and weaknesses of orthodox Humean metaphysics and to provide a thread and starting point for the development of the different accounts within or beyond the Humean intuition regarding our world. In a Humean framework nomological predicate-ascriptions, like “It is a law that p” or “The opening of my fist causes the glass I was holding to fall on the ground” refer, if true, to some arrangements of ontological primitives or to something determined by such arrangements. This is an instance of the truthmaker principle that is endorsed throughout the entire discussion that will follow. It says that a correct predicate ascription is true in virtue of the world being such as to make it true (see also Heil 2003, 9, 54-55, 61 for similar formulations). In what follows we focus on the ontological dimension of the question of truths and their truthmakers. Once we have introduced the conceptual tools and the semantic analyses in support of a Humean view of the world we can first ask whether the analyses succeed in reducing nomological concepts to more fundamental notions of the Humean ontology and second whether the truthmakers of nomological and causal claims do justice to the meanings we attach to those concepts. Humean metaphysics implies that the existence of nomological property sequences is reducible to the existence of more fundamental non-nomological property arrangements. In order to be useful and valuable as a metaphysics it has to support our prephilosophical conviction that in practise (scientific or folk psychological) we utter countless nomological statements that are true and meaningful. According to the truthmaker principle it must be something about the way our world is that makes true those statements. Humean supervenience says that it is nothing fundamentally nomological about the world that makes true nomological statements for the world consists only of a vast mosaic of point-qualities and there are no fundamental nomological features in the world. It must be some arrangement of such point-qualities that makes true nomological claims. If there are no necessary connections in the world, but we make claims about such connections that are true, it must be made explicit by the Humean what we really mean with necessity talk and what this talk refers to. Humean metaphysics is thus tightly coupled with the philosophical enterprise of providing truthmakers for nomological concepts as well as reductive explanatory analyses for the concepts of laws of nature and causation.

20

1.2

Humean laws of nature

Humean laws of nature

In this spirit David Lewis presents a reductive account of laws of nature that he develops on the basis of an idea of Frank Ramsey’s (1903 – 1930, outlined in his 1990, 150). He defines a law of nature as a contingent regularity in a world W that appears as a theorem or an axiom in any of the best deductive systems true at W (see Lewis 1973, 73 and Lewis 1994a, 478). A deductive system is a set of rules (and among them axiom-rules) and symbols that permits the deduction of general theorems from the axioms via iterated rule applications. A deductive system is true in virtue of its axioms and theorems being true. True theorems of a deductive system are true in virtue of referring to regularities in the world making them true. Every true theorem has the form of a regularity that refers to a set of co-instantiations of properties that in turn instantiate a similarity relation between sets of property instances. A best deductive system is the system that results if we knew everything and organised it optimally in what regards its simplicity and its strength. Simplicity is the syntactic measure of deductive parsimony. The simpler a deductive system, the better does it constrain the number of rule-applications as well as the complexity of the hypotheses. Both these characteristics being objectively determinable, simplicity is an objective measure applicable to any deductive system. In virtue of being objective the simplicity of a deductive system organising the regularities of our world supervenes on those regularities. There cannot be any difference in the simplicity of deductive systems without difference in the property instances of our world. However, supervenience only holds for simplicity relative to a reference language. Equivalent systems that imply the same truths may differ in simplicity because of the choice of different languages in which the hypotheses are expressed. Somehow, artificial language with too-remote-from-natural predicates constitutes a problem for the simplicity measure. Natural predicates are such that natural properties are their references. The problem has a remedy though, as we will see soon. The strength of a deductive system is a semantic measure of its pertinence and informativity. The stronger a deductive system, the more information it provides about the world’s properties in virtue of their being parts of regularities. Statements about regularities can be more or less informative. Compare, for example, the two following regularity statements: “Every planet turns

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around a spherical object” and “Every planet follows an elliptical trajectory when turning around a star”. In order to be informative deductive systems must talk about natural properties, where any natural property is composed exclusively of perfectly natural properties. Information can be objectively measured, as is done in information theory. However, the objectivity of the measure does not suffice to make a system’s strength objectively determinable if it is a subjective matter to which concepts it is applied. There can be dispute on the question what the perfectly natural properties are, how they are connected and how to evaluate the scientific prospects of formulating the regularities between them. Nevertheless, Lewis claims that matters of theory interpretation are excluded as a source of subjectivity, if we think of our best deductive systems as ideally organising all the knowledge available about our world. Subjectivity enters as a sign of knowledge insufficiency, whereas under perfect information an objective process might result in an objective value of the strength-measure of deductive systems. The strength of a deductive system would thus be objectively determinable insofar as it is independent of the one who accomplishes the process that leads to a value of strength. Therefore the strength of an ideal deductive system supervenes on the arrangement of basic point-like qualities. The strength of a deductive system is intuitively given by Lewis’s claim that the axioms of the strongest systems are talking about perfectly natural properties (see Lewis 1983a, 367-368). The objectivity of the process sketched above intends to meet this criterion. But the considerations on simplicity show that a language restriction to natural predicates is necessary a priori in order to warrant the possibility to objectively determine its value. Deductive systems using the same natural language might nevertheless differ in the regularities they incorporate. Strength is thus a characteristic of deductive systems that is indispensable for their qualification. The possibility of an a priori language restriction is based on the realist principle that the world is such that with its properties instantiated it imposes objectively a distinction between natural predicates that correspond to classes of sparse (qua natural) properties and artificial predicates that correspond to abundant (qua unnatural) properties. There is an objective distinction between natural and artificial classifications of the world’s properties. Realism concerning this distinction is a premise of Lewis’s account of laws of nature.

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Humean laws of nature

In restricting the language of deductive systems, the former independency of simplicity and strength (there might be very simple and very strong systems using artificial language) is converted in a mutual trade off between them. The strength of a deductive system can be augmented by ceding simplicity and vice versa. In order to determine the best systems it is therefore necessary to introduce a balance-measure over a system’s simplicity and strength. This measure has to be objective as well. The value of the measure must not depend on the one who applies it. Given the objectivity of its arguments the optimal balance between strength and simplicity depends on the weighing one adopts. To the extent that such a weighing is objectively determinable the measure is going to yield constant results in system comparisons. The class of best deductive systems will consist of all those systems that equally well trade off simplicity and strength. Laws of nature are those theorems that are shared by every member of the class of best deductive systems. A valid argument against Lewis’s account consists in saying that in case of more than one equally good competing deductive systems the sharing of theorems is unlikely so that the definition of natural laws would leave us with few or even no laws at all. It might also leave us with unimportant laws that do not suffice to accomplish further tasks such as the evaluation of statements about causal relations or the distinction between law-like and purely accidental regularities. In response, Lewis postulates that it is up to the way the world actually is how fine-grained the classification and hierarchisation of competing deductive systems can be. Theory is always underdetermined by the way the world is, but underdetermination admits of degrees. Things in the world can be simple or complicated. If nature is kind (not deliberately but accidentally), then it does not allow for competing equally best deductive systems. If point-qualities are accidentally thus arranged that the fundamental regularities between them impose themselves objectively to the observer as being fundamental it is likely that they do not admit of competing deductive systems that refer to different regularities with their axioms. The few-laws problem on this point of view is not as implausible as it seems. If nature really is so irregular that it coarsely underdetermines theory building and the choice of natural language why should we think that nevertheless we dispose of many laws that describe the world including our reasoning about it? Few laws may seem counterintuitive to us, because as a matter of contingent fact we happen to live in a world that is com-

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paratively kind in that it leaves us (for the moment) with a robustly best system of axioms. The postulation that we live in a kindly arranged world is justifiable as an objective belief of world affiliation given our actual evidence and state of knowledge of the world. To sum up, Humean laws of nature on the Ramsey-Lewis view are those regularities that are sufficiently fundamental as to figure as theorems of our best deductive systems. The statements expressing these axioms are made true by the regularities they refer to. Implicitly Lewis has to accept a realist principle of correspondence between perfectly natural fundamental properties of the world and the primitive vocabulary introduced in the sciences. In conceiving this vocabulary in an idealised way, composed of those predicates that are simple predicates in the axioms of the best deductive systems that we would build if we knew everything, Lewis is guilty of endorsing some form of the picture theory of representation (see Heil 2003, 26-27). The picture theory states that our predicates read off features of reality in a systematic way. Philosophers like John Heil denounce the picture theory of representation as an unserious principle for ontology, because language does not provide us with a privileged access to the properties of the world. However, it is not clear how any properties can be identified at all if even ideal fundamental physics is condemned to remain silent about the question what the fundamental properties of the world are. Heil himself shrinks back from the denial of the picture theory when it comes to fundamental physical predicates and properties (see, for example, 2003, 44 footnote 8). A principled denial of the picture theory contradicts the basic intuition of scientific realism, namely that it is best up to science to tell us what properties there are in the world and how they are connected. These technical considerations allow us to proceed from the question what Humean laws of nature are to the question whether they are satisfactory in the sense that they meet the scientific and folk psychological intuitions we have about laws of nature.

1.3

Humean laws of nature at work

The most fundamental features laws of nature should display is that they are true. Truth implies there being truthmakers in virtue of which law-statements are true. Humean law-statements are trivially true for only true deductive sys-

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Humean laws of nature at work

tems are candidates for best deductive systems and the truth of a deductive system is equivalent to the truths of its constituting axioms and theorems. For any regularity statement that is a law-statement in virtue of its reference to a sufficiently fundamental regularity there is a truthmaker. Yet the truth of a lawstatement does not supervene on the relevant regularity only, for the following situation is possible: suppose that regularity R is instantiated co-extensionally in worlds W1 and W2 . Suppose further that in W1 regularity R is among the fundamental regularities, whereas in W2 there are many more fundamental and more general regularities besides R. The mere existence of regularity R does not determine the truth of the sentence “It is a law that R”. Without a change in regularity R there may be a difference in the truthvalues of law-statements contradicting supervenience of laws on individual regularities. Furthermore, assume that Lewis’s account of laws of nature allows for the existence of true law-like statements that do not refer to any actual regularity at all, that it allows for so-called empty laws of nature (justification for this assumption will be given later in this section). True empty law-statements do not have local truthmakers in a trivial sense. In general, any law-statement’s truthmaker embraces more than the instantiation of the relevant regularity. It includes the instantiations of such a regularity and its comparative importance in the deductive organisation of all regularities. A law-statement is therefore true in virtue of there being a regularity and in virtue of this regularity being an important one compared with other regularities. Relative importance of regularities is measured by the support they provide to the simplicity and the strength of deductive systems when taken as theorems. A regularity of relative unimportance may not be integrated in the theorems of a deductive system without lowering the simplicity and the strength of the system. The supervenience basis for single law-statements consists of the whole distribution of contingent point-qualities for it consists in the whole set of regularities that exist in virtue of the whole property distribution. Therefore, on the Ramsey-Lewis view of laws of nature, it is not possible to delineate the truthmakers for single law-statements to a proper subregion of the whole of space-time. There is no local supervenience basis available for the determination of the truthvalues of such statements. Alternative, anti-Humean accounts of laws of nature (like dispositionalist accounts, for instance) take this point to be disadvantageous. They look for

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a local supervenience basis for law-statements in order to provide local truthmakers for instances of generalised law-statements. The problem of truthmaker delineation generalises from laws of nature to causation. If the evaluation of causal statements is dependent on the way the laws of nature are, then causal statements are also made true in virtue of maximal truthmakers. In the case of causation, unlike in the case of laws of nature, this strikes us as more problematic, for maximal truthmakers are incompatible with the idea of localised causal responsibility and agency when it comes, for example, to mental causation. But do anti-Humean accounts really provide remedy there? These questions are being addressed later. A major advantage of Lewis’s Humean laws consists in the clear criterion it gives to distinguish between accidental and law-like regularities. Laws of nature are often appealed to in order to distinguish between regularities of the following kind: “All spheres of uranium235 have a diameter inferior to one kilometer” “All spheres of gold have a diameter inferior to one kilometer” Not only can Ramsey-Lewis laws state that there is a difference between the two regularities, that the first is law-like and the second is purely accidental, but they can explain why this is the case. While the first and the second statement are equally important as individual regularities, both have a comparable number of instances and no counterinstance, there is a difference in the relations they have to other regularities. The first statement is implied by more general regularity statements about particles’ stability and radioactive decay, whereas the second is not implied by any regularity statement that would count as more fundamental. Intuitively, the uranium regularity is a necessary one, while the gold regularity is only accidental. There being true necessary statements about the world is in conflict with the Humean conviction that there are no necessary property connections in the world that could make them true. In general, laws of nature have to satisfy two modal intuitions. What laws are instantiated in a world should be a contingent fact, for - pace actualists - the majority of philosophers agrees that the laws could have been different. However, once disposed with the actual laws of nature, the law-like behaviour of a world’s properties should be necessary and not merely accidental. The first intuition can be easily met by the Humean. Her definition has it that laws are

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Humean laws of nature at work

contingent regularities that satisfy further conditions. It is entirely contingent what properties are instantiated at our world. As the laws of nature supervene on the whole distribution of point-qualities in space-time, there can be a difference in the laws provided that there is a difference in the point-quality distribution. Lewis’s ontology offers countless ways our world could have been different. Each point-quality instantiated could have been different because it is intrinsic and therefore independent of accompaniment or loneliness (following the standard definition of Langton & Lewis 1998, where a property is intrinsic to an object if and only if the having of the property is independent of accompaniment and loneliness with regard to properties of other objects). Moreover, there could have been point-qualities that are altogether alien to our world, like the properties of alien fundamental particles or point-sized souls. Finally, Humean supervenience is itself conceived as a contingent metaphysical thesis. Humean laws of nature are coupled with the notion of necessity in the following way. Lewis defines a set of possible ways the world might have been as nomologically accessible from a world W if and only if at every world of the set the laws of W are true. For the moment ways the world might have been may be called possible worlds. Note that this does not imply that these possible worlds have the same laws. There may be laws over and above the laws of W in the worlds of our set. Furthermore, a statement p is nomologically necessary at a world W if and only if p is true at every world that is nomologically accessible from W. It follows that a statement p is nomologically necessary at W if and only if p is implied by the laws of W. The reasoning goes as follows: – The first direction: If the laws of W imply a statement p then this statement is itself a theorem of the best deductive system in W. It is therefore true in every world that is nomologically accessible from W. Hence, it is p is nomologically necessary. – The second direction: If p is nomologically necessary at W then p is true at every world that is nomologically accessible from W. Any law of W is also true in each of those worlds. The statement p is true wherever the laws are true as well. This defines an implication (the reasoning is borrowed from Van Fraassen 1989, 44). Therefore any statement implied by the laws-of-nature statements (including themselves) are nomologically necessary. The uranium-statement is implied

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by the laws, but the gold-statement is not. That is, the first is necessary and the second is not. Yet, the Humean cannot say that the uranium statement is necessary, because it is implied by our laws of nature. This would be a misinterpretation of the logical connection between the notions of law and necessity. They are interdefinable via the biconditional relation above. The Humean laws do not explain why some statements are necessary, they rather define some statements as necessary. The need of explanation when it comes to alleged necessity in the world reflects the need of a more-than-nomological necessity that grounds the modal force of law-statements. Only some kind of metaphysical necessity provides the means to explain in a non-circular way why some statements are necessary. This is an ontological burden the Humean is not ready to bear, while anti-Humean approaches (like the dispositionalist approach) take it to be an advantage that they can say that statement p is necessary, because it is implied by laws that are made true by the existence of necessary property connections in the world. Nomological necessity is then the derived expression of real metaphysical necessity making true the relevant law-statements. The Humean, however, contents herself with the criterion that distinguishes between law-like and accidental regularities, even if she cannot explain nomological necessity by the means of her laws and their truthmakers. The two modal aspects mentioned above are also difficult to reconcile on an anti-Humean account of laws. That is to say that the anti-Humean might have the resources to explain where the necessity of the laws and the statements implied by them comes from, but in turn they face difficulties in providing a clear criterion to distinguish between accidental and necessary regularities. If the Lewis-laws do not explain the necessity of some statements p, what about their ability to explain the phenomena that obtain in our world? Philosophers like David Armstrong reproach to any regularity analysis of laws of nature that the identification of laws with their manifestations (regularities) makes it impossible that the laws can explain those regularities (Armstrong 1983, 41). They only explain themselves. However, it is part of the Humean intuition that there is nothing over and above the phenomena that could serve as their explanation. Hence, the Humean does not look for explanations of phenomena in this sense. She has to commit herself to a different conception of explanation.

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Humean laws of nature at work

To say that a regularity is a Lewis-law is to say that it is part of the theorems of our best deductive system and can therefore be derived from it. It can thus be logically connected and implemented in a system of regularities. A deductive system of regularities is a unification of the phenomena of our world. In best unifying those phenomena Lewis’s laws of nature explain them (for support to the claim that explanation is attained by systematisation or unification see Loewer 1996, 114 and Friedman 1974, 14-19). Unification explains phenomena in that it regards them from the point of view of their position and importance relative to an explanatory framework given by a deductive system. Thus, unification increases our understanding of those phenomena in telling us a story about their connections to other phenomena. Humean laws of nature have a privileged position in the deductive system of knowledge about our world and can therefore serve the purpose of being the relevant reference frame for the evaluation of particular phenomena. In this sense they can explain phenomena. Laws of nature do not only have to be explanatory, but also projectable to future or other counter-to-the-fact situations. They must support hypothetical claims about the alleged behaviour of uninstantiated possible property sequences. In other words, unlike accidental regularities, laws of nature must support and license counterfactual reasoning. Take the two regularities: “All the objects in this room are heavier than 1 kg” “All the objects in this room have a certain weight” Counterfactually formulated, they are “If x were an object in this room, x would be heavier than 1kg” “If x were an object in this room, x would have a certain weight” A counterfactual statement is true if and only if it is either vacuously true, which means that the antecedent is impossible, or in all the nomologically and factually similar worlds the antecedent and the consequent are always coinstantiated. This is a simplified version of the definition in Lewis (1973, 16). The criterion for the antecedent and for the consequent of the counterfactual to be co-instantiated in all most similar worlds might prove too strict and can be weakened by demanding co-instantiation in most of those worlds (see Gundersen 2002, 393). Nomological similarity is defined as before by the respect of

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the laws of nature in our world. There being an object in the room of a possible world that is not heavier than 1 kg is compatible with all our laws of nature being true at the possible world. Hence, there exists a similar world in which the antecedent and the consequent are not co-instantiated. Therefore, the first counterfactual is false. There being an object in the room of a possible world that has no weight is not compatible with all our laws being true. Especially a law-statement connecting positive extension with positive weight of objects could not be true in such a world. Hence, there exists no nomologically similar (or accessible) world in which the antecedent and the consequent are not co-instantiated. Therefore, the second counterfactual is true. Again the notions of nomological necessity, laws of nature and counterfactual truth are interdefined. By being nomologically necessary, laws of nature are counterfactual proof and permit to distinguish between accidental and lawlike regularities. Counterfactual statements may contain antecedents and consequents that are altogether uninstantiated at our world. For example: “Were element 118 of our periodic table of elements to exist in our world, it would decay with chance c after time t.” Such counterfactual claims seem to have definite truthvalues for definite values of c and t. From the definition of counterfactual truth it follows that they can have definite truthvalues only if there are corresponding laws of nature supporting them and licensing their inference. Thus, the question is if there may be vacuous laws of nature on Lewis’s account. More about the truthmakers of counterfactual statements will be said in section 1.4.2. Vacuous laws state regularities between properties that are uninstantiated in our world. Typically such laws are introduced in the deductive system in order to increase the simplicity of the system without affecting its strength concerning the properties of the actual world. Vacuous laws are regularity statements that do not refer to any regularity instantiated at our world for there are no such co-instantiations that could make true those statements. Rather what makes vacuous laws true is the overall distribution of instantiated regularities. They suffice as a supervenience basis for our best deductive systems that present an increased degree of simplicity. Of two equally strong deductive systems without vacuous laws, one can always be made simpler by introducing vacuous laws in virtue of their import of generality. The best deductive system there-

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Humean laws of nature at work

fore necessarily comprises such law-statements that have none of the relevant properties in their extensions. For those law-statements having instantiated properties as extensions the problem of intensionality can arise. It would be a disadvantage for any lawaccount if by means of the definition of a law of nature one could not distinguish between co-referential descriptions that differ in their meanings. A difference in meaning between two descriptions implies that they are not equivalent and thus they should not be interchangeable as theorems of our best deductive systems. At first glance it seems as though the measures of simplicity, strength and balance could not distinguish between the two following sentences: “All electrons are attracted by positive charges” “All particles with a mass of 511 keV are attracted by positive charges” Both descriptions are true and have the same extensions. Nevertheless, we would only like the first to express a law of nature but not the second. Two equal deductive systems comprising each one of the above statements cannot be distinguished by means of the ressources of Lewis’s laws. But “It is a law that p” is true at a world if and only if there is a best deductive system (that is unique when nature is kind) for that world and among the theorems of the system is a statement that expresses the same regularity as “p”. The question is whether the segment “it is a law that” can create an intensional context that permits to distinguish between intensions such that it is possible both to hold that “It is a law that F’s are followed by G’s” and “It is not a law that F ∗ ’s are followed by G’s” with F and F ∗ co-extensional (for a positive answer using the notion of proposition see Loewer 1996, 107). Only something intensional can create an intensional context. Neither simplicity, nor strength nor balance provide intensional ressources if they are applied to actual property instances and their arrangements exclusively. Therefore an additional specification has to be added in order to account for the intensions of theorems of the deductive systems. The strength of a deductive system can for example be measured not only for the actual way the property instances are arranged in our world, but for all nomologically possible ways such properties can be arranged. To the extent that there cannot be a difference in the set of those possible ways the world might have been, without a difference in the property arrangement of the actual world, no additional onto-

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logical primitives are added (this is probably what is meant by Loewer when he talks of propositions creating the intensional context, if he adopts a Lewisian definition of propositions as sets of possible worlds). If the set of nomologically possible worlds including particles of 511 keV proves to be smaller than the one including electrons (for there are fewer worlds where the relevant lawstatements are true) the deductive system containing the latter is stronger than the one containing the former statement. The account of laws of nature of David Lewis presents all the characteristics that are typically satisfied by such statements (see Van Fraassen for a list of those characteristics in his 1989, chapter 2.4). Only aspects such as the explanatory force or the delineation of truthmakers demand concessions from the Humean, because in the first case she has to abandon generality in the benefit of a special account of explanation and in the second case she cannot determine any proper subregion of the whole arrangement of particular matters of fact that can serve as a truthmaker for law-statements. For laws of nature this does not seem to be a big price to pay. On the contrary, by appeal to deductive systems and their characteristics Lewis’s laws make it plausible that with our currently best deductive system and its laws we dispose of good candidates for the ultimate “real” laws of nature. As an account that picks up the idea of the dynamics of deductive systems during scientific discovery, it naturally incorporates the intuition that our scientific practise tends to the discovery of the ideal laws of nature and at the same time to the knowledge of what the fundamental properties of our actual world are. Humean laws of nature as conceived by Lewis supervene on the arrangement of Humean ontological primitives and support the intuition of a contingent world. As a next step we will check if the same is valid for statements about causal dependencies and their Humean interpretation.

1.4

Humean causation

From a Humean point of view the truthmakers for causal statements are exclusively composed by a contingent arrangement of contingent property instances. The truthvalues of causal statements have to supervene on this basis in order to be objective and determined by the way our actual world is. There are different accounts of causation that may serve the Humean cause. The historical

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Humean causation

Hume (1711 – 1776) defines causation as being an object followed by another and where any objects similar to the first are followed by objects similar to the second, or in other words where, had the first object not been, the second would have never existed (see Hume 1999, 37). Hume regarded the two ways of analysing causation as equivalent. However, they gave rise to two apparently different Humean strategies to define causation. The first part of Hume’s statement expresses the core idea of a regularity view on causation, whereas the second part captures the idea of a stronger than material implication between causes and effects in the form of a counter-to-the-fact implication.

1.4.1

The regularity theory

Regularity theories of causation claim that two entities instantiate a causal dependency in virtue of their affiliation to a regularity. Entities are part of regularities in virtue of their similarity with other entities, which can be therefore called “of a kind”, and in virtue of their actual co-instantiation with entities of different kinds. Thus, not entities as individuals are causally dependent, but the kinds they are affiliated to are the analysanda of any regularity account of causation. The primary interest of regularity accounts of causation lies in the analysis of general causation as causal relevance between kinds. Causal relevance is considered to be a necessary condition for singular instances of causal dependence between individual entities. Claims about general causation however are not sufficient for singular causal instances of entities. The truthvalues of general causal claims like “A’s are causally relevant for B’s” do not depend on a singular causal claim like “a causes b” for there may be no instances of A and B or some ceteris paribus clause admits of exceptions. The truthvalues of general causal claims do therefore not supervene on the truthvalues of singular causal claims. Rather the truthvalues of singular causal claims supervene on the truthvalues of general causal claims. What makes true general causal claims by itself might not be sufficient to make true individual causal claims. The possibility of void regularities is given through the systematisation of all instantiated regularities in a simple and strong deductive system. In the framework of a regularity theory philosophers intend to find appropriate conditions under which the statement of a general causal claim is correct. Examples are Mackie’s INUS conditions that roughly define causes as

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Insufficient, but Necessary parts of an Unnecessary, but S ufficient condition for the effect. Imagine the following scenario: The lighting of match (l) causes a hut to burn down (b). The lighting of the match by itself is not sufficient for the hut to burn down for there are many matches lit in huts that do not burn down. However, l is part of a set x of conditions that are jointly sufficient for the effect b to occur (the presence of oxygen, the dryness of the match, the actual contact of the lit match with combustible material, and so on). Moreover, given this set of conditions occurred, rather than some other set of conditions sufficient for fire (y), the lighting of the match was necessary. Fires in huts do not occur in such circumstances, if lit matches are not present. Finally the set of conditions x is not necessary for b because the hut could have burned down upon a lightning stroke (y). Formally defined, l is an INUS condition for b if and only if, for some c and y, (l ∪ c or y) is necessary and sufficient for b, l is not sufficient for b and c is not sufficient for b (see Mackie 1965, 246). For l to cause b it must be at least an INUS condition, l and c (if any) must actually occur and no y that does not contain l occurs. The analysis of causation via INUS conditions intends to provide us with purely logical criteria of what can be regarded as an instance of causation. What makes those condition-ascriptions true or false are the regularities instantiated at our world and referred to by the analysis. It does not suffice only to take into account the actual regularity between kinds of entities referred to by the concepts of a general causal claim, but the notions of sufficiency and necessity that constitute the analysans are to be made explicit as well. On Mackie’s view they are defined as simple counterfactual dependencies (see Mackie 1974, chapter 2 and Mackie 1965, 254; see also Lewis 2004, 77, who confirms that the counterfactual move is hardly evitable in Mackie’s account). He recognises that an analytic account of them must be given and therefore defines them as incomplete deductive “patterns” that need further premises to licence inferences. Those premises consist of universally quantified statements about properties in the world (“true universal propositions”). This is the general form of regularities. Such propositions exist (whether as linguistic or as ontological entities Mackie does not make explicit) and connect the antecedent and the consequent of a counterfactual. They might not be epistemologically accessible. But the inference from counterfactuals to regu-

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Humean causation

larity statements is nevertheless possible. Mackie claims that “[...] [it] is an important point that someone can use a non-material conditional [i.e. a counterfactual] without [...] being able to complete the argument [i.e. the inference] [...] and similarly that we can understand such a conditional without knowing exactly how the argument would or could be completed” (Mackie 1965, 254). Hence, the inference of causal statements from counterfactual statements (via necessity and sufficiency statements) is possible in principle, but Mackie gives no arguments to support his claim. He owes both a semantic account and an ontological account of counterfactuals to his readers, because counterfactual dependence might prove not to be an innocent notion when it comes to causation. Unless an explicit account of counterfactuals is given, Mackie’s regularity analysis is incomplete for his analysis of general causal claims connecting types of entities amounts to counterfactual dependencies between individuals. Such dependencies can themselves be regarded as stating a causal dependence between individuals. While Mackie’s account is based on counterfactual dependencies contemporary regularity theories of causation do not commit themselves to the acceptance of counterfactual definitions of necessity and sufficiency. Their necessity and sufficiency definitions only comprise material conditionals (see Baumgartner 2005, 254). However, it is not clear whether truth conditions for material conditionals include irreducible modality or not (see Baumgartner 2005, 7 against this claim and Lewis 1986a, 150-151 in favour). The existence of irreducible modality goes against the Humean program to reduce modal notions (like causation) to non-modal notions.

1.4.2

Counterfactual theories of causation

Rather than concentrating on the statements of general causal relevance between property types by means of regularities between them, singular causal statements about particular instances of causation between individuals can be examined. Such individuals might be the only instances of their types in the world and might not constitute a regularity. The existence of particular causal instances licences general causal relevance claims between types as their necessary condition. But the existence of a general causal type-dependence does not licence the inference to their particular instances. Therefore, an account of

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singular causation, where particular causal instances constitute the analysanda, must be pursued in any case. Hume suggests that singular causal statements can be conceived as counterfactual dependence, for example: “If it had not rained, the forest fire would have continued” to account for “The rain causes the forest fire to end”. The evaluation of counterfactuals is dependent on whether the regularities they refer to are important or unimportant. Whatever the comparative factor may be (positions in deductive systems for example), the evaluation of counterfactuals on a Humean account involves an inter-regularity comparison. Thus, general causal claims on such an account are true in virtue of the whole arrangement of regularities in our world. Since the truthmakers of causal counterfactuals involve much more than the relevant singular property instances a counterfactual account of causation on a Humean ontology is not a singularist approach in the strong sense. Singularist accounts typically succeed in delineating truthmakers of causal or nomological statements to singular occurrences. Singular causation means that causal relations can be regarded as causal independently of the occurrence of other properties. In particular they are independent of the regularity or law of nature that they are part of. Singularist approaches are, for example, those considering causation as a primitive feature of the world (mainly dispositionalist accounts presented in chapter 2). Primitive causation is obviously beyond the Humean framework that denies necessary connections among distinct existences in the world. However, singularist approaches need not be anti-Humean. Any reduction of causation to features that do not include general laws of nature may have non-global truthmakers and may therefore not involve regularities. The most popular accounts of this sort are so-called process theories of causation. They define causation as the transfer or exchange of a conserved physical quantity between intersecting processes (the accounts presented in Dowe 2000, Kistler 1999 and Salmon 1998 are good candidates for such theories). It is an independent question whether such causal processes are to be considered as necessary or contingent relations. Certainly Humean regularity and counterfactual accounts of causation do not involve necessary connections. Formal semantics for the evaluation of counterfactual statements are introduced by David Lewis (1973) and have become standard since. On his account a counterfactual C: A € B (read “If A had not occurred, B would not have occurred”) is true in a world W and for a sphere S of system $ of possible worlds

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that are accessible from W if and only if A is part of no world in S or all the worlds in S that have A and B as parts are more similar to world W as is any world that has only A as a part (see Lewis 1973 with slight modifications that do not affect the content of the definition. A material implication between two entities is equivalent to their co-instantiation once the empty case is excluded.) Similarity enters at two stages in the definition. First, aspects of similarity constitute the extent and the content of the system $ of possible worlds. Second, similarity is the distance that determines the extent and the content of a sphere S with respect to a reference world W. Equidistant worlds with respect to W are part of the same sphere S of the set of concentric spheres $. The similarity at stake is not primitive similarity between fundamental entities. It should be supervening on this basis though if the evaluation of counterfactuals is supposed to be an objective matter. Overall similarity regroups several similarity aspects in a hierarchically ordered set that determines accessibility distances between worlds. The whole set defines an overall comparative similarity relation. The relation compares the overall similarity of two possible worlds with respect to a common reference world W. The system of spheres is therefore centred on W and the resulting distance relation cannot provide a quantitative measure of accessibility but only a qualitative one. It is also nested in the sense that for any two spheres S and T either S is included in T or T is included in S . Any two worlds in $ are therefore comparable with respect to their similarity to W. The system of spheres furthermore satisfies closure under union and intersection, which means that any union of parts of $ is in $ and any intersection of non-empty parts of $ is in $ (see Lewis 1973, 14). For the evaluation of counterfactuals Lewis adopts the following hierarchy of similarity measures between possible worlds (see Lewis 1986b, 47-48): (1) It is of first importance that worlds minimise big, widespread violations of actual laws of nature (that minimise big miracles, in other words). (2) It is of second importance that worlds maximise spatio-temporal regions that are identical with our world in matters of particular facts. (3) It is of third importance that worlds minimise small, punctual violations of actual laws of nature as well (small miracles). (4) It is of fourth importance that worlds maximise approximate similarity in matters of particular facts with our world.

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Together the four similarity respects define a parameter p that determines an ordering on the set of possible worlds. There are several aspects that have to be satisfied by the set of four similarity respects in order to define an evaluation basis $ for counterfactuals as described before. The set of spheres S of $ is centred on the world W, because W is at least part of an equivalence class of most similar worlds. That is W is exactly p-similar to W. The criterion that spheres must be nested is at first glance only given between the first and the third similarity aspects. Possible worlds minimising small miracles necessarily minimise big miracles if the latter are a combination of the former. The inverse is the case for the second and the fourth respect of similarity. Possible worlds showing maximal spatio-temporal regions of identical base property distributions show also maximal approximate similarity in what regards particular matters of fact. Therefore, it is not clear what the import of the fourth similarity aspect is given the existence of the second. Approximate similarity of particular matters of fact seems to be a limit criterion as it figures in parameter p. Most pertinent counterfactuals can be attributed definite truthvalues without making use of the fourth similarity aspect. Note that counterfactuals may be true of singular, unique events as well, like statements about a nuclear holocaust or the Big Bang. Statements about the nuclear holocaust may be implied by and statements about the Big Bang may even be located within the theorems of the best deductive system (see Lewis 1983a, 367). But they are not among the laws of nature, because they do not express regularities. In turn statements about the Big Bang may themselves imply further regularity statements. The laws may be affected by a variation of the Big Bang. It is possible that the state of the world shortly after the Big Bang is a state of high entropy (contrary to actuality), which would affect certain laws of nature. The similarity measure of maximisation of regions that are approximately similar with respect to matters of particular fact applies for example to cases where small events change significantly the further development of the world (as it is the case with Nixon pushing the button and starting a nuclear holocaust). The counterfactual “Had Nixon pushed the button, a nuclear holocaust would have occurred” is under evaluation. A world where he pushes the button, but a small miracle occurs to stop the launch missile, is intuitively closer the actual world than is one where he pushes the button and

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the nuclear holocaust occurs. With the priority of minimising small miracles over maximising approximate similarity the pushing-with-holocaust world is ranged closer to actuality than the pushing-without-holocaust world (for detailed discussion see Schaffer 2004). Hence, it is necessary that the criterion of approximate similarity is only of fourth importance. The similarity between the pushing-without-holocaust world and actuality is only approximate, because some traces of the pushing might not be erased by the introduction of a small miracle. However, the question remains if the first three similarity criteria yield a nested system $ of spheres of possible worlds. Violations of laws of nature imply localised divergences in matters of particular fact. But there may be a difference in matters of particular fact without there being a violation of laws of nature. Supervenience of laws of the distribution of particular facts is thus respected. The second criterion of similarity has to be amended. The set of possible worlds that are ordered with respect to the size of the regions that are factually identical has to be restricted to those containing small miracles. This is equivalent to the assumption of determinism in worlds of $ with identical initial conditions. The proof goes as follows: Under determinism any possible world with the same initial conditions than ours that diverges in matters of particular fact is beyond nomological accessibility. At least the claim about the diverging property instance is not implied by our laws of nature. Thus, there is at least one small miracle, that is one violation of our laws of nature. Therefore, measuring the size of factually identical spatio-temporal regions applies only to worlds with small miracles. If measuring the size of factually identical spatio-temporal regions applies only to worlds with small miracles, there cannot be a world diverging in matters of particular fact that is nomologically accessible. If there is a factual difference, there is a nomological difference as well. A necessary condition for indeterminism (probabilism) is that a factual difference without nomological difference be possible. Unless the factual difference concerns the initial state of the world the initial conditions are the same in all the possible worlds by the maximisation of identical regions. Nevertheless, counterfactual reasoning about the initial state of the world can be accounted for by Lewis’s semantics for counterfactuals. If the second respect of similarity applies (as assumed) the initial conditions of the possible worlds of $ are identical and determinism is

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true. Thus, the set of spheres of possible worlds is nested under the assumption of determinism. Any two possible worlds of $ are therefore comparable with respect to their similarity with W. For cases of probabilism Lewis upgrades his account in changing the first and the third similarity aspect as to include socalled quasi-miracles. Quasi-miracles are very rare events that are compatible with actual probabilistic laws, for example, an event that prevents current to pass the wire between Nixon’s button and the launch missile. The constitution of $ has to be an objective process. It must not depend on the one who evaluates counterfactuals whether they are true or false. The set of possible worlds included in $ are all beyond nomological accessibility. They contain worlds with the same history before and the same future after the region that the counterfactual refers to. But the relata of the counterfactual claim are actually not instantiated, they are counter-to-the-fact. Although the worlds of $ are nomologically inaccessible, they are in close nomological vicinity to our world. They are not nomologically accessible for the following reason: the instantiation of the counterfactual relata requires the existence of miracles. However, miracles are quantifiable. Big, widespread miracles are composed of small, punctual miracles that are countable. The divergences in point-qualities (as in the case of Humean supervenience) are objectively determinable insofar as their mere number is concerned. To the extend that the laws of nature are objective themselves (see section 1.3) the measures of similarity are objective. But are there objective reasons for the hierarchy and arrangement of the different respects of similarity? Intuitively, the parameter p correctly embraces criteria of similarity of particular fact and laws of nature. Their ordering satisfies pragmatic needs in that it permits to assign truthvalues to those counterfactuals intuitively taken for true (among the cases that are covered also figure the alleged counterexamples in Bennett 1974, 394-395 and Fine 1975, 452). For David Lewis however, the distinction between small and big miracles has a more fundamental meaning. In the perspective of a counterfactual analysis of causation he claims that small miracles typically take place before the antecedent’s instantiation, whereas big miracles typically take place after the consequent’s instantiation. This asymmetry is supposed to represent the asymmetry between causes and their effects. The cause determines and the effect is determined. Thus, Lewis bases the asymmetry of miracles on what he calls the asymmetry of overdetermina-

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tion (see Lewis 1986b, 49-50, 199). He gives the example of a drop producing concentric waves when hitting a liquid’s surface. There are, he claims, many distinct parts of those concentric waves that permit to determine the position and properties of the drop. So the drop is overdetermined by parts of the waves. But there is only the position and velocity of the drop that determines the form of all the resulting concentric waves. So the drop does not overdetermine the waves. It has been shown that the composition of the similarity aspects in p assumes determinism. Determinism in the Humean framework may be defined as the thesis: same cause implies same effect (provided the Humean is a realist about causation). It is equivalent to the denial that the laws of nature holding at our world comprise proper probabilities p (0 < p < 1). In this sense Humeanism is compatible with determinism. Humeanism is not compatible with a conception of determinism that makes use of the idea that certain entities in the world completely determine and ground the existence of other entities. Such a notion of determinism comes with a commitment to strong singular causation instantiated as metaphysically necessary connections in the world. Given an entirely contingent arrangement of properties in the world, as the Humean wants it, and assuming determinism (in the deflationary form that is compatible with Humeanism), the determination from the effect to the cause and from the cause to the effect are completely symmetric. There is nothing in the contingent arrangement of property instances that permits to found an asymmetry between the cause and the effect. Lewis’s reasoning is wrong, because given deterministic laws any spatio-temporal region with its properties instantiated permits the inference towards its history and its future in a completely symmetric way. Asymmetries of miracles in causal situations are only present from a subjective point of view, when regions of space-time are deliberately privileged (like the region of the drop) as causal agents. There is no ontological foundation for the asymmetry of causation, or miracles in Humean ontologies. Therefore, under determinism the parameter p can be simplified and defined as only comprising one aspect of nomological similarity. Still, the appropriate definition of p has a specific semantical function. Counterfactual reasoning in general is affected by vagueness in various ways. It depends on the context of utterance, on the vagueness of the concepts involved and on the degree of epistemological sufficiency in what regards the

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arrangement of base properties in our world. Only the first, contextual vagueness can be semantically accounted for by the definition of a parameter that fixes the evaluative context (see Lewis 1983b, 228-229 and 244-247). Thus, the set of possible worlds $ defined in order to evaluate counterfactual reasoning satisfies the following semantic needs: – it permits to assign determinate truthvalues to counterfactual claims that are uttered in a sufficiently specific context of nomological and factual circumstances, for example: “If the tennis ball had been hit by a racket, it would have accelerated.” – it permits to identify those counterfactuals that have no such determinate truthvalues, because the reference to a given context does not objectively determine a truthvalue, for example: “If stones could talk, they would express their sadness for being ignored all the time.” The development of Lewis’s account of causation shares at all stages the conviction that at the core of a conceptual analysis of causation there is a counterfactual dependence between the cause and the effect. Beginning with a simple counterfactual analysis he defines C to be a cause of E if and only if C and E are actual distinct events and were C not to occur, E would not occur either (see Lewis 1986b, 159-171). Events are property instantiations at space-time points or regions. The Lewisian account is independent of the property theory one adopts, although it is designed for event-ontologies. Every occurrence of “event” could be replaced by “particular, spatio-temporally located entity”. This first definition has the problem that it is insensitive to cases of redundant causes. Redundant causes may be causes of early, late or simultaneous preemption (where the latter is often called a case of trumping causes). 1.4.3 1.4.3.1

Counterfactual theories of causation amended Preemption and causation as influence

Cases of early preemption include the idea that there are causal chains in the world that may be blocked or deviated by the presence of other causal chains. Thus, the idea of early preemption is always connected to the idea of interference between alternative causal chains. In case of early preemption the causal chain of the preempted alternative is cut short before the preempting causal

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chain leads to the effect. Think about the following example of early preemption: Hannah and Emma throw stones at a bottle, one after the other. Hannah wants to throw her stone when she notices that Emma’s stone actually hit and smashed the bottle. She finally keeps her stone in her hand, because her throwing has been cut short by the loss of the target. Late preemption as well incorporates the idea of alternative causal chains, but this time the preempted causal chain is only cut short after the preempting causal chain has led to the effect. The preempted causal chain does not lead to the effect it had led to had the preempting causal chain not taken place. Both causal chains are independent of one another and target to the same effect. A case of late preemption excludes by definition that the effect be overdetermined, one of the causes is preempted after all. Again, think of the following example: Hannah and Emma throw stones at a bottle at the same time and Emma’s throw strikes just a bit before Hannah’s. If Emma’s stone had not smashed the bottle, Hannah’s would have. Emma’s hit cuts short Hannah’s causal chain only after the occurrence of the effect. Hannah’s causal chain is subject to late preemption. The possibility of late preemption cashes out the idea of a slight time difference between two causal chains that, once started, continue independently of interaction, be it on the part of an agent or between themselves. This idea can be developed into cases of preemption without short cutting at all, but including cases of overdetermination. These examples allow for exact simultaneity of causes and include the additional feature that one of the causes is inefficient in presence of the other, because the second is more important and trumps over the first. They constitute a problem for a counterfactual analysis of causation. Imagine the scenario where a sergeant and a major simultaneously shout “Fire!” at their troops. As a consequence of the major’s shouting the troops advance. The shouting of the sergeant, however, is not the cause of the advancing of the troops. His order is being trumped by the order of his chief. The three variants of preemption have forced David Lewis to amend his account, because they are counterexamples to the simple counterfactual analysis he proposes at the beginning. Take for example the following case of early preemption (figure 1). There are two neural chains (C − D and A − B) leading to the same event E and an element of the first (C) may inhibit the second chain (the example is borrowed from Dowe 2001). Suppose the first neural chain is

causation. Imagine the scenario where a sergeant and a major simultaneously shout "fire" at their troops. As a consequence of the major's shouting the troops advance. The shouting of the sergeant however is not the cause of the advancing of the 43 troops. He order Orthodox Humeanism on laws of nature and causation is being trumped by the order of his chief. C

D E

A

B Figure 1

Figure 1

The three variants of preemption have forced David Lewis to amend his account because work (C − D), leading totoE the and cutting the second neural chain. Lewis’s they atare counterexamples simpleoffcounterfactual analysis he proposes at the beginning. Take for example the following case of early preemption (figure initial account states no counterfactual dependence between C and E for if C 1). There are two neural (CE–would D andhave A –occurred B) leading to the same event an element of the had notchains occurred nevertheless as a result of Etheand second first neural (C) may inhibit the second chain his (theaccount example from chain. Therefore, Lewis amends with is theborrowed result that for C Dowe 2000 unpublished). thebefirst neural chainchain is atbetween work (C D), That leading to E and cutting to cause E Suppose there has to a counterfactual the–two. means solution does not work for cases of late preemption (figureno2)counterfactual where, for example, two off the second chain. Lewis's initial account orstates they either neural are directly counterfactually connected there are intermediate dependence stones CCand C* are thrown atnot a bottle bothEtargeting but occurred C* is a tick later and misses the between forthat if Care had occurred would have nevertheless as a result events and D1 ...E D each counterfactually dependent on their neighbours n bottle merely neural becausechain. thereTherefore, is no bottle anymore. It his has account been smashed by C. of the second Lewis amends with the(E) result thatThe for (see Lewis 1986b, Postscript E). E is not counterfactually dependent on any D between that lies the between andmeans E for they the Cevent to cause E there has to be a counterfactual chain two. C That bottle are would still have been smashed by C*. or there are intermediate events D1…Dn tha either directly counterfactually connected are each counterfactually dependent on their neighbours (see Lewis 1986, Postscript E,). The amended definition worksCout for E is counterfactually dependent on D (remember that the closest worlds are non-B worlds) and D is counterfactually dependent on C which E is not the case for the sequence of events (A – B) because the closest A-worlds comprise C-events which inhibit B.C* Therefore, the closest A-worlds are not-B-worlds. But this Figure 2

Figure 2

19

Lewis therefore introduces an additional regularity feature in the form of quasiThe amended definition works E is counterfactually dependent on D similar to the dependence. C quasi-depends on Eoutif for in most situations that are intrinsically actual situationthat there counterfactual dependence the C-type event and the E(remember the is closest worlds are non-B worlds)between and D is counterfactually type dependent event. Thus causes E if if sequence there is either counterfactual on CCwhich is not theand caseonly for the of events (A− B) becausedependence or quasi-dependence between C andC-events E. Although the example E does counterfactually the closest A-worlds comprise which in inhibit B. Therefore, the not closest depend on C, are it quasi-depends on C. of does late and early for preemption can be included A-worlds not-B-worlds. But thisCases solution not work cases of late in this counterfactual analysis by means of a regularity relation between the cause and the preemption (figure 2) where, for example, two stones C and C ∗ are thrown at a effect that is merely a possible one. The revised analysis of causation however cannot bottle both targeting but C ∗ is a tick later and misses the bottle merely because cope with cases of simultaneous or trumping preemption. is no bottle anymore. has been smashed by C. Thesimultaneously event E is not shout “fire” Takethere the example from aboveItwhere a major and(E) a sergeant at their troops. The major’s (C) but not the sergeant’s shouting is the cause for the firing (E). But the sergeant’s shouting is the reason that there is no counterfactual dependence between C and E. In the most similar worlds without C there is still the sergeant and the troops still advance (E). There is no counterfactual chain between C and E either. For any

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counterfactually dependent on any D that lies between C and E for the bottle would still have been smashed by C ∗ . Lewis therefore introduces an additional regularity feature in the form of quasi-dependence. C quasi-depends on E if in most situations that are intrinsically similar to the actual situation there is counterfactual dependence between the C-type event and the E-type event. Thus C causes E if and only if there is either counterfactual dependence or quasi-dependence between C and E. Although in the example E does not counterfactually depend on C, it quasi-depends on C. Cases of late and early preemption can be included in this counterfactual analysis by means of a regularity relation between the cause and the effect that is merely a possible one. Still, the revised analysis of causation cannot cope with cases of simultaneous or trumping preemption. Take the example from above where a major and a sergeant simultaneously shout “Fire!” at their troops. The major’s (C) but not the sergeant’s shouting is the cause for the firing (E). But the sergeant’s shouting is the reason that there is no counterfactual dependence between C and E. In the most similar worlds without C there is still the sergeant and the troops still advance (E). There is no counterfactual chain between C and E either. For any intermediate event D between C and E it is true that had D not occurred, then E would have occurred nevertheless by the existence of the causal chain between the sergeant and the troops. However, E quasi-depends on C, because in most intrinsically similar situations of C- and E-kind events they would be counterfactually dependant. But the quasi-dependence clause makes the sergeant’s command also a cause of the troops advancing (as Dowe 2001 correctly states from whom this overview is borrowed). In intrinsically similar cases with sergeants and troops the advancing of the troops (E) would counterfactually depend on the sergeants’ commands. Thus, the disjunctive definition of Lewis does not cover trumping situations. The idea of quasi-dependence, Lewis agrees at a later stage, is a bad one in that it presupposes that causation is an intrinsic relation. A relation (as any property) is intrinsic if it can occur independently of accompaniment or loneliness of properties of other objects (again, this definition is the actual standard definition as borrowed from Langton & Lewis 1998). Recurrence to intrinsic features of causal relations is an illicit move for Lewis anyway, because the truthmakers of counterfactual statements comprise global regularities and thus

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extrinsic relations to the causally related events. Because what is a causal relation on a Humean regularity view is determined by what goes on in the rest of the world, previously uncausal connections as in the case of trumped causes (where there is no connection between the sergeant’s order and the troops’ advancing) can turn out to be causal connections when intrinsically duplicated and put into a different environment (see Lewis 2004, 83-85). Therefore causation is not independent of accompaniment and thus not a priori to be considered an intrinsic relation. In order to analyse causation without appeal to the premise of intrinsity Lewis presents another amended account of a counterfactual analysis of causation that should account for trumping situations. The definition goes as follows: for two actual distinct events C and E, C causes E if and only if there is a chain of stepwise influence from C to E (see Lewis 2004, 91). The idea of causation as the ancestral of a more fundamental relation is again present. Whatever the notion of influence will prove to be its ancestral has thus the property of transitivity. “Where C and E are distinct actual events, let us say that C influences E if and only if there is a substantial range C1 , C2 , ... of different not-too-distant alterations of C (including the actual alteration of C) and there is a range E1 , E2 , ... of alterations of E, at least some of which differ, such that if C1 had occurred, E1 would have occurred, and if C2 had occurred, E2 would have occurred, and so on.”(Lewis 2004, 91)

The relation of influence sets up a pattern of dependence of the whether, when and how of the effect on the whether, when and how of the cause. This is an extension of the idea of simple counterfactual dependence at earlier stages of Lewis’s analysis where causal dependence was analysed as counterfactual dependence of whether the cause exists on whether the effect exists only. The intuition captured with the concept of influence is that those actual events are to be called causes of a given distinct actual event that constitute the latter in what regards its existence, but also position in space-time and its actual intrinsic make-up. Alterations of the cause event are meant to represent those slight variations that would change the aspects of the effect event a lot were they to occur. Formally, an alteration of an event C is defined as being either a very fragile version of C or a very fragile alternative event that is similar to C, but numerically distinct from C (see Lewis 2004, 88). Lewis remains neutral where the line has to be drawn between still-enough-similar events to count as the same and already-too-distinct events to count as numerically distinct.

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Causation as influence provides a neat solution to the standard problems of early and late preemption as well as to trumping situations. In the case of the two stones thrown at a bottle only the range of alterations of the actually bottle-hitting stone is in counterfactual correspondence with alterations of the bottle’s smashing. It does not matter whether the other stone would have hit the bottle, had the first one missed it, because not enough alterations of this event stand in counterfactual relations with alterations of the effect. Nor does it matter what the sergeant would have shouted given the order of the major, whose alterations are in counterfactual correspondence with the alterations of the troops’ behaviour. Although Lewis’s tuned analysis seems to have captured an essential idea of causal relation, there are several problems remaining. First of all his new account makes essential use of alterations and presupposes that one can confer objective sense to their properties of being “distinct” and “not too distant”. Alterations are only distinct if they are counterparts. The counterpart relation in turn applies similarity relations of various degrees across possible worlds including perfect similarity of intrinsic features. Intrinsically perfectly similar counterparts may count as distinct alterations only if they do not share all of their relational features as well (like space-time positions, etc.). As stated before, counterfactual reasoning as such is already a vague matter, but one that can be amended by the attribution of constant truthvalues relative to a given evaluation context. The choice of a given context has consequences for what counts as a “distinct” alteration as well. Intuitively, it is clear that in considering the situation of a smashed window “distinct” alterations of the causally responsible baseball will not be obtained in removing one of its electrons. They will be obtained in doubling its mass, changing its direction and the like. Hence, the mere distinction criterion for alterations does not necessarily have a subjective flavour if considered relative to a determinate context. There is no principled problem to the fact that what is a “not too distant” alteration depends as well on the global context of a given causal claim. But the context only fixes the lower boundary of not enough distant alterations for being distinct. Certainly, any alteration that is “not too distant” from actuality will be part of a world in nomological vicinity, hence of a world that is nomologically accessible except for the miracle that is needed to make possible the alteration. Only such a criterion guarantees that pertinent alterations for the

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evaluation of causal claims supervene on the actual alteration of the event plus the laws of nature of our world. But can one make objective sense of Lewis’s idea that an event is to count as a cause of another event, if small changes in the first lead to greater changes in the second? Another “not too distant” alteration of the baseball could be a change in its colour. Lewis has no possibility to exclude such epiphenomenal alterations from the set of pertinent alterations, because it seems that any attempt to define pertinence will lead to circularity of his account. Therefore, such cases are admitted in the analysis even if they do not lead to alterations of the effect. Only “some” of the effect alterations must be distinct. The idea is of course that in case of a real causal relations most of the effect alterations will be distinct, whereas in non-causal relations only very few of the effect alterations will be distinct. A subjectivity problem arises here that has been pointed out by Jonathan Schaffer in a critique of Lewis’s influence account (see Schaffer 2001). It is not clear how one could possibly distinguish in an objective way many effect alterations from few effect alterations. Of course one can count them, but where should one draw the line between enough and too few distinct effect alterations and hence between genuine and artificial cases of influence? Now assume that there is a way to discriminate between enough effect alterations and too few effect alterations. The global context of causal claims may provide only environments where causal and epiphenomenal relations are neatly separated. Even then, Schaffer shows, one can make up examples where influence takes place but not causation (see Schaffer 2001, 17-18, where he thinks of a person’s watching the electrocution executed by a second person while having the possibility to stop it. You have how and when dependency sufficient for influence, but not causal responsibility for the electrocution). Therefore, influence is not sufficient for causation. Schaffer’s counterexample consists in showing that the way an actual epiphenomenon abstains from causal interaction can be considered as how-influence. Any restriction of the “not too distant” clause to exclude such epiphenomena seems to be unjustified. Furthermore, you can think of instances of causal relations that do not even admit the construction of alterations. If this is correct then there are cases of causation that are instances of the influence relation. Therefore, influence is not necessary for causation (see Schaffer 2001, 12-17).

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Schaffer advances three criteria for believing in the presence of a causal relation: predictability, explicability and moral responsibility (Schaffer 2001, 12-13). In case a person watches another person executing an electrocution and does not interfere while having the (“not too distant”) possibility to do so (and she does so in alterations of her actual abstention), he argues for unique causal responsibility of the executor. He did it, after all. But Schaffer’s argument is based on an ambiguity of the event that someone watches an electrocution. Only watching suffices for not counting the watcher as causally responsible, but watching while having the possibility to intervene makes for her influence on the scene. Therefore, I claim only the second specification of the event (watching plus presence of intervention devices to prevent the executor’s action) should be relevant for the intuition test whether or not we have a case of causation here. The insufficiency claim presupposes that omissions can always be interpreted as influences, but not as causes. It seems, however, that non-interference as well can be cited as an element in the prediction of the electrocution, may be used as an explanation of the electrocution and could be blamed by a judge for the electrocution. If this is correct, then one faces the following choices: either to accept the non-interference as a cause (and to count omissions as causes in general), or to exclude omissions from the definition of influence from the beginning (by not considering them as events, for example).

1.4.3.2

The non-sufficiency challenge: causation by omissions

There are independent reasons why omissions should not be considered as causes. Imagine the following situation of omission as a causal event: everyone has remembered to bring his lifejacket on the boat except for yourself. The boat sinks and your neglect is the cause of your drowning. I think the friend of causal omissions will accept to call the fact to forget something as an omission in the sense of not having thought about it, or in general, in the sense of a some feature not having taken place. She will, of course, also assign complete causal responsibility to this omission for your death. But what is considered as being the cause of your death is a specific event in the world. Events are instances of properties at space-time regions. It is only a description of this event that uses negative concepts such as absence, neglect and the like. If every description of

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the very same event includes such concepts we have reason to believe that we get involved with an instance of a negative property here. Only the existence of such a property instance licences the inference that the causally responsible event is actually an omission. But there are other descriptions of the same event that do not include negative concepts. One can give a positive description of the situation in which you were supposed to think about your lifejacket but did not. In the end one can always give a fundamental physical description of the event in question. Of course, what is interesting is to refer to the event from the point of view of your neglect. The choice of a certain perspective of description does not influence the properties of what is described from this perspective. The description of an event using negative concepts can be true even if negative properties do not exist. Omissions are purely conceptual. This argument presupposes two additional hypotheses: first, a sparse theory of properties and second that there is a non-causal way to define natural properties. By a sparse theory of property I mean that any property must somehow be a construction out of fundamental properties. I do not deny that any gruesome recombination of such properties are properties themselves. In addition, fundamental properties are natural. Suppose that something like Lewis’s criterion is correct that the axioms of our best system identify natural properties. There are no omissions among the natural properties. Hence, omissions qua events clearly comprise an element that resists composition by natural properties. That is, omissions are no properties. Therefore, negative concepts do not refer to real omissions. Applied to Schaffer’s case we have to distinguish between innocent conceptual omissions and erroneous ontological omissions. Omissions in the ontological sense do not exist. A fortiori they cannot give rise to existing alterations. Hence, they cannot figure as relata for the influence relation. Therefore, Schaffer is wrong in accusing Lewis’s influence account as insufficient. But still there is a sense in which omissions play a role in the above situation. When Schaffer says that the watching of the person influences the electrocution, we have seen that what makes for the influence is the possibility of intervention (for example a device activating a trap door where the executor stands). The event comprises the person’s watching plus the possibilities of intervention. Note that intervention is a relational concept. In the present case it is intervention to prevent the executors action. Hence, the omission refers to the watching, the

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intervention facilities and the executor’s action. Admittedly, this is a big and complex event, but not bigger and more complex that the situation set out. The mere fact that we may refer to this event by the concept of omission (this is the innocent move!) does not imply that the event itself is an omission (in the erroneous sense) and is compatible with the claim that the event is genuine and also influences the electrocution. It is also compatible with the claim that this event is a genuine cause for the electrocution. Why should it be considered a genuine cause? Because it does under Schaffer’s criteria. It allows to predict, explain and denounce the electrocution. Schaffer is conscious of the objection above, but argues that the watching alone (as a causally distinct event from the watching without intervention) influences the electrocution while not causing it. I claim that if such a causal distinction between events can be made, the two relevant events are watching without possibility to intervene and watching with possibility to intervene. Where the first neither influences nor causes anything, the second can be considered as doing both. Schaffer’s distinction is merely a difference of discription of one and the same event in more or less precise ways. It is not true that only Kate’s saying “I love you” but not Kate’s speaking in general is responsible for John’s flushing, if these are descriptions of the same spatio-temporal region at the same world. One and the same individual cannot instantiate distinct sets of causal possibilities at one time. In our case we do have one and the same individual once supposed only to influence another event, once supposed not to cause it. It is, of course, in virtue of the possibility (or the power, in an innocent sense) to intervene that the person’s watching influences the electrocution. Hence, it is also in virtue of exactly this possibility that one could consider her a cause.

1.4.3.3

The non-necessity challenge: no alterations available

The claim that influence is not necessary for causation is more severe. Can you consider causal situations where no alterations of the cause event are at hand at all? Schaffer makes the following case (2001, 15): imagine an electrocution executed by pressing a single button. Clearly there is no how dependency on the effect for it is irrelevant in any sense to the electrocution how the button is pressed. There is neither when-how, nor when-whether dependency either.

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There only seems to be a when-when and a whether-whether dependency in this case. Schaffer argues that those two dependencies can be driven to zero such that the one who presses the button causes but does not influence the electrocution. When-when dependency can be driven to zero by integrating a preempted backup (that is a potential preempted cause) that would press the button should the executor hesitate just a little bit and by setting up the wiring of the button such that it would not have worked before a fixed time anterior to which a second person would have executed the electrocution. By means of the preempted backup there is no whether-whether influence either. So there is no influence, but still causation. As influence is being sufficient for causation, it does not seem to be enough. There is no influence, not because “not too distant” alterations of the causes are not counterfactually connected to alterations of the effect, but because there are no alterations of the cause and of the effect at all. There is no influence by default. The possibility of alterations as defined by Lewis presupposes a permissive principle of property recombination. Lewis provides such a principle in considering almost any rearrangement of fundamental property instances as a possible way the world could have been (see his 1986a, 89-90 for the restriction he imposes). Thus on the Humean account impossibility if existing at all is rather an uncommon feature. The situation sketched above is highly complex, but admittedly a possible contingent scenario. Whereas in the majority of cases influence and causation come together, rare cases might not show all of the dependencies built in the notion of influence (nine in total, namely all combinations between whether, when and how dependencies). For rare cases, Lewis estimates that some of those dependencies suffice in order to qualify a relation as influence and in a second step as causal. For example, on the rare occasion where a preempted backup takes over the role of the cause in case it does not take place, a counterfactual relation between how-and-when alterations of the cause and how-alterations of the effect suffice to qualify for influence. Then, making things even more complex one can envisage situations like above with no possible alterations available at all. Schaffer’s argument examines the executor’s action in pressing a button as the cause for the electrocution. Alterations thereof may not go as far as to affect the carefully constructed set-up, of course. One looks for something like the minimal cause. This means the impossibility at stake is not of a metaphysical or

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logical sort, but purely of a semantical or methodological sort. You may only build alterations by holding the actual alteration’s environment fixed. Else, probably anything in the world would count as a case of influence and hence causation. But this is not an exclusive alternative. It admits of degrees. However, any spatio-temporal delineation of the region around a putative causal event that strictly includes the event seems to be subjective, ad hoc and, worse, subject to further counterexamples. There are two possibilities at hand to resolve this situation: first, to deny that the pressing of the button is actually a cause for the electrocution or second to look for an amendment to the actual definition that goes beyond the idea of influence. The first is, at first glance, intuitively hopeless. The person actually pressed the button even if someone or something else would have done it had she hesitated a little. Maybe the person was not free to do it, but she has done it. Maybe she only had exactly this possibility to do it, but she has done it, etc. The reason not to count this situation as an instance of influence is the presence of the preempted backup. Lewis could argue that the event of pushing the button and the possible intervention of the backup are so closely intertwined that the pushing alone cannot be regarded as a sufficient cause for the electrocution. It is only part of a sufficient cause, as the watching above is only part of a sufficient cause for the electrocution, the watching that together with the intervention device and the executor’s pushing is sufficient for the occurrence of electrocution. In this sense, the counterexample is just not accepted as such, it is considered as spoils to the victor. After all, common sense intuition is already considerably forced during the construction of the counterexample. The second way out is to amend or change the account. Amendments within the counterfactual approach are not excluded by Schaffer’s criticism. One might look for a slightly more general notion than influence in order to get a necessary condition for causation. Influence is sufficient for causation after all. If not identical with causation influence is at least very close to causation. Schaffer, however, concludes his discussion of Lewis’s analysis by pointing out a concrete morale. Causation is not about influence, but effluence, that is process connection (see Schaffer 2001, 18). Even if he does not exclude that effluence admits of a counterfactual analysis as well, he seems to opt for a singularist process account of causation. Processes are sequences of events that may transfer or exchange conserved physical quantities (energy, in most accounts).

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The main difficulty for process theories consists in the tension between looking for a physical account of causation while having physical problems with the mere notion of a conserved physical quantity, because general relativity only recognises conserved quantities in relation to a fixed reference frame (see Esfeld 2008b, 151-152). From the physical point of view an event E is determined by the properties of the spatio-temporal region included in the lightcone that opens in the backwards direction of E. Asymmetry between past and future enters only contingently in the Humean picture. Given the entire distribution of fundamental property instances some laws of nature expose temporal asymmetry (for example, laws that describe dynamics like the laws of entropy or of quantum state reductions). The conceptual analysis of causation as influence provides us with a criterion to identify among all the events included in this lightcone those that play a privileged role in the determination of whether, when and how event E is instantiated. The events thus distinguished are called causes, because from the point of view of their influence on E they are salient to us. Given the objectivity of counterfactual reasoning and the construction of alterations for actual events, cause-events can be objectively designated. The way they actually influence event E is a contingent matter and has to be identified a posteriori by empirical investigation of what the laws of nature are at our world.

1.4.4

Regular causation vs. counterfactual causation

Lewis’s conceptual analysis of causation is the currently most developed account of Hume’s initial intuition that distinct entities can be called cause and effect under the condition that had the one not been, the other one would have never existed. He considers this criterion to be equivalent to regular succession between first-kind entities and second-kind entities. From a Humean point of view regular succession means law-like succession if it is part of the important regularities that make true law-statements in our world or if it is implied by the laws. A regularity account of causation in the Humean framework therefore holds that causal relations are law-like relations for it is a law of nature (or entailed by a law of nature) that entities of the same kind as the cause are followed by entities of the same kind as the effect (see Armstrong 1983, 11).

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Moreover, those regularities are completely contingent and might have been different from what they actually are. Intuitively, causal relations are individual instances of particular events satisfying certain conditions. Counterfactual approaches to causation share the advantage that their relata are particulars. Regularity approaches to causation do not share this advantage at first glance. Whether this intuition is correct or not depends on the question whether all cases of causal relations under the regularity view are also cases of causal relations on the counterfactual view and vice versa. The regularity theorist accepts that a causal relation between two entities is a law-like relation and that law-like relations are regularities that are either of sufficient importance as to figure among the theorems of our best deductive systems or that are implied by such theorems. It has been shown that being implied by the laws of nature (that are defined as theorems of our best deductive systems) is interdefinable with being nomologically necessary. Causal relations are therefore nomologically necessary. In all the worlds that are nomologically accessible from our world statements about our causal relations are true. Nomologically necessary statements support counterfactual statements about them. Therefore any instance of causation on a regularity account is an instance of causation on a counterfactual account in the form of a simple conditional analysis. Whether this result generalises to the more sophisticated Lewisian account depends on the question whether the system of spheres $ that determines the truthvalues for counterfactuals remains sufficiently constant throughout the construction of alterations of events and their counterfactual evaluation. Counterfactual dependence between alterations of two events is evaluated by the same laws of nature as the actual alterations are: by the actual laws of nature. The maximisation of identical regions in matters of particular fact may vary for example in the case of alterations concerning the spatio-temporal positions of events. Therefore the system of spheres $ varies in that it is centred on the alteration of the cause-event under evaluation. However, those alterations are defined as either being versions of the same event or alternative but intrinsically similar events to the actual event. In the first case the system of spheres $ is centred on the same event and can therefore not affect the attribution of truthvalues for counterfactuals by its mere variation in constitution. In the second case the

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system of spheres $ is centred on numerically distinct but intrinsically similar events that are sufficiently similar in that they do not affect the attribution of truthvalues for counterfactuals either. Intuitively, this is provided by the clause that the alterations be “not too distant” in whatever respect compared with the actual alteration of the counterfactual antecedent-event. Therefore any instance of a causal relation on a regularity account is also an instance of causation on a counterfactual account, even on Lewis’s specific analysis. For the inverse direction of implication it has to be tested whether a regularity view of causation can account for a causal relation between two singular and unique events C and E. By definition there exists a chain of influence between C and E. Assume that C and E have a unique occurrence in our world and for simplicity that the chain of influence actually consists of only one link. There are alterations of C and E that stand in the appropriate counterfactual one-to-one relation. The system of spheres of possible worlds $ is defined by the laws of nature and the identity of particular matters of fact. In adopting a regularity account of laws of nature the regularities of our world that appear in our best deductive system co-define $ together with considerations of factual similarity. The best deductive system of our world is maximally strong. That means that it embraces true statements about the whether, when and how of both singular unique events in question. Such statements about the singular unique events C and E can figure as unique instances of the relevant regularities. The number of instances is not essential to the existence of a regularity (there can be empty regularities in the form of uninstantiated laws of nature). As events C and E are not part of a purely accidental regularity (they are causally related) the regularity they are part of is implied by the theorems of the best deductive system. The regularity containing C and E is therefore constitutive for the evaluation context $. The necessary and sufficient conditions for being a causal relation (INUS conditions, for example) are likely to be fulfilled by the nomological context thus created. Hence, there exists a regularity that accounts for the causal relation between the singular unique events C and E and it is possible for the regularity theorist to claim that events of kind C cause events of kind E even though this regularity has but a single instance. Statements about the singular unique events C and E can also figure as singular claims without being instances of regularities. Such claims, if there are

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any, are likely to be situated among the theorems of our best deductive systems. Claims of that kind may be claims about the initial conditions of our world, like claims about the Big Bang, for example. It has been shown that Lewis’s counterfactual account of causation is able to attribute truthvalues to counterfactual statements about such unique claims. The context of their evaluation contains nomologically accessible worlds. However, the regularities that define nomological accessibility do not embrace or imply statements about the singular unique events C and E. It is impossible to account for them in terms of regularities. Therefore, on a normal regularity account causal claims about singular unique events that make true theorems of our best deductive system cannot be attributed definite truthvalues. In particular, the Big Bang cannot be called a cause of any other event, because statements about it are good candidates to figure among the theorems of our laws of nature. Hence, all relations that are identified by a regularity theory as being causal are also identified by a counterfactual theory as being causal, but the inverse is not the case. Humean regularity theories and Humean counterfactual theories are therefore not equivalent. It has to be tested whether they share the same ontological commitments in order to license the conclusion that a counterfactual theory is superior to a regularity theory. While regularity theories are ontologically innocent in that they do not explicitly allude to possibilia, Lewis’s counterfactual theory does at least make semantical use of possible ways the world might have been. Possible ways the world might have been enter in the account at the evaluation set of possible worlds $ and when alterations of actual events are introduced. Lewis himself is a modal realist. For him every way our world or its parts might have been exists as a spatio-temporally and causally independent entity apart from our actual world (see Lewis 1986a, 3). He defines property instances (as events and for him also propositions as properties of worlds) as transworld entities, in other words as sets of parts of worlds. If such an ontology is implied by his accounts of causation in particular and of counterfactuals in general, then they have an important disadvantage, namely to multiply ontological primitives disproportionately to the greater import of his theoretical account. If, in the other case, possible ways the world might have been prove to be merely semantic devices to make explicit the meaning of causal and counterfactual statements and if their truthvalues therefore supervene on the actual arrangement of point-

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quality instances, then standard Humean ontology is sparse and fruitful at the same time. It is beyond doubt that true statements about an actual singleton event E, like ”I scored a goal” are made true by this event itself. Alterations of this event cannot be conceived in an ontologically innocent way unless they are conceived as rediscriptions (be it of a linguistic, pictural or set-theoretic kind). Rediscriptions can be picked out in virtue of the similarity relation S they bear to the initial exhaustive description of event E. If alterations of E are designated by E1 ,...,En then the set of alterations of E is E ∗ = {Ei such that Ei S E}. It depends on the specification of the similarity relation S whether the set E ∗ can be different given the actual alteration E. In other words, it depends on S whether E ∗ supervenes on E. E ∗ does not supervene on E in the case where S is subjective, varies or regroups an infinity of similarity aspects. The only explicit specification of S that is given by Lewis is that it does not produce too distant alterations. But the evaluation of counterfactuals is conducted by reference to a set of worlds $ that is in immediate vicinity of the sphere of nomologically accessible worlds. More precisely, nomological accessibility is only transgressed for the specific creation of counterfactual situations relative to the world on which the set $ is centred. Therefore, it must be the case that the similarity relation S is restricted to nomological accessibility. Only alterations that do not violate our laws of nature are admitted in the set E ∗ . Alterations that are nomologically accessible have a certain degree of approximate similarity in matters of particular fact, because they have approximately the same constituents distributed in a similar way. Nomological accessibility is an objective matter, does not vary and is obviously finite as a similarity criterion. Therefore, the artificial construction of alterations such as needed for Lewis’s causal analysis supervenes on an exhaustive description of the actual alteration. It does not follow that any instruction for the construction of alterations supervenes on the initial alteration. Think of alterations consisting partly or wholly of alien properties. Existing possible worlds might be needed in order to make true statements about those alterations if they want to be accorded definite truthvalues. It does not follow either that the construction of a set of possible worlds $ for the evaluation of counterfactual reasoning about alterations is ontologically innocent. Again it must be shown that the truthvalues of

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counterfactual statements supervene exclusively on the way our actual world is. The comparative similarity relation that defines $ compares two possible worlds in what regards their similarity to a reference world W on which $ is centred. The counterfactuals involved in the analysis of causation are supposed to have definite truthvalues, because, although vague to a certain degree, their truthvalues are objectively determinable relative to a given nomological and factual context. It has been shown that the similarity criteria at stake in the counterfactual analysis of causation are objective, finite and constant. The set of possible worlds in $ thus supervenes on the actual arrangement of particular facts. From the description of the actual world a set of objectively similar worlds is constructed. There may not be a difference in $ without a difference in the world that $ is centred on (in the case of Lewis’s analysis). It does not matter whether a given system of possible worlds $ is centred on an actual or merely possible alteration of an event E as long as the set of alterations E ∗ of E supervenes on the actual event, because supervenience is transitive. Again it does not follow that the truthvalues of any counterfactual statement supervene on the actual arrangement of particular matters of fact. Existing possible worlds might be needed in order to make true statements about those counterfactuals if they want to be accorded definite truthvalues. However, more likely those counterfactual connections among relata that are parts of too remote or dissimilar possible worlds should not have definite truthvalues at all (like cases of depressed stones, for example). Modal realism is therefore not implied by the characteristics of the semantic accounts for causation and counterfactuals. Possible worlds and alterations are intended to make explicit the meaning of causal statements and not to constitute it. Regularity theories and counterfactual theories of causation therefore share the same ontological commitments in that their ontological basis is restricted to the arrangement of actual property instantiations, but their strength differs in favour of the counterfactual account. Therefore, the latter is preferable to the former. Counterfactual accounts of causation are just sophisticated regularity accounts. From the point of view of a counterfactual theory of causation one can now ask what exactly the truthmakers for causal claims are and if they permit to be identified more specifically. In general, the truthvalues of causal statements supervene on the laws of nature and the distribution of particular matters of fact. Law statements in turn supervene globally on the distribution

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of particular matters of fact. Therefore, causal statements supervene globally on those facts as well. Consider for example the following simple causal statement: “My throwing of the stone causes the water to splash.” If this claim is true, then there exists an influence chain from my throw to the splash. This means that had I not thrown the stone, no water would have splashed, and had I not thrown the stone then, the water would not have splashed then, and had I not thrown the stone thus, the water would not have splashed thus. Those counterfactuals are true in virtue of the sufficient nomological and factual distance of worlds where I threw the stone, but the water did not splash, etc. In other words, those counterfactuals are true, because the worlds with our laws of nature (with very few exceptions) instantiate both the stone-throw and the water-splash or their alterations. The set of closest worlds that makes true a counterfactual can be regarded as instantiating a possible regularity. Note that this is more general than the requirement that there has to be an actual regularity in order to license causal claims about them as it is the case on regularity accounts on causation. Hence, if the counterfactuals are true they are true in virtue of there being a (possible) regularity between stone-throws and water-splashes or their alterations. Therefore, causal claims like our example are true in virtue of it being a regularity that stone-throws are contiguously co-instatiated with watersplashes. But it is not enough to be a regularity that stone-throws are followed by water-splashes. Accidental regularities do not support counterfactual reasoning about them. In addition those regularities are regularities in the nomological context defined by our actual laws of nature. In other words, those regularities are important regularities in the sense that they are implied by our laws of nature. To be implied by our laws of nature means that compared with other regularities of our world, they appear to be more important. This is the reason for the global supervenience of Humean laws on the whole distribution of particular facts. Therefore, causal claims like in our example are true in virtue of it being a regularity that stone-throws are contiguously co-instantiated with water-splashes and in virtue of this regularity being an important one compared with all the other regularities, because it is implied by the theorems of our best deductive system. The truthmaker of a simple counterfactual claim thus appears to be the whole distribution of particular matters of fact. The lack

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of a local supervenience basis for causal claims is due to the lack of a local supervenience basis for nomological claims.

1.4.5

Humean causation in the mental domain

Although a simple causal claim like our example from above seems to refer to the actual particular events that are engaged it is only in virtue of their affiliation to an actual or possible nomological regularity that their causal connection can be truly attributed. This has unwelcome consequences that show up most stringently in the case of mental causation. The lack of local supervenience bases and therefore of local truthmakers for causal claims is counterintuitive, because it subtracts the idea of localised agency from the concept of causation. My mental states are causal not merely in virtue of what is going on in my body (or brain), but they are causal in virtue of other actual or possible bodies to which they are similar and in virtue of all those bodies’ regular behaviour being implied by the most fundamental regularities in the world. Thus, Humean causation does not account for agency as a localised, particularised process that can be instantiated by something independently from what is going on elsewhere in the world. Global supervenience of counterfactual causation counters the intuition of localised agency of causal events. An ontology can be called Humean if it implies a global supervenience thesis whose basis is an entirely contingent arrangement of property instances. It can be called physicalistic as well if its supervenience basis contains only physical entities. Conceptually it is not excluded that among physicalistic Humean ontologies there are some that satisfy local supervenience theses for causation (like, for example, process theories of causation). However, if she is a realist concerning the laws of nature the Humean needs to accept globally supervening laws. Lewis’s analysis of these concepts entails global supervenience bases for both, because causation supervenes on the laws and the laws supervene globally on particular matters of fact. Besides the discussion of the implications of Lewis’s causation from the point of view of its being Humean, it can also be examined what the implications of Lewis’s causation are from the point of view of its being physicalistic (in an ontologically reductionist perspective). An imminent task of physicalistic metaphysics is to come to a decision for the problem of causal exclusion for so-called “higher-level” causation, as bio-

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logical or mental causation. Some adherents of Humean causation claim that Lewis’s counterfactual account is such a deflationary view on causation that it does not engage its defender to accept causal exclusion as a problem at all. Jaegwon Kim famously presents the causal exclusion problem for physicalistic theories (see Kim 2003, 151-152). He starts with the premise that a mental event m1 causes another mental event m2 . In a physicalistic world (that is a world where psychophysical supervenience holds) the only way m1 can cause m2 is to cause its supervenience basis, the physical event p2 . Kim holds thus that higher-level causation implies trans-level causation in physicalistic worlds. He goes on in claiming that there are strong independent reasons from science to accept the causal closure of the physical domain (see also Papineau 2004, appendix). So, every physical event has a physical cause to the extent that it has a cause at all. The physical event p2 , has a cause (m1 ), hence, by closure, it has a physical cause p1 . This is a situation of overdetermination. The physical event p2 has two causes p1 and m1 . Kim claims that overdetermination is rare and that systematic overdetermination is therefore implausible (this is the causal exclusion principle). One of the causes has to go (or, in other words, is excluded). Because of closure we are always stuck with the physical cause. Therefore we face the choice between either eliminating the causal relation between m1 and p2 and to make the mental epiphenomenal, or to identify m1 to the physical event p1 and to save its causal efficacy. As most philosophers try to avoid epiphenomenalism we have a strong case for reductionism. Causally effective “higher-level” properties are identical with arrangements of fundamental physical properties. The alleged counterfactual solution of Kim’s exclusion problem has it that overdetermination is not as bad a way out under the condition that a counterfactual account of causation is adopted. With a counterfactual account of causation we do not have genuine overdetermination. Therefore the exclusion principle does not apply. The problematic decision between causal effectiveness and distinctness of “higher-level” properties can be avoided. Consider the situation of overdetermination between m1 , p1 and m2 . The argument has the following structure (following Loewer 2001, 318-319): a counterfactual connecting a mental event and another mental event can remain true while the counterfactual connection between the mental event’s supervenience basis and the second mental event may turn out to be false. For example, first, if I had

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not felt the desire for an ice cream, then I would not have remembered my last summer holidays in Italy. Suppose this is a true counterfactual for my desire actually caused my memories. Second, if the physical supervenience basis for wanting an ice cream had not been instantiated, I would not have remembered my holidays. The argument claims that this counterfactual can be false for there might have been another supervenience basis (sufficiently similar to the actual) for the same wanting of an ice cream that would have been a sufficient cause for my thinking about Italy. Because the truthvalues of the two counterfactuals may differ they refer to different relations. Both relations share the effect relatum. Therefore they must differ in their cause relata. Hence, there are two causes that overdetermine the effect. But the overdetermination is not a bad one, like the case of two independent killers shooting a victim at the same instance. Rather the overdetermination is harmless, for there is metaphysical dependency between both causes via supervenience. The problematic assumption in the reasoning above consists in claiming that “higher-level” events are not particulars in the sense that they remain unchanged if their composition changes (see Sparber 2005). Such multiple realisation usually holds for types or kinds of property instances. An event like my desire for ice cream is exactly localised and determined by its physical constitution. As individuals events are maximally determinate. A change in the physical constitution may not affect the affiliation of the event to a certain property type, but it affects the identity of the token-event. Therefore, it is not true that we can have numerically the same “higher-level” property token with two different physical base property constitutions. The truthvalues of the corresponding counterfactuals cannot diverge simply by making small changes in a property’s base that leave unchanged the type-affiliation of the “higherlevel” token. The truthmakers of causal claims on a counterfactual account do not license the inference that a given ‘higher-level” property instance and its corresponding base property instance differ. The causal exclusion problem is independent of the fact whether a Humean account of causation is adopted, because counterfactual causation (and therefore regularity causation as well) does not permit to evade the causal exclusion problem. The Humean faces the same problem as anyone else. In this sense Humean causation might well be considered deflationary, but not just as deflationary that it need not be regarded

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as causation anymore, for it is also subject to the problem of causal exclusion and overdetermination. There are presuppositions underlying the overdetermination approach advanced by Barry Loewer. On standard semantics the attribution of truthvalues to counterfactual statements crucially turns on the actual laws of nature. Kim’s argument (as Loewer’s) starts with dualism as a premise in the framework of physicalism. Loewer adds the premise that causation is essentially counterfactual. He thus adopts something at least close to Lewis’s standard semantics for the evaluation of counterfactuals. The truthvalues of the mental and the psychophysical counterfactual differ, because different laws of nature apply in their evaluation. Mental events, in being distinct from physical events, do not allow an evaluation by physical laws of nature (after all they are non-physical by hypothesis). So mental counterfactuals refer to possible worlds that are ordered in a more coarse-grained way than physical counterfactuals. Of course, because of supervenience there are no mental laws without underlying physical laws. So mental-law-ordering is necessarily compatible with physical-law-ordering. The difference between the two counterfactuals resides in the fact that many worlds that play an important role in the evaluation of physical counterfactuals do not play a role in the evaluation of mental counterfactuals. In general, different possible worlds play decisive roles in the evaluation of the two kinds of counterfactuals. The dualistic premise therefore presupposes that there are laws of nature relating mental events. Certainly, such laws are not general in that they admit for exceptions. They include ceteris paribus clauses. My desire for an ice cream only causes the memories of my holidays if in sufficiently many cases recent desires remind me of older desires and the situations in which I experienced them and if no more fundamental intervening feature comes up during the process (for example, I simultaneously hit my toe on the foot of the table and feel sudden pain). It is far from clear what psychological events are within the Humean framework. In principle, for the Humean (on the Ramsey-Lewis account at least) anything is a law that is deducible from the axioms of the best deductive system that truly describes our world. It may be possible that psychological laws follow from fundamental physical laws, but this has not been shown yet. Even more, if it is possible the reduction should be accomplished. Note that the reductionist does not have the same problem

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for she does not have to recur to non-physical laws of nature for mental counterfactuals. The second presupposition is the possibility that an individual (e.g. a token or an event) may be multiply realised. Under this assumption one and the same individual may be differently composed. There is plausible argumentation for the fact that, for example, a person as an individual may be differently composed through her temporal evolution. Typically persons persist while their body is subject to change. But Loewer makes a more audacious claim, namely that one and the same individual may be differently composed at one and the same time. For the sake of clarification suppose that possible worlds exist. The claim is that two identical worlds may differ in your physical composition at only one moment. Loewer’s token multiple realisation hence presupposes trans-world identity for property tokens. One and the same token exists in different possible worlds. These worlds are distinct by a difference in the instantiation of particular matters of fact. Differences in the instantiations of particular matters of facts may result in differences in laws of nature. This need not say that those worlds are far beyond nomological accessibility. Worlds that play a role in the evaluation of counterfactuals typically are worlds beyond nomological accessibility because they include miracles, but not far beyond. In particular, one may not hold constant the laws including the events counterfactually related to one another. Therefore, one and the same event may behave differently across possible worlds. What identifies events is then not reducible to what they actually are and to what laws they actually figure in. In other words, the knowledge of what composes properties and of what laws these properties figure in does not suffice to identify their instances. Their identity is irreducible, they have so-called primitive thisness: a haecceity. Haecceitism is a consequence in property theory that should be avoided (see Chisholm 1967 for some unwelcome consequences of a haecceitistic ontology). David Lewis, the most important advocate of contemporary Humeanism, rejects haecceitism himself and develops a counterpart theory of property instances across possible worlds. Counterparts are similar individuals that may nevertheless differ in some of the intrinsic properties they have. You might be actually sitting, while your counterpart in a closely similar possible world is standing. Haecceitism has among its unwelcome consequences that one can make up intrinsic differences within one and the same individual (see Lewis

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2007, 7-8). On counterpart theory no individual can be located in two different possible worlds, but only counterparts of individuals can occupy the same spatio-temporal region in different possible worlds. Therefore no haecceitistic difference between indiscernible possible worlds can arise. Note that transworld identities of individuals do not suffice per se for haecceitism. They do so in the framework of standard Humeanism, with exclusively intrinsic, categorical properties at the fundamental level. Hence, for the standard Humean the multiple realisability of property tokens bears a heavy metaphysical burden: haecceitism. Without the general possibility of multiply realised property tokens she lacks an argument for the claim that when we have two different physical supervenience bases, we may have one and the same property token. At least, it does not follow automatically that the truthvalues of the mental and the psychophysical counterfactual can differ. There is no free solution to the causal exclusion problem in mental causation in adopting a counterfactual account of causation. Actually, the ontological price is high. If the causal exclusion problem generalises to properties of the special sciences, then every higher-level natural property instance has a primitive thisness on Loewer’s account. Kim has put forward that the exclusion problem is a general problem for any supervenient property instance (see Kim 2003, 164-167). Therefore, one can conclude that Humean regularity causation (the normal or sophisticated counterfactual one) can be labelled “causation light”, but not just as light as to avoid general metaphysical problems for higher-level causation. Somehow, Humean causation still is “enough” causation to run into the same trouble as any other account of causation, even if causation is not a fundamental property of nature.

Chapter 2

Orthodox dispositionalism on laws of nature and causation From the early 1980’s on a rival metaphysical account to standard Humeanism as presented by Lewis has gained more and more adherents. Based on an article by Sydney Shoemaker (1980) the view has been propagated that the properties in the world are not merely contingently arranged in space-time, but rather that they have characteristic powers that determine the causal and nomological behaviour of objects in a necessary way. In acknowledging necessary causation and laws of nature, Shoemaker’s position represents a metaphysical account that is incompatible with the Humean commitment to pervading contingency in nature. In what follows, such views are referred to as dispositionalist ontologies or power ontologies, powers being the ontological features that determine a property’s dispositions. This chapter proposes an analysis of dispositionalism in its different versions and its conceptual connections with notions like necessity, intrinsity, and in a second time with the notions of counterfactuals, laws of nature and causation.

2.1

The ontology

Shoemaker’s properties are identified via the functions they have in nature. Thus, the property of charge is identified via the causal features this property has, corresponding to what we know from physics about charge. To be identified through functions does not restrain the reality of a dispositional property (see Martin & Heil 1999, 53). Moreover, from an ontological point of view Shoemaker claims that all there is to the charge property are the powers that give rise to properties of other objects. Properties for Shoemaker are identical with their functions in nature. They link sets of characteristic causes and effects to their underlying powers (see Shoemaker 1980, 114). Only the second thesis is straightforwardly anti-Humean. Humeans also identify fundamental properties via physical theories. For Lewis fundamental properties are those

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that correspond to the simple predicates in the axioms of our best descriptive systems. Those axioms might be interpreted as functions as well. Humeans object to the view that the identity of fundamental properties is nothing over and above the functions of properties. Dispositionalists hold that properties cannot be distinguished in another way than by the set of characteristic effects they give rise to. These effects do not have to be manifest all the time. They may be considered as mere possibilities in case the disposition is instantiated in inappropriate circumstances. In general, dispositionalists claim that functional properties are sets of characteristic potential causes and characteristic potential effects. Nevertheless, these properties are natural properties and therefore perfectly actual even if the physical behaviour of things they determine is not actually instantiated in the world. Characteristic potential causes therefore come together with appropriate circumstances under which the property is instantiated. In this sense, dispositional properties do not have to be manifested all the time, but if they are, they are necessarily manifested.

2.1.1

Metaphysical necessity

The necessity at work is stronger than the nomological necessity in Humeanism. It is a metaphysical necessity. Under the assumption of determinism (i.e. that the laws of nature do not contain probabilities) the instantiation of a certain set of manifestations M could not have been different given the instantiation of a dispositional property D where M is the set of all manifestations of property D. In other words, it is not possible that in certain circumstances of certain possible worlds D is instantiated and gives rise to manifestations M 0 such that M , M 0 . For D to give rise to M it has to be instantiated in appropriate circumstances C (that may in some cases be empty). Given C and D, there is no possible world where M is not instantiated, nor is there a possible world where M is instantiated without the instantiation of C and D, because M defines D as just the dispositional property it is. An analogical reasoning in the field of formal logic is available: take C, D and M to be propositions. If and only if it is not possible to for the conjunction of C and D to be true without M being true and it is not possible for M to be true while the conjunction of C and D is false, the relation obtaining between the conjunction of C and D to M is called an implication. This is the semantic definition of the relation of impli-

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cation. Logical implication between two propositions A and B is equivalent to the claim that A is logically sufficient for B. Analogously, it follows that C and D together are metaphysically (or ontologically) sufficient for the instantiation of M. Moreover, the instantiation of C and D together is ontologically prior to the instantiation of M. In order to account for the instantiations of the properties C, D and M the set of ontological primitives only consists of the instantiations of C and D. The fundamental difference between dispositionalist ontologies and Humean ontologies is thus a difference in the extension of the set of ontological primitives. Whereas the Humean accepts the distribution of fundamental properties at the entire space-time as primitive the dispositionalist only accepts the distribution of fundamental properties at a proper subset of the entire space-time as primitive. The ontological priority of C and D over M is the priority of the causeevents over the effect-event, as the relation of C and D to M (i.e. the relation of the manifestation of a certain disposition) is an asymmetric causal relation. One can think of it as a “thick” causal relation of genuine production. Such relations are singular in the sense that for their instantiation the only elements of C, D and M suffice, unlike in the Humean case where causal relations have bigger supervenience bases. The supervenience basis of a dispositionalist causal relation has exactly the extension of the instantiation of their relata. Because the existence of a causal relation does not depend on other instantiations of properties that are not directly related by the causal relation, dispositionalist causation cannot be reduced to such external relations. It is a primitive, irreducible fact of the world. It is of course presupposed that the extension of the set of circumstances C is such that it does not comprise big or maximal environments of a given disposition D, but only local instances of properties in the neighbourhood of D. One particular way how the extension of C is restricted follows from the asymmetry of the causal relation and the ontological priority of the cause over the effect. First and foremost the causal relation is asymmetrical, because it is time-irreversible. The production of an event on the basis of another set of events implies an order of time. Both the disposition D and the circumstances C in which it is instantiated are temporarily prior to the instantiation of the effect M. As to exclude action at a spatio-temporal distance they are contiguous in

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space-time. Hence, the extension of C is restricted to the temporarily prior and contiguously neighbouring region of the manifestation M. For the dispositionalist it is a primitive necessary fact about the world that there exist causal relations. From conceptual analysis it follows that causation is an asymmetrical and irreversible relation. Causation is irreversible with respect to time. Therefore, the existence of causal relations implies the existence of a time order. The direction of time does not follow from the existence of causation itself (allowing for example for backwards causation). Imagine two deterministic worlds W1 and W2 consisting only of one disposition D that is manifested as M. From the identity of M follows the identity of D. The existence of the causal relation implies a time order. Suppose that W1 and W2 have opposed directions of time such that W1 is a world with normal causation and W2 is a world with backwards causation. Suppose, that is, that W1 and W2 are distinct. The difference between W1 and W2 is merely conceptual and not founded on any physical feature of both worlds. Their difference amounts to a primitive fact about what world happens to be picked out metaphysically. Dispositionalism generally tries to ban primitive identity features from ontology (see Bird’s discussion on haecceitism and quidditism in his 2005b, as well as chapter 3.2.2.5). Let us therefore assume that for the standard dispositionalist there is no metaphysical feature that distinguishes the two worlds from the point of view of time directions. This means that on standard dispositionalism the direction of time corresponds to the direction of causal determination. Primitive causation comes with a causal theory of time and backwards causation is conceptually excluded as a genuine physical possibility.

2.1.2

Defining dispositionalism and categorialism

Standard dispositionalism holds that every fundamental property is dispositional insofar as it has a causal impact in the world. Every fundamental property instance is hence the manifestation of a certain dispositional property D. The set of property instances that constitutes the state of the world at a given time t0 is the set of manifestations of a certain set of dispositions at time t, where t0 immediately follows t. From an ontological point of view the set of property instances at time t is ontologically sufficient for the set of property instances at time t0 . Under the assumption of determinism, it is sufficient to take the initial

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state of the world (the set of property instances at time t0 ) in their particular arrangement under initial conditions, in order to account for any subsequent state of the world at any time tn later that t0 . Any subsequent state follows necessarily from the initial set of primitives and their particular arrangement. The identity of initial states makes for the identity of possible worlds. For the dispositionalist, the set of ontological primitives contains a smaller number of elements than the set of primitives of the Humean. In turn the dispositionalist accepts primitive productive causation integrated in the form of powers to bring about different property instantiations, a claim the Humean rejects. Note that under the assumption of determinism any two worlds are identical that have a state of the world at the same time in common. Both, for example, the final state of the world or the actual state of the world suffice to unambiguously identify possible worlds. It is, however, not a mere matter of convention that we privilege the initial state of the world as forming the set of ontological primitives, because the initial state is the only world state that determines all the others. Humeanism and dispositionalism offer different metaphysical interpretations of the nature of properties. They leave aside the question what kinds of properties are actually instantiated at our world (the latter being a question of scientific investigation). The following discussion focuses exclusively on fundamental properties unless specified otherwise. A property is fundamental if and only if it does not supervene on a single or the arrangement of several other properties (supervenience being a relation of synchronic existential determination). In the framework of physicalism that is adopted here fundamental properties are expected to be physical properties. Actual candidates for fundamental physical properties are mass, charge and spin among others. Both the physicalistic Humean and the physicalistic dispositionalist agree on the fact that ideal physics will pick out the fundamental properties with its fundamental concepts. While the Humean claims that fundamental properties are categorical in nature, the dispositionalist conceives them as being dispositional. Let us define a property P as categorical if and only if the causal role it plays (provided it plays a causal role at all) depends on instantiations of other properties than P. It follows that a change in these property instantiations may result in a change of the causal role of property P. That is to say that a property P can play

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a causal role R in a world W and a causal role R0 in a world W 0 , such that R , R0 and W , W 0 . Inversely, a property Q is dispositional if and only if the causal role it plays depends only on the instantiation of Q. Note that along this definitions, the causal role a categorical property plays is contingent on what other properties are instantiated in the world, whereas dispositional properties have their causal roles wholly determined by themselves. One can translate this fact by attributing essential causal roles to dispositional properties (see Bird 2005b, 438 and Bird 2007, 514). Ontologies may be defined as categorical or dispositional on the basis of their properties. Lewis’s fundamental physical qualities are categorical properties for they only play a causal role in virtue of the fact that they are part of fundamental and sufficiently widespread regularities. Causal relations supervene on the distribution of fundamental properties in the whole of space-time (see chapter 1.4). On a dispositionalist ontology causal relations only supervene on the disposition D, the circumstances C under which it is instantiated and the manifestation M. Note that the definition allows for mixed ontologies with both dispositional and categorical properties on the price of a different metaphysics of causation for the two kinds of properties. Ellis (2001) presents such a mixed ontology, but accords no causal roles at all to categorical properties, thus strictly falling short of our definition (for another mixed approach see Molnar 2003). His categorical properties are edge cases and might be called categorical by default (certainly they are non-dispositional). It is important to note that to qualify an ontology as Humean is not equivalent to qualify it as categorical (Armstrong 1983, for example, defends an anti-Humean categorialism). Humean ontologies form a subset of categorical ontologies. What turns a categorical ontology into a Humean ontology is the additional commitment to the thesis that there exist only first order fundamental properties. Armstrong recognises both first order intrinsic categorical properties (universals) and second order extrinsic categorical properties (universals) relating them as fundamental. These second order relations have primitive modality in that they install a dependency of nomic necessitation between the related property instances. Hence, laws of nature do not supervene globally (as in Humeanism) and violate the Humean credo that distinct existencies are not necessarily connected. Nomic necessitation relations are sufficient to qualify an ontology as anti-Humean, even though they seem to be contingent from a metaphysical

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point of view. First order properties (universals) have their causal and nomological roles determined by second order relations (universals). Therefore, they are not dispositional properties. Second order relations of nomic necessitation are not sufficient by themselves either to determine their causal roles. In fact, in being second order properties, the relations of nomic necessitation are not adequate candidates for causes at all, as causes are usually conceived as first order properties. In contrast with the second order necessary relations that the dispositionalist recognises, those of the categorialist are external relations that do not supervene on the properties of the relata. They are ontological surplus. The anti-Humean categorialist takes the distribution of the first order properties and the second order properties at the entire space-time as ontologically primitive. By the preceding definition, they are both categorical. The categorical/dispositional distinction is exclusive for properties playing a causal role. The definition of categorical properties makes use of a proviso excluding “inert” property types. Causally inert properties are commonly regarded as obsolete for the following reason: two worlds that are strictly identical in their arrangement of properties, but one of which contains additional, causally inert properties are not distinguishable by physical means. As before, a purely metaphysical distinction between physically identical worlds is considered by the dispositionalist as philosophically idle. Moreover, from a dispositionalist point of view a property that does not potentially play a causal role is an undefined object. Therefore, one can consider properties that have no potential causal roles at all as edge cases and as categorical by default. Causally inert properties may be excluded from ontology by adopting the following principle: “Everything that exists makes a difference to the causal powers of something” (Armstrong 1997, 41, who calls it the Eleatic Principle). Hence, what does not make a difference in the causal (or dispositional) makeup of the world does not exist. The dispositionalist holds that every property that exists in our world is a power identified by the specific manifestations it gives rise to. What does not give rise to any causal manifestation cannot be identified as a property and therefore is not to be regarded as a property at all. The identity criterion of dispositionalist properties conceptually entails the Eleatic Principle. Nothing commits the Humean to subscribe to the Eleatic Principle. One can think of a point-sized, fundamental quality that does not make any potential causal (i.e. no counterfactual) difference in the behaviour

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of the world. The Humean can, however, adopt the Eleatic principle, as Lewis does, when he admits only perfectly natural properties in his basic ontology (Lewis 1986b, ix - x) and natural properties are those identified by the axioms of fundamental science (1983a, 367-368). No causally inert property could be identified by science. The adoption of the Eleatic Principle also cuts short Humean attempts to include dispositional properties in their ontology that need a distinct categorical basis to be instantiated. Such properties are doomed to be epiphenomena (see Prior, Pargetter & Jackson 1982), because they fall short of Kim’s causal exclusion principle (see Kim 1998 and 2003 for an analogous case in the field of mental properties). Adopting the Eleatic Principle for a class of properties is incompatible with epiphenomenalism of the same properties. In any case, dispositional properties that need a distinct categorical basis to be instantiated are not pertinent to our discussion, because they lack fundamentality. In their standard versions, Humeanism and dispositionalism both claim that fundamental physical properties are intrinsic. Remember the definition of intrinsity from the previous chapter. A property is intrinsic to an object if and only if the having of the property is independent of accompaniment and loneliness with regard to properties of other objects (see Langton & Lewis 1998). Humean qualities and dispositions are intrinsic for different reasons. Lewis’s Humean supervenience defends an atomistic ontology composed of point-sized objects that instantiate local physical qualities. No fundamental physical relations exist (only geometrical relations between space-time points). Every physical relation supervenes on the mosaic of point-qualities, in particular causal relations. Each point-quality instantiated at a space-time point or point-sized bit of matter is intrinsic, because it is not dependent (qua being related to) on the existence of properties of other objects (the potential relata). Lewis’s fundamental qualities are ontologically self-sufficient.

2.1.3

The intrinsity of dispositions

Dispositionalists, however, recognise fundamental physical relations, namely primitive causation. Still the fundamental dispositions are conceived as intrinsic. The main reason in favour of intrinsic fundamental dispositions stems from an analogy with macro-dispositional properties. Dispositional properties

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of macro-objects, like a glass’s being fragile, are intrinsic because the having of property F (being fragile) is independent of the fact whether it is instantiated in such circumstances C as to manifest itself as S (shattering). F is intrinsic because its having is independent of the accompaniment and loneliness of the instantiation of the manifestation M (see Martin 1997, 203-204), which in turn depends on the instantiation of the appropriate circumstances C. But intrinsity does not seem to be pervading as in the Humean case. Manifestations themselves, for example, are metaphysically necessitated by the disposition and the appropriate circumstances. Hence, they could not have occurred without their occurrence. They are dependent on their accompaniment and are therefore extrinsic properties. Every dispositional property instantiated at our world is, according to dispositionalism, itself the manifestation of another set of property instances that precedes it. This is valid for every property except of course for the non-preceded dispositions of the initial state of the world. Dispositionalists hold that it is a contingent matter what properties are instantiated in the world. There might be a world composed of alien properties or the same properties arranged differently at the beginning of the world. There might also be a world, where a property that is always the manifestation of a disposition in our world, belongs to the properties of the initial state. If this scenario is metaphysically possible for a given property, then this property is not dependent on the existence of a preceding disposition and is not extrinsic with respect to that property. Insofar as the initial arrangement of properties is contingent, these properties are not dependent on the accompaniment of specific circumstances either. Thus, it is not possible to think of dispositional properties as extrinsic with respect to preceding or simultaneous properties, if there is an initial state of the world composed of dispositional properties. But is it possible to think of dispositional properties as extrinsic with respect to subsequent properties? Dispositionalists presuppose that, by analogy to macro-dispositional properties, fundamental dispositional properties are intrinsic because the may remain unmanifested. The notion of a fundamental unmanifested disposition proves to be problematic. Assume for the following argument that the manifestations of fundamental dispositions do not depend on circumstances C (i.e. let C be empty). Let us grant the metaphysical possibility of unmanifested fundamental dispositions in a world Wu . Let us also grant the metaphysical possibility of a world without unmanifested fundamental dispo-

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sitions Wm . Call the adherent of the view that we happen to live in a world like Wu a Dispu and similarly call a Dispm someone who believes we live in a world like Wm . Imagine the following worlds W1 the actual world except that actual charge is augmented to schmarge, including the disposition that like charges very rarely do nothing at all (instead of repel) W2 the actual world except that there are no unmanifested fundamental dispositions Suppose that the very rare case in W1 never manifests itself (that is, W1 is a world like Wu ). For a Dispu W1 and W2 are possible worlds. The first is possible if it is a contingent matter what kind of properties form the initial set of fundamental properties in the world, the second is possible if it is a contingent matter whether or not we live in a world with unmanifested fundamental dispositions. Schmarge is different from charge, because their causal roles are different despite the fact that there is no difference in the particular manifestations they give rise to in our sample worlds. The actual causal relations between the objects of both worlds are exactly the same, yet they can be distinguished by the metaphysical set-up of their properties. In the manner of W1 other possible worlds can be constructed that are not physically distinguishable from W2 . There is a brute metaphysical fact about the difference between W1 and W2 . This difference between worlds can be quantified by the number of unmanifested fundamental dispositions. For a Dispu the number of possible worlds that are physically indistinguishable, but still metaphysically distinct from W2 is the cardinality of the number of unmanifested dispositions she is prepared to admit. Let us assume for the moment that purely metaphysical distinctions between physically identical worlds are to be avoided in metaphysics (reasons for this claim are given in chapter 3.2.2.5). There are two objections to the claim that W1 and W2 are physically identical and metaphysically distinct that cross the mind. First, world W1 might be distinguished from W2 through the fact that they make true different counterfactuals. Second, the argument is only valid, if there are types of unmanifested dispositions, whereas the Dispu is only interested in tokens of a given type that remain unmanifested while other tokens of the same type manifest themselves in bringing about an effect.

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The first objection holds that the difference between charge and schmarge entails a difference in counterfactuals and that a counterfactual difference between worlds is a physical difference between worlds. We agree with the first part, but contest the second. For hermeneutical reasons let us adopt standard counterfactual semantics (as proposed in Lewis 1973 and outlined in chapter 1.4.2) and let us thereby assume that such hermeneutics are also available to the dispositionalist (nothing substantial turns on that point). Now, a difference in counterfactuals is a difference in the order of possible W1 -worlds and possible W2 -worlds. Of course, if one does not want to be a realist about possible worlds, such a difference implies that W1 and W2 are themselves distinct (what they are). Nevertheless, this distinction is not necessarily one between the actual causal relations instantiated at these worlds. As in our case, it may be a distinction between merely possible causal relations. A purely metaphysical distinction distinguishes identical arrangements of physical relations via the kinds of properties their underlying objects instantiate. Therefore, W1 and W2 show a purely metaphysical difference. Their difference is merely a non-actual, counterfactual one, because the truthvalues of counterfactuals do not supervene on the distribution of actual physical properties. Non-actual differences are not physical, but nomological or metaphysical differences. Besides that point, we cannot answer the question unambiguously whether we live in W1 or in W2 . There is no actual physical evidence to settle the question. The second objection says that the kind of pure metaphysical distinctness the Dispu is confronted with is not bothering, because there is no reason to be a Dispu . The distinction between Wu -worlds and Wm -worlds concerns types and not tokens of properties. The dispositionalist only claims that there are tokens of fundamental physical properties that may lack manifestations. She can grant that there is always a token of the same type that actually manifests itself. The choice between being a Dispu or a Dispm is not exclusive, because it is not the pertinent choice to make. This line of argumentation makes the controversial assumption that in such a situation we can nevertheless subsume manifested and unmanifested tokens under the same type of property. But dispositionalists only give us one criterion of property classification at hand, namely a similarity in their manifestations. Hence, a difference in manifestation (and one might take the absence and presence of manifestations to be a difference) makes for a difference in types. In ontological terms, it is of course the case that

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a macro-disposition may remain unmanifested (think again of the fragile glass). Nevertheless, an object can be safely said to instantiate the relevant property, because it is similar to other objects whose relevant property has manifested itself. What is similar, however, is the composition of the constituting objects with their lower-level properties (think of the molecular composition and its properties). Such underlying properties are already less likely not to manifest themselves. The present case discusses fundamental properties. There is nothing underlying a fundamental property that could possibly make for the similarity of its bearer with others, if the property is unmanifested. There is no reason to attribute such a property instance to one kind rather than to another. Therefore, in case of fundamental properties the choice between being a Dispu and being a Dispm is exclusive. Indeed, dispositionalists may find it hard to believe that properties like schmarge are instantiated in our world. They might want to commit themselves to be Dispm and exclude the possibility of unmanifested fundamental dispositions. In other words, they believe that fundamental dispositions necessarily manifest themselves. But then the instantiation of a disposition is not independent of the instantiation of the manifestation it brings about: it must be accompanied by its manifestation. Therefore, if the dispositionalist wants to avoid the metaphysical possibility of worlds like W1 and its problems, the fundamental properties are to be extrinsic. Even if the way in which these properties are extrinsic is not the standard way in which, for example, the relation of being bigger than is extrinsic, intuitively permanently manifested dispositions lack a sort of independence that makes their behaviour similar to that of relational properties.

2.1.4

Variations of dispositionalism

Still, dispositions as fundamental intrinsic properties, that give necessarily rise to specific manifestations are the common ground of the dispositionalist metaphysics. There is, however, considerable variation inside the dispositionalist camp to spell out a metaphysics of fundamental dispositional properties. Dispositionalists currently defend the following positions: – Properties are dispositional and categorical/qualitative at once. This position is defended as the limit view (Martin 1997, 201-205, Martin & Heil

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1999, 47-48, Heil 2003, 111-115) and as neutral monism (Mumford 1998, 192-195, Kistler & Gnassounou 2007, chapter 4). – Properties are actual powers to bring about specific effects. The specificity of the effects is the essence of a property. This position is known as dispositional essentialism (Harr´e & Madden 1975, Shoemaker 1980, Mellor 2000, Bird 2005b, 437-443, Bird 2007, 514-515). We have defined categorical and dispositional properties according to their capacity to play causal roles by themselves. While categorical properties play causal roles in virtue of the arrangement of properties other than themselves, dispositional properties play causal roles solely in virtue of their instantiation. This definition is exclusive for causally efficacious properties. Hence, the first position as it is formulated here conflicts with our definition of dispositional and categorical properties. In other words, Martin’s and Heil’s dispositional/categorical distinction cannot be one that cashes out a difference in the way they play their causal roles (this point is also made by Bird 2007, 514-515). There are two options to interpret Martin’s and Heil’s distinction. Either the distinction is taken to be one situated at the conceptual level, such that their thesis merely maintains that dispositional as well as categorical predicates have universal applicability (an option promoted by Mumford 1998, 193). Or, what seems to be suggested at some places by the authors themselves, for a property to be categorical or qualitative simply means that it is an actual and real property of the world (Martin 1997, 203 and Heil 2003, 97-120 where he contrasts his view with the position that dispositions are pure potentialities). The first thesis is not apt to settle the debate between Humeans and dispositionalists, because one can both be a Humean and accept universal applicability of dispositional predicates (that will be shown in chapter 2.2.1) or be a dispositionalist and accept universal applicability of categorical/qualitative predicates. In addition to the limit view Heil defends the claim that our practice of predicate ascription does not permit us to read off what kinds of properties exist in the world. He rejects a correspondence principle between predicates and properties (a principle he calls the picture theory of representation, 2003, 26-27). Together with the claim that we can truly ascribe dispositional and qualitative predicates to the objects and properties instantiated at our world it follows that from this practice we are not allowed to infer to the existence of these two

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kinds of properties. If we accept the dispositional/qualitative distinction to be conceptual together with rejection of the picture theory, it is at least problematic to maintain a realist position concerning dispositional and qualitative kinds of properties (see Freland 2006). Heil claims to be a dispositional as well as a qualitative realist. But there seems to be only one realist criterion left while rejecting the picture theory, namely that there is a truthmaker for the dispositional and qualitative predicate ascriptions. This is problematic to accept for a full-blooded realist as it amounts to a neutral monist position (see Sparber 2007, 305). According to the second interpretation, dispositional properties are real, actual and concrete properties in the world. Thus, according to the second interpretation the distinction between dispositional and categorical/qualitative does not amount to the distinction between purely potential, conditional properties and fully actualised and concretely existing properties. Remember that the metaphysical discussion between Humeanism and dispositionalism has as an object the fundamental physical properties constitutive of our world. They are the sparse properties that make for the physical similarity and dissimilarity of objects. In being physical they are concrete properties that exist in the world. In playing causal roles they are actual, their causal role being the only feature of the property that may remain purely potential. The power defined by the causal roles it plays (i.e. the manifestations it characteristically gives rise to), however, is an actually instantiated property. This much being granted to the dispositionalist, the second interpretation of Martin’s and Heil’s categorical/dispositional distinction proves pointless from a metaphysical point of view. Neutral monism agrees with the claim that the dispositional/categorical distinction is in the first place a conceptual distinction. Both kinds of concepts are truly ascribed to object and property instantiations in the world. According to neutral monism they apply to one and the same kind of properties (monism) the nature of which cannot be stated in terms of dispositionality or categoricity (neutrality). One aim of a metaphysics of nature, however, consists exactly in the examination of the nature of fundamental properties. Since the conceptual distinctions of the limit view and of neutral monism do not have the potential to formulate the problem from an ontological point of view, there are attempts in literature to define dispositional and categorical properties in another way.

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These form the second class of positions (defended for example by Shoemaker and Bird) where dispositions are coarsly defined as actual powers that bring about specific effects. The latter constitute a property’s essence. The definition of dispositional properties presented here conforms to their project. Dispositional essentialism is the claim that properties have their causal roles essentially (see Bird 2007, 515). The causal roles a property plays could not have been different. In a world that only consists of one dispositional property D, this property still plays the characteristic causal roles that it would play were it instantiated as part of a larger arrangement of property instances. There is no external factor to determine a property’s causal roles. Hence, the causal roles a property plays are entirely determined by and depend on the kind of property in question that is instantiated. Therefore, dispositional essentialism implies that there are occurrences of dispositional properties according to our definition presented above. If there are properties with causal roles that are entirely determined by and depend on the instance of the property itself, these causal roles could not have been different leaving the property unaltered. The only way to change the causal roles of a property is to change the property itself. Hence, for dispositional properties according to our definition, their causal roles are essential. There being dispositional properties in this sense implies that essentialism is true. Categorical properties having their causal roles inessentially cannot determine their causal roles by themselves and if they cannot determine their causal roles by themselves these roles are determined by or depend on instances of other properties (provided they have causal roles at all). In turn do properties whose causal roles depend on instantiations of properties other than themselves not have their causal roles necessarily or essentially. Again, the definition in terms of determination and dependence implies the definition in terms of essence. I take it to be an advantage of the former to be more explicit in analysing the meaning of essentiality. Standard dispositionalism claims that every fundamental property is dispositional, whereas standard Humeanism defends the thesis that every fundamental property is categorical. Note that in order to refute Humeanism it is sufficient to show that there exists one fundamental physical property that is dispositional.

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2.1.5

The ontology

The prima facie plausibility of dispositionalism

As a rival metaphysical position to Humeanism, dispositionalism has first of all to prove its prima facie plausibility. The following plausibility problems have been raised against dispositionalism: – Dispositionalism never surmounts potentiality and never catches actuality (Armstrong 1997) – Dispositionalism leads to a vicious regress (Psillos 2006) The first argument is called the ‘always packing, never travelling’ argument, following Armstrong’s claim that all fundamental properties being dispositions of objects is analogous to “[...] particulars always re-packing their bags as they change properties, yet never taking a journey from potency to act” (1997, 80). The idea is that if dispositionalism is true for all fundamental properties in the world, then once a disposition manifests itself as a particular effect, this particular itself is nothing, but a potential to be manifested as yet another effect, etc. The argument presupposes that being a dispositional property is incompatible with being an actual, concrete property. The motivation for this presupposition resides in the Humean tradition to analyse dispositional predicates in purely counterfactual terms. If the meaning of a dispositional predicate is exhausted by what an object that instantiates the corresponding property would do, were it placed in such and such conditions, then it is describing a merely potential behaviour of the objects instantiating dispositional properties. Only if the mere potentiality of dispositional predicates is projected to the ontological level of properties is there a reason to claim that dispositional properties never get into a status of full actualisation. There are two reasons against this conclusion. First, an analysis of dispositional predicates by means of counterfactuals does not necessarily lead to anti-realism concerning dispositional properties (this will be shown in the next section). The counterfactuals can have dispositional property instances as their truthmakers. The dispositionalist is not committed to consider these property instances to be themselves conditional properties. They can be fully actual in nature. Therefore, an effect might be only potential as long as the dispositional property instance that is its cause lacks accompaniment of the appropriate circumstances. Once these are instantiated the effect is also instantiated and fully actualised, bearing, however, intrinsically the potential to bring about further

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effects. Second, the definition of dispositional properties that is propagated here is based on the particular metaphysics of causation they come together with. Whether they are actual properties or merely conditional properties is an independent question. The fact that dispositional properties do not necessarily manifest effects (i.e. that they do not necessarily instantiate causal relations) has no implication to the state of actuality they have themselves. Second order causal relations between property instances may be merely potential, while the underlying first order property instances are fully actualised once they are instantiated. The dispositionalist is hence free to conceive the fundamental physical properties that are effects of a manifested disposition as actual ways the world is. The second argument is distinct from the first in that it does not question the status of the dispositional effects (i.e. the manifestation), but rather the status of the cause (i.e. the disposition) itself. What are disposition or what do they do when they are not manifested (the question is thus put in Psillos 2006)? The dispositionalist might answer that they are nothing but the potential to bring about a certain effect. They are, in other words, directed towards the manifestation of a particular effect. Either, says Psillos, this directedness of dispositions is itself considered to be a disposition, namely the disposition to be directed to their manifestations, even if the latter do not occur, or it is not a disposition and then dispositions are not fundamental (see section 2.2). Dispositionalism is of course only open to the first horn of the dilemma that seems to point to a vicious regress from dispositions for directedness to dispositions for dispositions for directedness, etc. Standard dispositionalism of the essentialist flavour stops the regress by admitting primitive modal essences at the fundamental level (McKitrick 2003, 366). There is no regress because the dispositions of fundamental objects are just primitively directed to manifestations. This point is, depending on the preferences of the debater, either non-problematic or completely opaque. In any case there is no straightforward way to compare the intuitiveness of the ontological primitives admitted into one’s ontology. Another way so far not cashed out by dispositionalists against the vicious regress objection is the following. The literature on the metaphysical debate about the prima facie plausibility of dispositions often mingles two important kinds of dispositions: macrodispositions and fundamental dispositions. Macro-dispositions like the fragility

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of a glass can undoubtedly remain unmanifested. They do not face the viciousregress objection directly, because the disposition in question and its directedness are very complex states composed of simpler and more fundamental elements. A property like the fragility of a glass does not face the vicious-regress objection if its composing properties do not run into the same objection. The vicious-regress objection is hence to be settled at the level of fundamental properties. At the fundamental level, however, we have candidate-properties from actual physics that might be dispositions and have primitive modal essences and directedness towards manifestations: we have charges manifesting their dispositions in being attracted by opposed and repelled by like charges, etc. In an earlier discussion of this section there has been given independent metaphysical argumentation why a dispositionalist should not believe in fundamental unmanifested dispositions (they lead to primitive facts about the identity of worlds that should be avoided as claimed in chapter 3.2.2.5). The shortest answer to the question what dispositions do when they are not manifested is thus: there are no fundamental unmanifested dispositions. The primitive modal fact about fundamental dispositions is that they are sufficient to instantiate a causal relation by themselves and in a necessary way. There is no point in analysing their directedness independently of an actual causal relation with an effect. If this claim is accepted dispositionalism does not face the prima facie implausibility of leading to a vicious regress or being incompatible with the actuality of properties. Moreover, important work has been done to show that dispositionalism is a conceptually consistent metaphysical position in that dispositions do not necessarily need non-dispositional bases (McKitrick 2003 and already Blackburn 1990). There is nothing logically inconsistent with the idea of fundamental (and hence ungrounded) dispositions. In comparison with Humean orthodoxy purely conceptual arguments or even logical considerations do not have the potential to decide the matter. Let us assume from now on that dispositionalism provides a coherent conceptual framework for a metaphysics that challenges Humean orthodoxy. One class of highly debated conceptual arguments between dispositionalism and Humeanism deserves discussion though, namely the specific ways the two rival positions semantically account for dispositional predicate ascriptions.

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2.2

The conceptual level of dispositional predicates

2.2.1

Semantic reductionism of dispositional predicates

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The semantic analysis of dispositional predicate ascriptions by means of conditional statements has a tradition in the philosophy of science that goes back to the logical positivists (mainly Carnap 1936 and 1937). With the possibility of a semantic analysis of dispositional predicate ascriptions by means of nondispositional conditional statements comes the possibility to eliminate dispositional properties from ontology, a process promoted by the adherents of Humeanism. For exactly this reason dispositionalists have shown principled hostility towards semantic reductionism of dispositional predicate ascriptions (for example Martin 1994 and Mumford 1998). There is a vast amount of literature on the adequacy of specific reductive accounts on dispositional predicate ascriptions from the 1990’s until 2003. Both the adherents and the opponents of semantic reductionism seem to believe in the importance of the debate, because of the following reasoning: (1) Dispositional concepts can be truly applied to the world. (2) The meaning of dispositional concepts is exhausted by an appropriate analysis in terms of counterfactual relations. (3) The relata of these counterfactual relations are not dispositional concepts themselves. (4) Therefore, you can exhaustively describe the properties of the world by means of non-dispositional predicates. (5) It follows that dispositional properties do not exist in the world. In other words, semantic reductionism of dispositional concepts implies ontological eliminativism of dispositional properties. While Humeans attempt to show the adequacy of their reductive semantic approaches in order to get ontological eliminativism for free, dispositionalists try to show its inadequacy in order to avoid a knock down argument in favour of ontological eliminativism. Furthermore, the inexistence of an appropriate semantic analysis of dispositional concepts that can be truly applied to the world points to the existence of properties in the world that cannot be captured by non-dispositional concepts. They believe in the truth of the claim that semantic anti-reductionism of dispositional concepts implies ontological realism about dispositional properties.

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Think again of the concept . It is clear that the discussion between reductionists and anti-reductionists presupposes that dispositional concepts can be truly applied to the world (1). Were true application of dispositional concepts impossible, then ontological eliminativism would follow straightforwardly (an example is given by Churchland 1981 in the domain of conscious state ascriptions). Let us therefore suppose that a glass can truly said to be fragile. Premise (2) is obviously the most debated. Humeans believe in the adequacy of something along the line: a glass is fragile if and only if it would break, were it thrown out of a third floor window onto the street. Dispositionalists try to deny this. Both can agree that the concepts of breaking and being thrown out of the third floor window to the street are non-dispositional concepts. That is what the dispositionalist seems to acknowledge at least, when she tries to argue against (2). Let us therefore grant (3) for the moment. Now, if (2) were true, it would follow that a complete description of the glass’s fragility is available that does not use dispositional concepts. In other words, a complete non-dispositional description of the glass’s fragility is available (4). Does it follow from this that there are no dispositional properties in the world? Possibly, but not necessarily. There are specific accounts of semantic reduction that entail (5). If the analysis of a dispositional concepts involves the existence of a certain non-dispositional property that has a certain counterfactual behaviour, then obviously the subscriber to such an account is committed to eliminativism of dispositional properties. Lewis (1997, 157) defends such a view in saying that an object is disposed to a certain behaviour if and only if it has a certain intrinsic (supposedly non-dispositional) property B and keeps it for a given time as to show response r to a stimulus s (i.e. in more technical terms, that s and the having of B are a complete cause for the object to show response r). Other reductive semantic accounts by means of counterfactuals that do not mention the existence of non-dispositional properties in the analysans are compatible with dispositional truthmakers for the counterfactual statements. It is compatible with a counterfactual analysis of fragility – in terms of throwing and breaking – to consider the relevant feature of reality that distinguishes between the true and the false application of the concept as the dispositional property that is fragility (this point is made by Malzkorn 2000, 464467). In general, a reductive counterfactual analysis of dispositional concepts

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does not entail anti-realism about dispositional properties. (5) does not follow as a general conclusion. The dispositionalist can advance further, independent reasons to posit dispositional properties in her ontology. The ontological stigma is thus removed from the semantic enterprise to analyse dispositional concepts counterfactually. It is at least removed for the dispositionalist. Still, on the other side, the ontological stigma persists for the Humean. Should it not be possible to adequately analyse dispositional concepts with counterfactually related non-dispositional relata, then there might be reason to believe in the existence of irreducible (and hence fundamental) dispositional properties. Humeanism would be false. Therefore, we will examine in the following paragraphs the prospects of semantic reductionism of dispositional concepts in the lights of common inadequacy objections from the dispositionalist camp. In early attempts the logical positivists have analysed the meaning of dispositional concept through material conditionals. If an object x is thrown out of a third floor window to the street then, if x is fragile, it will break (examples along this line are given in Carnap 1936, 1937). The statement conditionalises over an object’s fragility, and therefore does not serve the purpose of being a definition of the term fragility. The purpose of an appropriate definition is rather to start from a given true dispositional predicate ascription and to give necessary and sufficient conditions to account for its meaning. An object being truly described by a dispositional predicate has something to do with the behaviour it displays in an actual or possible situation. Therefore, counterfactuals have emerged as the appropriate tool to account for potential behaviour in general (starting with Goodman 1965). The simple standard formulation of a counterfactual analysis of dispositional terms is the following: an object is fragile if and only if were it thrown out of a third floor window onto the street, it would break. Given standard possible worlds semantics for counterfactual statements, fragility can be safely attributed to a normal household wineglass.

2.2.1.1

Finkish dispositions

There is, however, fierce opposition against the claim that such analysis is generally valid (the line of defense follows Sparber 2006). Martin (1994 and later 1999) argues as follows: there is reason to postulate dispositional properties, because the most serious and common enterprise to reduce dispositional state-

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ments to classes of counterfactual statements can be discarded as inadequate. The task for those, says Martin, who set out to reduce dispositional statements is double. First to show that a counterfactual account is necessary and sufficient for dispositional statements, second to show that it is not dispositional properties that make true counterfactuals. Martin attacks the first point (the task of providing independent reason for or against dispositionalism will be tackled in the next chapter). The main point of criticism Martin advances against a counterfactual analysis is the case of finkish dispositions. Finkish dispositions are supposed to be counterexamples to the prevailing counterfactual accounts of dispositions. They are supposed to be dispositions that escape counterfactual determination. The most famous example is the following one: the wineglass is fragile (disposition), but each time fragility is about to manifest itself God intervenes and makes the glass lose its fragility. This refutes the first direction of implication between fragility (disposition) and its counterfactual analysans: (A) Fragility ⇒ x would break if it were thrown out of the third floor window onto the street (A) is false since the glass is fragile, but the counterfactual is false. For the second direction of implication consider the following slightly modified situation: imagine a God that each time a previously non-fragile thing (a tin cup, for example) is dropped he interferes and makes it fragile. Here we get the refutation of the implication from the counterfactual to the disposition: (B) x would break if it were thrown out of the third floor window onto the street ⇒ fragility (B) is false since the counterfactual is true, but the disposition ascription is false. Hence, counterfactuals are neither necessary nor sufficient to analyse dispositions. Since they are not further analysable in this way they must refer to something “of the kind” in the world, namely dispositional properties. There are a couple of options in the literature destined to answer Martin’s argument: (1) David Lewis (1997) and others (Malzkorn 2000 and Manley & Wasserman 2007 as well as 2008, for example) propose conditional analyses that are finkproof: Lewis excludes the loss of the pertinent property (the dispositional basis) during the counterfactual analysis, but this approach is open to new counterexamples (for example antidotes from Bird 1998). Malzkorn introduces formal normality constraints that seem to exclude finkish cases.

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Manley & Wasserman introduce a proportionality criterion for manifestations over pertinently varying trigger-situations. (2) Finked situations can be considered as bad or invalid counterexamples that, on a proper analysis, turn out to be mostly harmless: Gundersen (2002) and Cross (2005) favour this position, and in what follows I put forward a variant of their insights. For the one who thinks that examples of enchanted glasses are difficult to grasp, one can think of the more common tool of a circuit breaker. The disposition of a wire to let pass a current is finked each time current is actually present, because the circuit breaker prevents its passing (that is Martin’s example in his 1994). Nothing substantial turns on the choice of example. Therefore, let us stick to the fragility case. So God is responsible for the wineglass losing its disposition right at the moment the appropriate trigger conditions for its manifestation obtain. As we have seen the counterfactual in (A) is false. Other situations can be construed where the objects does not lose its disposition right at the moment of manifestation, but the disposition is masked by another one that annihilates its potential to manifest itself (think of an antidote to ingested poisons as promoted by Bird 1998, 2000 and Choi 2003). They share the commitment that the relevant counterfactual in (A) is false. More precisely, and presupposing counterfactual possible worlds semantics, there is a very (or sufficiently) similar world where the glass hits the street and does not break. Actually such a world would be exactly similar. Nevertheless, the dispositional statement “The glass is fragile” remains true. So at least says Martin. When the truthvalues of two different statements diverge, the meaning of their concepts cannot be identical. Hence, there are dispositional predicate ascriptions that are not accounted for by a counterfactual analysis. The case of finkish dispositions cashes out the apparent tension between a disposition’s actuality even if unmanifested and its pure counter-to-the-fact analysis through subjunctive conditionals. This tension is apparent because, as we have seen before, not the property itself (be it dispositional or categorical) is conditional or actual. On our account both dispositional and categorical properties are actual, concrete properties. What can be regarded as a conditional or counter-to-the-fact feature is only the relation between the property and the actualisation of its causal role. Therefore, the simple conditional analysis presented above (x is fragile if and

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only if it breaks if dropped) can only stand for the claim “x is fragile if and only if x is such that it breaks if dropped”. It refers to an actual way the object x is (i.e. to a physical property of x in the widest sense). In proposing a conditional or counterfactual analysis the Humean does not want to deny the existence of a property that is (part of) the referent of the concept fragility. She only denies that this property is dispositional. The counterfactual analysis serves the Humean purpose of analysing the meaning of dispositional predicate ascriptions without explicit recurrence to dispositional truthmakers. The analysis does only serve this purpose, because it comes together with specific Humean semantics for counterfactuals. The dispositionalist can, of course, propose different semantics or additional independent reason in favour of dispositional truthmakers. Still, for the Humean the success of a counterfactual analysis is more important than for the dispositionalist. How can then the problem of alleged counter-examples to the counterfactual analysis of dispositional predicate ascriptions be established? We have a situation of finkishness that is supposedly a metaphysically possible scenario. First let us state the two situations that one needs to compare: I The normal situation – The glass is fragile (= has disposition F). There is a set of conditions C (being thrown out of the third floor window onto the street) that is typically sufficient for his disposition to manifest itself as B (the breaking). – If C obtained, then F would manifest itself as B. II The finked situation – The glass is fragile (= has disposition F). There is no set of conditions C 0 that is typically sufficient for its disposition to manifest itself, because as soon as any set of conditions C 0 becomes sufficient for F to manifest itself as B, C 0 entails the loss (or the masking) of F and therefore the absence of B. – It is not the case that if C 0 obtained, then F would manifest itself as B, because C 0 entails that the glass loses F (or that the glass’s F-ness is masked). Such is the initial situation. But what does “typically sufficient” mean? In general it means to be often sufficient but not always. There are situations where it is not the case that C is sufficient for the glass’s fragility to manifest itself as B.

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Think of the following un-finked (therefore type (I)) situation: the glass is fragile, it is thrown out of the third floor window heading for the street and right at that moment two people carry a mattress beneath the window that safely catches the glass. Disposition F is still there but the manifestation B has not occurred, because of non-occurring but necessary physical contact of the glass with the street. What this is about could be called circumstances or context (see Mumford’s α-conditions in his 1996, 90-91 and Cross 2005). Circumstances are also conditions for F to become manifested as B, but they are conditions of another kind than C (or equally C 0 ). While the latter are properly called trigger conditions (appealing to causal sufficiency), the former can be qualified as background conditions commonly referred to as normality (basic necessary conditions). The most economic way of describing what we should consider as normal is a negative characterisation: the lack of interference that blocks the entailment connection between F and B given some conditions C. If we want to specify the content of this negative characterisation we should rather refer to sets of specific descriptions than to statistical normality (see Hauska 2008). In any case, if a situation is not normal there is blocking interference. This would qualify a fink as a sufficient feature to render a context abnormal, if added to a set of normal conditions. The context would contain an inconsistency in as much as normality is required for dispositional talk. Abnormality entails the emptiness of C 0 . But is it allowed to consider the fink as a part of the background conditions? Martin intends to take the fink to be part of the trigger conditions or the overall dispositional make-up F of the glass. In our formulation of the problem the fink cannot be part of the trigger conditions C 0 because C 0 is empty. The only way to conceive C 0 as non-empty is when one accepts that “typically sufficient” is compatible with the existence of some counter-fink that trumps over the initial fink in making the manifestation possible again. This is no viable solution, because the pair of fink and counter-fink causally neutralises itself. It is hard to see how to distinguish the result from a normal type (I) situation. There is also a problem to imagine how finks can be parts of the trigger-conditions if “trigger” is to mean something at all in connection with the respective disposition. What if the fink should be part of the glass’s overall dispositional make-up? What would the result-disposition R of disposition F be in presence of a “trumping” disposition E (the enchantment)? I claim that

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whatever R might be in detail surely it satisfies the predicate non-F. This is very intuitive in the example case. The enchanted glass is no longer fragile as there is no metaphysically possible way (remember that the relation is logical entailment) it could break (likewise the wire with a circuit breaker attached is not supposed to let pass current, although the wire itself is). The hidden premise of this claim is that in order to ascribe the disposition F (fragility) truly to an object x it is necessary that some R-similar (similar in what regards the having of the finked fragility) object really manifests F at least once. If no finked-fragile object ever could manifest fragility (because there is no metaphysically possible set of conditions jointly sufficient for this) we should not think that it is fragile. Or weaker: its fragility does not possibly matter. This means that the glass (I) is not similar to the glass (II) from the point of view of its dispositional make-up. It is possible, however, to hold an account of unmanifested disposition ascriptions that does not involve the hidden premise spelled out above. This matters when it comes to physically relevant properties. David Lewis’s account of laws of nature, for example, integrates unmanifested laws, but does not license the inference to unmanifested actual dispositions making them true. The truth of such ascriptions might not be determined by actual and unmanifested dispositional properties, but by the lack of instantiations of the corresponding properties in our world. Unmanifested laws are non-instantiated properties (more of that later). Admittedly, it is arguable that finks are (always) components of the dispositional make-up, but if they are not, they enter at least in the background conditions that are presupposed in any case of dispositional talk. In whatever way the preferences lie it follows from the above discussion that it is impossible that (a) a fink is truly ascribed to an object and that (b) the finked disposition does not behave correctly under counterfactual analysis. Thus the amended situation (II) is either: II’ The pseudo-finked situation 1: – The glass is fragile (= has disposition F). – If the situation were normal, there would be a non-empty set of conditions C 0 typically sufficient for F’s manifestation as B. If C 0 were a non-empty set of conditions C 0 typically sufficient for F’s manifestation

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as B, then F would manifest itself as B. This counterfactual is vacuously true, since a non-empty C 0 is metaphysically impossible. or: II” The pseudo-finked situation 2: – The glass is not fragile (= has disposition non-F). It’s having F is trumped over by the presence of the intervening God-fink, which makes it impossible for it to break. – It is not the case that if some triggering conditions for the breaking C (typically the ones from case (I)) obtained, then F would manifest itself as B, because the glass does not have F. Therefore, the case of finkish dispositions does not show that in principle a counterfactual analysis of dispositional predicate ascriptions is false. Simple counterfactual analyses have mistakenly been thought of as not involving circumstantial and background conditions (Mumford 1996 supports the view that dispositional predicate ascriptions come with implicit assumptions on the background conditions, 91-92). Note that no step of the argument depends on the supposition that dispositions could not be lost or gained in time (as postulated by Martin). Rather this view is adopted and constitutes a part of the premises. In a more general context Gundersen (2002) shows that finks and more recently antidotes are no engaging counter-examples to a counterfactual analyses, because they either disrespect a serious principle of object composition (x having F does not imply that x + y has F), or abuse to a certain point the counterfactual semantics. For valid counterexamples “[...] a scenario is called for in which the masker [fink or antidote] prevents the characteristic manifestation from appearing, not merely on some particular occasion, but in a systematic and non-accidental manner” (Gundersen 2002, 393). 2.2.1.2

A counterfactual analysis for all predicates

Besides this point there is a second objection to the claim that dispositional statements are typically analysed as counterfactual dependence statements advanced by Mellor (1974). His claim is inconsistent with Martin’s objection because it says that strictly anything that is a true factual statement, be it dispositional or categorical, can be appropriately analysed in terms of counterfactuals. The objection to counterfactuals is then (unlike in Martin’s case) that

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counterfactuals cover too many statements, especially not only dispositional ones. Mellor concludes to the exclusive existence of dispositional properties as the truthmakers for these counterfactuals (and thus meets with Malzkorn in uniting counterfactual analysis and dispositional realism). This is a deliberate choice that the Humean can also make in her favour. In any case additional argumentation is needed for such a decision. For Mellor there is no substantial difference between the following two statements where the first contains a dispositional and the second a categorical predicate: (1) ‘x is fragile’ entails ‘If x were thrown out of a third floor window onto the street then it would break’ (2) ‘x is triangular’ entails ‘If the corners of x were counted the result would be three’ There is, however, a difference (promoted by Mumford 1998) in that (1) is true with conceptual necessity, whereas (2) is only contingently true, because it depends on the laws of nature (that include most remotely the laws that govern our mental activities) whether the result after counting the corners of a triangle will be three. In stating that difference Mumford sees justification that there is a criterion to distinguish dispositional from categorical concepts. Neither the existence nor the non-existence of such a distinction on the conceptual level have logical implications on the ontological choice between dispositionalism or Humeanism. The Humean has the possibility to ontologically eliminate dispositional properties in the following way: the idea is to indicate an a priori semantic reduction from dispositional to categorical vocabulary. Propositions consisting exclusively of the latter have in turn only categorical (intrinsic or relational) truthmakers. This is sufficient to make the project eliminativist. Note that the project of ontological elimination via a priori intensional semantic reduction is different from the project of ontological reduction via a posteriori extensional semantic reduction. As an example for the latter, think of the case of the reduction of higher-level kinds. No intensional semantic analysis is provided, but only extensional bridge-principles can be identified a posteriori which opens the possibility of ontological conservative reductionism leaving the higher-level kinds their status as existing properties.

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2.2.1.3

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Ontological elimination of dispositions

The following is an outline of an eliminativist account in the first sense: dispositions are names for classes of counterfactuals. Counterfactual analyses are adequate and exhaustive to account for the meaning of those names. Such a reduction can be accomplished by an appropriate counterfactual analysis, according to the lessons learned from a seventy years old tradition working with reduction sentences from the simple conditional analysis (Carnap 1936 and 1937), Ramsey sentences composed of counterfactual relations (Mellor 2000), to more complex variants of the simple counterfactual analysis (Lewis 1997, Malzkorn 2000, Gundersen 2002). We only have to suppose that an analysis of dispositional concepts by means of counterfactuals can be adequate in principle. Counterfactuals are important as an expression of nomological status. Thus, laws and causal relations are typically more than simple actual truths and more than material implications are needed to acknowledge their status. Hence, dispositions can label laws and causal relations or even property instances that might (but did not yet) causally matter, insofar as they fall under laws. In any case it has already been shown elsewhere that the support of counterfactuals is an important feature of laws (see Van Fraassen 1989, chapter 2.4). Remember that on Lewis’s semantics it is an analytic truth that laws make the correspondent counterfactuals true. Laws might label types of causal relations in the sense that to support counterfactuals is widely accepted as a necessary condition for causation. Humean causation is supervenient on the laws of nature. Many laws of nature state causal dependencies between property types. In this sense common examples of dispositions are: – Fragility as the name for the law that in appropriate circumstances things of a certain molecular structure break when sufficiently struck, where sufficiency is thus specified that it does not render the statement circular. – Alcoholism as the name for the type of causal relation that humans are in such a condition (in the sense of a state) that they cannot resist to drink alcohol, as soon as they have the opportunity, that they feel nervous, sick, etc. when they lack the opportunity. – Mass conceived dispositionally (intended is rest mass, not relativistic mass) as the name for the law that describes the behaviour of things as regards their resistance to acceleration.

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The Humean can be a realist about dispositional properties only in the way she is a realist about causation and laws of nature. Dispositions are only global features of the world. Hence, dispositions qua properties of individual objects are eliminated. The mass case exemplifies well why many philosophers think of the fundamental physical properties as dispositional instead of taking them as properties governed by laws and dispositional concepts to name these laws. To the extent that properties fall under laws the latter can be called or classified by concepts that facilitate their usage in common and scientific language. Dispositions are supposed to be necessary by those who believe in their actual existence. This necessity is not metaphysical but conceptual. Fragility conceptually implies its counterfactual analysis, which in turn might well express relations or features of the world that have modal priority by being nomologically necessary. For the Humean nomological necessity is of course all that is available.

2.2.2

Counterfactuals for dispositionalists

For the dispositionalist the status of counterfactuals is merely heuristic. As we have seen before, it is a viable option to suppose the adequacy of a counterfactual analysis of dispositional predicate ascriptions. Both the Humean and the dispositionalist believe in the actuality of natural properties. Both believe that these properties have causal roles that might be conditional only: for the dispositionalist there are unmanifested dispositions, for the Humean there are uninstantiated laws of nature. Therefore, both should adopt a conditional or counterfactual analysis of dispositional predicate ascriptions. The Humean project is to eliminate dispositional properties. Therefore, it is necessary for her to come up with an appropriate Humean semantics for counterfactuals. The dispositional project is to show that dispositional property instances make true dispositional predicate ascriptions. Therefore, it is necessary for her that the occurrence or non-occurrence of dispositional property instances make for the truth or falsity of the corresponding counterfactuals. That does not seem to be a problem in principle. However, one can ask whether the idea of a necessary world as propagated by the dispositionalist is compatible with the idea of counterfactuals that suggests things could have been different in different circumstances. In other words, can a specific glass at a specific time truly be

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said to break were it smashed on the floor, when – determinism assumed – the states of the world are necessarily produced such that if you take the glass and put it in different circumstances you might change the whole state of the world in the past and future lightcone of the actual glass? Dispositionalism implies that you have different possible worlds only if you either take the actual fundamental properties at the beginning of the world and arrange them differently or under different initial conditions or if you take properties alien to our world and arrange them in whatever way you like. If the evaluation of counterfactuals involved alien properties, then it would imply realism about possible worlds, because the truth of counterfactuals would not supervene on the actual world only. What the dispositionalist needs are counterfactual situations with actual laws of nature. Laws describe what properties do which in turn is the properties’ essence. Actual laws of nature imply actual properties, because for the dispositionalist there cannot be alien properties governed by actual laws, nor can there be actual properties governed by alien laws. Standard counterfactual semantics, however, implies the existence of miracles (i.e. small local violations of laws of nature) for the implementation of the antecedent. Therefore, standard counterfactual semantics seems to need actual properties and alien laws of nature. The laws are alien if they are actual laws that cover the miracle as well (see also Schaffer 2005, 8). This violates dispositionalism (Armstrong 1999, 33-34 agrees). To construct counterfactual situations for actual happenings (like an actual glass) seems hopeless, when it has to be done by different arrangements of the properties at the beginning of the world or by adopting different initial conditions. Positing the glass that is actually in my hand, say, 1’000’000 years ago under a falling rock, involves complete back- and forth-tracking of the past causes and future effects of this event. It is hard to believe that such a situation could be construed. But maybe it does not have to. There is a third option for the dispositionalist to account for counterfactual statements. Remember that the Humean semantics for counterfactual statements involves the similarity between worlds as a whole. Even if only one specific event is under examination, the past and future history of the event enter into account as well. In fact it is advocated that they be identical across possible worlds. They cannot be left out, because the evaluation of counterfactuals depends on the actual laws of nature, and those in turn supervene globally on the distribution of property instances

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at the entire space-time. For the dispositionalist the situation is different. The past and future history of the event under examination does not play any role in the evaluation of the counterfactual statement, the only truth condition being the occurrence or non-occurrence of the dispositional property. The truth or falsity of counterfactuals can be determined locally. Hence, all global or general aspects (as the past and future history of the event as well as the supervening macro features of the event) can be abstracted. The mere ontological possibility must of course be given that the event in question has a past and a future history within the framework of actual laws and properties, but for the evaluation of the counterfactual it is not decisive. It does not have to be construed or made in any way explicit (whereas in the Humean case the laws are descriptive for the world history). Thus the existence of a handcrafted glass under a rock 1’000’000 years ago might be considered as philosophically idle or impossible, but note that for a Humean as well the existence of such a glass requires more than just a small local miracle. In other words, the alien Humean law that includes that miracle is very alien compared to standard cases. For the pertinent question how a glass – with its particular constitution – behaves, if put under a falling rock – with its particular constitution – the dispositionalist can account. This is a situation that can be tested for a particular kind of glasses. Test situations are essentially thus that they exclude circumstances that supposedly have no influence on the causal relation. They isolate and simplify systems by only admitting a limited number of objects and properties. Dispositionalists cannot cash out the ontological contingency of initial property rearrangements, but they also have the contingency of isolating objects and properties from their environment. More precisely, there are not two ways the dispositionalist has contingency entering her picture, but two different points of view on the same contingency. The first, of rearranging the beginning of the universe such that a certain test situation obtains is hopeless. The second, of presupposing a possible backtracking history of a given test situation without alien properties seems acceptable. No reasons come to the mind why a world where the actual glass slips through my hand and breaks on the floor should contain alien properties and laws of nature. They are actual properties and actual laws of nature. For standard scientific test situations the presupposition of having a past and future lightcone that only include actual properties and actual laws of nature seems acceptable.

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Again, how the exact property distribution in the lightcones of specific test situations looks like does not play any role in the determination of the truthvalue of the counterfactual. In general, semantics for counterfactuals do not necessarily need actual properties and alien laws of nature (as claimed by Schaffer 2005), because they do not need revert to the notion of miracles. Miracles are only an essential part in a Humean evaluation of counterfactuals. Counterfactual reasoning is hence available to the dispositionalist and to the Humean. Moreover, there are reasons that both should adopt a counterfactual analysis of dispositional predicates (the lack of pertinent counterexamples). That counterfactuals do not capture the essence of dispositional predicates, because the former refer to merely possible states while the latter refer to actual properties, is erroneous and misunderstands the fact that an appropriate counterfactual analysis of a dispositional predicate refers to an actual property and its merely possible causal role. If the Humean does not want dispositional talk to be flatly false, this holds for both the Humean and the dispositionalist. Martin claims that the Humean cannot account for the possible causal effects of a given property instance by itself (Martin 1994, 7). This is correct, but trivial, because it is restating the definition of categorical properties that constitute a Humean world. She does not want or have to. That does not undermine a counterfactual analysis of dispositional predicates as a consequence. By the Humean semantics for counterfactuals she undertakes a reductive enterprise for dispositional predicates and opens the way to an elimination of dispositional properties. By a different semantics the dispositionalist does undertake a non-reductive enterprise, while still accepting a counterfactual analysis of dispositional predicates. Moreover, there is no hindrance for the dispositionalist to have solely actual truthmakers for counterfactuals. The possible worlds that evaluate her counterfactuals can be conceived as being composed of actual properties and laws of nature alone, at least for standard cases. Hence, dispositionalists do not have to fear counterfactuals. They capture exactly the meaning of dispositional predicates. The question what makes true the counterfactuals must be settled separately. In Humeanism and dispositionalism the laws of nature have a central although different role in the truthmaking of counterfactuals.

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Dispositionalist laws of nature

Dispositionalist laws of nature

For the dispositionalist as for the Humean, laws of nature at first designate universally quantified statements about objects and their properties. They show logical dependence between predicates that refer to regular co-instantiations of kinds of natural properties. It makes for a law of nature that this dependence has modal priority over so-called accidental co-instantiations of properties. The modal priority of laws of nature consists in their reference to a kind of natural necessity. Humeanism only accepts nomological necessity for laws of nature (which is close to a triviality). Given the distribution of first order fundamental properties, necessarily, by supervenience, the second order nomological relations are determined. There is of course a metaphysically possible scenario, where the laws of nature are different. Nomological necessity is nothing over and above the fundamental contingent property distribution. The distinction between nomological and accidental regularities merely arises from systematic factors about the comparison of the theories those regularities are embedded in. Nomological necessity is weaker than and does not imply metaphysical necessity. In a Humean world there is no metaphysical necessity.

2.3.1

Strict laws of nature and ceteris paribus laws of nature

The dispositionalist ontology differs from the Humean in the following respects concerning ontological hierarchy and modality: Humeanism (at least Humean supervenience) takes the fundamental categorical property distribution as ontologically primitive and logically primary, the laws of nature as ontologically supervenient and logically secondary, truth determination for counterfactuals as ontologically supervenient and logically tertiary and truth determination for dispositional predicate ascriptions as ontologically supervenient and logically quaternary. The initial property distribution determines the laws of nature, which are necessary to evaluate counterfactuals that analyse dispositional predicates. Dispositionalism takes the initial distribution of essentially dispositional properties as ontologically primitive and logically primary, as well as the truth determination of counterfactuals and the laws of nature, while regarding the world history as a whole as ontologically supervenient and logically secondary. The initial distribution of properties determines as an ontological

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consequence the world history as a whole (the entire distribution of property instances with their essences). The essences of the initially instantiated dispositions determine the truth values of counterfactuals. The truthmakers of laws of nature are also the essences of the properties among which lawlike connection is stated. Let us suppose that the counterfactual analysis of dispositional predicates is correct. A dispositional predicate refers to a property D of an object x that behaves such that it would bring about manifestation M, when triggered by stimulus S in the appropriate circumstances C (a similar reasoning without taking circumstances C into account is made in Bird 2005a, 2-3): (CA) Dx ⇔ (S x & Cx) € Mx It follows from the truth of (CA) that always if D, S and C hold together, M must follow. In other words, it is not possible to have D, S and C without getting M as well. Hence, we have the semantic definition of an implication: (Dx & S x & Cx) ⇒ Mx As this is true for every object x, it is possible to quantify over the range of objects: (L) ∀x ((Dx & S x & Cx) ⇒ Mx) Universally quantified statements of the kind of (L) are normally considered to be laws of nature. Therefore, an appropriate counterfactual analysis of dispositional predicates allows to deduce laws of nature. It depends on the adequacy of (CA) whether the correct laws of nature result. (CA) has the advantage over the simple counterfactual analysis ((SCA) (Dx ⇔ S x € Mx)) that it does not fall short of counterexamples like finked dispositions or antidotes (see preceding section). In this sense, the universal laws of nature that follow from (CA) not only include strict, exceptionless laws, but also ceteris paribus laws. The difference between these two kind of laws depends on the extension of the predicate Cx, namely the circumstances in which the object x with disposition D undergoes stimulus S . Strict laws are such that the underlying dispositions do not depend on the occurrence of particular circumstances C to be manifested as M. For strict laws the counterfactual analysis simplifies to (SCA) and law statements take the simple form of (SL) ∀x ((Dx & S x) ⇒ Mx). Ceteris paribus laws are such that they do not always hold. They admit of exceptions.

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Exceptions of laws of nature are found exactly in case when an object has disposition D and undergoes stimulus S , but fails to bring about the manifestation M. It fails because the appropriate circumstances C do not obtain. There are four possibilities why this can be the case: (1) Normal macro laws of nature: take for example the case of the fragile glass (D) that is thrown out of a third floor window (S ), but fails to break (M), because it is accidentally thrown on a mattress lying on the street. Circumstances (C) specified for the disposition fragility certainly contain features like the existence of a continuous trajectory of the glass that meets with the street surface. If such a trajectory is absent, then in (CA), −(Cx) leads to −(Mx) and in (L), −(Cx) leads to −(Mx). Typically such cases of accidentally interfering external factors are rare compared with the normal situations (Bird’s antidotes rank among them). There are other cases, however, where interference from external factors are steady (take, for example, the law of free fall with the gravitational constant that presupposes vacuum conditions that almost never obtain within the atmosphere of the actual world except in specially set lab conditions). (2) Abnormal macro laws: in opposition to the previous case, abnormal macro laws designate processes with systematic interference resulting in a necessary prevention of the manifestation. Such are finkish dispositions (like the intervening God fink) that either imply impossible circumstances (that is, necessarily −(Cx)) or do not even licence the ascription of disposition D (one can argue that God’s glass is not fragile at all, see previous section). (3) Normal fundamental laws: fundamental laws that admit of exceptions strike us as improbable. Still there is no reason to rule them out on conceptual grounds. If they do not exist in our world, it is metaphysically cautious to take this as a contingent matter of fact. (4) Abnormal fundamental laws: nothing restricts the idea of finkish interference to the level of macro objects. God might intervene in preventing an electron of being attracted by a proton. If we suppose that our world is not governed by abnormal laws the extension of the set of circumstances under which x is instantiated (Cx) defines the following kinds of laws of nature:

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(Cx) non-empty: the circumstances can be non-instantiated, hence the law admits of exceptions: ceteris paribus laws (it is supposed that a (Cx) that specifies circumstances that are always met, can be left out of both (CA) and (L)) (Cx) empty: the circumstances cannot possibly influence the manifestation of the disposition, hence the law does not admit of exceptions: strict laws Fundamental physical laws like the laws of quantum mechanics or the laws of general relativity state dependencies among kinds of properties without reference to specific conditions for their manifestation. They have time- and spaceuniversal applicability and are good candidates to be fundamental laws of our world. Moreover, no actual candidate for a fundamental law is at hand that does only hold in specific circumstances. Let us therefore suppose that there are no fundamental ceteris paribus laws of nature. In other words, our fundamental laws are strict and only supervening macro laws include ceteris paribus clauses. At a more macroscopic level the special sciences abstract from fundamental physical facts in order to find macroscopic regularities grasped by functional concepts. The concept of a gene that produces red petals in roses, for example, is both a functionally defined concept and abstracts from such microphysical details as, for example, the exact quantum physical states that compose both the gene and the petals. By leaving aside compositional physical aspects and the specific fundamental physical circumstances under which a gene of a given kind is instantiated, the laws describing a gene’s behaviour admit of exceptions. One way one can think of these exceptions is as a result of finkish interference of some external physical factor (the contact with a DNA destroying acid, for example). An exact physical description of a situation including a finkish interference does not itself mention laws that admit of exception. To the extent that the laws invoked in a physical description or explanation of the situation are the fundamental physical laws they can be considered as strict laws. Hence, by abstracting from physical detail the special sciences and their object (macroscopic supervening properties) formulate laws that admit of exception and depend on a set of circumstances. They are called ceteris paribus laws, because they invoke a set of circumstances under which the law is supposed to apply that is held constant. Therefore, the laws of nature stated by the special sciences are

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not strict laws in principle. The distinction between strict and ceteris paribus laws is equivalent to the distinction between fundamental and supervening laws (at least for our world).

2.3.2

Probabilistic laws of nature

For the following discussion let us focus on laws of nature that do not need specific circumstances to be always true. In other words, let us focus on fundamental, strict laws in the framework of a simple counterfactual analysis of dispositions (SCA) and a simple account of laws (SL): ∀x ((Dx & S x) ⇒ Mx). Two possibilities for the stimulus S are at hand (analogically to the discussion of the circumstances C). Either the disposition D needs stimulus S to manifest itself as M or it does not need a stimulus S to manifest itself as M. If the disposition needs a specific stimulus to be manifested and if there are no particular circumstances necessary to the manifestation, then the existence of the disposition plus the stimulus is ontologically sufficient for the instantiation of the manifestation. Always and exactly when the former obtain, the latter follows as an immediate metaphysical consequence. It is not possible for the manifestation as an individual to remain uninstantiated. Therefore, the sequence of events (D & S at time t and M at time t + 1) is entirely metaphysically determined. Dispositions that need triggering by a stimulus give always rise to deterministic sequences of events. On the other hand, if a disposition does not need a stimulus to be manifested and if there are no particular circumstances necessary to the manifestation, then the existence of the disposition is ontologically sufficient for the instantiation of the manifestation (leading to even simpler law statements (SSL) ∀x (Dx ⇒ Mx)). As the instantiation of the manifestation is not triggered by any stimulus, it depends on the essence of the disposition itself whether it gives rise to an effect. Its manifestation is spontaneous. Spontaneous manifestations either always occur immediately after the disposition itself has come into existence or there can be a larger difference in time between the instantiation of the dispositions and the manifestation. In the first case, we have non-triggered deterministic dispositions. In the second case, the average period of time can be calculated between the instantiation of the disposition and the instantiation of the manifestation, for the instances of a given kind of dis-

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positions. For the individual instance of a disposition it follows that there is a ratio of the probability of its manifestation per time period. Insofar, as probability for the instantiation of the manifestation is not 100% immediately after the instantiation of the disposition, the occurrence of the manifestation is only probabilistically determined. Probabilistically determined manifestations of dispositions give rise to probabilistic laws of nature ((SSL’) ∀x pt (Dx ⇒ Mx), with 0 < p < 1 and 0 < t). The formulation of (SSL’) leaves open the question what makes true such probabilistic laws of nature. Either the truth of the laws of nature still supervenes on the individual essences of dispositions or there is no essence of dispositions that determines the probability of an individual instantiation of a manifestation. In the first case, dispositions can be interpreted as incorporating an essential quantified tendency or propensity to manifest itself in a specific way. In the second case, the length of the time period between the instantiation of the disposition and the instantiation of the manifestation is considered to be non-essential to the disposition itself and is thus an external and entirely contingent fact about the disposition. If the truth of probabilistic laws of nature supervenes on individual occurrences of dispositional properties, then they are commonly conceived as incorporating individual tendencies or propensities (a view going back to Popper 1957 and 1959). A property has then not only the disposition for a particular manifestation, but also a propensity that determines when and to what extent the manifestation is likely to be instantiated. For the familiar case of radioactive decay, an atom of enriched uranium234 has the disposition to decay as well as the specifically quantified propensity to decay with 50% chance in the first 244’500 years of its existence. Another example of fundamental physics is the dynamics of reductions of entangled quantum states into quasilocalised unentangled states as proposed by Ghirardi, Rimini & Weber (1986). According to this theory an isolated, closed, quantum system will undergo a spontaneous transition localised within a spatial area of 10−5 cm roughly every 100 million years on average. Quantum systems not only have the disposition to reduce to quasi-localised states, but have in addition the propensity to do so within the time range specified above (see Su´arez 2007, for a detailed discussion). Propensities are irreducible and objective single-case probabilities. The propensity theory aims at giving an explanation of the occurrences

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of characteristic frequencies in numerous repetitions of random experiments via objective single-case probabilities. Propensities are thought to explain the results of experiments of radioactive decay, for example, by making it a matter of objective fact that manifestations are necessarily tied to dispositions. This is not the conceptual or metaphysical necessity that defines or identifies dispositions via their manifestations, but it is the necessary connection between the occurrence of the disposition and the period of time traversed until the occurrence of the manifestation. Thus on a propensity account of probabilities it is not a contingent fact when an individual enriched uranium atom decays. It is as a matter of objective fact more likely to decay at some times than at others, because it has a specific propensity to do so. The objective chances of probabilistic laws supervene on the individual essences of dispositional properties and their propensities for manifestation. Hence, the dispositionalist can account for any particular fundamental property instantiation in a probabilistic world by positing only an initial set of property instantiations that brings about all the rest (see also Esfeld 2008b, 173-175). In general, the dispositionalist is not committed to the view that irreducible propensities exist. She could think that in a probabilistic world there are dispositional properties, but the point of time when an individual disposition is likely to be manifested is entirely contingent. She could explain the probabilities in the laws of nature by a mere frequency that describes the history of such manifestations. The probabilities of kinds of dispositions to manifest themselves at a given time would then supervene on the distribution of particular fundamental property instances at the entire space-time. This is obviously a Humean conception of natural probabilities (as it can be found in Lewis 1994a). It is metaphysically questionable whether the dispositionalist should adopt a Humean view on probabilities, because she loses the advantage of providing an ontology that is smaller (in quantity) compared with the Humean one. From an epistemological point of view both accounts are problematic, although for different reasons. The propensity theory aims at explaining the objective frequencies of property occurrences in terms of objective single-case probabilities. Propensities cannot, however, explain why our subjective degree of beliefs in certain outcomes tends to accord with these objective single-case probabilities, which is arguably something a theory of objective probability should provide us with (see Rosenthal 2006). Lewis proposes such a bridge principle from subjective

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degrees of beliefs to objective chance with his “Principal Principle” (1986b, 83132 and 1994a). He proposes in addition an account that shows how objective probabilities are determined by the relative frequencies of instantiated properties in the history of specific experiments or the world history in general. He can therefore explain why our subjective degrees of belief about probabilities tend to accord with objective probabilities. In turn, his account has notorious problems when it comes to explain probabilities in terms of relative frequencies in case of rare or even single occurrences (see again Rosenthal 2006 for discussion). In any case, the relative advantage in explanation of the Humean conception of objective probability does not seem to outweigh its ontological drawbacks for the dispositionalist (global supervenience and maximal truthmakers), because standard dispositionalism comes with a propensity theory of objective probability even though it is not committed to it. Dispositions that incorporate propensities are the only way the dispositionalist can stick to the project of restraining the number of ontological primitives with respect to the Humean. If the probabilities in nature supervene on the essences and propensities of properties, then the dispositionalist only needs an initial set of property instantiations to account for the entire distribution of fundamental properties in the world. The set of properties at the beginning of the universe (supposedly at the time shortly after the Big Bang) is ontologically sufficient to bring about any subsequent event. In this sense, laws of nature that supervene on individual property essences govern the behaviour of the world (matters of particular fact supervene on these essences). There is fundamental modality within properties that necessitates that behaviour. The view that laws of nature govern (or direct or probabilistically guide) the world in determining particular matters of fact is not only shared by dispositionalists, but also by anti-Humean categorialists (like Armstrong 1983 and Dretske 1977; see Loewer 1996 and Beebee 2000, 578-580, who make this point). It contrasts fundamentally with the Humean view that laws of nature globally supervene on the entire distribution of fundamental properties and therefore do not govern nature’s behaviour, but rather describe it (or summarise it). It has been shown that among the many ideas connected to laws of nature governance is not a conceptual necessity for an account of laws of nature and insofar as it is motivated by a prephilosophical idea of a law maker not very well founded (see Beebee 2000 for details).

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There is no direct conceptual argument to rule out a non-governing account of the laws of nature. There are attempts to find direct arguments pointing to the inconsistency of contingent laws and therefore to the conclusion that laws of nature are necessary (as an example, see Bird 2001, for the solubility of salt in water). Necessity can indeed be found in the law governed behaviour of complex objects the composition of which presupposes the same law: salt dissolves in water by Coulomb’s law and does so necessarily, because without Coulomb’s law there is no salt at all. First, this does not work for fundamental objects and properties that are not composed and thus do not presuppose the validity of laws whose contingency is subject to test afterwards. There is no inconsistency with the law that two electrons repel each other with a ratio of the inverse cube of their distance. The objects picked out by the terms of the laws can still be electrons though. Second, even in the case of salt dissolving in water, the argumentation still does not rule out that Coulomb’s law could be different in another possible world, in such a way that the natural constant it postulates is (slightly) different or that it includes alien properties in addition to actual charge. Such a law could still account for the composition of salt and water, but might not imply the dissolution of salt in water. In conclusion, arguments in favour of the necessity of laws or of the governing conception about laws can at most motivate the search for more general, metaphysically independent reasons for a dispositionalist account of laws.

2.3.3

Truthmakers of uninstantiated laws of nature

One kind of independent reasons is covered by the claim that dispositionalist laws have a decisive advantage over Humean laws, because they can account for unmanifested laws whereas the Humean has problems to do so. The dispositionalist claims to have the advantage that even uninstantiated laws of nature have local truthmakers in the form of unmanifested dispositions. It is a fundamental intuition we have about laws of nature that there are such laws that are not always instantiated. Again it is useful to distinguish between macrolaws that include ceteris paribus clauses and fundamental, strict laws. Ceteris paribus laws are not always instantiated as they permit of exceptions, strict fundamental laws are not always instantiated (or rather never), because they might not actually occur at all in our world.

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As an example for the first, let us think of the gene again that causes the phenotype of red petals in roses. Assume that it is winter season such that the conditions for the gene to manifest itself are not given (there is not sufficient warmth, or light, or water, etc.). The rose in question does not flourish. The corresponding law statement is: “It is a law that all genes of type X cause petals in roses to be red. For the dispositionalist the truthmaker for this law statement is easily identified. It is the disposition of gene of type X instantiated by roses to cause their petals to be red. The law statement supervenes on particular dispositions of the genes of type X identified by the common essence to cause red petals in roses. This is the case even in winter, because the manifestation of gene X does not have to actually occur in order for the disposition to be instantiated. For the Humean the search for a truthmaker is more complex. Let us first suppose that a rose has gene x in springtime and has thus red petals. Remember that, according to the Humean account of laws, those regularities are laws of nature that are referred to by the theorems of the best deductive system that describes our world (see chapter 1.2). The truthmaker for the law statement involve the kind of property of being gene X, the kind of property of being red petals and their regular co-instantiation. In order to make true the laws statement the additional fact is needed that the regular co-instantiation is not just any regularity, but that it is such a regularity that is a theorem of the best deductive system. In other words, the regularity has to be sufficiently important compared with other regularities to count as a law. Therefore, the truthmaker for law statements involves comparison between regularities and supervenes globally on the entire distribution of properties in the world. In wintertime, when gene x is instantiated, but not the red petals, the truthmaker for the according law statement is the gene x and the structural similarity it bears with other genes of type x that happen to be co-instantiated with the property of being red petals. Hence, in both springtime and wintertime the Humean truthmaker for the law statement is the categorical property of being a gene of type X and the role the regularity plays in which it is co-instantiated with the property of being red petals. Even if there are cases the co-instantiation does not take place, the Humean is not committed to consider the same genes to be of type X in springtime and to be of type Y in wintertime. The similarity of their structure makes for their type identity, a structure that is regularly accompanied by the

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property of being red petals, if the conditions specified in the ceteris paribus clause obtain. Hence, it is clear for the case of ceteris paribus laws that the dispositionalist can provide local truthmakers while the Humean has only global truthmakers at hand. As an example of strict laws of nature that are not instantiated in the world think of Lewis’s famous element unobtainium349 (see Lewis 1994a, 476-477). Suppose that unobtainium is not only difficult to obtain but is flatly inexistent in our world (as maybe element 118 of our periodic table of elements, even though element 118 is unlikely to have fundamental properties not had by actually existing elements). Suppose further that there are true law statements about unobtainium as there are undoubtedly for element 118. The Humean best system analysis for laws of nature can account for strict laws that have no instances in the world. The key feature of the best deductive system is to organise our knowledge of what there is in the world in the simplest possible way while retaining a maximum of empirical strength. Such a system typically tends to have few axioms from which our knowledge can be deduced. Given the knowledge we have of our world and given a deductive system that covers all and only the properties actually instantiated at our world, it is possible to augment the simplicity of this system by the introduction of empty, noninstantiated laws of nature without altering its empirical strength. Therefore, a best deductive system describing actual matters of fact is likely to include uninstantiated laws of nature (about unobtainium or element 118, for example). The truthmakers for statements about such laws is the global distribution of property instances. For the dispositionalist the case is different from uninstantiated macro-laws. While all unmanifested kinds of dispositions are uninstantiated laws of nature, not all uninstantiated laws of nature are unmanifested dispositions. The existence of unmanifested dispositions implies that there is an object instantiating these dispositional properties. The property of being unobtainium (or being element 118) for example, to have a certain chance of decay p after time t must be instantiated by something and somewhere in space-time in order to count as an unmanifested disposition. Among uninstantiated laws of nature only those may correspond to unmanifested dispositions that talk about uninstantiated properties of existing objects. Those in turn that talk about properties of non-existing objects may not be regarded as unmanifested dispositions. If

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we admit that true law statements can be uttered about unobtainium, we have an example of a fundamental physical predicate ascription that does not have a local truthmaker in the form of an existing disposition (not even an unmanifested one). Hence, the dispositionalist is not right in claiming that she can provide local truthmakers for every uninstantiated law of nature. The dispositionalist does not have to (or want to) abstain from truthmakers for statements about uninstantiated laws of nature. It is not plausible to consider such statements as false in principle. One possible way to account for their truth is by adopting a Humean best system analysis. As the best deductive system (with maximal empirical strength) describing our world it certainly includes every disposition that we have empirical knowledge about. As we have seen before it might also include statements about unobtainium. The truthmaker, however, for such statements is global even for the dispositionalist. It supervenes on the totality of dispositions instantiated in our world, for it is in virtue of all these dispositions and their organisation in a deductive system that we are licensed to make true claims about certain alien properties like the one of being unobtainium. The dispositionalist can in a second time still claim that the global distribution of properties in the world supervenes in the end on the initial distribution of properties and the conditions of their instantiation. When the best system analysis is married with dispositionalism it has a merely heuristic value for the abundant number of cases (concerning all the actually instantiated properties in the world). For a small number of cases (concerning alien properties and objects), however, it bears ontological commitment insofar as it determines truthmakers. The discussion about counterfactuals and dispositionalism shows that no particular, but only general counterfactuals (about property types instead of instances) about alien properties can be accorded truthmakers, because the existence of truthvalues for particular counterfactuals presupposes local truthmakers. There is no particular problem about this point as stating general counterfactuals is as far as you can get in talking about alien properties that are covered by the best deductive system. The adoption of the best system analysis by the dispositionalist presupposes its objectivity and therefore its supervenience on objective physical facts (see chapter 1.3, for this discussion). Given the acceptance of the best system analysis the dispositionalist has no crucial disadvantage coming from her basic ontology, as she can account roughly for all the things and features of reality that the Humean can account

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for. There are, however, numerous arguments in the current literature that plead in favour of dispositionalism on various levels of argumentation. These arguments are addressed in the next chapter.

Chapter 3

Humeanism vs. dispositionalism The present chapter discusses the major arguments between the two competing metaphysical accounts presented in chapter 1 and 2, that is between Humeanism and dispositionalism. Both formulate ontologies for the fundamental properties identified by physical science. They are exclusive insofar as the definitions of Humean properties qua first order properties that do not play their causal roles essentially and dispositional properties qua first order properties that play their causal roles essentially mutually exclude themselves (for a more detailed discussion of the definitions see chapter 2.1.4). In the present discussion mixed ontologies are excluded from consideration and Humeanism and dispositionalism are taken to be claims about fundamental properties. In being the metaphysical position of the majority of analytic philosophers since the 1950’s Humeanism is the challenged position. Arguments against Humeanism therefore occupy the biggest place in the evaluation of the two positions. They have mainly been developed during the past ten years. Special emphasis is going to be given to the separation of the questions whether the position of orthodox Humeanism (i.e. Lewis’s Humean supervenience) is affected by these arguments and whether Humeanism in general (i.e. the position that there are only first order categorical fundamental properties) is also challenged by the dispositionalist objections. This separation presupposes that the postulation of fundamental Humean intrinsic qualities is not the only possibility to spell out a Humean ontology, a presupposition that will be justified in chapter 4. Before addressing the challenges for Humeanism we will recall the main reasons for its philosophical appeal.

3.1

Advantages of Humeanism

The rise and success of Humeanism in the second half of the twentieth century is due to two virtues of David Lewis’s formulation of the fundamental ontology of nature: its clarity and its simplicity. Humean supervenience is a clear ontological commitment, because it postulates fundamental entities that

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are familiar – objects and properties – and open to adequate interpretation by fundamental physical theories. Objects in Lewis’s sense are either to be seen as space-time points or bits of matter or fields located at space-time points (Lewis 1986b, x). These objects instantiate fundamental properties that need nothing more than one of these objects to be instantiated. The kinds of properties are entirely determined by what fundamental physics considers to be the fundamental ways our world is composed of. Hence, they are perfectly natural properties (Lewis 1986b, x). As all the instantiations of these properties are contingent, we have an atomistic conception of the world as a vast mosaic of objects and properties held together solely by the geometrical relations between spatio-temporal points. There is no fundamental modality inherent to the properties and objects that escapes a possible, reductive explanation. Because all the fundamental constituents of our world are scientifically and intuitively familiar, Humean supervenience can be considered an exemplar of a clear ontology. This is all there is to the world according to Lewis’s supervenience. Everything else supervenes: nomological relations, causation and modality altogether (if one considers modal realism about possible worlds to be an independent and problematic thesis). Therefore, Humean supervenience is also an exemplar of a simple ontology the formulation of which does not exceed a paragraph’s length. It is an open question whether the virtue of simplicity translates into the virtue of ontological economy. Humean supervenience is ontologically economical concerning the metaphysical characteristics of the types of properties it postulates. Humean properties are categorical and hence ontologically selfsufficient. In Lewis’s terms, they are qualities. In this respect, dispositional property types are metaphysically more loaded. In addition to Humean qualities, they include a power to bring about other properties in the world. Thus, dispositional properties are incomparably more endowed than categorical properties. From the point of view of ontological type economy Humeanism is qualitatively better off. From the point of view of property tokens, however, Humeanism is quantitatively worse off. The property distribution at the entire space-time is ontologically primitive. Dispositionalism in turn only has to accept the initial distribution of property instances as ontologically primitive. Hence, dispositionalism recognises less entities as primitive than Humeanism. How is one to decide which ontology is more economical on these grounds?

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Such a decision is only possible if qualitative type economy and quantitative token economy can be weighed up. The usual measure of inter-theoretical comparison is Occam’s razor according to which entia non sunt multiplicanda praeter necessitatem. Not to postulate entities beyond need admits of two different interpretations. Even if we grant for the moment the necessary condition for the application of Occam’s razor, namely that Humeanism and dispositionalism have equal explanatory value (a hypothesis that will be challenged within this chapter 3.2.2), opinions diverge whether “entities” refers to “number of primitives” or “metaphysical features of primitives”. There is to my knowledge no decisive argument for either interpretation. More precisely, the only undisputed application of Occam’s razor concerns comparisons of theories the axioms of one of which are a proper subset of the set of axioms of the other. As this is clearly not the case in the present discussion considerations of ontological economy cannot settle the debate between Humeanism and dispositionalism, that is between two theories that are qualitatively distinct in their approach on modality. In the tradition of David Hume the notion of modality is particularly seen as unclear and flawed (Hume 2003, 111-124). Hume argues that natural modality would not be graspable by our perceptive apparatus and concludes that necessary connections between distinct objects or properties do not exist (this is, of course, not a conclusive philosophical argument). More important than the negative part of Hume’s claim, is the philosophical program it gives rise to, namely to explain why we think that there is necessity in the world and how we can understand such notions as laws of nature and causation that allude to the idea of natural modality. Note that the existence of necessary relations in the world cannot be postulated conditionally (as restricted to higher-levels of existence or complexity). If the fundamental ontological primitives do not include natural and necessary connections, then it is difficult to understand how they could “emerge” at a higher level of existence or complexity. At least no explanation in terms of lower-level entities is available. As explanations must respect the principle of distinction between explanans and explanandum, it is not clear what could possibly serve as a proper explanation for necessity emergence. Let us therefore assume that the question of the existence of necessity in the world reduces to the question of the existence of necessity on the fundamental level of existence. Thus, the denial of primitive modality comes to-

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gether with a philosophical project to reduce (semantically and ontologically) the notions and properties that include the idea of natural necessity. The veritable reason for the predominance of Humeanism consists in the fact that the reductive philosophical program incited by the adoption of its ontological framework has been extremely dynamic and fruitful. Elaborate ways of analysing the concepts of laws of nature and causation have emerged (mainly on Lewis’s groundwork, presented in chapter 1) and substantially augmented our knowledge of their significance. Although the Humean is committed to a general reductive or eliminativist program regarding natural necessity, the anti-Humean can consistently defend the existence of natural necessity without denying the Humean achievements in the field of the analysis of the concepts referring to it. Such analyses do not bear reductive ontological commitment for the anti-Humean, but can be of heuristic value. The understanding of the fact that ontological anti-Humeanism does not come along with the global denial of its analytical achievements altogether has been a starting requirement to launch a new wave of anti-Humean philosophy during the past ten years. Its focus is not anymore on the question, whether the sophisticated Humean analyses of concepts impregnated with necessity is fully adequate or can be in principle, but on other kinds of arguments that shall be valid independently of such mostly technical subtleties. In this sense, general objections have been advanced that are going to be presented in the next section.

3.2

Challenges for Humeanism

General challenges against Humeanism are put forward on two different levels. First, for some philosophers Humeanism is at odds with our pre-philosophical vision of the world as we experience it in our everyday life and from the folk interpretation we have concerning the nature of the world as described by natural science. Second, there is a class of objections that denounce epistemological shortcomings of Humeanism. They vary from general worries about the explanatory value of such an ontology to problematic relations between different levels of descriptions of the natural sciences: between physics and biology, for example. Furthermore, Humeanism is confronted with the straightforward denial that a description in terms of non-dispositional predicates at the fundamental level of physical description is possible. On these grounds it is questionable

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whether the Humean theory of causation does lead to general ignorance about the kinds of properties instantiated at our world. An ontology that excludes the knowledge of its fundamental properties for theoretical reasons puts itself at a disadvantage with an ontology that does not. The underlying reason for the last objection is the primitive identity Humeanism accords to its fundamental properties, an identity that cannot be known. Such a primitive identity leads to possible ways our world could have been that clash with our philosophical intuitions about natural modality. These epistemological arguments and their underlying metaphysical reasons within Humeanism form the second class of challenges against Humeanism.

3.2.1

Pre-philosophical intuitions against Humeanism

In the following section two prominent challenges for Humeanism based on pre-philosophical intuitions are discussed: first, the intuitive need that the regular behaviour of the world is somehow founded on underlying necessary connections and second, the knowledge from science that our world shows dynamic development among its properties that needs proper ontological foundation in necessary and productive, irreducible causation. The Humean cannot satisfy either of the needs. Therefore, if the arguments are straightforward Humeanism is in trouble.

3.2.1.1

The status of Humean regularities

Everybody agrees that there is regular behaviour among the natural events occurring at our world. The difference between Humeanism and dispositionalism resides in the fact that the former takes the regularities as primitive ontological features whereas the latter claims that they supervene on more fundamental properties. These properties provide a connection between the events and metaphysically guarantee the existence of regularities. They are causal connections between singular property instances and as such hold the world together. It has been claimed that the conception of regularities without underlying necessary connections is absurd (for example by Strawson 1989, 21-22). What exactly absurdity means is not specified, but there are only two possible ways of interpretation: either logical inconsistency or extreme implausibility (Strawson

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himself seems to switch between both senses, see his 1987, 260-261 and 1989, 21, for the first sense and 254, for the second). One objection that aims at logical inconsistency of the Humean regularity view is the following of Strawson’s arguments (1987, 260-261, reconstructed and discussed in Beebee 2006, 528-531): (1) There are persisting objects in the world. (2) They persist in virtue of instantiating regular sequences of properties. (3) Their properties are regular in virtue of forces tying them together. (4) These forces include the idea of generating regular behaviour. (5) Hence, the concept of regular behaviour includes the concept of an underlying productive force. (6) Any attempt to conceive of regularities in the world without an underlying productive cause is therefore inconsistent. Let us grant that for the Humean there might exist persisting objects (1). Leaving aside the question whether objects have a primitive identity through time, we can state the minimal criterion for the persistence of an object by saying that it has properties at different times and these properties satisfy a certain identity condition (2). Some properties of an object might change over time, but their change is such that it is possible to identify the object in question via some other properties that remain identical (or to a sufficient degree similar). Thus, objects behave according to regularities that are known to us by scientific investigation. For example, according to Strawson, matter persists through time in virtue of a “stable nature” (Strawson 1987, 260, author’s italics). This stable nature itself exists in virtue of forces that hold together matter such that it can persist over time (3). In other words, the persistence of objects includes the idea that there is something in virtue of which it persists (4). For Strawson there is a productive force operating on which the properties of objects supervene and which, by all intuitive means, can be properly called causation (5). Therefore, it is logically inconsistent to conceive of regularities without admitting an underlying productive cause as their ontological supervenience basis (6). The argument targets Humeanism in general and Humean supervenience in particular. Even if it is not clear whether Humeanism is generally committed

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to a regularity theory of causation, also an account like the physical transference theory of causation – if compatible with Humeanism (as proposed by Handfield 2008) – does not provide the metaphysically necessary productive feature underlying regular behaviour in the world. It rather aligns with regular behaviour. In other words, the regular transference of a conserved physical quantity between physical objects does not admit of an underlying ontological explanation in the framework of Humeanism. The crucial premise of the argument from inconsistency resides in the claim that forces responsible for the regular and steady course of nature include the idea of generating this regular behaviour (premise (4)). There are two different ways to interpret the existence of such forces. Either, they are conceived as physical properties relating objects or they are thought of as the metaphysically necessary and irreducible productive causation Strawson has in mind. While the Humean can account for the existence of such forces qua physical properties, she cannot accept the second interpretation under which physical forces not only obtain as a matter of fact, but as metaphysically entailed features instantiated only in virtue of an underlying stable nature of things (see Beebee 2006, 529). Strawson’s argument mingles the two ways of interpreting the notion of ‘force’. The Humean can accept a purely physical interpretation of ‘forces’ used in premise (3), while denying that the term actually refers to a substantial nature incorporating metaphysical necessity as used in premise (4). Forces in the physical sense, as identified by scientific investigation, do not include the idea of metaphysical generation or production. Science is typically neutral on questions of natural modality. The conception of regular behaviour does not conceptually imply the existence of natural necessity and productive causation (against premise (5)). Therefore, it is not permissible to conclude that the mere existence of physical forces makes the postulation of regularities as ontological primitives inconsistent (against premise (6)). The second interpretation of Strawson’s claim imputes extreme implausibility to the Humean. The conception of fundamental regularities as ungrounded and contingent features of the world is utterly implausible, because the regular course of the world as we know it from scientific investigation would be such a miraculous coincidence as, for example, a monkey put in front of a typewriter and miraculously reproducing Kant’s Critique of Pure Reason. The argument states that such a non-foundation of our knowledge about the world is highly

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intellectually unsatisfying. The curative proposition is to introduce a so-called ”straitjacket” for the course of the universe, something “[...] in virtue of which the world has had and is going on having the order that it does” (Blackburn 2000, 103, author’s italics). It has not to be confused according to Blackburn with a simple causal nexus between individual events, for the straitjacket guarantees the continuation of a pattern of such individual connections (see his 2000, 104). One way to spell this out is to posit dispositional properties at the fundamental level of existence. Properties have powers in virtue of which regularities in the world arise. Powers are potential causal connections between individual events, and by the fact that they connect events according to a stable essence they guarantee the continuous existence of qualitatively similar patterns of causal connections. In other words, they also qualify as straitjackets. The powers’ essences cannot be specified other than being potentially, but necessarily directed to a specific effect. This is a primitive unexplainable fact. Nothing more can be said about the meaning of terms like production or the in-virtue-of relation. The mechanism of powerful causation remains opaque in principle. Thus, it can be seriously doubted by the Humean that intellectual satisfaction is achieved by the mere introduction of metaphysically necessary productive causation that holds the universe together and is by itself a purely theoretical postulation in the sense that science cannot provide us with a contentful concept of power. Or as Beebee concludes: “For the regularity theorist, inductive vertigo – that feeling one gets when one spends too long reflecting on the fact that everything may yet fall apart at any moment – is not an ailment to be cured by ontological inflation. If it is an ailment at all, it is better to suffer it than to accept the cure that Strawson offers us.” (2006, 532)

In other words, the ontological cure against the implausibility of ontologically coincidental regularities in the world consists itself in the postulation of metaphysical entities not above reproach from an intuitive point of view (both their nature and the method of ontological inflation that comes with their introduction). There being irreducible and thus unexplainable powers that hold the world together and necessarily bring about the regular behaviour of the universe is itself intellectually unsatisfying if only based on the reasons proposed by Strawson. The Humean can at least argue for intuitional stalemate. Therefore, the first argument based on our pre-philosophical intuitions is not compelling.

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3.2.1.2

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Humeanism and the dynamic world

The second argument from pre-philosophical intuition stems from intuitions we have from the scientific description of the world. It is true that Humean properties do not play causal and nomological roles on their own (for they are categorical). It follows that their causal and nomological roles are contingent to them. The same properties could be instantiated under different laws of nature or under no laws at all. The latter possibility is called a Hume world (Ellis & Lierse 1994, 28 and Ellis 2001, 45). It is not true that in the framework of Humean supervenience there is a possible world matching ours regarding its fundamental property distribution, but without any laws instantiated, because laws of nature supervene on the fundamental property distribution (unlike Ellis envisages in his 2001, 46). In other words, for David Lewis a Hume world is impossible. There cannot be a difference in the laws without a difference in the underlying property distribution. Humean laws of nature are contingent for individual property instances, but not for entire world sets of property instances. By themselves Humean fundamental properties cannot ontologically bring about instances of other fundamental properties. Therefore the Humean takes the entire distribution of fundamental properties as an ontological primitive. This fact seems to be sufficient reason to claim that a world governed by Humean supervenience is a static world (see Mumford 1998, 214, Ellis 2001, 1-2 and Molnar 2003, 135-137). The argument from science claims that fundamental physics gives us sufficient reason to conceive of the world as dynamic. Hence, Humeanism in general as committed to the form of statics described above is untenable in the light of contemporary fundamental physics. The line of attack against this claim consists in making the following points: (1) It is correct that contemporary fundamental physics identifies dynamic behaviour among fundamental properties. (2) It is not correct that this dynamics has to be interpreted metaphysically in terms of irreducible dispositions. Indeed, contemporary fundamental physics suggests a dynamical nature in two different ways: according to general relativity space-time is a dynamical entity and according to some interpretations of quantum mechanics (notably the one presented in Ghirardi et al. 1986) there are dynamical processes by which entangled quantum states are dissolved and result in (or are projected to) reduced

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physical states having properties with definite numerical values. On the one hand, spatio-temporal relations are dynamical in the sense that they interact with non-gravitational energy-matter and with space-time itself. This interaction can be interpreted as a causal process (therefore (1) is a justified claim). On the other hand, the process of dissolution (or reduction) of entangled quantum states into disentangled quantum states with properties that have definite numerical values can be interpreted as a causal process (therefore again (1) is a justified claim). In being causal both cases of fundamental dynamic behaviour of the world can be interpreted dispositionally. Spatio-temporal relations can be conceived as including the disposition to “[...] produce changes in non-gravitational energy-matter as well as in the metric structure of space-time itself” (Esfeld 2006, 198). Relations of quantum entanglement can be conceived as including the disposition to dissolve. Entangled quantum states include the disposition to reduce to unentangled quantum states (see Esfeld 2006, 199). Let us grant that this interpretation is conceptually possible. It is, however, not conceptually necessary. If it were conceptually necessary, (non-2) would follow as a straightforward conclusion. There would not be a coherent interpretation under which the dynamics in fundamental physics could be stated in non-dispositional terms. The Humean has to deny this consequence. It is beyond doubt that the fundamental dispositions that are postulated in the fundamental physical realm bring about regularities in the world. The disposition of spatio-temporal relations to interact with the metric structure of itself and with non-gravitational energy-matter gives rise to the regularities described by the theorems of general relativity, for example. Insofar as they are part of our best deductive system these theorems are accepted by the Humean to be laws of nature. In other words, the Humean can accept that some (or even all) laws of nature are regularities that are described by dynamic laws of nature. In this sense, it is not true that Humean metaphysics leads to a static world-view. These dynamic laws (as any Humean laws) do not have local truthmakers though. The truthmakers of Humean laws are global (see chapter 1.2). They are the regularities themselves and their import to the strength and simplicity of our best deductive system. Hence, for the Humean the truthmakers for dynamic laws of nature are only categorical properties. There is nothing underlying the fundamental

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regularities of the world (remember that regularities are simply property coinstantiations). If the Humean accepts the dynamic behaviour of fundamental physical properties, then these dynamics are a primitive contingent fact about the world (see also Esfeld 2006, 198-199). Thus, it is a primitive fact for the Humean that spatio-temporal relations develop dynamically in accordance with the laws of general relativity. It is also a primitive fact for the Humean that entangled quantum states reduce according to the dynamics proposed by Ghirardi, Rimini & Weber. In other words, the acceptance of a dynamic behaviour among fundamental entities (1) is independent of their metaphysical interpretation (against (2)). Both the Humean and the dispositionalist can provide a conceptually coherent interpretation of fundamental dynamics. (2) only follows from (1) with the additional hypothesis that regularities that are described by dynamic laws of nature are ontologically secondary. Qua being ontologically secondary regularities supervene on a different ontological basis, for example in the form of irreducible dispositions or second order universals (as postulated by Armstrong 1983). This is begging the question, because both the presupposition of irreducible dispositions and of second order universals imply the falsity of Humeanism, a claim that is supposedly to be shown by the argument. Therefore, the intuitions that fundamental science suggests to us are insufficient for the metaphysical claim that Humeanism is false. Humeanism in general and Humean supervenience in particular are compatible with the dynamic nature of our world. At most, the dispositionalist can assert an epistemological advantage, because primitive dynamics do not admit of an underlying explanation within Humeanism.

3.2.2

Epistemological challenges

Hume’s argument against necessary connections is based on the epistemological insight that knowledge about fundamental natural modality is a divine privilege. Mere epistemological argumentation of this type is, of course, insufficient for the metaphysical conclusion that necessary connections do not exist. In the best case it motivates a metaphysical choice that has to be justified additionally. This much being granted to the dispositionalist it might strike us as peculiar that an important class of arguments against Humeanism also advances epistemological hypotheses for its purpose. Even though they suffer in principle

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from the flaw of underdetermination of the metaphysical by the epistemological realm, they intend to point to determinate explanatory and epistemological advantages of dispositionalism over Humeanism. All other merits of the two ontologies being equal, that might be reason enough to adopt dispositionalism on these grounds. First, dispositionalists argue that they have an advantage by being able to explain the existence of regularities and property instances by their causal history. Second, they argue for the existence of functional properties in the form of higher-level kinds of the special sciences. Functional kinds, so the argument goes, are not available to the Humean. Therefore, Humeanism cannot adequately pay tribute to the properties of the special sciences. Third, dispositionalists claim that science can describe the fundamental properties of the world only dispositionally. If that were not the case, we could not even know what the fundamental properties of our world are. In other words, we would be ignorant in principle on what properties occupy what causal roles. The metaphysical feature of properties that underlies the Humean ignorance consists in the fact that the identities of categorical properties are independent of their causal roles and can thus vary across possible worlds. If these arguments are correct, then the Humean has an epistemological disadvantage that the dispositionalist avoids. For any metaphysics of science the central test of adequacy consists in its ability to embed the results of scientific investigation within a comprehensible framework. If from this point of view Humeanism is worse off than dispositionalism, then it has to be abandoned. The aim of the following sections is to discuss the epistemological challenges for Humeanism. 3.2.2.1

Explanation of regularities and property instances

If they do not have a decisive intuitive advantage in grounding regularities on powers, dispositionalists might insist on an epistemological surplus by the fact that they can explain the existence of regularities. In order to explain fundamental regularities of the type R : ∀x(F x → Gx) two minimal conditions must be satisfied: (1) The explanans must be intensionally distinct from the explanandum. (2) There must be a reductive relation between the entities they refer to such that the concepts are co-extensional.

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Regularities are fundamental insofar as they relate fundamental properties. More precisely, both for the Humean and the dispositionalist they are internal relations among fundamental property instances. For the Humean fundamental regularities are ontological primitives. They are contingent relations, even if they are exceptionless. Contingency does not call for explanation. Hence, for the Humean the meaning of being a fundamental regularity just is to be a contingent internal relation between fundamental property instances that belong to different kinds. As all fundamental property instances are primitive, so are the internal relations between them. There is no distinct, more fundamental concept available to explain regularities (against (1)). In the framework of dispositionalism regularities between fundamental properties are necessary. They are necessary, because they have an underlying reason. Dispositionalists explain regularities of type R by F’s essence to bring about G’s. The concept of differs from the concept of , because the meaning of the concept does not contain a reference to a determinate causal essence (hence (1)). Else, the Humean would not even have the right to use the concept of regularity (a claim shown to be false in chapter 3.2.1.1). For the dispositionalist, a regularity of type R refers to a set of individual internal relations between instances of property F and instances of property G. We leave aside the question whether dispositionalism is compatible with non-causal or accidental regularities. The interesting case of regularities is the class of necessary relations between kinds of contiguously instantiated properties. As a working hypothesis, let us assume that this class is identical with the class of causal regularities. Dispositionalism holds that property F has the essence that its instances produce instances of property G. If we assume that fundamental dispositions are always manifested, then the set of internal relations supervenes on the essences of F-instances. Regularities of type R just are manifested essences of the dispositional property F. Both concepts are coextensional (hence (2)). A reductive explanation of regularities is available for the dispositionalist, because her set of ontological primitives is distinct from her set of fundamental properties. Fundamental properties and the internal relations among them can therefore be explained reductively by the smaller set of ontological primitives. In our case both F and G as well as the internal relation R between them are fundamental properties, but only F is ontologically prim-

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itive with respect to G and R and potentially explanatory. If F is potentially explanatory for G and R, then it might also be potentially explanatory for G and its instances. An explanatory surplus of dispositionalism concerning regularities might also be an explanatory surplus concerning individual property instances. Conditions (1) and (2) are minimally necessary for explanation. It is a matter of further investigation whether irreducible dispositions (i.e. irreducible causal essences) have a real additional explanatory value. It is important to distinguish between two different kinds of explanations here. On the one side, it is the aim of metaphysics in general to give a unified theoretical account of the nature of natural properties. In the sense of providing a conceptual unification and a theoretical subsumption of particular knowledge under general principles metaphysics is explanatory. On the other side, there are scientific explanations to the question why certain objects instantiate the properties they actually do. If dispositionalism is a coherent metaphysical account of the nature of natural properties, it is explanatory in the first sense. It increases our comprehension of nature by postulating a limited set of ontological primitives (an account of explanation along these lines is presented in Friedman 1974). There is nothing, to my knowledge, that represents a serious threat to the logical consistency of dispositionalism. Dispositionalism has, however, not an explanatory surplus over Humeanism in the first sense given that the Humean position also presents a unified account of the nature of natural properties and postulates a limited set of ontological primitives. The difference between the two accounts is just a difference in the nature and number of primitives they posit. As we have seen, it is difficult to find an objective measure to quantify and compare the degree of unification the two accounts achieve. Whereas dispositionalism achieves greater unification in reducing regularities to causal property essences, Humeanism achieves greater unification in reducing causation and modality to categorical property distribution. Occam’s razor is not apt to settle the question. Nor are our pre-philosophical intuitions. If the explanatory force of dispositionalism is greater than the one of Humeanism, then it must provide a better account of explanation in the second sense. Scientific explanations of individual property instances can be classified into two different groups. There are vertical explanations of property instances by means of their compositional properties and there are horizontal explanations

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by means of their causal history. The instance of a property like being a certain gene, for example, may be explained by its chemical or physical composition or by the history of its individual development in a given organism. Vertical explanations are equally available for the dispositionalist and the Humean. If they are physicalists they ought to agree on the fact that ideal science informs us about the ultimate constituents of nature and shows how higher-level properties are composed of lower-level properties. From the point of view of vertical explanation the dispositionalist has thus no explanatory advantage with respect to Humeanism. On both accounts the regularity between being a gene of type X and having red petals can be explained by the more fundamental regularities between the chemical and ultimately physical components of the two properties. From the point of view of horizontal explanation the causal history of events is important. The only property instances that do not admit of vertical explanation are those ones that are not composed. The question reduces thus to what kind of explanation dispositionalism and Humeanism can provide for fundamental property instances. Take, for example, the case of two electrons e1 and e2 that repel each other according to Coulomb’s law. Humeanism can provide an explanation of the position of electron e1 in citing e2 as a cause for its determinate spatial deviation. Causal dependence is determined by what the laws of nature are. The law of nature that covers the behaviour of electrons is simply the contingent regularity that all instances of electrons satisfy Coulomb’s equation with respect to one another. No other explanation is available for the Humean. For the dispositionalist, however, the behaviour of the two electrons is metaphysically necessary. The explanation of the necessary behaviour of electrons is provided by the existence of irreducible dispositions that bring about the specific behaviour. Therefore, the dispositionalist offers additional explanation with respect to the Humean. The dispositions of electrons are their essential features. They make for their identity. The essence of electrons consists precisely in the fact that they repel other electrons according to Coulomb’s equation. The behaviour of the two electrons e1 and e2 as described by Coulomb’s equation is thus explained by the fact that in being electrons it is their essence to behave according to Coulomb’s equation. The explanation of a certain fundamental regularity is given by the fact that the essence of the fundamental properties involved consists exactly in bringing about the regular

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behaviour in question. The additional explanation the dispositionalist offers is hence an analytical truth without empirical content. This kind of explanations once incited Moli`ere to mock philosophers (in his Malade imaginaire 1673) by describing a philosophical doctor who answers the question why opium puts people to sleep by saying that it has the power to put people to sleep (cited in Armstrong 1973, 15). Even though the dispositionalist has an additional metaphysical explanation of regularities and individual property instances in terms of irreducible dispositions, she has no explanation that adds to our scientific understanding of the fundamental behaviour of nature. Therefore, dispositionalism has no empirical explanatory surplus with respect to Humeanism. The previously stated potential explanatory value of irreducible dispositions vanishes once it is spelled out. From the point of view of scientific explanation Humeanism and dispositionalism are on a par. Still, the irreducible causal essences the dispositionalist postulates might prove to have important advantages when it comes to our global understanding of science as a multi-layered approach to describe the world at different levels of complexity.

3.2.2.2

Conservative reductionism

If physicalism is true then all fundamental properties are physical properties in the sense that they are the referents of fundamental physical concepts. And everything else at least globally supervenes on the distribution of fundamental physical properties (see Jackson 1998, 1-28). If Kim’s causal exclusion argument is correct, then non-reductive physicalism is a flawed metaphysical position (see Kim 1998 and 2003). According to Kim every property that exists in the world and plays a potential causal role is either identical with a fundamental physical property or composed of several fundamental physical properties. There are no levels of being, only levels of complexity. At some levels of ontological complexity predicates are available that can be truly applied to classes of individual property instances. Thus, simple predicates of fundamental physics (e.g. ) refer to simple property instances (e.g. the singular property of one object to have mass x). To the complex arrangements of fundamental properties that constitute, for example, genes of a certain type X the biological predicate of can be

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applied. The complex arrangements of fundamental properties that can be correctly described as being genes of type X can also be described individually by listing the physical descriptions of the constituents and their arrangement. Ontological reductionism says that there is nothing more to being an instantiation of a gene of type X than its physical constitution. Ontological reductionism qua token identity raises the question how the predicates on different levels of scientific description are related to one another. There is a tradition of arguments claiming that predicates of higher-level descriptions (for example biological descriptions) cannot be co-extensional with predicates of fundamental physical descriptions (they are called arguments from multiple realisation as presented, for example, in Fodor 1974). These arguments claim that entities that fall under one higher-level predicate (like being a gene of type X) cannot be captured by a single physical concept. To the extent that these entities differ in fundamental physical aspects they are described by different physical predicates. On these grounds the argument concludes that predicates of higher-level descriptions cannot be put into one-to-one correspondence with predicates that constitute physical descriptions. There can hence be no co-extensionality between them (for an overview of these arguments see Sachse 2006, 96-99 and Sachse 2007, 116-132). It can be shown, however, that the mere fact of multiple realisation does not prevent the development of a reductionist strategy to reduce predicates of the special sciences to predicates of fundamental physics (a strategy that introduces theoretical subpredicates that are co-extensional with physical predicates is presented for biological predicates in Sachse 2006, 99-107 and Sachse 2007, 138-166). If this strategy is successful and if physical descriptions are sets of fundamental physical descriptions, then it is possible in principle to identify biological predicates with sets of fundamental physical predicates. The argument from conservative reduction against Humeanism presupposes that epistemological reductionism (in the sense of theory reduction) is a consistent position. It goes as follows: in the framework of Humeanism all there is to causation – be it in the form of a counterfactual account or in a simple regularity account – are contingent patterns of regular property co-instantiations. The instantiations themselves are identical with arrangements of fundamental categorical property instances. Functional properties in turn are defined by the characteristic effects they bring about. Causation figures as a primitive intrinsic

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feature of these properties. They are causally effective by themselves. Therefore, functional properties are not categorical properties and are not available to the Humean in general. The Humean can of course acknowledge the true ascription of functional predicates within the special sciences, but the truthmakers of such ascriptions are not instances of functional properties. There are various proposals for semantic reduction of functional and dispositional predicates that come along with such a position (see, for example, Lewis 1997, Gundersen 2002, Choi 2003 and Cross 2005). The referents of true functional predicate ascriptions are, for the Humean, configurations of fundamental physical property instances that make true higher-level, functional descriptions in a secondary way (see Esfeld 2006, 204). For dispositionalists, in turn, true functional predicate ascriptions have direct referents in the form of functional property instances. Hence, according to the argument, the Humean commitment to the exclusive existence of non-functional properties implies a model of epistemological reductionism that has an eliminative flavour with respect to the properties of the special sciences in contrast to the dispositionalist who can opt for a conservative model of epistemological reductionism. The difference in the metaphysics of causation is responsible for this fact. Because Humean causation is reducible to non-causal, contingent and regular property co-instantiations, true functional predicate ascriptions refer in the first place to a certain property configuration, but are only true in virtue of this configuration being regularly co-instantiated with other configurations of the same type. The argument from conservative reductionism is a general argument against Humeanism. The crucial premises to fall short of conservative reductionism are the absence of functional properties and the global supervenience of causal relations as a necessary condition for their reduction. Although the potentially coherent combination of Humeanism and a transference theory of causation (which is left out from consideration here) does not necessarily imply global supervenience, any causal relation on this account reduces directly to causal relations between conserved physical quantities. There are no functional properties on the higher levels of complexity. Thus, any form of Humeanism is under pressure from the argument from conservative reduction. In other words, Humeanism in general faces the challenge that it is unable to properly account for the properties described by the special sciences.

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The Humean makes a deliberate choice on the metaphysics of causation in claiming that there are no irreducible functional properties in the world. In this sense it is not justified to impute eliminativism to the Humean with respects to functional properties. They have just never been introduced. From the common ground of true functional predicate ascription the Humean provides truthmakers that are categorical only. Nothing commits the Humean to consider these ascriptions to be false. In this most fundamental sense the Humean does justice to the special sciences. From the ontological point of view the Humean as well as the dispositionalist defend positions compatible with token identity theories. Token reductionism entails a compositional principle in accordance to which every instance of a property is either identical to a fundamental property instance or an arrangement thereof. Neither the Humean nor the dispositionalist is therefore committed to a layered view of the world. For both of them there need not be levels of being. Still, there are levels of complexity in the sense that arrangements of fundamental property instances can be more or less complex. An individual gene, for example, is a less complex arrangement of fundamental properties than a cell which in turn is less complex than an organ, etc. The difference between both positions consists in the fact that the Humean not only reduces a higher-level property to its composition of lower-level properties, but that she also reduces the functional aspect of a property like being a gene of type X. Strictly speaking there are functional properties in a Humean world, but they are global properties of the world and thus not delimitable to a proper subregion of space-time. On the fundamental level of complexity there are no isolable functional properties and therefore the fundamental distribution of categorical properties makes true in the first place (or so the argument goes) a fundamental description in non-functional terms. If a model of epistemological reductionism (i.e. of theory reduction) is available then this fundamental description must have the resources to serve as a basis for the deduction of the functional concepts and laws of higher-level descriptions of the special sciences. There are different accounts on how the deduction of special science descriptions can be qualified. Let us grant that a complete description of the fundamental physical nature of the world plus the functional definitions of higher-level concepts entails a description of all there is in the world. Either the translation between fundamental descriptions and higher-level descriptions are

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a priori and the functional definitions of the higher-level concepts are known to us analytically, thus leading to a so-called a priori physicalism – where the deduction of higher-level descriptions is executable without further empirical knowledge – (for this position see Lewis 1994b, Jackson 1998, Chalmers & Jackson 2001) or the translations are a posteriori and the functional definition of higher-level predicates presupposes empirical knowledge, leading to a position called a posteriori physicalism (defended, for example, by Block & Stalnaker 1999 and Laurence & Margolis 2003). A priori physicalism has come under attack, because higher-level descriptions of the special sciences are not accorded the scientific and epistemological value one commonly associates with them. Strictly speaking, their concepts are superfluous, as they do not have epistemological import over and above the knowledge we have about the fundamental physical functioning of nature. A priori physicalism has an eliminative flavour. To the extent that conservative reductionism is a reductionist strategy at all it disposes us with a manual to deduce higher-level predicates from lowerlevel predicates. Conservative reductionism does not entail a particular form of physicalism. It is compatible with the idea that fundamental descriptions of the physical nature permit a priori deductions of higher-level descriptions and that our functional definitions of higher-level concepts are in fact analytical. It is also compatible with the idea that there is no a priori deduction of the higher-level descriptions and that the functional definitions of our higher-level concepts depend on the empirical knowledge we get of the properties they refer to. From this point of view, the challenge from conservative reductionism consists in the claim that Humeanism is only compatible with austere a priori reductionism. There is no doubt that David Lewis as Humeanism’s most ardent defender embraces a priori reductionism (see Lewis 1994b). Nevertheless, it is hard to see why a Humean should not be able to adopt the view that the functional predicates of the special sciences are empirically defined through scientific investigation. The Humean can defend the view that concepts like are rigid designators of specific causal roles as to bring about phenotype P without being committed to the existence of dispositional properties. In other words, having the function to bring about phenotype P might be rigidly true of certain complex properties despite the fact that the

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property has this specific function in virtue of being part of a law-like regularity of several instances of the same properties and the particular effects they bring about. The question, however, remains whether Humeanism faces eliminativist charges. In other words, the question remains whether Humeanism has to admit that there is only one direct relation of truthmaking at the fundamental physical level and that every other truth about the world – for example truths about genes – is only made true indirectly in virtue of being deducible from the fundamental physical facts. Does the fact that causation (and with it dispositions) reduces to contingent arrangements of property instances entail that complex properties cannot directly make true their functional descriptions? Let us first consider this question at the fundamental level of description. Humeanism is committed to the claim that there must be a description of fundamental properties in non-dispositional terms (for a justification of this claim see chapter 3.2.2.3 where structural definitions of fundamental properties are proposed). Still, those same properties can be described in dispositional terms as well. In the framework of Humeanism the true description in dispositional terms of the behaviour of a particle having a certain mass x refers to the property instance in question. The description is true of this property instance in virtue of the law of nature that summarises the behaviour of all instances of the mass property, because the causal roles of the mass property are horizontally reduced to just these laws. It will be claimed in what follows that the mere fact that the truthmakers for true dispositional predicate ascriptions at the fundamental level have a bigger extension than the truthmakers for true categorical predicate ascriptions (although structural definitions of fundamental properties might have considerable extension as well) does not suffice to qualify the relevant truthmaking relation as indirect. For the Humean the description in terms of dispositional predicates is deducible from the whole inventory of categorical descriptions of fundamental properties. It does not follow that the description in terms of dispositional predicates does not refer to fundamental properties. Besides the properties themselves, their behaviour as well is a fundamental property of the world in the sense that it is nothing over and above regular co-instantiation among fundamental properties, which is itself an internal relation among fundamental property instances. Hence, it makes sense to call the dispositional description

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itself fundamental. The fundamentality of the dispositional description points to an important distinction concerning the relation of deduction. Assume that for two sets of descriptions A and B, the following deductive relation holds: A → B (B can thus be deduced from A). There are numerous mathematical and metaphysical interpretations for this relation only two of which matter in our context. First, A → B can be interpreted as a relation of abstraction. B can be deduced from A, because it is determinable, whereas A is its corresponding determinate. Think of the familiar example of A = burgundy and B = red or as an example from science A = primates and B = mammalia. Second, A → B can be interpreted as structural inclusion. B can be deduced from A, because the structure described by A can be mapped onto the structure described by B. Think of A = the set of descriptions of every chessboard field as black or white and B = the description of a 8 × 8 square consisting of black-and-white alternating fields. The first interpretation of deduction fits the model of vertical epistemological reductionism in both the conservative and the eliminative flavour. Both positions agree on the fact that higher-level descriptions abstract from lower-level descriptions. Abstraction is an irreversible relation. The second interpretation of deduction can be situated on the same level of description. In this case deduction is horizontal and not necessarily irreversible. Applied to our case, the deduction of the dispositional description of the fundamental property distribution from the categorical description of the fundamental property distribution is horizontal. Both are descriptions of the fundamental properties. Moreover, from a complete dispositional description of the fundamental properties a complete categorical description of the same properties can be deduced. Hence, this specific deductive relation is reversible. In the case of a reversible, horizontal mapping relation between two sets of descriptions it makes no sense to talk of a direct relation of truthmaking for one set of descriptions in contrast to an indirect relation of truthmaking for the other set of descriptions. The previous considerations are independent of the metaphysics of causation one likes to adopt. In particular, they are independent of the extension of the supervenience basis of causal relations. Hence, for the fundamental level of complexity the metaphysics of causation does not impute a hierarchy between the truthmaking relations for categorical and dispositional descriptions.

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Naturally the question arises whether this point generalises to other levels of descriptions and the corresponding levels of property complexity. I take it to be uncontroversial that Humeanism can account for natural complex property types. They are classes of complex natural property tokens sharing an aspect of similarity. The similarity aspect consists in a similarity of structural aspects. Thus, for the Humean there is a complex natural property referred to by the concept of . Of course all tokens of this property are composed by fundamental properties being arranged in accordance to a specific structural principle (i.e. as a specific DNA sequence). But these tokens also share a common structural aspect that can be specified at the same level of complexity. Their underlying structure gives rise to a global qualitative feature that is specific to all and only the genes of the given type X. The Humean can even accept that the common feature of complex property instances is identified functionally, by the ascription of functional predicates through scientific investigation (just like at the fundamental level where we get in touch with properties through the effects they have). With the functional identification of property types comes, of course, no commitment to functional essences. What is identified is just regular co-instantiation. The regular co-instantiation of the gene tokens with other complex natural properties – namely those referred to by the concept specifying the phenotype – accords them the functional role to bring about a specific phenotype. It is only this co-instantiation that matters for causation. Again, for the dispositionalist this functional role is an essential feature of the complex natural property. As in the case of fundamental properties the set of categorical descriptions of each instantiation of the two complex natural properties permits to deduce the dispositional description of the very same complex property tokens. This is a case of horizontal structural inclusion. There is no point in distinguishing between direct and indirect relations of truthmaking for the two alternative descriptions of the same entities. Therefore, Humeanism is not worse off in that it is committed to a specific model of theory reduction. In particular Humeanism is not committed to first ontologically reduce the complex property to an arrangement of simple properties, making true a privileged description in fundamental physical terms, just to deduce from this description in a second move the higher-level functional concepts that refer to the complex entity. Complex arrangements of properties can directly make true descriptions in higher-level dispositional terms.

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To sum up, conservative reductionism challenges Humeanism with the eliminative charge. Its complex properties are nothing but fundamental physical property arrangements making true a privileged fundamental description in physical terms. Everything else can be deduced from that description. As a matter of fact, neither Humeanism nor dispositionalism challenges the principle of property composition (if they find themselves to be ontological reductionists). Neither of the two challenges the deducibility of higher-level descriptions from lower-level descriptions (if they find themselves to be epistemological reductionists). So the argument can only consist in the claim that complex Humean properties cannot directly make true higher-level descriptions whereas complex dispositional properties can. The Humean counterargument consists in pointing out that causal descriptions of higher-level entities are made true within one and the same level of complexity. Causation is not reduced vertically. Complete descriptions at a given level of complexity in terms of categorical and dispositional predicates are mutually deducible, in virtue of constituting structurally inclusive sets of descriptions. Thus, in case of higher-level predicate ascriptions the need for first an ontological reduction, then a description of the fundamental properties and then a deduction of the higher-level predicate ascriptions does not arise. The choice of this particular model of austere a priori reductionism is independent of the metaphysical account of causation one chooses. There is, however, a different aspect (mentioned in Esfeld 2006, 204-205) that is potentially problematic for the Humean: the case of mental causation. Dispositionalists claim that the Humean cannot admit the experience of conscious, human agency as being veridical. As in the biological case, structurally (or in this framework better qualitatively) similar conscious states (like the state of being in pain) bring about a typical behaviour (namely to moan, to writhe and to cry). It is our psychological conviction that we as subjects bring about this behaviour with our personal mental states. It has been shown that even highly complex states can be direct truthmakers for higher-level descriptions and that the metaphysics of causation has no bearing on this question. But something additional to the problem of direct truthmaking is important within the field of mental causation. In the framework of Humeanism a complex state is never sufficient by itself to bring about an effect (this is in the very definition of categorical properties). The veracity of our experience of mental causation

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is tied to the metaphysical choice one makes with regard to causation. Once again, the question of direct or indirect truthmaking is not. Therefore, the two problems should not be mingled. It is correct to say that for the Humean our pain states are causes of typical behaviour. It is also correct to say that this is only the case in virtue of there being other pain states that bring about other behaviours of the same type. In reducing causation to regular behaviour, Humeanism implies radical externalism about the referents of concepts as pain. Externalism clashes with our everyday experience of ourselves as agents. So much the Humean has to grant, knowing that she can meet the challenge of conservative reductionism. Mental causation exists, but not as we imagine it in our everyday experience. The next section discusses a central premise of the Humean response to the challenge of conservative reductionism: that there can be a description of fundamental physical properties in non-dispositional terms.

3.2.2.3

The ungrounded argument

The ungrounded argument is named after Stephen Mumford (2006) who develops it in order to show that our world contains irreducible dispositions that are not grounded on a more fundamental categorical basis. His central hypothesis is that at the fundamental level of description science necessarily uses dispositional predicates (for a different interpretation of the argument and an according objection, see Williams 2008). It is the aim of this section to argue to the contrary. On the basis of this claim the argument concludes that there must be fundamental and irreducible dispositional properties and hence that Humeanism is false. In order to support this conclusion the ungrounded argument examines the vocabulary contemporary fundamental science uses to describe the world. Dispositionalists claim that the vocabulary of fundamental physical science is immerged by dispositional terms. They argue that fundamental physics can only talk in a causal way about at least one of the fundamental properties instantiated at our world. The ungrounded argument takes the following form: (1) The fundamental physical properties can be defined as dispositions of an object instantiating them.

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(2) There exists at least one fundamental physical property for which there are empirical reasons to think that this is the only possible description. (3) Therefore, there exists at least one fundamental physical property that is irreducibly dispositional. (1) and (2) are premises for the conclusion (3). Mumford (2006, 475-476) defends the stronger claim that every fundamental property identified by physics is dispositional. He applies universal quantification to premise (2) and conclusion (3). For our purpose it suffices to consider the weak version as formulated above, because however weak the conclusion remains anti-Humean. The argument targets Humeanism in general. No step of the argument confines its scope to a particular form of Humeanism (i.e. to Humean supervenience). Suppose that the premises are correct. There exists a fundamental physical property for which there is only a dispositional, that is a causal, definition available. In order to license the inference that the physical property thus described is itself irreducibly dispositional a principle of concept-property correspondence must be invoked. Philosophers interested in the ontology of science commit themselves to take science in general and physical science in particular as a guideline to learn about nature’s properties. If there is a robustly best world-description employed by the sciences, then there is reason to think that it captures features of our world. The only way a theory can do so is when its concepts correspond to something in the world. A concept-property correspondence principle must guarantee that fundamental physical concepts (of ideal physics) catch the essence of the fundamental physical properties of nature and the objects instantiating them. Scientific realism provides such a principle. I take it for granted that scientific realism is adopted both by adherents and opponents of the ungrounded argument. Nobody contests that fundamental scientific vocabulary may be interpreted as being dispositional (1). The vast majority of Humean philosophers admits that dispositional descriptions of fundamental physical properties have referents in the world, only do they not refer to fundamental dispositional properties. These Humeans defend reductive semantic accounts for dispositional predicate ascriptions (as Lewis 1997, Gundersen 2002, Choi 2003 and Cross 2005). But premise (2) makes the additional claim that a description in dispositional terms is the only valid description available. Stathis Psillos has argued that this is not the case (2006, 152-154). He claims that fundamental physics

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admits of purely structural definitions of mass, charge and spin, for example, by referring to symmetry relations. On such a view properties of the fundamental objects (particles) are determined by symmetries that exist in the world. The properties of having mass, charge and spin are defined as remaining invariant under certain sets of mathematical transformations that form a mathematical symmetry group (that is a set together with an associative binary operation with an inverse and an identity element). They are distinguished by the different sets of transformations under which they remain invariant. Symmetry relations play a crucial role in the identification of fundamental physical properties. But even if there is a definition of the fundamental properties in terms of structural vocabulary, nothing so far specifies the status of the symmetries that appear in the definiens. The question remains whether a structural definition of fundamental properties has to be interpreted as the attribution of a disposition to a certain object to behave in a specific way. Two things must be distinguished here. On the one side there is the mathematical description of the world that makes use of symmetry groups and transformations. On the other side there are the truthmakers of these description. Scientific realism claims that the difference in description (invariance under different symmetry groups) picks out or individuates different fundamental properties. The Humean suggests that these properties are categorical. An immediate dispositionalist objection comes to the mind: the fundamental properties obviously have the disposition to remain invariant under certain symmetry groups and therefore they are irreducibly dispositional. But it is a categorical mistake to think of a disposition as a function mapping the realm of existence onto the realm of description. The dispositionality in question would be analogous to the “disposition” of any truthmaker to make true a corresponding statement. Still, a problem remains. The Humean truthmakers of mathematical symmetry relations seem “to bring about” alleged fundamental properties like mass, charge and spin. Thus, the ungrounded argument does not apply to the standard candidates for fundamental physical properties, but to some underlying more fundamental properties. If it is between these two property sets where the dispositionalist wants to have irreducible dispositions, then, according to premise (2), she has to claim that the unique interpretation admissible for the formulation “to bring about” is a causal interpretation. The Humean can object

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that the appropriate dependence is rather one of regular co-instantiation than of productive causation. To the extent that this is a valid claim for the Humean dispositionalists cannot confirm premise (2). The dispositionalist can of course hold that among the set of all the fundamental properties, some suffice for the instantiation of all of them, that there is at least one privileged subset of fundamental properties that has the disposition to generate other fundamental relations. This claim is in need of physical justification that has not been given so far by dispositionalists. The physical explanation of the fundamental properties in the world does not prima facie appeal to dispositional vocabulary. This is not to say that a dispositional characterisation of fundamental properties is excluded, but “[...] at least, we can equally well see them as non-powers too” (Psillos 2006, 154, where non-powers can be replaced by non-dispositional, categorical properties). The Humean may therefore object to premise (2) of the ungrounded argument that she can offer a conception of fundamental properties as truthmakers for mathematical symmetry relations that does not prima facie refer to irreducible dispositions. The Humean is free to adopt a standard regularity view for these fundamental properties and their co-instantiations (see Dieks 2006, who defends a Humean regularity account for fundamental quantum physics). Similarity makes for sets of fundamental relations that are picked out by specific mathematical descriptions by means of invariances under different similarity groups. She thereby admits the whole distribution of fundamental relations in the world as primitive. The ungrounded argument is based on what physics tells us about the world by the way it talks about nature. In a more ambitious attitude than in the argument presented above Mumford concludes that all properties of fundamental particles are dispositional. This, he says, follows from science, because we can detect properties only by their effects and thus science can only talk in dispositional vocabulary about those properties (see Mumford 2006, 475-476). The latter point, however, has proofed not to be uncontroversial. In general, knowledge can be gained of relational properties, not only of primitive fundamental causation (this point will be addressed in the chapters 3.2.2.4 and 4.4.2). Mumford at best establishes that dispositional vocabulary is a possible way to talk about fundamental properties and hence that the existence of irreducible dispositions is conceivable. This is what follows as a logical consequence of

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his argumentation, once it is deprived of premise (2). As a merely hypothetical consequence, Mumford’s argument need not bother the Humean. Still, a general worry persists whether fundamental Humean properties are knowable at all. 3.2.2.4

The argument from humility

Humility is a name for principled ignorance. The argument from humility concludes to the truth of dispositionalism and equally to the falsity of Humeanism on the basis that the first has a major epistemological advantage over the second, namely that only for the dispositionalist it is possible to know what fundamental properties are instantiated in the world. It takes the following form: (1) The only properties that are knowable to us are the relations an object entertains with other objects. (2) Fundamental Humean properties are intrinsic properties of objects and not relations between objects. (3) Dispositionalist properties are knowable. (4) An ontology with knowable properties has a decisive advantage with respect to an ontology with unknowable properties. (5) Therefore, there exists at least one fundamental property that is irreducibly dispositional. Premise (1) holds that the only possible way for us to get to know objects in general is via the relations they entertain with each other. This is not to say that immediate introspective awareness of an object’s non-relational properties is flatly impossible. Such knowledge may be available in the case of conscious experience of qualia. As to fundamental physical properties immediate acquaintance with them may be excluded. There is, however, a recent attempt to dismiss the unknowability of Humean intrinsic properties in principle (Schaffer 2005). Schaffer claims that such a general humility towards properties is analogous to general scepticism. He argues that therefore, whatever relieves us of general scepticism towards the external world equally well frees us from humility about the essence of the properties instantiated at the external world. The argument is flawed, because it is hard to see how the relationship between causal roles and role occupiers could be equalled to the relationship between the realm of appearance and the realm of reality. Scientific realism provides a

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bridge of correspondence between the latter two. It can be justified by independent reasons (for example, by the miracle argument, see Putnam 1975,73). There is no such bridge of correspondence between causal roles and role occupiers in the framework of Humeanism. Even worse, the very intention of Humeanism is to deny its existence by claiming that it is wholly contingent what property occupies what causal role. It is not clear how we can get to know a property’s essence through the causal role it plays if there is only a contingent link between the two (pace Ney 2007). Let us therefore take premise (1) for granted (at least within the scope of fundamental physical properties). Lewis’s Humean supervenience only recognises intrinsic and categorical properties instantiated at space-time points and the metrical relations between them as fundamental. Thus, the fundamental physical properties are not relations between objects and are not knowable (premise (2)). Fundamental dispositional properties, however, manifest themselves as actual causal relations. Hence, they are knowable in principle (premise (3)). Note that, if all there is to a property is its causal roles and if we can know these roles by scientific investigation it is straightforward to claim that our knowledge can be completely expressed by dispositional vocabulary (a point made in chapter 3.2.2.3). These premises being granted, the argument crucially turns on the justification of premise (4). Humility is a problem for Humeanism because a thesis like Lewis’s Humean supervenience creates a gap between ontology and epistemology. The fundamental entities it postulates escape our conceptual grasp in principle. Humean philosophers may react in biting the bullet. David Lewis does so when he defends humility as something we have to live with (Lewis 2007 accepts premises (1) and (2), remains silent about (3) and denies (4)). Given the structure of human knowledge, humility is, after all, the general case and not a limited particularity. Humility regarding the world seems to be principled in some fundamental domains of knowledge (as, for example, in the choice of a particular quantum mechanical model or in string theory with its mathematically equivalent but dual geometric interpretations, although admittedly string theory might not yet meet the requirements for a full-grown scientific theory). But even if the perspective of pervading knowability proves to be too optimistic, there is still an argument of relative advantage for the dispositionalist over the Humean. Towards the set of fundamental properties the dispositionalist is less humble than the Humean, because for example disposi-

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tionalist charge is knowable, whereas the Humean occupier of chargish causal behaviour is not knowable. The Humean can, as the argument goes, only know the relations between, say, two particles of like charge, but the fundamental Humean properties are different from these relations, they constitute their supervenience basis. The supervenience basis determines the causal structure of the world, but it is contingent what essences the properties figuring in the supervenience basis have, because the essences of Humean properties are not determined by the causal roles they actually occupy. Given that two ontologies are stalemate from the perspective of our pre-philosophical intuitions about the world, the one that avoids humility (to a greater degree) has a decisive advantage (premise (4)). If on epistemological grounds dispositionalism has a decisive advantage over Humeanism, it is preferable ceteris paribus. If the argument is correct dispositionalism justly figures as the winning ontology. It has fewer drawbacks. Therefore, the argument from humility presents a point against Humeanism and in favour of dispositionalism. But if Humeanism is false and dispositionalism is true then there exists at least one fundamental property that is irreducibly dispositional (conclusion (5)). The target of the argument from humility is Humeanism in general. That is what the conclusion states. And admittedly Lewis’s Humean supervenience is in trouble, because it postulates intrinsic properties of objects that are distinct from the relations these objects entertain and that are distinct from the second order relations between the property instances themselves, at least as far as causal and nomological relations are concerned. But premise (2) only constitutes a general attack against Humeanism if the additional claim is accepted that the set of fundamental categorical and natural properties necessarily consists of intrinsic properties only. In other words, Humeanism in general is only targeted insofar as a Humean metaphysics that does not postulate fundamental intrinsic and natural properties is inconceivable. It will be argued in the following chapter that this is an unjustified claim. An ontology is conceivable that recognises only categorical and extrinsic (qua relational) natural properties that are fundamental (such ontologies will be subsumed under the label of unorthodox Humeanism as opposed to Lewis’s orthodox version). Ontologies that share the commitment to fundamental extrinsic properties are called structural realist positions. The logical possibility of structural realism about categorical properties will prove to follow from the fact that the classification

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of the set of properties into an intrinsic and an extrinsic subset is independent from their classification into a dispositional and a categorical subset. To the extent that this is correct there is a live perspective that the epistemological challenge for Humeanism presented above can be met. Even if the epistemological threat of humility advanced by the dispositionalists can be repelled there is an underlying metaphysical reason for the principled unknowability of Humean properties that has to be discussed.

3.2.2.5

The argument from quidditism

The argument from quidditism is connected to the argument from humility as follows (for their dependency as well as the formulation of both arguments see also Sparber 2008). For Lewis’s orthodox Humeanism the perspective to avoid humility is not open. Even though the orthodox Humean can know the causal and nomological structure of the world (i.e. the causal and nomological relations that are instantiated by the properties of objects) this knowledge does not determine on what kind of properties the structure supervenes. What bears the causal and nomological roles in the world cannot be known. There is a hidden non-causal and non-nomological essence to the intrinsic properties that are related by the causal-nomological structures. There are reasons to think that the existence of such essences is philosophically idle. Hence, the crucial question will be whether Humeanism in general is committed to their existence. The claim that Humean properties are not knowable whereas dispositional properties are has not been given other that epistemological justification so far. The underlying metaphysical reasons that underpin the foregoing argument are presented at different places in the literature under the name “the argument from quidditism” (see Black 2000, Lewis 2007 and Bird 2005b). It takes the following form: (1) Humean properties are not essentially dispositional. (2) Humeanism entails quidditism. (3) Dispositionalism does not entail quidditism. (4) An ontology that does not entail quidditism has a decisive advantage with respect to an ontology that entails quidditism. (5) Therefore, there exists at least one property that is irreducibly dispositional.

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As before, the argument depends at first sight on the acceptance of premise (4). Again opinions about premise (4) diverge. While Lewis thinks that quidditism is a harmless ontological consequence, Black and Bird argue that it should be avoided. Quidditism (named as such by Robert Black who invokes Scotist tradition, see 2000, 92) is a feature of properties and in what follows it will tacitly be taken to be one about fundamental properties. It is the claim that properties (qua types) have a primitive thisness. Property types have a primitive essence that constitutes their identity. The identity of a property is primitive if it is independent of the identity of its causal roles or dispositions (see Bird 2005b, 444). Quidditism is then the claim that the identity of property types does not supervene on the causal roles of those properties. The sameness of dispositions of two property types does not make for their identity. Nor does the identity of two properties make for the identity of their dispositions. In more detail, for two worlds one of which is ours, quidditism is the claim that “[...] [n]othing constitutes the fact that a certain quality playing a certain nomological role in that world is identical with a certain quality playing a different role in ours; they are just the same quality, and that’s all that can be said” (author’s italics, Black 2000, 92). Quality can be replaced by the more general notion of property type, and likewise can the notion of disposition stand for a certain nomological role. Quidditism then becomes the claim that for some fundamental property F and distinct sets of dispositions X and Y there is a possible world in which F has X, one in which F has Y or maybe even one in which F lacks any disposition at all. It is not claimed that the definitional variants for quidditism presented above are equivalent. Quidditism admits of degrees (see Bird 2005b, 443-453 for the distinction between strong and weak quidditism). The change in the causal roles of a property while holding the property itself identical admits of degrees. In order to confer maximal strength to the argument let us define quidditism in the weakest possible way. Bird’s weakest definition equals quidditism with the idea that two worlds may be identical in all respects, except that they contain two distinct properties that have the same dispositional make-up (see Bird’s definition QB1 in his 2005b, 446). They have the same causal structure brought about by a different metaphysical set-up. Quidditism can be defined as the claim that two sets of identical causal structures are metaphysically distinguishable by the property types their underlying objects instantiate, where

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causal structures are arrangements of actual causal relations between objects. In this sense quidditism is a feature of sets of second order properties, as causal relations are properties of properties. Sameness in all respects between worlds might, however, include the sameness of first order relational properties as well as the sameness of other than causal second order relations, if such exist. In principle, quidditism is a feature of sets of physical relations regardless of their order or kind. Thus, one can make sense of quidditism involving first order physical relations and non-causal second order relations. Due to maximal generality let us define quidditism as the claim that two sets of identical physical structures are distinguishable by the fundamental property types their underlying objects instantiate, where physical structures are arrangements of actual physical relations. Lewis’s Humean supervenience thesis says that there are only intrinsic and categorical physical properties. The essence of such properties does not depend on the causal roles the property plays (premise (1)). Their essence is a primitive metaphysical given. Consider the following situation: W1 consists of all the properties instantiated at the actual world W2 consists of all the properties instantiated at the actual world except for one charge particle replaced by a schmarge particle that behaves exactly chargishly To behave chargishly is to adopt exactly the causal roles of actual charge. Schmarge is a property distinct from charge and alien to our world. Lewis’s Humean supervenience cannot exclude W2 as a genuine possibility, because in his ontology nothing determines the essences (and hence the identities) of fundamental properties. There are even more extreme examples of worlds consisting of swapped actual properties (see Bird 2005b, 447-450 and already Chisholm 1967 for similar and easily applicable cases). W1 is physically identical to W2 , because it instantiates exactly the same actual causal (and noncausal) structure, but it is metaphysically distinct from W2 by the types of properties it instantiates. Therefore, Humean supervenience entails quidditism (premise (2)). Note that in a dispositionalist framework where properties have their causal roles essentially schmarge is not a possible property (nor are worlds with swapped properties and the like). Therefore dispositionalism does not entail quidditism (premise (3)).

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There are two main reasons to adopt premise (4). First the mere possibility of worlds like W2 seems philosophically counterintuitive. Whereas W2 is only slightly quidditistic there is in principle no limit within Humean supervenience that restricts the construction of more and more fancy quidditistic worlds. Second, given that only relations between objects are knowable to us (premise (1) from the previous argument), our knowledge never allows us make inferences to the world we actually live in. Our knowledge of causal roles and our ignorance of the Humean role occupiers leave us “blind” to quidditistic differences between worlds. In other words, we can never tell whether we live in W1 or W2 (Lewis 2007 acknowledges this point himself). Hence, quidditism of fundamental properties is the underlying metaphysical reason for humility towards them. The two arguments are logically dependent. An objection to the argument from quidditism might open the way to meet the argument from humility as well. Humean supervenience is affected by quidditism, because, even though the causal-nomological structure of the world supervenes on the distribution of fundamental property instances, nothing determines how these instances are regrouped into kinds. The obvious way to do so is via the notion of perfect similarity. Perfect similarity, however, cannot be spelled out in terms of their causal-nomological behaviour (i.e. in terms of similarity with respect to causal-nomological role occupation). It must be a perfect similarity of primitive essences. It is contingent how these essences are distributed among the fundamental natural property instances. The question remains whether the argument from quidditism is an argument against Humeanism in general (that is whether premise (2) is justified). So far we have seen that Humean supervenience with its fundamental physical properties, which are both intrinsic and categorical, is in trouble. Remember that a property is intrinsic to an object if and only if the having of the property is independent of accompaniment and loneliness with regard to properties of other objects (see Langton & Lewis 1998). Likewise, a property is extrinsic to an object if and only if the having of the property is dependent of either accompaniment or loneliness with regard to properties of other objects. In chapter 2.1.2 we have provided a definition of the classification of the set of properties into dispositional and categorical properties. Both orthodox Humeanism and orthodox dispositionalism posit fundamental intrinsic properties. In the first case they are categorical (so-called qualities)

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and in the second case they are dispositional (so-called powers). This suggests that the two distinctions cross-classify fundamental properties. In other words, the distinctions seem to be orthogonal. Orthogonality follows from the logical consistency of all four resulting categories. As before, we assume logical consistency for orthodox Humeanism and orthodox dispositionalism. Now consider an extrinsic property that plays a causal role: for example, the property to collide with a certain particle. The property relates two particles and may have specific effects. Nothing determines logically whether this property alone suffices to identify the two events as a causal sequence or whether a larger set of properties needs to account for the same. Nothing does so physically either (according to actual scientific knowledge). Hence, the exclusion of one of the two possibilities will be based on an entirely metaphysical reasoning. For the moment there is nothing inconsistent with the classes of extrinsic and categorical, as well as extrinsic and dispositional properties. In order to spell out orthogonality properly the property of colliding with a particle had better be a good candidate for a fundamental property, which it is arguably not: it is composed of the direction of two trajectories and the velocity of particles. The argument from humility and the argument from quidditism are declared anti-Humean (as shown in detail before). Dispositionalists claim that Humean supervenience is false, because it postulates categorical properties only. Now, orthogonality provides us with the following logical possibility: if it is the case that the arguments actually target at the postulate of intrinsic fundamental properties, then Humeanism might be saved if spelled out as an ontology of categorical and extrinsic fundamental properties. A case has been made in chapter 2.1.3 that under certain circumstances dispositionalism faces quidditistic problems as well, namely exactly when it postulates unmanifested fundamental dispositions. The existence of unmanifested fundamental dispositions serves as a motivation for the dispositionalist to consider her fundamental properties as intrinsic. Hence, it is justified to make the hypothesis that the woes of humility and quidditism actually affect ontologies that posit fundamental intrinsic properties. The orthodox Humean is of course worse off in the sense that she has to admit more possible worlds differing from ours only quidditistically. But if it is the case that intrinsic fundamental properties lead to humility and quidditism, then Humeanism might admit of an ontology that evades the problems of humility and quidditism. Such an ontology would have to posit exclusively

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fundamental relational and categorical properties. An attempt to spell out such an unorthodox Humeanism will be made in the next chapter.

Chapter 4

Unorthodox Humeanism Orthodox Humeanism, in the form of David Lewis’s Humean supervenience, is under pressure from arguments advanced by orthodox dispositionalists. The properties of orthodox Humeanism have quiddities that cannot be known (see chapters 3.2.2.5 and 3.2.2.4). Regarding the fundamental physical properties orthodox Humeanism consists of two fundamental postulates: first, that fundamental physical properties are intrinsic and need nothing more than a point (of space-time or matter) to be instantiated and second, that they are categorical. Everything else in the world supervenes. From the first claim (i.e. the intrinsity postulate) it follows that the complete physical state of the world (or even the complete state of the world simpliciter) supervenes on the intrinsic properties of fundamental physical objects, be they points of space-time or point-like bits of matter. These objects or the space-time points at which they are instantiated stand, of course, in spatio-temporal relations. The intrinsity postulate “[...] posits, in essence, that we can chop up space-time into arbitrarily small bits, each of which has its own physical state, much as we can chop up a newspaper photograph into individual pixels, each of which has a particular hue and intensity. As the whole picture is determined by nothing more than the values of the individual pixels plus their spatial disposition relative to one another, so the world as a whole is supposed to be decomposable into small bits laid out in space and time” (Maudlin 2007, 50, who calls the intrinsity postulate the doctrine of separability). This is philosophical atomism. Orthodox dispositionalism, as committed to fundamental intrinsic physical properties, is also an atomistic ontology in the above sense. Just like in the Humean case one could go and chop up space-time into point-sized bits and find there definite properties of objects such that we have definite physical states at these points. From the second claim (i.e. the categoricity postulate) it follows that no proper subset of the set of fundamental physical properties is ontologically sufficient for the instantiation of a different proper subset of the same fundamental physical properties. Categorical properties do not include the kind of primitive natural modality that is a prerequisite for ontological sufficiency. In

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fact, they do not include any kind of primitive natural modality at all. Still, we have reason to believe in the existence of some sort of modality in the world, for example in the case of causal and nomological relations. Such relations can only supervene on the whole arrangement of fundamental properties in the world. In the absence of primitive modality only the whole arrangement of fundamental categorical physical properties can determine causal and nomological relations. Thus, the categoricity postulate amounts to the claim that “[...] all facts about a world, including modal and nomological facts, are determined by its total physical state” (Maudlin 2007, 50, who calls the categoricity postulate the doctrine of physical statism, a misleading name in the light of chapter 3.2.1.2). The categoricity postulate is in principle independent of physicalism. One can be a physicalist without being a categorialist (as the orthodox dispositionalist) or a categorialist without being a physicalist (if one believes in the existence of fundamental categorical souls instantiated in our world). For our case, physicalism is a general assumption. The combination of the intrinsity postulate and the categoricity postulate excludes dispositionalist positions as well as categorialist positions that posit irreducible categorical physical relations (as, for example, the second order nomological universals in Dretske 1977 and Armstrong 1983). In what follows, I will take Lewis’s Humean supervenience thesis as the main representative of a coherent combination of both postulates (knowing that there may be others, maybe like in Earman 1984, will not narrow the range of application of the subsequent argumentation). Conceptual non-circularity demands that the adherent of Humean supervenience recedes from attempts to define intrinsic properties via the causal or nomological relations in which they stand. The combination of both postulates is logically possible. It is not necessary. In other words, both of the postulates are logically compatible with the negation of the other. Fundamental physical properties could be intrinsic, but dispositional (that is orthodox dispositionalism), or they could be categorical and extrinsic (an example of fundamental physical and categorical relations are Armstrong’s and Dretske’s second order nomic necessitation relations). The postulates are orthogonal (or, alternatively, logically independent of one another). All four combinations of the postulates and their negations are prima facie logically possible. The present chapter consists in the conception and the evaluation of one of those possibilities: unorthodox Humeanism. It first explains what the unortho-

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dox turn consists in and how it is motivated from a physical and from a metaphysical point of view. What is here called an unorthodox ontology will prove to satisfy the principles of a metaphysical position that is commonly referred to as structural realism. The chapter continues with the formulation and the discussion of the principles of such a structural realist ontology, in particular within a Humean framework. It then asks what the metaphysics of causation in accordance with a Humean structural realism looks like (in particular concerning regularities, laws of nature and counterfactuals). Once the metaphysics is spelled out unorthodox Humeanism is evaluated with regard to its potential to meet the dispositionalist challenges from the arguments of humility and quidditism. Besides these two arguments there exists a class of new dispositionalist challenges that target specifically at unorthodox Humeanism: arguments from anti-realism and empiricism. They are discussed together with a general evaluation of the potential for the dispositionalist to advance new challenges against unorthodox Humeanism. The chapter ends with a general comparison between unorthodox Humeanism and unorthodox dispositionalism and an appraisal of the Humean perspectives to have a competitive metaphysical system with respect to the ontology of science as compared to the dispositionalist. First of all, however, let us focus on the question what exactly the unorthodox turn consists in that leads to both unorthodox Humeanism and unorthodox dispositionalism.

4.1

The unorthodox turn

Both standard dispositionalism and standard Humeanism postulate fundamental intrinsic properties. They advocate an atomistic worldview. Giving up this perspective means to adopt a non-standard position. This is what will be called subsequently an unorthodox ontology. Motivations for such a move are located on different levels: physical, epistemological and metaphysical. First to physics: from the intrinsity postulate it follows that all fundamental properties are intrinsic properties except for the fundamental external spatio-temporal relations between the objects that instantiate them. The objects are points of space-time or point-sized bits of matter. In any case the objects that instantiate the fundamental properties have a definite location. As the fundamental physical properties (except for spatio-temporal relations) are such that they can be instantiated at point-sized locations, it is possible in principle to account for

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the physical state of a fundamental individual object by listing the intrinsic local properties instantiated by that object. In other words, every fundamental point-sized object has its own (that is what intrinsic means) physical state and is thus separable from any other fundamental object in the sense that their properties can exist separately and independently (again with the exception of spatio-temporal properties). Orthodox Humeanism explicitly makes the intrinsity postulate (in Lewis 1986b, x). I conjecture that something along these lines must be intended by orthodox dispositionalism as well. It is at least difficult to see how the postulation of fundamental intrinsic properties could be combined with a non-separability principle. The principle of the separability of a fundamental object from other fundamental objects is well respected from the point of view of classical Newtonian mechanics. It will be shown in the next section to be problematic when it comes to non-classical quantum mechanical objects and their quantum mechanical properties. Contemporary fundamental physics is both a well-established and confirmed scientific theory (pace Lewis 1986b, xi) and proves to conflict (on all major attempts of interpretation, according to Maudlin 2007, 61) with the principle of separability inherent to orthodox ontologies. As the intrinsity postulate naturally leads to the principle of physical separability, there is physical motivation for an unorthodox turn. From the epistemological and metaphysical point of view the motivation for an unorthodox turn lies in the prospect that the challenges raised by the arguments from humility and quidditism can be met. On the one hand, we have seen (in chapters 3.2.2.5 and 3.2.2.4) that orthodox Humeanism is affected by humility and quidditism. If the Humean wants to amend her account on this background her choice consists in either giving up Humeanism or orthodoxy, that is either the categoricity postulate or the intrinsity postulate. On the other hand, we have also seen (in chapter 2.1.3) that there are cases in which orthodox dispositionalism is also affected by humility and quidditism, even if these cases are considerably rarer compared to the number of examples of humility and quidditism that Humean supervenience permits. This situation at least suggests that what makes for humility and quidditism is the intrinsity postulate (in being the one that is shared by both orthodox Humeanism and orthodox dispositionalism). On these grounds the unorthodox turn is methodologically motivated by epistemological and metaphysical shortcomings of orthodox on-

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tologies. Whether the prospect to overcome humility and quidditism proves to be justified is discussed later in this chapter. The next section deals with the explanation of the physical reasons in favour of an unorthodox ontology and the discussion and explicitation of its metaphysical principles. 4.1.1

Physical reasons in favour of an unorthodox ontology

There are two different aspects of the intrinsity postulate (as stated above) the interdependence of which is important to our case: (1) The principle that all fundamental physical properties (except for spacetime relations) are intrinsic (intrinsity). (2) The principle that the state assigned to a compound physical system at a given time supervenes on the states assigned to its component subsystems at this time (separability). Principle (1) is a metaphysical thesis whereas principle (2) makes a physical claim. Supervenience here means physical determination and the state of an object are the physical properties the object instantiates. Within classical mechanics the principle of separability is tacitly respected. Think, for example, of an object like a billiard ball. This complex physical system has physical properties as a whole. It has a mass, a momentum, a location, etc. According to classical mechanics, all the properties of the compound system are determined by the well-defined and distinct properties of their composing objects. Suppose that a billiard ball is composed of fundamental atoms. Each classical atom of the classical billiard ball has a well-defined distinct classical state and the classical state of the classical billiard ball is wholly determined by these states. All of these atoms have, according to classical mechanics, the very same kinds of properties as the compound with determinate numerical values that are such that together they determine the numerical value of the compound properties. Fundamental objects can instantiate, in principle, any combination of fundamental properties each with determinate numerical values. All fundamental properties are in this sense independent of and compatible with one another. From the idea that, according to classical mechanics, physical properties have definite numerical values, it follows that every object has also a definite location (i.e. a property of being located that has a definite value). Thus, according to classical mechanics, the properties of a compound physical system super-

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vene on the properties of the composing systems that have determinate spatial coordinates. Hence classical mechanics claims that it is physically possible to locally isolate subsystems and their properties. In principle the identification of subsystems can be repeated until reaching the fundamental level of complexity (if there exists such a level). Therefore the idea of physical separability at least strongly suggests that fundamental physical properties instantiated by the fundamental physical objects are intrinsic (in the sense that they are metaphysically independent of the property instances of other objects and in the sense that if they are fundamental they only need small localised regions, maybe only points, of space-time to be instantiated). Classical mechanics reaches its scientific limits when it comes to the prediction and explanation of the behaviour of microscopic (subatomic) objects. The contemporary science that provides a description of the behaviour of such physical objects is the theory of quantum mechanics. In quantum mechanics the physical independency of the numerical values between any of the properties instantiated by an object does not hold in general. It holds, however, for some properties, namely exactly for those properties whose numerical values are independent from time: rest mass, charge and spin. Exactly those properties are independent from time that have constant numerical values throughout the existence of the objects that instantiate them. This is why independent properties can figure as definitional or essential features of microscopic objects. An electron could be defined as that kind of particle that has a rest mass of exactly 0.51 MeV, negative elementary charge and spin 21 . Thus, even in quantum mechanics, rest mass, charge and spin are considered classical properties. All other properties identified by quantum mechanics have values that are time-dependent. For these properties the general independency of their values does not hold anymore. Some of these properties are incompatible with one another. For example, both the position and momentum of a particle and the components of its spin (i.e. the three orthogonal directions x, y, z of its spin) are incompatible sets of properties. Two or more properties are incompatible exactly if not all of them can have definite numerical values when instantiated by an object at the same time. Only one property at a time can have a definite numerical value. Thus, if two properties are incompatible, the value of one of the properties at a time restricts the range of possible values the other property can have at the same time. The spin of an electron can, for example, only

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take two possible definite numerical values in each direction: + 12 and − 21 (or equivalently up-state and down-state, or formally | x ↑ > and | x ↓ > where x designates the direction in which the spin is measured). If it is the case that an object is measured to have the spin-value − 12 in x-direction, it follows from incompatibility that it has no definite spin value in either y- or z-direction. Only a probability distribution can be given for all possible values the object’s spin could have in the y- and z-direction. The specificity of quantum mechanics, in contrast with classical mechanics, is that the two values the spin of a particle in one direction can have give rise to more than two possible spin-states the particle could be in. In addition to the + 21 and − 21 spin-states, for example in the x-direction, any linear combination of the two (α | x ↑ > + β | x ↓ >, for α and β complex and α2 + β2 = 1) represents also a possible spin-state for the particle. Linear combinations of the definite numerical values a quantum state can have are called superpositions of values (see, for example, Albert 1994, 1-16, Maudlin 2007, chapter 2.1 and Esfeld 2008b, chapter 3). The probability distributions over the ranges of possible spin states in all three directions are correlated with one another. The probability distribution over the range of possible spin states in the x-direction determines, for example, the probability distributions over the ranges of possible spin states in the y- and z-direction. Suppose, for example, an electron is in the x-spin up state and we want to determine its z-spin. Then the correlation is given by | x ↑ > = √1 | z ↑ > + √1 | z ↓ > and the probabilities of getting a z-spin up or 2

2

a z-spin down result are both ( √1 )2 = 21 (something similar holds for the x-spin 2 | z ↑ > − √1 2

down state: | x ↓ > = | z ↓ >). The same reasoning applies for the correlation between possible positions and momenta of a quantum object (with the particularity that the correlation is represented by Heisenberg’s uncertainty relation). The possibility of superpositions of values of properties in an object qualifies the property as a non-classical, quantum physical property. So far, we have only discussed the case of a single object and its quantum properties. Thus, until now it cannot be decided whether the separability principle holds within quantum mechanics, because separability talks about compound systems that are composed of several subsystems. Let us therefore consider the situation of two particles and their spin states in the x-direction. There is a straightforward possibility to account for such a situation, namely by √1 2

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the so-called product states of the two particles. Product states of a compound system consisting of two particles assign any state the first particle alone can be in to this state and any state the second particle alone can be in to that state (see Maudlin 2007, 56), for example | z ↑ >1 | z ↓ >2 for the joint state consisting of particle 1 being in a z-spin up state and particle 2 being in a z-spin down state. Product states are separable. In our example, the joint state of the two-particle system supervenes on the individual states of the composing subsystems (consisting of particle 1 and 2). But the product states of the component quantum systems are not the only states in which the compound can be. Actually, in the same way that individual quantum states are subjected to the principle of superposition (spin states, for example, can have definite values up or down or any linear combination thereof), so are their product states. In other words, in the same manner as the probability distributions of some properties of individual quantum objects are correlated, the probability distributions of some properties of compound quantum systems (described by product states) can be correlated in a way that classical systems cannot. If this is the case for two or more quantum objects, then the objects are in an entangled state. The compound state of a two particle system (think of two electrons issued simultaneously and orthogonally from a common source) can be, for example, a so-called singlet state, where the spinstate of the compound z12 = √1 | z ↑ >1 | z ↓ >2 − √1 | z ↓ >1 | z ↑ >2 . For two 2 2 particles to be in a singlet state means that always when one particle has a definite value of spin in a certain direction, then the other particle has also a definite value of spin in the same direction and the two values are exactly opposite. In such a state, if the objects have a definite value of spin in the z-direction, there is a 50% chance that | z ↑ >1 | z ↓ >2 obtains and a 50% chance that | z ↓ >1 | z ↑ >2 obtains (chances for | z ↑ >1 | z ↑ >2 and | z ↓ >1 | z ↓ >2 to obtain are 0). It is, however, not the case that, taken by themselves, the two objects have definite values of spin in any direction. Therefore, the singlet state cannot be written as a simple product state, but only as a superposition of product states. An important support for the claim that the two objects taken individually are not in a spin state with definite numerical values is given by a theorem of the mathematician John Bell (in his 1964 paper). Bell’s theorem claims that if two or more objects are in an entangled state (of spin-directions, for example) and if the objects taken individually are also in a state with a definite numerical

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value (of the respective spin-direction), then it is impossible to obtain (through measurements during empirical experiments) the correlations as predicted by quantum mechanics. Bell’s theorem is commonly considered to claim that either quantum mechanics in its actual state is false (a thesis at least problematic in the light of its tremendous empirical success), or the objects that are in an entangled state cannot be in the respective states with definite numerical values of their own. This feature is called non-separability in the literature, because if a two particle system is, for example, in a singlet state (in a state of superposition of product states), then the determination of a definite numerical value of one of the particles (through a measurement) determines instantaneously the opposite definite numerical value for the second particle, no matter where or how far apart the two particles are. Thus, what Bell’s theorem shows is that non-separability “[...] is necessarily [...] a feature of every possible manner of calculating (with or without superposition) which produces the same statistical predictions as quantum mechanics does; and those predictions are now experimentally known to be correct” (Albert 1994, 70). To be precise, it does not follow from Bell’s theorem that the world is non-separable. The relevant correlations that are empirically known to be true can also be derived from theories that postulate a separable world (think of hidden variable theories like the one presented in Bohm 1952 or theories postulating time reversed or backward causation). These theories face independent problems. For Bohm’s theory there is a threat of incompatibility with special relativity as it requires an absolute standard of simultaneity (see Albert 1994, 160-161), an absolute standard that is denied by special relativity. Theories including backward causation face the charge of presenting counterintuitive ad hoc solutions. Let us, therefore, assume with the majority of philosophers of physics that the world is, in cases, non-separable. If several objects are in an entangled state such that they are in a superposition of spin-product-states, then these objects do not have definite spin values on their own. They do not instantiate determinate intrinsic spin-properties in the sense that their spin properties are not independent of the spin-properties of other objects. They depend on the spin-properties of the whole entangled state. Therefore, there exists a property of a compound physical system (i.e. the entangled spin-state) that is not determined by underlying properties of the component physical subsystems. In other words, for some physical systems

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and states, the state assigned to a compound physical system does not supervene on the states assigned to its component subsystems at this time (see also Teller 1986). Therefore, the existence of entangled states violates separability (without taking notice of the reservations from above). As entangled states of physical systems do not supervene on properties of the component subsystems, such states can be considered as candidates for fundamental properties in the same right as the component objects’ intrinsic properties could have counted as fundamental, had there been any. They are properties of the objects that compose the compound systems. But for any such object the property of being in a certain spin-state is not an intrinsic property. Hence, quantum mechanics also contradicts (or is problematic in combination with) the intrinsity principle. More precisely, because the world is not separable, fundamental physical properties cannot all be intrinsic (besides the spatio-temporal properties that are extrinsic anyhow). Thus, at least some of the fundamental physical properties that were previously considered as intrinsic really are extrinsic. A valuable interpretation consists in considering superpositions of product states of compound physical systems as relational properties of the objects that are in these superposed states. This will be spelled out in the next section. There are two questions to be addressed before. First, does physics suggest that all fundamental properties are extrinsic and relational? Second, are cases of quantum entanglement rare or common in nature? As we have seen physics pleads for relational properties in cases where there exist entangled states. Entanglement obtains only for timedependent properties. Thus, physics suggests that the properties of momentum, location and the components of the spin in any of three orthogonal directions can be conceived as irreducibly relational properties. Quantum physics, however, does not suggest that compatible, time-independent properties like mass, charge and spin are relational. The argument from the possibility to be entangled in certain physical systems does not affect these properties. Therefore, they are not affected by the non-separability as described by quantum mechanics. The most quantum physics in its actual state can aspire to accomplish is to show that “[...] the relations which the physical theory in question treats do not call for any intrinsic properties of the related systems. Nonetheless, since quantum theory is our fundamental theory, it would be desirable to derive stateindependent properties within the formalism of quantum theory. The idea then

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is to get to state-independent properties such as charge and mass on the basis of state-dependent properties” (Esfeld 2004, 611-612). State-dependency can be read as time-dependency. In any case, properties like mass and charge cannot provide for identity conditions of quantum mechanical objects, because they are instantiated with identical values by every fundamental quantum object of a certain kind. If we assume that electrons can be defined as the objects that have negative unitary charge, a rest mass of 0.51 MeV, etc. then all electrons instantiate these properties with identical and definite numerical values and cease to exist as electrons as soon as they cease to instantiate the properties. Therefore two electrons cannot be distinguished for example by the properties of mass and charge. Concerning the second question, the formalism of quantum mechanics considers the superposition of states not as an exception, but as the normal and pervading case. As for the individual object, which in most cases does not have time-dependent properties with definite numerical values, but is rather in a state of superposition of the possible numerical values the properties can have, the case where a physical compound is in a state where each of its components has properties with definite numerical values is the rare exception. In the normal situation a physical compound is in a superposition of all possible product states that consist of the components’ respective properties with definite numerical values. Consequently, if we have reason to think that quantum mechanics or some extension of it is a true theory, then we have reason to think that our world is not separable. It is not separable in the sense that the world cannot be “chopped up” into deliberately small pieces and one could still find all fundamental physical properties instantiated there. Such properties would be intrinsic properties. But quantum mechanics suggests that there are relational properties (and this is the rule) that do not supervene on underlying intrinsic properties. Therefore, there are irreducible relational properties. It is not possible to “split up” two objects that are in an entangled state without changing the objects themselves. Thus, quantum physics pleads for non-intrinsity, the claim that the fundamental physical properties are relational. The metaphysics of this thesis will be presented next.

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4.1.2

The metaphysical principles of an unorthodox ontology

On the ground of the physical motivations in favour of irreducible relational properties one can defend the following metaphysical thesis: All fundamental physical properties that provide for identity conditions of fundamental objects are extrinsic relational properties (structural realism). This position is called structural realism, because at the fundamental level of complexity there are only structures. Structures are sets of extrinsic properties. Structural realism is a thesis about fundamental physical properties. Just like, in the orthodox case, mere Cambridge properties (as being grue) are excluded as abundant, in the unorthodox case extrinsic properties in the form of internal relations (like being bigger than) do not figure among the fundamental properties. If restricted to fundamental physical properties, the class of extrinsic properties is coextensive with the class of relational properties (as intrinsic relations like being identical with are excluded). Structural realism as presented here is a metaphysical thesis that is independent from the epistemological claim that our knowledge of natural properties is exhausted by the knowledge of the relations that obtain between objects. The literature therefore distinguishes between metaphysical or ontic structural realism and epistemic structural realism (for the distinction see Ladyman 1998, who also launches the project to develop a metaphysics of structures; epistemic structural realism has been revitalised by Worrall 1989 on the basis of the work of Poincar´e, for example his 1905). The following discussion exclusively focuses on ontic structural realism unless specified otherwise. It follows from structural realism that there are no fundamental intrinsic properties that provide for identity conditions of the fundamental objects. Thus, the fundamental extrinsic properties that provide for identity conditions of objects cannot be internal relations. They do not supervene on the intrinsic properties of their relata (the physical example from above supports this claim). A relation is supervenient on underlying intrinsic properties if and only if necessarily each of the related things has a certain intrinsic property and these intrinsic properties determine the relation (see, for example, Cleland 1984, 25 for a formal definition). Spatio-temporal relations (even according to Lewis) and relations of quantum entanglement are non-supervenient relations in this

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sense. There exists a distinctive characterisation of how non-supervenient they are. Relations (according to Cleland 1984, 27-29) can fail to supervene in a strong or a weak way. Weakly non-supervenient relations have relata that necessarily instantiate intrinsic properties that do not, however, determine the relation in question. Strongly non-supervenient relations have relata that might instantiate (but do not have to instantiate) intrinsic properties. Obviously, these intrinsic properties fail to determine the relation. Spatio-temporal relations can be conceived as weakly non-supervenient (Cleland, for example, claims that one cannot think of spatio-temporal distances between ordinary objects without their having typically intrinsic properties like a certain shape or size). Relations of quantum entanglement, however, can only be characterised as strongly non-supervenient (see French 1989, 17-18, Esfeld 2004, 606 and Ladyman & Ross 2007, 150). On the one side it is clear that, in the case of structural realism, both spatiotemporal relations and relations of quantum entanglement have to be conceived as strongly non-supervenient relations, because there are no fundamental intrinsic properties of objects at all, even if they are independent of the relations in question. On the other side does the claim that all fundamental properties are strongly supervenient relations per se not exclude the existence of fundamental intrinsic properties. They just do not have any importance (in any sense of determination) regarding the relations. The possibility to conceive of strongly non-supervenient spatio-temporal relations (for such an interpretation see Esfeld & Lam 2008) shows that the mere specification of the supervenience type does not suffice to account for the specificity of spatio-temporal relations and relations of quantum entanglement. Both kinds of relations are worldbound and strongly non-supervenient, but they are distinct in the following sense: whereas any two objects in a given world are spatio-temporally related, not any two objects are related in quantum entanglement (such relations are actually dependent on the states of the objects). In virtue of being strongly non-supervenient and world-bound both kinds of relations somehow unify the world in relating its objects at the fundamental level. Every structural realist commits herself to this much. From this common ground, opinions considerably diverge about how to spell out structural realism furthermore. Structural realist positions can be classified into radical versions and moderate versions. Radical structural realism

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defends an eliminativist version of the claim that there are only fundamental relational properties. In addition to what has been said above the radical version holds that the set of beings (or existents) at the fundamental level of complexity is exhausted by the relational properties that are instantiated. In other words, all there is is structure. There is nothing more to the world than structure. In particular, there are not even objects (hence the label of eliminativism). The radical version of structural realism is due to Steven French and James Ladyman (in Ladyman 1998, French & Ladyman 2003b, French 2006 and with modifications Ladyman & Ross 2007). The argument against fundamental objects consists in pointing out that physics gives us no reason to believe in fundamental quantum particles or space-time points in the sense of physical individuals. There are two ways to interpret this claim metaphysically. Either there exist relations at the fundamental level of being or complexity that simply lack relata. Or relations lack relata in the sense that there is no fundamental level of being or complexity at all and the world is structure all the way down (where “all” does of course not allude to completeness). Every object that stands in a physical relation turns out to be a structure (or set of relations) itself and thus the question what the fundamental objects in the world are becomes pointless (if not absurd) by the fact that there are, by metaphysical postulation, no such things as fundamental objects. If there are objects in any relevant sense they are ontologically secondary or supervenient. The first interpretation faces difficulties when it comes to the question how to make sense of the existence of a fundamental relation that lacks relata altogether. Any familiar kind of relation (“being taller than”, “being composed of” or even “being in a state of entanglement with”) seems to have its ontological status tied to the ontological status of its relata. In other words, the reality of relations familiar to us seems to depend on the reality of their instances. How could instantiated relations possibly fail to relate something? If we consider the instance of a relation at the fundamental level, no other issue to the problem seems to be at hand than to question the ontological priority of the instances over the kinds of properties under which they are subsumed. In order to confer reality to relations that lack relata the commitment to a universalist theory of properties seems inevitable. But a universalist metaphysics of relations means not to be interested in the contingent specificities of their instantiations, but rather in their formal, ideal properties. Thus, in the first interpretation, recog-

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nising relations without relata at the fundamental level brings a commitment to a certain form of Platonism, because reality is conferred not to the concrete instantiations of relational properties, but to the formal abstract features of relational properties as kinds (this point is also made in Esfeld & Lam 2008, 5 and granted by Ladyman & Ross 2007, 152). I take it for granted that Platonism is at least highly problematic for a scientific realist position and should not be pursued within the framework of the search for a natural ontology. The second interpretation of the claim that relations can exist without relata presumes that there is no fundamental level of being or complexity. Let us from the outset leave aside the conception of a layered world with different levels of being or reality. Such ideas have been shown to be problematic (see Kim 1998 and Heil 2003). Insofar as the existence of a fundamental level alludes to an ontologically layered world let us ignore this line of interpretation. In other words, let us take the claim that there is no fundamental level in the world to mean that there is no fundamental level of complexity or composition in the world (something along these lines is suggested in Schaffer 2003). From this point of view the radical version of structural realism claims that relations are real, they have instances and what they relate turns our to be another relation (or a set thereof) and so on. There is no final level of complexity or, differently put, there is no level of compositional simplicity. What has previously been considered to be particles or space-time points really are structures (or patterns) that behave like particles or space-time points (see Saunders 2003b, 129 and Ladyman & Ross 2007, 178-179). Such a conception of relations and the structures they build up breaks the hierarchical conceptual link between the concept of relation and the concept of relatum. We are now in a situation that resembles rather conceptual circularity. Each relation has relata and relata are nothing but relations. It is not clear how something can be a relation and a relatum at the same time unless there is a hierarchy of composition or complexity in place. This is in principle no problem, for the radical structural realist can and should accept a principle of composition and with it levels of complexity on independent grounds. From this point of view the world is a system of pyramiding relations of higher and higher order (more precisely, every relation will be of maximal or infinite order). Let us assume for a moment that we are in such a situation where the world might be depicted as one of Calder’s mobiles (however,

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of infinite size and ramification). Take for example a water molecule that is a structure consisting of a specific arrangement of the composing three atoms that are themselves structures consisting of specific arrangements of protons, electrons and neutrons, and so on ad infinitum. This leads to the following problem: if there is no fundamental level of composition or complexity, then every entity in the world is equally and infinitely complex, because every entity (or structure) is composed of an infinity of other entities (or structures). Thus, there is no objective point to make about the relatively smaller complexity of an electron with respect to an atom or of an atom with respect to a molecule or of a molecule with respect to a cell, etc. Hence, there is no principle of composition (at least in the metaphysical sense). Ladyman & Ross (2007) bite the bullet and give reason for even doubting that there is disadvantage in doing so. Coarsely speaking, according to them scientific research always leads to model-dependent composition relations between entities, whereas metaphysics looks for a model-independent composition relation. The existence of the former cannot motivate the postulation of the latter, because abstraction in models reaches so far that no meaningful claim about causal relations or dispositions can be made independently of the model itself (this, they claim, is at least so for economical models, see Ladyman & Ross 2007, 21). But metaphysical composition is composition of causal relations or dispositions. Hence, no metaphysical principle of composition could possibly follow from scientific practice. Still, most philosophers have interest to stick to a metaphysical principle of composition on independent grounds. Even if abstraction might only lead to model-dependent causal claims, there is sufficient inductive ground that modeldependent abstraction decreases when the numerical extension of the scientific concepts augments. In other words, there are more electrons than free markets and models that cover the first have to make less abstraction than models that cover the second in order to identify causal relations. In this sense, there is a hierarchy of conceptual complexity between scientific concepts that opens the way towards the possibility of an epistemological reductionism. Epistemological reductionism in turn comes together with ontological reductionism. In particular, ontological reductionism provides the reason for the fact that higherlevel concepts do not capture something about an entity in addition to the composing entities referred to by the lower-level concepts (note that the inverse is

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not the case). But ontological reductionism postulates the identity of synchronically instantiated entities. What provides the identity is a relation of composition (pace Ladyman & Ross 2007, 253). Thus, the existence of a relation of composition (and accordingly the existence of levels of complexity) is motivated by the entire philosophical programme of epistemological reductionism. There are historical examples of successful inter-theoretic reduction that plead in favour of epistemological reductionism (see the example in Sachse 2007). Other versions of structural realism are compatible with a principle of composition and levels of complexity even if its radical form is not (or only at the cost of Platonism). Therefore, we adopt a moderate version of structural realism as presented in (Esfeld 2004 and Esfeld & Lam 2008). Moderate structural realism postulates that every fundamental property is relational and that the relata of fundamental properties are objects. In virtue of postulating objects moderate structural realism is compatible with a compositional principle. Complex objects and their properties are composed of less-complex objects and their properties. Property holism, the claim that a property is not generally independent of properties of other objects, does not affect the possibility of a compositional principle as such. Note that the moderate structural realist also needs to postulate a fundamental level of complexity in order to have comparative complexity between objects. Unlike the radical structural realist she is able to do it. There is no hierarchy of being between fundamental objects and the fundamental relations they entertain. The objects do not have intrinsic properties and are therefore nothing, but that what stands in relation to other objects. The relations themselves are concrete, irreducible physical relations that are instantiated by real objects. Thus, insofar as they exist, they exist as properties of objects (the avoidance of Platonism is another advantage of the moderate version of structural realism). In other words, “[...] objects can neither exist nor be conceived without relations in which they stand, and relations can neither exist in the physical world nor be conceived as the structure of the physical world without objects that stand in the relations” (Esfeld & Lam 2008, 32). The fundamental objects that moderate structural realism postulates have a primitive numerical identity in the sense that they are countable. As any form of primitive metaphysical identity should be avoided (see chapter 3.2.2.5) the question is whether the relational properties the fundamental objects entertain

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are discriminative enough to individuate the objects from a physical point of view. Let us assume that it is sufficient for an object to count as an individual entity if the properties it instantiates (or it may instantiate) distinguish it physically from all other objects. In other words, assume a principle of identity of physical indiscernibles for individual entities. It can be shown that in principle relational properties may suffice to individuate objects if they satisfy certain conditions (Bird 2007 proposes asymmetric second order relations). But actual candidates for fundamental physical relations do not satisfy these conditions (they are symmetric and first order). There are well-documented arguments that show how spatio-temporal relations and relations of quantum entanglement fail to provide sufficient discriminative power to physically distinguish all numerically distinct fundamental objects that are postulated by orthodox ontologies and moderate structural realism (see French & Redhead 1988, French & Ladyman 2003b, 36, Esfeld 2003, Esfeld 2004, 611-612 and Ladyman & Ross 2007). From a physical point of view two entangled quantum objects of the same kind (two electrons, for example) are indistinguishable. To be precise, there exists a criterion (presented by Saunders 2003a) according to which two electrons in an entangled state are weakly distinguishable. An irreflexive two-place relation applies to them, namely “is of opposite spin to”. It is not clear whether weak distinguishability in this sense makes for a physical difference between two electrons in an entangled state. Anyway, there are examples of physical objects, like elementary bosons, that can be in states such that no two of them are even weakly distinguishable. Hence, spatio-temporal relations and relations of quantum entanglement unify the world in relating its objects, but they do not individuate every fundamental object therein. From the point of view of contemporary physics only few of the fundamental objects are individual entities. Moderate structural realism not only claims that this physical situation need not be amended by the introduction of metaphysically primitive identities (that science must in principle ignore), but also that it should not. Both from the physical point of view and from the metaphysical point of view nothing speaks against fundamental objects that have only numerical identity but no irreducible intrinsic properties. As we have seen, radical structural realism is under double metaphysical strain. First, there is the threat from Platonism and second, it is incompatible with a compositional principle that, in turn, has inde-

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pendent advocacy. Both shortcomings can be avoided by the moderate version of structural realism. Let us therefore adopt moderate structural realism as a metaphysical principle for the following discussion. Besides the differences between the radical and the moderate form of structural realism there is a second criterion that allows for different structural realist accounts: the reducibility of natural modality. This criterion will be discussed in next section.

4.2

Humean and dispositionalist structural realism

Natural modality stands for the feature in nature that makes true causal and nomological (deterministic or probabilistic) predicate ascriptions. It is common to think of such ascriptions as including the notion of necessity. In our case, the question of natural modality is the question whether this conceptual necessity refers to natural metaphysical necessity in the world (the dispositionalist view) or whether there is not such thing as natural metaphysical necessity (the Humean view). Note from the outset that the metaphysical necessity defied by the Humean comes in the form of second order necessary relations. Causal relations and nomological relations do not obtain between objects directly, but between properties of objects. A majority of philosophers agrees, for example, that the causal relation of a window shattering upon a stone throw obtains between the events (qua property instances of objects) of stone-throwing and window-shattering. Assume now that moderate structural realism is true. Every fundamental property is a relation between fundamental objects. In other words, every fundamental property is a first order relation. As such the thesis of moderate structural realism says nothing about the existence of second order necessary relations. It is prima facie consistent both with their existence and their non-existence. But a closer look at things is appropriate here. We have seen previously that the fundamental objects of moderate structural realism, for most of the cases, fail to be individual entities in the physical sense. Responsible for this fact are the fundamental physical properties that are instantiated in our world that fail to distinguish every fundamental object from any other fundamental object. In particular, two quantum objects that are in a superposition of product states - that is, two quantum objects that are in an entangled state - cannot be distinguished by any physical means by the

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state-dependent properties they are in a superposition of. Relations of quantum entanglement are first order relations that do not supervene on intrinsic underlying properties of the related objects. They are structures directly instantiated by objects. In being first order and fundamental the relations cannot be modified by a modification of underlying intrinsic properties unless they have primitive identities over and above the fact how they relate their objects. Let us assume that this is not the case (with good reason to be found in chapter 3.2.2.5). Because it follows from moderate structural realism alone, the Humean and the dispositionalist ought to agree on the following claim: structures are holistic in the sense that a given structure relating a number of objects cannot be subject to local or isolated modification. Change one element and you change the whole structure. For the dispositionalist, this is not uncommon. Already in the atomistic version of dispositionalism local or isolated modifications of components of the world (for example, of a fundamental intrinsic property at a given spatiotemporal location) lead to changes in the past and the future light-cone of the property instances (determinism and permanent manifestation of fundamental dispositions assumed). If you change the first order properties, you change the second order causal and nomological set-up of the world. And with a change in the second order causal and nomological set-up of the world you change the first order property distribution, because the first order property distribution supervenes on the dispositions that are manifested as second order causal and nomological relations. Each fundamental object, insofar as its properties stand in causal relations, is necessarily related to other objects in virtue of the necessary causal and nomological connections between its properties and the properties of other objects. Remember that the essence of dispositional properties consists exactly in the potential causal relations with other properties. On the atomistic worldview, the properties in virtue of which objects stand in causal and nomological relations are intrinsic. All fundamental objects are individual entities in the physical sense, because there is always a determinate intrinsic property instance that distinguishes the object in question from any other object. Thus, for every fundamental object it is possible that its properties figure as relata of causal relations. Moderate structural realism has it that fundamental objects do not have properties of their own. Contemporary physics tells us that not every funda-

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mental object is an individual entity in the physical sense. Two necessary conditions are missing for a fundamental object to be able to entertain causal relations via its properties by itself: the intrinsic properties and a physical identity (the two are of course dependent). Therefore, in the case of moderate structural realism, not every fundamental object by itself instantiates properties that can figure as a relatum in a causal relation. But still, every fundamental object can figure as part of system that has properties that can be the relatum of a causal relation. Take again our example of two quantum objects in an entangled state. From the physical (or causal) point of view they are indistinguishable. As parts of an entangled system of quantum objects, however, their joint properties can stand in a causal relation. The entangled quantum system, for example, develops as a whole according to the dynamics described by Schr¨odinger’s equation. This dynamics permits to distinguish one quantum state at a certain time from the same state at a different time. According to dispositionalism this can be interpreted as a metaphysically necessary, causal development. In other words, any given quantum state (even if the state itself is a complex structure among several objects) can be said to have the disposition to develop according to Schr¨odinger’s equation. If one accepts an additional dynamics of state reductions (as presented by Ghirardi et al. 1986), then an entangled quantum state of a number of objects can be interpreted as having the disposition to reduce to disentangled localised states of these objects with definite numerical values. In sum, the unorthodox turn towards structural realism is not particularly problematic for the dispositionalist. There has already been considerable restriction on her possibilities to recombine fundamental objects and their properties in the orthodox framework. The second order, metaphysically necessary, causal relations still obtain as well as the fact that any modification of the first order property set-up leads to a modification of the second order causal and nomological structure, which, in turn, is responsible for a change in the first order property distribution. Her account is only to amend insofar as contemporary science informs us that, in general, causation is not a local process (as supposed by atomism) and that causal processes might exist between nonlocalised complex systems of fundamental objects (for the claim that locality is a contingent feature of causal relations, see Esfeld 2008b, 180). Instead of having dispositions themselves, objects enter into complex arrangements with dispositions. It is, however, inappropriate to think of fundamental objects as

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sic properties nor a primitive identity (a feature to be rejected on independent grounds). They are nothing but that what stands in the relations. Therefore, from a moderate structural realist point of view figure 2 does not represent a genuine possibility (not even for the Humean). Any variation of an element of a structure leads to a global change of the structure (as represented by figure 3). Structures are global properties of groups of objects that do not admit of local changes. Because she loses cases like those represented in figure 2 as genuine possibilities the unorthodox Humean has to restrict her free combinatorialism (a restriction that has consequences for her account on causation, discussed in chapter 4.3.2). Some properties of some objects are not capable of local, isolated change. In other words, some properties, namely the first order fundamental relations, are necessary connections even for the Humean. This is only at first sight incompatible with the Humean commitment to the absence of necessary connections in the world. Precisely, what the Humean is committed to is only the absence of necessary connection between distinct existences. Even though we recognise numerically distinct objects in our example of a state of quantum entanglement, we cannot conceive these objects as distinct existences in the sense of individual physical entities. The entangled quantum system as a whole is not per se necessarily connected to other quantum objects. Such a claim demands additional justification. Hence, the existence of fundamental necessary relations is compatible with Humeanism, because Humeanism is not a claim about the intrinsity or extrinsity of first order properties, but about the metaphysics of causation (and thus about second order properties). Above we have seen that it is possible for the dispositionalist to postulate for a state of quantum entanglement to have the disposition either to develop according to Schr¨odinger’s equation or to be reduced to disentangled states according to the Ghirardi-Rimini-Weber dynamics. In the same way is it possible for the Humean to accept both these fundamental dynamics as primitive metaphysical features in the sense that they only describe contingent and regular behaviour among fundamental physical entities in the world. In other words, it is possible for the Humean to consider the second order causal and nomological relations as merely contingent and internal relations of regular co-instantiation among physical states. Regular co-instantiation can serve as a sufficient supervenience basis for causal and nomological claims (it has done so in the orthodox case). Orthodox models are at hand. Consequently, on these accounts

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the causal roles physical systems play depend not only on the properties of the system itself, but on the properties of other systems that are similar to the first. In this sense, the first order properties of unorthodox Humeanism are categorical, even though they are necessary relations. They are categorical, because they only serve as a supervenience basis for causal and nomological relations as a whole, but not individually. Unorthodox Humeanism combines first order necessity with second order contingency. Like in the orthodox case, only the distribution of fundamental properties at the entire space-time is sufficient to account for causal and nomological second order relations. Therefore, the entire first order property distribution is an ontological primitive. Still, there are particularities of an unorthodox ontology such that standard Humean accounts of laws of nature and causation cannot simply be adopted. In the next section the question is raised whether a standard Humean view on laws of nature and causation is in principle available within an unorthodox ontology and how it can be spelled out.

4.3

Unorthodox Humean metaphysics of causation

Left aside the possibility of a Humean transference theory there is no account within the framework of Humeanism that provides a singularist account on causation. Only those accounts are singularist for which isolated and more or less local causal processes are ontologically primary with respect to the regularities they build up. For the Humean it is the other way round: more or less local causal processes or relations reduce to regular (and non-causal) behaviour. Irreducible, local causal processes conflict with our working definition of Humeanism saying that the world only consists of first order properties that do not play their causal roles independently of other objects and their properties. Any Humean metaphysics of causation (whatever the first order properties are like) should be committed to the following principles: (1) Realism: correct causal statements are strictly true. They have truth-values and refer to something in the world. There are some determinate features of the world in virtue of which causal relations obtain. (2) Reducibility: causal relations reduce to non-causal properties or arrangements thereof. Reduction comes down to identity. Therefore causal relations are identical with non-causal properties or arrangements thereof.

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There are currently two accounts within the orthodox Humean framework that are compatible with these principles: the standard regularity view and the sophisticated regularity view (or counterfactual theory) of causation. They differ in that the first accords priority to the causal dependence between property types and derives individual causal relations between property tokens (or events) whereas the second accords priority to the causal relation between property tokens (or events) and derives causal dependency between property types. On both accounts causation is intimately linked to the laws of nature. Remember that laws of nature state dependencies between property types. They quantify universally over every object that instantiates a given property type in order to establish a type of second order nomological relation between the properties themselves. For example, the classical law of gravitation quantifies over every object instantiating the property of having a determinate mass and its determinate property of being accelerated towards other determinate masses in order to establish the well known correlation between the properties of having a determinate mass and having a determinate acceleration. For the standard regularity theory every causal type-dependence is also a law of nature. For the sophisticated regularity or counterfactual theory there are laws of nature that point out important regularities in the world. These regularities determine the truth-values of statements about causal relations between particulars. In both cases, regularities and laws of nature play a fundamental role in the analysis of causation. Reasons have been presented (see chapter 1.4.1) why the counterfactual analysis is to prefer. The next section examines first in what sense there can be laws of nature and regularities within unorthodox Humeanism and whether a regularity view on causation is in principle tenable. Second, a discussion follows if and how the currently standard analysis of causation (Lewis’s counterfactual theory) can be amended such that it is compatible with unorthodox Humeanism.

4.3.1

Regularities and laws of nature in unorthodox Humeanism

In the present section we consider the question whether there can be Humean laws of nature within the framework of moderate structural realism. Moderate structural realism is a position that is informed by contemporary physical knowledge. As we have seen there are properties according to quantum me-

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chanics that cannot be conceived as intrinsic and fundamental at the same time. As our best actual deductive system the theoretical framework of quantum mechanics is supposed to provide us with theorems that, according to Lewis’s standard account, can be interpreted as laws of nature. Take, for example, the theorem of quantum mechanics according to which quantum states (usually denoted by Ψ) evolve in time as stated in Schr¨odinger’s equation. One peculiarity of quantum mechanics resides, for example, in the fact that the value of the position (as determined by Schr¨odinger’s equation) of a single quantum particle at a given time cannot be determined with security, but rather does the position function (Ψ(x)) for such a particle yield a probability distribution for different positions of the particle that can be found upon measurement. In this sense, the position function of a single particle contains not only information about the actual outcome that can be measured in an experiment, but it contains information about all possible outcomes of all possible experiments that can be carried out in order to find the position of the particle. The function itself is empirically corroborated insofar as repetitions of the experiment in which the position of, let us say, a single electron issued from a constant source is measured yield different outcomes with exactly the probabilities determined by the position function for this particle (actually by the norm of its squared value | Ψ2 |). On these grounds the following argument against the compatibility of a Humean account on laws of nature and the theorems of quantum mechanics has been stated (for a detailed development see Dieks 2006): (1) The position function of, say, an individual electron provides us with a probability distribution for possible measurements in which the position of the electron is determined. (2) Nothing within quantum mechanics permits us to distinguish between the status of the actual outcome of a measurement and the status of the nonactual possible outcomes of the measurement. (3) Thus, according to quantum mechanics all possible outcomes of measurements are on a par with regard to their existence. (4) Hence, if the actual world with the actual measurement outcome exists, then the possible worlds with possible measurement outcomes exist. (5) Therefore, the theorems of quantum mechanics are not mere regularities in our world, but trans-world regularities.

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Premise (1) is univocally accepted on empirical grounds. According to quantum mechanics the quantum state of a single particle like an electron has not, in general, a determinate value of position, but the state of the electron is rather a superposition of all possible states of position. It is also true that nothing within the theory of quantum mechanics confers actuality to only one of these possible states before a measurement is actually carried out (2). (3) has to be specified as it stands. It is correct that before any position measurement is actually carried out any measurement outcome has the same ontological status: it is possible (therefore (3)). It is not correct that before any measurement is carried out the single particle is actually in the state that is going to be measured afterwards. Rather the single particle is in a superposition of all states that can be measured afterwards. That we cannot determine the state of the particle before a measurement has actually been carried out is thus not due to our ignorance, but to a real indeterminacy of the state of the particle. (4) claims that if several outcomes for a measurement are possible, then all must be attributed the same ontological status. This claim as such is not implied by the theory of quantum mechanics. It is a claim about the ontological status of probabilities. An analogous thesis can be made about the reality of the possible outcomes of a play of dice. If all possible outcomes of such a play are regarded as equally real (let us say that there are six possible worlds instantiating the different outcomes), then the law that describes the play in stating the probabilities of its results supervenes not only on the actual world, but on the six possible worlds with their different results (5). Conclusion (5) implies modal realism. Only what exists can be part of a regularity. But if existing non-actual worlds contribute to the laws of nature that describe our world, then the Humean view is false that our laws of nature supervene on the arrangements of this-worldly regularities. There are several ways to spell out modal realism. The only form of modal realism that concerns us here consists in the introduction of real natural modalities within the actual world in the form of dispositions. On this view, an electron (or a play of dice) has a certain disposition (or rather propensity in the probabilistic case) to be at a given position at a given time. All the probabilities of all the possible outcomes are supposed to be explainable via the propensities of the quantum object to be at the relevant location. First of all, remember that the empirical explanatory surplus that comes with the introduction of propensities (or dispositions in general) is illusionary

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(see chapter 3.2.2.1). Therefore, from the point of view of quantum mechanics and its explanatory power there is no need to introduce propensities into one’s ontology even though their introduction is possible (according to Su´arez 2007). Second, the introduction of a modal realist account on objective probability is only compelling if no alternative account on objective probability is available that does not include primitive natural modality. As a matter of fact there exists a standard account on objective probabilities within the framework of Humeanism in terms of relative frequencies (see Lewis 1994a). The major drawback of such a theory (see chapter 2.3.2), namely its problems to account for rare or single occurrences of outcomes, does not affect the field of quantum mechanics where probabilistic dependencies are typically stated after a large number of experiences. Third, it is at least a misrepresentation of our practice of theory building if one supposes that non-actual possible states of affairs can inform our theories about the world, when rather the inverse is the case. We only have an epistemic access to non-actual states of affairs through our theories and not through direct acquaintance with such facts (see Dieks 2006). In other words, the unification that we perform in organising our knowledge about particular matters of fact into an empirically sound and deductively organised theoretical system brings us to believe that some laws of nature include probabilities. Whether or not these probabilities refer to primitive natural modality is independent from the empirical knowledge itself. The vantage point of our theory building rather suggests that our probabilistic laws of nature supervene on actual non-modal matters of fact. From these considerations it follows that contemporary physics is compatible with a standard regularity account on laws of nature. The existence of fundamental regularities is neither questioned by dispositionalists nor by Humeans. Lewis’s best system analysis of laws of nature permits to explain why in the process of organising our knowledge into a deductive theoretical system we might come to the point of introducing objective probabilities into our generalisations (it makes the system simpler while holding at least constant its explanatory strength). Nothing within contemporary physics commits us to a specific interpretation of these probabilities as primitive natural modalities (for example in the form propensities). An alternative account on objective probabilities is available that does not posit such entities. Therefore, the argument as stated above is not sound. Although fundamental physics informs us of

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the question whether there are intrinsic or relational fundamental properties and it suggests that there are objective probabilities in the world it does not preclude the existence of Humean laws of nature. Insofar as a regularity view of laws of nature is necessary for a regularity account on causation, the development of the latter within unorthodox Humeanism is possible. For the simple regularity account on causation every causal type-dependence is a law of nature. A simple regularity account on causation is thus a viable option. We will not enter into a discussion of how the standard account has to be amended in order to include probabilistic causation. The next section focuses on the sophisticated, counterfactual account within the framework of unorthodox Humeanism.

4.3.2

Counterfactual accounts on causation in unorthodox Humeanism

With the development of an unorthodox ontology as a physically informed unification of our knowledge, questions arise concerning the compatibility of a Humean counterfactual account of causation and the physical features of the world as stated by contemporary fundamental physics. As before, two different (and independent) aspects deserve discussion: the existence of probabilistic laws of nature and the fact that, in general, fundamental quantum objects are not localised. First, a brief reminder of the basics of a counterfactual analysis of causation (for details see chapters 1.4.2 and 1.4.3). According to Lewis’s standard account (1973, 1986b, 2004) causation is the ancestor relation of influence from an event C to a distinct event E. Influence is a class of counterfactual dependence between alterations of C (all of which are distinct) and E (some of which are distinct). A counterfactual dependence obtains between two events C and E if in all the closest C-worlds E also obtains. In other words, a C-world without E must be less similar to our world than any C-and-E-world. Similarity between worlds is determined by the following hierarchically ordered parameter: of first importance is the minimisation of widespread violations of actual laws of nature (so-called miracles), of second importance is the maximisation of world regions with identical matters of fact, of third importance is the minimisation of small local miracles and of forth importance is the maximisation of world regions with approximately similar matters of fact.

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We have shown (see chapter 1.4.2) that if the criteria of the similarity measure lead to nested sets of possible worlds (as they should), then the counterfactual semantics presuppose determinism. But Lewis also provides amended semantics for probabilistic laws of nature (1986b, 58-65). Instead of talking about violations of laws of nature, he introduces the notion of quasi-miracles to designate those states of affairs that are nomologically possible according to our current probabilistic laws, but that are “[...] chance outcomes [that] seem to conspire to produce a [highly improbable] pattern” (Lewis 1986b, 60). Quasi-miracles qualify as miracles not because they are improbable per se, but rather because the extension of the pattern determined by the many chance occurrences contributing to it is considerable (think of the quasi-miracle that is needed to rematch a possible world with our actual world in case of a nuclear bomb drop). Therefore, everything in the probabilistic account is standard except that divergences between previously identical worlds do not need small miracles anymore (they are just single chance occurrences according to Lewis 1986b, 61) and convergences of previously different worlds do not need big or widespread miracles anymore (they might only need quasi-miracles). The system of possible worlds still seems to be nested under probabilism in the sense that the third parameter (about small miracles) simply drops out (pace Schaffer 2004, 301). Lewis’s theory of probabilistic causation is not restricted to the macro-level. Consider, for example, two electrons in a singlet state (at time t0 ), the spinstate of which is being measured (at time t1 ). Undoubtedly, we are confronted with a causal relation between the state of the electrons and the state of the measuring device. There is a 50% chance to get result up-down and a 50% chance to get result down-up. Suppose that in the actual world the result is up-down. There are possible worlds that match ours exactly until the time of the measurement and contain result down-up. This is an ordinary chance outcome that does not need a violation of the laws of nature to be possible. Any attempt to converge both worlds after their different measurement proves to be more difficult, because states of measuring devices are typically very complex macro states (think of pointers and the like). It might be that such a convergence does not strictly speaking violate our actual laws of nature. But at least a quasi-miracle is required in the sense of a somehow “coordinated” (in an innocent interpretation) counterfactual arrangement of single chance occurrences

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that bring about the pattern in question. The actual best theory of causation (causation as influence, see Lewis 2004) requires counterfactual relations not only between the actual events, but also between alterations thereof. In our case, we can at least think of spatial and temporal alterations that establish a where-and-when dependence of influence between the singlet state and its measurement. From this perspective there does not seem to be a particular problem for the Humean with causation, but a more detailed examination will follow. The foregoing considerations are of course independent of the question whether one defends an orthodox or an unorthodox ontology. But it is noteworthy that the motivation behind the defence of a probabilistic account on laws and causation and the defence of an unorthodox ontology come from the same camp: contemporary fundamental physics. The importance of discussing probabilistic causation here lies in the fact that there is an element within the Humean account of causation that is present in both its deterministic version and its probabilistic version and that might prove to be problematic for an unorthodox ontology: the assumption of locality. The deterministic semantics of counterfactuals presupposes the possibility of local miracles and the indeterministic account presupposes the possibility of quasi-miracles that are a composition of specific outcomes (according to a pattern) of localised single chance occurrences. As we have seen, in general, fundamental objects (or particles) are not localised, in the sense that they do not instantiate a property of being located with a determinate numerical value. They cannot be said to be instantiated at a space-time point. Single chance occurrences are also in general not located at precise spatial locations, because they are instantiated by fundamental objects themselves or systems of such objects (as in the case of states of quantum entanglement). Moderate structural realism accounts for this fact in positing a holistic ontology where it is not possible to consider objects with properties independently of other objects and their properties. Holism, however, does not have to be considered universal. As far as physics is concerned, a network of first order relations between fundamental objects does not have to exceed the size of those physical systems that are experimentally considered as individual physical entities. It is a coherent interpretation of the quantum physical formalism to conceive of the world as composed of huge entangled states that encompass the whole of space at a given time and their development in time (as, for example, spelled out in Maudlin

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2007, 77-103, who vindicates a global structuralism that does not admit of any possibility for individual manipulation, see, in particular, 103). If this is the case though, there is not much interest in singling out objective causal processes within the world’s development, because there are no such processes besides the general quantum physical behaviour of the world as a whole (neither for the Humean nor for the dispositionalist). Let us therefore assume that there are sufficiently small physical entities that are apt to figure as causal relata (in Lewis’s conception of being distinct physical events) as, for example, a system of two fundamental objects whose states are entangled. So what we get is not a precise location of every fundamental object, but we get sufficiently small physical individuals that are contingently co-instantiated with other physical individuals and can therefore be modified. Even if in unorthodox Humeanism local miracles or quasi-miracles are not always available still there is physical individuality and thus manipulability (in the orthodox case every fundamental object is both localised and a physical individual) in spatio-temporal regions that are approximately determinable. Physical individuality is not tied to a causal interpretation of properties. The standard Humean account on natural properties can do. Exactly those properties are natural and constitute physical individuals that correspond to the predicates of the theorems of our best deductive system that describes the world. Thus, two spatially separated electrons in an entangled state do not admit of independent modification (of their incompatible properties), but their global state does. There are miracles on unorthodox Humeanism even if they are not always exactly localisable and even if they sometimes affect properties that are instantiated at disconnected space-time regions. Note that, in the case of quantum entanglement, it is not possible, according to Lewis’s account, to consider the entangled objects as entertaining a causal relation between themselves (that is to consider the relation of entanglement itself as causal). Physically speaking this makes no sense, because the relevant objects behave strictly synchronically (in the case of a measurement, for example), even if they are spatially separated by a long distance. According to the special theory of relativity no kind of information could be transmitted between the objects themselves. But it is commonly accepted that in case of a causal relation some information actually is transmitted from the cause to the effect (even if the information is as meagre as counterfactual influence).

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In addition, from the metaphysical point of view, causation is regarded as an asymmetrical relation. Two events cannot exchange their roles as cause and effect. No criterion (metaphysical or physical) is at hand to univocally assign the role of the cause to one object as opposed to the other object in the case where their states are entangled. Even if the behaviour of two objects that have their states entangled could be said to depend counterfactually, their relation is not causal per definitionem. Lewis’s definition of a causal relation presupposes the presence of two distinct events. Events are property instantiations of objects. There is no physical property supposedly making for causal influence between objects in an entangled state, because the objects in such a state do not instantiate underlying intrinsic properties. In other words, quantum entanglement is not a relation between properties of objects (and thus a second order property), but rather a relational property of quantum objects (and thus a first order property). Therefore, not the state of quantum entanglement between objects itself is causal, but only its development in time according to the dynamics identified by contemporary quantum mechanics (or maybe its reduction to separate individual states). Physics gives us no upper delimitation of what to consider as an individual entity, because the world can be physically interpreted as just the development of one all encompassing entangled state. It does give us a lower delimitation of what to consider an individual entity in saying that not every fundamental object is physically distinguishable from every other fundamental object. We make the additional metaphysical assumption that individual physical entities (like systems of objects whose quantum states are entangled) exist within appropriate dimensions (i.e. that they are sufficiently small). Thus, their properties can stand in contingent causal relations in a way compatible with our intuition that causal relations are more or less local in our world (think of macroexamples like billiard balls). But if we say that fundamental physical entities like a system of two entangled quantum objects can potentially entertain causal relations, it is still an open question whether Lewis’s theory of causation is applicable to such entities. According to Lewis, causation is influence. Influence establishes a whether-when-how dependence between distinct events and their alterations. Take, for example, a system of two entangled objects and its development from time t0 to time t1 as described by Schr¨odinger’s equation. Certainly the

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states at both times are when-when-dependent. Consider alterations of the first event instantiated at t0 +∆ and there will be a counterfactual dependence with alterations of the second event at t1 +∆, because time is an external parameter in quantum mechanics. It might be problematic to consider time as an external parameter, because in doing so one neglects the relational spatio-temporal network quantum mechanical processes happen to be embedded in. This network as described by the theory of general relativity is not merely a passive background for mechanical processes, but contains itself gravitational energymatter that interacts with the spatio-temporal network in determining its geometry. The existence of gravitational energy-matter, as interpreted according to moderate structural realism, is a global property of space-time and does not admit of local counterfactual variations (for this point see Lam 2007 and also Esfeld 2008b, 164). In the light of a missing unifying theory, it might be enough for the existence of temporal alterations of entangled states to resort to a simplified picture of the spatio-temporal network in considering it as a passive background and thus breaking the mutual dependency between mechanical processes and spatio-temporal relations. Furthermore, Schr¨odinger’s equation provides other kinds of alterations that are independent of the spatiotemporal network they happen to be instantiated in. It determines the way in which how-alterations of the first event counterfactually depend on some how-alterations of the second event. Even if point-like temporal alterations prove to be physically inconceivable still there is a sort of influence between the cause-properties and the effect-properties. Whether-whether dependence is a limit case of how-how dependence. Therefore, one can maintain that a certain extent of counterfactual influence can be identified within the dynamics of quantum mechanical processes. In case one accepts a dynamics of probabilistic state reductions in the sense of spontaneous localisations (as proposed in Ghirardi et al. 1986), these processes also admit of counterfactual dependency with different subsequent events. If, however, the future development of fundamental physics proves the impossibility of alterations within stable global property arrangements two alternatives are at hand for the Humean. First, she can still adopt a simple regularity theory on causation as outlined in chapter 1.4.1. Second, she can provide amended semantics for counterfactual statements that are based on the actual laws of nature, but do not include local manipulations. Thus, the Humean can

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for example defend the claim that events are related as cause and effects if and only if they fall under laws of nature that involve a temporal asymmetry. But for now, no such move seems to be necessary. Lewis’s idea of causal influence, namely that “wiggling” with the features of the cause-event lead to changes in the features of the effect-event, can be applied to the case of instances of fundamental relational properties. This is the case even though some alterations of these instances are not allowed. It might not be allowed to construct spatio-temporal alterations and one certainly cannot “break up” a relation of quantum entanglement between two objects, because these relations are fundamental and necessary. But just like the world is not the point-mosaic Lewis postulates, it might be conceived as a contingent arrangement of individual entities occupying spatio-temporal regions (even if not precisely delimitated), having relational properties and standing in causal and nomological second order relations. The next section deals with the potential of unorthodox Humeanism to meet the problems that its orthodox version faces.

4.4

The arguments against Humeanism in a new light

Before we have shown that the standard accounts for laws of nature and causation are available (with modifications) to the unorthodox Humean. The question to answer now is whether the unorthodox version of Humeanism is better off than the orthodox version when it comes to dispositionalist objections. Two objections seriously affect orthodox Humeanism: quidditism (chapter 3.2.2.5) and humility (chapter 3.2.2.4). Both objections are connected in the sense that quidditistic differences between possible worlds cannot be known in principle. But not only intrinsic and categorical properties are affected by quidditism and humility. Also unmanifested dispositional properties can lead to quidditistic differences between possible worlds. This suggests that quidditism and the humility that comes along with it are features of a theory of properties that is independent of the question whether properties are defined functionally (that is along the possible effects they can have) or in a Humean way (for example, through a principle of correspondence between fundamental predicates of our best descriptive theory and fundamental properties). It is the aim of the present section to cash out this assumption to the result that Humean properties can

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be conceived such that they do not include unknowable primitive identities, insofar as they are structures.

4.4.1

Quidditism

Humeanism in general holds that laws of nature and causation supervene on the arrangement of fundamental first order properties independently of the choice one takes in either postulating they are intrinsic or that they are extrinsic. Quidditistic differences between possible worlds typically arise either when one and the same property plays different causal roles in different possible worlds or when different properties assume the same causal roles in different possible worlds. Supervenience of causation includes the possibility of a difference in the arrangement of fundamental physical properties leaving the set-up of causal relations identical. But this difference is not a quidditistic difference, because it is not a difference in the kinds of fundamental properties instantiated. Supervenience only includes the idea that the same properties actually instantiated can be arranged a little bit differently without altering the actual causal relations between them. Remember our definition of quidditism. Quidditism is the claim that two sets of identical physical structures are distinguishable by the fundamental property types their underlying objects instantiate, where physical structures are arrangements of actual physical relations. The simple response for the unorthodox Humean against the charge of quidditism is the following: on a Humean regularity account (sophisticated or not) causation is nothing over an above certain regular patterns in the distribution of fundamental property instances. In our case, these property instances are exclusively extrinsic and form fundamental physical structures. According to the definition of quidditism two identical physical structures can be distinguished by the fundamental property types their underlying objects instantiate. On unorthodox Humeanism the underlying objects do not instantiate fundamental properties over and above the fundamental extrinsic properties that relate them to other objects. Therefore, unorthodox Humeanism lacks the potential to distinguish two identical physical structures. This answer is too short, because the extrinsic properties, if they are real, have identities themselves. Either they have a primitive identity distinct from the way they relate objects or the way they relate objects constitutes

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their essence. Of course, only the second possibility has the potential to avoid quidditism. Let us therefore assume that the essence of fundamental extrinsic properties is determined by the specific way they relate objects. It constitutes such a property’s essence that it relates two objects in a state of spin entanglement, for example. Note that in this case the essences of fundamental extrinsic properties are not defined by their dispositions, for their essences have nothing to do with causal features the properties actually give rise to. As we have seen before, the fundamental relations are first order properties and synchronic (and hence non-causal). The relations are metaphysically necessary connections between objects. However, the second order causal relations between the necessary structures are contingent as they depend on the contingent arrangement of the first order structures. Because the underlying objects lack intrinsic properties and the fundamental extrinsic properties have no primitive identity over and above the way they relate the objects, there is no quidditistic difference within unorthodox Humeanism between two identical physical structures. Humeanism in general does not entail quidditism (although orthodox Humeanism normally does) and the argument from quidditism as an anti-Humean argument is false. It follows that from the point of view of quidditism we have no reason to switch to a dispositionalist ontology. One step of our reasoning must be highlighted though: the relevant meaning of necessity, essence and manipulability of fundamental relations. The claim that first order properties instantiate metaphysically necessary connections between objects whereas second order properties that relate the properties of these objects are only contingent introduces a duality within ontology that might seem stunning at first glance. A closer look, however, reveals that the idea of necessary first order relation is not as far fetched as one might think. It draws basically on the distinction (that is physically and not metaphysically justified) that not every fundamental object is a physical individual in the sense that its identity is determined by the physical properties it instantiates. Complex and fundamental physical individuals (as entangled states) are necessarily constituted as they are, because the relational properties their component objects instantiate are wholly described and identified by the particular way they relate these objects. Imagine that this would not be the case. The following situation would then be possible: we have two fundamental objects that are related by

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one fundamental property that is extrinsic to each of the objects. However, the same property could have been different in different possible worlds. Two possibilities cross the mind how this could be the case. Either, it is possible that the two objects are not related at all, or they are related by the same property (in a metaphysical sense) that is, however, physically different. On the first possibility, we have now two objects that are not related by the fundamental property in question. In order to be individual physical entities the two objects must instantiate other properties instead. Structural realism has it that those can only be relational properties, in which case the argument iterates. What we get in the end are objects that do not have properties at all. But moderate structural realism has it that objects are nothing over and above that what instantiates the relational properties. Such objects would be nothing at all in the physical sense and from moderate structural realism it follows that that which does not stand in relations at all is not an object. On the second possibility, we have two objects that are related by the same relation (from the metaphysical point of view) that are, however, physically different. One way to conceive of physical difference is to cite different causal or nomological roles the property in question plays. The Humean has no problems to accept distinct causal and nomological roles for the same kind of properties (that is precisely what her position consists in). These roles are determined by extrinsic factors, namely the particular arrangement the relational property instance is a part of. The fact that causal and nomological roles are assigned externally is independent of the fact that the role occupiers (the objects and their properties) do not themselves instantiate any form of primitive identity. Even Lewis’s orthodox Humeanism is not conceptually committed to quidditism, because it is compatible with a trans-world counterpart theory for property kinds (admittedly, a very problematic move). Quidditism is a claim about the metaphysics of properties and not about the metaphysics of causation. It is a claim about the nature of physical structures and their discernibility by means of the property kinds instantiated. The natural possibility to distinguish physically identical structures is given if they are said to supervene on non-structural more fundamental properties (as in the case of both orthodox Humeanism and dispositionalism). A non-natural possibility to distinguish them arises if structures themselves (or the relations that compose them) are conceived as having primitive identities.

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What is of interest to us presently are physical differences that are inherent in and determined by the property instance alone. Imagine therefore two possible worlds consisting only of the two objects and their relation to one another. According to moderate structural realism there are three ontological entities present (two objects and one property). In lacking a distinct supervenience basis for the relational property (in the form of intrinsic properties), there is nothing that ontologically justifies the claim that the relation can stay metaphysically identical while being physically distinct. I take this as a reason to consider the attribution of primitive identities to fundamental physical relations as metaphysically ad hoc. It is at least an ontological possibility not to consider the relations as having a quiddity. What makes for the identity of fundamental kinds of relations is that the predicates of our best descriptive system refer to them. If they differ physically, this is because they are referred to by different predicates. These first order properties are what they are in virtue of the specific way they relate fundamental objects. This is their essence. Under these assumptions their manipulation while maintaining metaphysical identity does not represent a genuine possibility. They instantiate necessary connections though not between distinct existences. Still, a clarification for our example is necessary. It includes the notion of possible worlds. Quidditism can be defined as the possibility of trans-world identity of property kinds that play different causal and nomological roles and as the possibility of trans-world distinctions between property kinds that play the same causal and nomological roles (as proposed by Lewis 2007). Then the simple argument can be made that the fundamental relation in our example is of the same kind than, say, the relation that obtains in a world with four objects, two and two of which are related respectively. Hence, we get quidditism. The problem with this line of argumentation is that such a definition of quidditism is erroneous or at least inappropriate for our case. The first conjunct of the definition is problematic for the Humean, because in structurally different worlds the laws of nature are likely to be different as well, thus falling short of satisfying our definition of quidditism in terms of structural identity. In any case, realism about possible worlds is implied with the conception of properties as trans-world entities. The second conjunct is equivalent to our definition, if one adopts realism about possible worlds. A definition implying realism about possible worlds is problematic for independent reasons. There-

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fore, let us conclude that for unorthodox Humeanism there is no metaphysical difference between structurally identical worlds (used in an innocent heuristic way) and that it can meet the objection from quidditism that affects its orthodox version. In the framework of unorthodox Humeanism primitive identities of property kinds are dealt with by restricting the number of possible ways our world could have been. The next section discusses whether such a restriction also diminishes our lack of knowledge concerning the question which world we actually inhabit.

4.4.2

Humility

Scientific realism claims that our descriptions of the world capture something about the properties instantiated in the world. In particular, we can describe the behaviour of objects and detect regularities concerning this behaviour. Regularities in the behaviour of things are similarities between relations objects entertain between one another. Unorthodox Humeanism considerably reduces the number of possible worlds compared to its orthodox version. Worlds with identical physical structures (arranged in the same way) are identical simpliciter. The ignorance about which possible world we actually inhabit shrinks accordingly. In order to know exactly to what extent our ignorance diminishes let us briefly return to the underlying metaphysical reasons for the humility objection affecting orthodox Humeanism. Orthodox Humeanism is affected by a double contingency. First and foremost, every Humean postulates the contingency of second order causal and nomological relations. From the point of view of the individual property instance it is externally and contingently determined what causal and nomological role it plays according to the global arrangement of property instances it is a part of. This contingency is preserved under unorthodox Humeanism. Second, it is also contingent under what property types these instances are subsumed. It is a primitive fact about their identity that makes for their membership to a certain type. It is only in virtue of this second fact that orthodox Humean properties can swap causal and nomological roles without altering the whole second order relational set-up of the world. The second contingency consists therefore in the undetermined and therefore primitive distribution of property type identities under which the particulars fall that are instantiated in a particular world.

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This second contingency claim is problematic in itself even if one leaves aside the problematic consequences that arise from quidditism. Suppose that Lewis is right. We have a true theory about the world. Let us pass over the subtleties of the different ways such a theory can be obtained. That is, let us abstract of the difficulties that come along with methods like Ramsification and so on. Thus, our theory provides us with a complete description of the causal and nomological roles instantiated in our world. The theory describing the world, according to the Humean account, also truly describes any world where properties of the same category (monadic, dyadic, and so forth) swap positions. If this is a possible scenario, the predicates of the theory’s theorems at most determine the relevant category under which the properties (or role occupiers) fall. Or, as Lewis says, “[...] it is one thing to know that a causal role is occupied, another thing to know what occupies it” (Lewis 2007, 1). Lewis insists, however, that his account for laws of nature (that is based on considerations about the theory that best describes the world) has the advantage to provide an explanation for the fact that in scientific practice the discovery of the so far fundamental physical properties is tied to the discovery of the laws of nature that describe their behaviour (Lewis talks of a package deal in his 1983a, 368). There is a tension between these two claims. According to the first claim, we can only know the world’s structure and not the objects and properties that are structured in this particular way, besides the merely formal knowledge about their category membership and the metaphysical postulate that the properties happen to be real physical entities. According to the second claim, our theorising about the world leads us to a certain physical knowledge of the properties actually involved in the laws of nature (and subsequently in causation) above the fact that they are mere placeholders for second order causal and nomological relations. One can interpret this claim in considering the relation between predicates of our theory and kinds of first order properties as necessary (conflicting thus with the double contingency specified above). Only the second claim provides the grounds for a full-blooded realism (pace Worrall 1989; reasons for this claim can already be found in Newman 1928). Epistemic structural realism, the claim that we can only know how our world is structured, is by itself insufficient for ontological realism (as discussed in Esfeld 2008b, 117-119). The combination of an atomistic ontology (consisting only of intrinsic fundamental physical properties) and the denial of direct acquaintance with the

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essence of fundamental properties leaves no room for the orthodox Humean to go beyond the idea of fundamental properties as mere placeholders for relations. To give up the idea of atomism, however, provides us with the following possibility: nobody contests that second order causal and nomological relations are knowable. That, however, is not all we can know. We can also gain knowledge about first order relations that obtain directly between objects. Macroscopic examples of first order relations that we get to know in our everyday life are spatio-temporal distances between objects like the beginning and the end of a football game or the left and the right goalpost. Even if our experience of everyday first order relations proves to be mediated by the causal relations they entertain with us the existence of specific kinds of macroscopic first order relations is common knowledge. In other words, through our everyday experience of the world we are familiar with there being non-causal first order relations between objects. It is a different question whether the knowledge of macroscopic first order relations licences the conclusion that so-called theoretical entities in the form of first order relations are knowable as well. Contemporary physics gives us the example of a fundamental type of property about which we have both physical knowledge and physical reasons to believe that it is relational and first order: relations of quantum entanglement. Again, our physical knowledge of relations of quantum entanglement might prove to be mediated by the causal relations in which they stand. So far, on inductive grounds (founded on our everyday experience) we do not have reason to believe that relations of quantum entanglement are in principle unknowable or that they lack a proper ontological status (a claim that will be challenged subsequently). In this sense, nothing restricts the knowability of relations to a specific metaphysical kind of relations (first order or second order). Like in the orthodox case, the unorthodox Humean still has her placeholders in the form of fundamental objects. Unlike in the orthodox case these placeholders do not instantiate intrinsic qualitative features in addition to the physical relations they stand in. Therefore, the properties postulated by the unorthodox Humean can in principle be known. Insofar as these fundamental first order relations do not have an essence (or identity) over and above the particular way they relate objects it is in principle possible for us to gain exhaustive knowledge about them. The unorthodox Humean has at least the perspective to defend an ontology that is a full-blooded realism. In other words, in ruling out fundamental intrinsic

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properties and the contingency of the distribution of identities among properties of the same category (and thus quidditism) the epistemological uncertainty about what world (of a class of structurally identical worlds) we inhabit shrinks accordingly. Classes of structurally identical worlds as postulated by orthodox Humeanism are single member sets under unorthodox Humeanism. The question whether unorthodox Humeanism has the resources for a fullblooded realism is not settled by the foregoing considerations. It has only been shown that the switch to an unorthodox ontology makes it easier for the Humean to remain within the realist framework. In particular, it is not clear whether the knowability of first order relations is independent of the question whether they are manifestations of underlying powers or categorical ontological primitives. If the knowability of first order relations were indeed independent of the metaphysics of causation then everything that is knowable on the dispositionalist account would also be knowable on the unorthodox Humean account (contrary to the premises of the argument from humility as outlined in chapter 3.2.2.4). From the point of view of humility the Humean would not be worse off than the dispositionalist. Surprisingly the challenge of antirealism has not been commonly addressed to the orthodox version of Humeanism (as we have done here). There are, however, arguments developed within the structural realist literature concluding to the point that general considerations about realism provide sufficient reason to adopt a dispositionalist instead of a Humean version of structural realism.

4.5

A new challenge for Humeanism: anti-realism

This section discusses the question: “Can unorthodox Humeanism be a fullblooded realism?” In answering the question positively the unorthodox Humean tries to separate herself from the view that our theories about the world are only empirically adequate for the phenomena we directly observe, but do not license any realist conclusions about the unobservable entities that are postulated by this theory. This position is known as constructive empiricism and mainly defended on the grounds of Van Fraassen (1980). According to constructive empiricism, we cannot get in touch with unobservable entities because we cannot know whether our scientific theories are true or false. The reference of the predicates of our theories to properties instantiated at our world is not guaranteed. A relation like predicate-property reference is typically inaccessible for

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us. Evidence for this is mainly coming from the argument of pessimistic induction that claims that we have no reason to believe in the truth of our current best theory or even an ideally best theory, because history has shown that any theory about the world so far has been subject to refutation. The adoption of epistemic structural realism by itself is insufficient for scientific realism, because there is no objective criterion within this position to determine which part of the structural description of the world’s behaviour corresponds to real properties of the world (see Van Fraassen 2006, 287-290). The featured solution for this problem has it that what remains structurally stable within a given theory throughout the progress of science corresponds to real entities. If all our knowledge about the world (as represented in our scientific theories) is structural in nature, then it is the case that whatever remains stable through theory changes are only formal mathematical correlations between concepts that themselves have their meaning changed in accordance with the new inferential role they adopt within the new theory. Thus, there is no positive content of concepts that remains stable when they are embedded in a new theory and therefore there is nothing the structures themselves positively tell us about the objects and properties in the world (see already Newman 1928 and Esfeld 2008b, 118-119). This feature is nicely demonstrated by the fact that within orthodox Humeanism the theoretical structure best describing the world does not supervene on the distribution of the identities (or essences) of the intrinsic properties that make this description true: free intra-categorical redistribution is possible. The lack of direct realist arguments from within epistemic structural realism has lead philosophers to add the following ontological premise to their accounts: not only can we not know the intrinsic properties of natural objects by means of our theories, but such properties do not exist at all. Therefore, the structural descriptions of our theories refer to irreducibly structural properties of the world (see Ladyman 1998, French & Ladyman 2003b and Ladyman & Ross 2007). In claiming the reality of non-supervening structural properties, this new thesis (described in detail in chapter 4.1.2), now called ontic structural realism, is developed in order to satisfy the demands of a full-blooded realism. As we have seen, however, the radical form of ontic structural realism faces the challenge of Platonism concerning the supposed structure of nature it describes (see Esfeld & Lam 2008). A Platonist view on structures brings

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with it the commitment to structures as abstract existing entities in the sense of universals. More precisely, by challenging the existence of objects in the world radical structural realism as it stands is not able to account for the reality of the structures themselves. Or as Van Fraassen has it, “[...] if there is no nonstructure, there is no structure either” (Van Fraassen 2006, 293). As it stands, radical structural realism is insufficient to be qualified as a realist position. There are currently two alternatives to amend this problem: first, to adopt a modal version of structural realism and second, to switch to a moderate form of structural realism. For the sake of simplicity let us assume that the term modal refers to that kind of entity that is ontologically sufficient to ground the existence of something else (objects, properties, structures and the like). In this sense, we consider the primitive modality postulated by a modal version of structural realism as functionally (or dispositionally) interpretable (conceptual proximity between the two notions is granted by Ladyman & Ross 2007, 130). Therefore, we consider modal versions of structural realism to be dispositionalist ontologies. The first alternative to amend the problem of anti-realism (as defended by Ladyman 1998, French & Ladyman 2003b, French & Ladyman 2003a, Ladyman & Ross 2007, chapter 3) holds that the structures referred to by our theories (or models) are real natural structures, because they instantiate natural modality. Note that the existence of natural modality is compatible with the radical structural realist’s conviction that there is only structure in the world. Instead to conceive of modalities as second order intrinsic properties of structures, it is also possible to accept them as second order necessary connections between structures. In any case, it is claimed that this modality ultimately provides a principle of necessary correspondence between our conceptual or mathematical, descriptive structures and the properties in the world. As natural structures are inhabited by primitive modality, they have the potential to ground second-order causal patterns. Any familiar and observable causal relation on the macroscopic level of consideration supervenes on the distribution of primitive modalities in the sense that it is identical with a specific arrangement of structures displaying necessary causal behaviour. For radical structural realism the existence of primitive modality coupled with some sort of reductionism therefore secures the passage (or inference) from the structure that is observable for us to the structure that is unobservable for us. Thus, the modal version of radical structural realism is not a form of constructive em-

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piricism. This conclusion, however, is flawed in one aspect. It presupposes the possibility of reductionism. Reductionism is broadly accepted as the vertical, compositional identification between entities. It is not at all clear how the reconstruction of macroscopic causal processes can be accomplished without acknowledging the existence of levels of compositional complexity (see chapter 4.1.2). But if reductionism is not compatible with radical structural realism, then it is hard to see how realism about non-observables can be justified. Thus the modal version of radical structural realism suffers from the tension between a need for realism and the hostility to a principle of composition and thus reductionism. Among other things, it is the intention of the moderate version of structural realism to break this tension. As before, it is possible to defend a modal, dispositionalist or a non-modal, categorialist version of moderate structural realism. The dispositionalist contends that the mere shift from the radical to the moderate version of structural realism does not suffice for the Humean to claim to be a realist concerning unobservable properties. In general, for an ontology to satisfy realist standards it must respond to the following demands: (1) Its properties must be real. (2) It must be possible that properties have instances. (3) It must be possible to identify objects by the properties they have. (4) It must be possible to distinguish kinds of properties. As we have seen above non-modal radical structural realism faces the objection that the properties it posits are abstract mathematical structures and that realism with regard to the structures comes down to Platonism about abstract mathematical entities. Moderate versions of structural realism, however, differ from the radical position exactly in the defence of a two-category ontology. There are objects and properties that are instantiated by them. Objects are nothing over and above what instantiates the properties. Objects and properties hence share their ontological status. There are no objects without properties and no properties without objects. If one is a realist about objects, then realism about properties follows and vice versa. As a primitive metaphysical postulate unorthodox Humeanism adopts realism about both (therefore (1)). In particular, unorthodox Humeanism posits fundamental extrinsic properties in the sense of fundamental physical relations between objects. Relations are kinds of properties that can have instances in the world. Both Lewis’s exam-

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ple of a physical relational property (see the discussion about the consideration of like-chargedness as a candidate for a fundamental relational property in his 1986a, 77) and relations of quantum entanglement obviously have instances independently of their being considered fundamental. Both are extrinsic (2). To a certain extent relations conceived as concrete physical entities in the world permit to identify objects and to distinguish them from other objects just like intrinsic properties. They have a certain discriminative power. Unlike intrinsic properties, they cannot do so independently of the existence of other objects. David Lewis argues that certain extrinsic properties as like-chargedness have too little discriminative power to unify the world (see Lewis 1986a, 77). They are bad candidates for fundamental physical properties, because they only give relative information about the states of, say, two particles. Now, consider our candidates for fundamental physical relations (relations of quantum entanglement). If two quantum objects are in a certain entangled state the relation of entanglement does not determine a relevant state of the systems taken individually, because there is no such individual state. If these relations lack the discriminative power to individuate quantum objects in such a way, this is not a metaphysical sign that they do not sufficiently unify the world and its objects, it is rather a physical sign that there is no unification over and above the one provided by these relations (see Esfeld 2004, 5-7). In Lewis’s orthodox Humeanism what unifies the world are spatio-temporal relations only. In addition to that, for the unorthodox Humean fundamental physical relations between objects unify the world. These relations have a certain discriminative power on objects. It is shown at length (in Bird 2007) with graph theoretic considerations that in principle intrinsic properties can be discriminated by asymmetric second order relations (e.g. causal relations) between them. The case applies to our situation in the sense that nothing substantial turns on the fact that our objects stand for Bird’s intrinsic properties and likewise our first order relations for his second order relations. There are fewer possibilities for identification in our case for we do not want to restrict ourselves to asymmetric relations. But in any case, fundamental extrinsic properties can (to a sufficient extent) identify objects (3), even if, for physical reasons, there is less identity in the world than Bird dreams of. Unorthodox Humeanism is still Humeanism and therefore cannot distinguish between kinds of properties via the different effects they give rise to. As

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natural properties their instances are supposed to display qualitative similarities and dissimilarities with other instances that permit to subsume them into kinds. Let us adopt the view that from an ontological point of view kinds are nothing over and above their instances. In the orthodox Humean case, we have seen that the postulate of such a primitive similarity that determines the kind membership of instances of a natural property (in other words the property’s essence or identity) leads to quidditism and humility, because there primitive similarity is a relation between qualitative aspects of intrinsic properties that are not determined by the causal and nomological role they play and thus not knowable through our theory. In other words, an orthodox Humean cannot guarantee that the predicates of theorems of her best descriptive system actually pick out kinds of natural properties (in the sense of a one-to-one correspondence relation). If she happens to be able to distinguish kinds of properties via scientific predicates this is at most a coincidence. For unorthodox Humeans the possibility to individuate property kinds also turns on their naturalness. This time, however, fundamental relations are defined by the qualitative way they relate their objects. And the qualitative way they relate objects are described by the scientific theory itself. Two electrons instantiate the relation of quantum entanglement if and only if their product states (of the relevant spin directions, for example, or their positions and momenta) are in a superposition. The terms of the product states in superposition determine the kind of relation that is instantiated. Unorthodox Humeanism postulates that this is all there is to the qualitative identity of the relation. The unorthodox Humean can hence distinguish kinds of properties (therefore (4)). One might hold that by postulating qualitatively discriminated relational properties we reintroduce the notion of primitive type identity (see, for example, Ney 2007, 57). The question is whether orthodox and unorthodox Humeanism are in an equally bad situation concerning primitive identities, or whether the structuralist version of Humeanism is better off. Remember that the orthodox Humean faces the problem of maximal contingency in the distribution of property type identities. Any causal description of an arrangement of intrinsic and categorical property instances therefore falls short of the Newman objection according to which the description lacks qualitative, concrete content. More precisely, insofar as we cannot get directly acquainted with the qualitative nature of fundamental properties our theory tells us nothing about

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these properties (see Newman 1928 and Demopoulos & Friedman 1985). Unorthodox Humeanism, however, avoids the Newman objection in the sense that our theory succeeds in discriminating fundamental properties qua concrete and qualitative physical relations. There is obviously something contentful about a theory that distinguishes, for example, between metrical relations and relations of quantum entanglement (see also Chakravartty 2004). In this sense, our theory allows us to grasp qualitative aspects of the fundamental properties even though, taken individually, they realise causal roles only contingently. Insofar as the qualitative aspects of the fundamental properties constitute their identity we are not in a similarly humble situation as in the orthodox case. Unorthodox Humeanism is better off. On these grounds, the unorthodox Humean can claim that she can in principle gain epistemological access to the nature of fundamental properties, because she postulates concrete, qualitative, physical structures at the fundamental level. But here another, more general objection threatens Humeanism: the fundamental concrete and physical structures are not properties of the realm of the observable phenomena. In being fundamental they are structures of theoretical entities that underly the realm of the observable phenomena. Theoretical entities (as postulated by our scientific descriptions) ground the observable phenomena. The existence of theoretical entities is only justified in virtue of the causal explanation they offer of the realm of the observable phenomena (see Esfeld 2008a, 8). But the causal relation between the unobservable and the observable is contingent for the Humean. Therefore the following situation can arise: suppose that the Humean has a complete theory about the world in the form of a Ramsey sentence. The Ramsey sentence describes the causal network that obtains at our world for we can gain knowledge of properties only insofar as they stand in a causal relation with the cognitive apparatus of the observant. In the course of our theory building we causally explain what we can observe directly by entities and properties that we cannot observe directly in postulating theoretical entities. Because causation is only contingent for the Humean the observable causal structure is compatible with the postulation of different sets of theoretical entities. In other words, the structure of the observable phenomena can be correlated with different kinds of unobservable structures. One can say that for the Humean one type of observable structure can be realised by different kinds of

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unobservable structures (as claimed by Esfeld 2008a, 7-8). Note that this is not a standard case of multiple realisation where the realisers of a higher-level property belong to different kinds of lower-level properties. Still, both the standard example and the present situation share the characteristic that there may be “[...] different minimal sufficient physical conditions to bring about the effects that define the multiply realized type” (Esfeld 2008a, 7). In our case the multiply realised type is the macroscopic and observable structure that is identified by the part of the scientific theory that describes our observable world. The argument from multiple realisation consists in the claim that within the Humean framework fundamental and unobservable physical structures of different kinds are sufficient to make true one and the same causal description of the realm of the observable phenomena. If the foregoing considerations are correct then unorthodox Humeanism has no grounds to plead for the existence of theoretical entities. That is, unorthodox Humeanism leads to anti-realism with respect to the unobservable in the manner of constructive empiricism. According to the argument dispositionalism does not lead to anti-realism with respect to the unobservable, because by metaphysical necessity any difference in the fundamental unobservable structure between two possible worlds entails a difference in the realm of the observable phenomena between these worlds. Thus, “[...] only a causal conception of the concrete, qualitative, fundamental physical structures ties them to the observable phenomena so that we can in principle know their qualitative character on the basis of the observable phenomena” (Esfeld 2008a, 8). The Humean faces hence a humility challenge much more general than the one based on quidditism that has been previously discussed. Her general agonsticism concerning the fundamental structure underlying the observable phenomena points to a case of general underdetermination of the observable by the unobservable, an underdetermination allegedly due to the specific Humean metaphysics of causation. The aim of the subsequent discussion is double. On the one hand it seeks to determine whether the unorthodox Humean (or the Humean in general) is in principle subject to the problems of underdetermination and multiple realisation. On the other hand it intends to check whether dispositionalism as it stands is safe from underdetermination and multiple realisation and has therefore an advantage over the Humean.

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Unorthodox Humeanism is affected by multiple realisation if the following situation is possible: two different kinds of fundamental unobservable structures realise the same kind of macroscopic observable structure. To be different kinds of unobservable structures does not mean that the same types of properties be differently instantiated (a contingency that even the dispositionalist allows for), but that different types of properties are actually instantiated. Realisation in this context means that tokens of one kind of structure (i.e. the structure of the observable) can be conceived as being identical with tokens of different kinds of lower-level structure (i.e. the structure of the unobservable). Conceivability means logical compatibility of the theoretical structures that correspond to concrete, physical structures in the world. So, let us suppose that we have a theory that is empirically confirmed by what is observable. By the theoretical entities the theory postulates we make conjectures to what there is at the unobservable level. The conjecture itself does not reflect an epistemological uncertainty, because, as we have stated before, we can grasp qualitative aspects of relational properties (relations of quantum entanglement and metrical relations are obviously qualitatively distinct). Rather the conjecture represents the possibility of multiple interpretation of one theory or even the presence of several distinct theories that are empirically adequate descriptions of the observable phenomena. In the first case, the uncertainty is due to the immature state of the theory itself, a fact that is normally not considered to plead for anti-realism. In the second case, we have theories that describe exactly the same observable phenomena, but differ in the postulation of what kinds of unobservable phenomena there are. The construction of such empirically equivalent theories is in principle always possible. In this sense, unorthodox Humeanism (and Humeanism in general) is always subject to multiple realisation. This sounds worse than it is, because Humeanism provides us with additional conditions a theory has to satisfy in order to be a candidate that picks out fundamental kinds of properties or that determines the kinds of theoretical entities that exist in our world: theories must display a good balance between empirical strength and deductive simplicity (see chapter 1.2 for details). Most of the theories that are empirically equivalent are going to be discarded as candidates for the best deductive system on the basis of their lack of simplicity compared with the theories that are actual candidates for best deductive systems.

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Still, it is possible that there is a tie between several theories in the sense that they display an equally good balance of simplicity and strength that cannot be discriminated further by any objective standards. Two cases have to be distinguished: if the theories are only partly distinct, then the theorems that are shared by all the candidate theories are those that determine the laws of nature and the theoretical entities that exist in the world. If the theories are wholly distinct, then we cannot determine what has to be considered a law of nature in our world, nor a fortiori the theoretical entities the behaviour of which these non-existing laws are supposed to describe (see again Lewis 1994a, 478-479). Lawhood would then be an entirely psychological matter and we would indeed have to abandon realism about theoretical entities, because the detection of laws of nature and fundamental kinds of properties is a “package deal” even under Humeanism (see Lewis 1983a, 368). As a matter of contingent fact, however, we happen to live in a fairly regular world (that is at least what the general consensus among scientists makes us believe). The chances for more than one equally good deductive systems shrinks accordingly. Therefore, in a world like ours best deductive systems do not tend to diverge with respect to theoretical entities as there is the perspective of a robust winner among the competing theories. Thus, the whole domain of the observable phenomena of the actual world is, as a matter of contingent fact, not realised by different types of arrangements of fundamental physical structures. That we happen to live in a world with the live perspective of a single robustly best deductive system is a metaphysical postulate of world-affiliation. Lewis refers to it as the kindness of nature (see Lewis 1994a, 479). It might be considered a disadvantage that the Humean can adopt realism only by postulation. In sum, there seems to be heavy metaphysical burden for a general and rather vague postulate pleading for a kindly arranged world. However, we will see later in this discussion that the dispositionalist cannot dispose herself either of the need to resort to a postulate when it comes to the problem of realism about theoretical entities. Even if the Humean can respond to the problem of multiple realisation the problem of a principled underdetermination of the unobservable by the observable phenomena remains. Apparently two forms of underdetermination have to be distinguished: the first principled and concerning the entire domain of observable phenomena in the world (and grounding thus the possibility of mul-

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tiple realisation), the second relative to the actual standard of our knowledge about a restricted set of observable phenomena. The second kind of underdetermination is unproblematic, as, given our actual limits of scientific knowledge, there “[...] always are cases in which a given set of observable phenomena available at a time underdetermines the theoretical entities posited by different theories of the same domain or different interpretations of a given theory” (Esfeld 2008a, 8). General anti-realism about theoretical entities should not be justified by the contingent state of development of human knowledge. Think, for example, of standard quantum mechanics and Bohmian mechanics that imply the same observable consequences (for the time being), but differ in the set of theoretical entities they postulate. One can be optimistic that the further development of quantum field theory or even a potential theory of quantum gravity and the empirical predictions that come along with them will discriminate between these diverging theories. This much being granted, we still face the first kind of principled underdetermination of the set of unobservable phenomena by the entire domain of the observable phenomena. It is well known (at the latest since Quine 1951) that in principle true theories are underdetermined by the world they describe. Again, the unorthodox Humean can accept this point without problems. The general underdetermination diagnosis is compatible with the claim that the entire domain of observable phenomena does not underdetermine the existence of a single best and true deductive system and does therefore not underdetermine the existence of a single set of theoretical entities or, equivalently, a single kind of unobservable structure. What is at stake here is an ideal theory that we would develop, if we knew everything. Still the dispositionalist can claim that the underdetermination problem depends on the metaphysics of causation that one adopts. Contingent causation allows for identical causal roles with underlying property changes whereas metaphysically necessary causation does not. This is important for our case, because, after all, unobservable entities are postulated in order to causally explain the observable world. From the point of view of individual property instances it is true that they play their causal role only contingently. From the point of view of the entire distribution of property instances the causal and nomological network instantiated in the world is metaphysically necessary (if supervenience holds). As opposed to orthodox Humeanism in the unorthodox framework the free redistribution of property identities is re-

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stricted by the fact that we can qualitatively identify natural kinds through our theory. Under appropriate circumstances (i.e. a kind enough nature) the whole domain of observable phenomena does not underdetermine the domain of unobservable phenomena, as long as we have reason to believe that our current best theories approach an ideal, single best deductive system. Therefore, the orthodox Humean can expect that different kinds of unobservable structures lead to different theories about the world in the long run (i.e. in the case of pervading knowledge) even if they are indistinguishable by the actual means of scientific investigation. The challenges from underdetermination and multiple realisation can be met. Let us turn to the second point, that is to say, to the question whether dispositionalists are safe from underdetermination and multiple realisation. Recall that dispositionalists claim that only primitive modality can guarantee the passage from observable to unobservable facts. The argument in favour of a dispositionalist version of moderate structural realism goes as follows: in order to have reasons to believe in the existence of structures that are unobservable for us, there must be a necessary connection between these structures (and ultimately the fundamental structure) and the properties that we experience directly through our senses. Moreover, this connection must be grounded in features of the unobservable structure itself. Only the dispositionalist provides an ontological foundation of the relevant connections by means of fundamental structures that have the dispositions to bring about the property instances such as they are experienced directly by our senses. By means of this ontological foundation (through the postulation of primitive modality) there is a necessary one-to-one correspondence between the structure of the observable and the structure of the unobservable. It is helpful for the discussion of this argument to distinguish the following two senses in which it is possible to infer from the observable to the unobservable. First, it is clear that our direct scientific experience of the world is restricted to a small region of space-time. From this experience we try to establish general causal and nomological claims between types of properties and assume that they hold at any spatio-temporal region throughout the universe (call this horizontal inference). Second, our direct scientific experience of the world is restricted to a certain level of complexity. It is not possible for us to directly observe sub-atomic particles, for example. The theory that

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has been established on direct observations above a certain level of complexity includes claims about unobservable entities and their behaviour beneath this level and maybe ultimately about the fundamental, simple constituents of nature and their behaviour. It is thus an inherent feature of our scientific theory building that we infer from the more complex observable to the less complex unobservable (call this vertical inference). Given the possibility that our scientific predicates pick out natural kinds of properties, the Humean licenses horizontal inference by simply postulating that we inhabit a regular world (this is the often cited kindness of nature, see Lewis 1994a, 479). The dispositionalist, however, conceives of the properties instantiated at the space-time region that is observable to us as necessitated in time. Via the observable causal structure she identifies the relevant dispositions at work and constructs theoretical claims about the behaviour of the world in the future and the past as well as in spatially inaccessible regions of the universe on their basis. At first glance she has an explanatory principle (the existence of dispositions) to license these horizontal inferences. At second glance, though, the dispositionalist also needs a metaphysical postulate not so different in nature from the one of the Humean. She postulates that in spatio-temporal regions inaccessible to our direct scientific experience exactly the same kinds of dispositional properties are instantiated as in the directly observable region. Were this not the case no nomological generalisation on the basis of observable dispositional properties would be true, because the actual course of the world is compatible with countless different dispositional property distributions (of different kinds) in the past and in the future. In any case, for the dispositionalist non-observable structure brings about the observable structure (this is the fundamental dispositionalist postulate). But we can only be realists about the types of unobservable structure if we postulate a natural similarity between the instances of unobservable structure and the instances of observable structures (by means of a similarity of the effects they cause), such that they can be subsumed under the same property types. To stress this point think of the following situation (as depicted in figure 4). Let o be the realm of the empirically observable (here simplified as a pointsized spatio-temporal region) and let o be the intersection of the two continuous straight lines that represent the light-cones (past for the lower triangle and future for the upper triangle) corresponding to the empirically accessible property

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o e

d

Let o be the realm of the empirically observable (here simplified as a point-sized Figure 4 temporal region) and let o be the intersection of the two continuous straight lin represent the light-cones (past for the lower triangle and future for the upper t corresponding to the empirically accessible property instances on the basis of w instances on the basis of what is observable to us. Let d be the instance of a disobservable to us. Let d be the instance of a dispositional property within the past lightpositional property within pastdispositionalist light-cone of what for dus.causes For what is observable for us. Forthethe theis observable effects that in the the dispositionalist the effects that d causes in the world determine under what determine under what kind of property the instance d is subsumed. Let e be such an ef kind property the instance d islight-cone subsumed. Let be such an effect. As upper it hap- dashed tr it happens e isofboth within the future of de (delineated by the e is bothfor within future light-cone of d (delineated by the upper which is pens necessary any the possible causal connection between the two,dashed and outside th is necessary any empirical possible causal connection betweensuppose the cone of triangle), o such which that we do not for have access to it. Now, that two, and outside light-cone such not that we do to notbe have accessIn other w characteristic effect of the d (note that of it odoes have theempirical only one). to it.(maybe Now, suppose that e is a characteristic effect of d (note thatanit instance does not of. If th determines co-determines) what kind of property d is to be the one).be In sure other what words,kind e determines (maybe possible have situation, weonly cannot of property d isco-determines) an instance of, becau property d is an instance of. If thisthat is aispossible situation, we know ab possible what that kind e is of itself the instance of a property alien to what we world. Incannot otherbe words, the kind kindofofproperty property is instance an instance of might be instantiate sure what d ise an of, because it isnot possible realm of that the eobservable or what empirically for we us know on that basis. Thus is itself the oinstance of is a property that isaccessible alien to what about case the the dispositionalist realist about the kinds of properties instantiated world. In othercannot words, be the akind of property e is an instance of might not spatio-temporal regionin that is physically accessible to us, because she cannot uni be instantiated the realm of the observable o or what is empirically accessubsumesible the forinstances this inregion under types of properties. us on thatwithin basis. Thus, this case the dispositionalist cannot be a Without assumption they might kinds of properties are alien to what we can obse realist about the instantiate kinds of properties instantiated in that the spatio-temporal region Hence, inthat excluding thisaccessible kind of situation, the she dispositionalist postulates is physically to us, because cannot univocally subsumealso the a sort of kindness, namely that only few types of dispositional properties are instantiated in th and that the types of observable structure are also the types under which unobs structure can be subsumed (this is, of course, only the case for horizontal infe Regularity in the course of the world follows thereof. Therefore, insofar as the lic

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instances within this region under types of properties. Without further assumption they might instantiate kinds of properties that are alien to what we can observe. Thus, dispositionalism suffers from horizontal underdetermination and multiple realisation. There are several ways the dispositionalist can address this problem in the sense of denying the possibility of the above situation. She can avoid horizontal underdetermination and multiple realisation in claiming that any effect e that is alien to our actual domain of observation will necessarily lead to some future differences in the course of the world that will be observable for us. She thus denies the possibility that our universe is such that causal changes can propagate indefinitely outside the future light-cone of the realm of the observable. This is a hypothesis about the structure and dynamics of space-time itself. If one does not want to make general assumptions on the topology of space-time there is an elegant way for the dispositionalist to exclude situations of the above kind. She can deny the possibility of fundamental multi-track dispositions (i.e. dispositions with more than one kind of manifestation). If only single-track dispositions exist at the fundamental level then e cannot be an effect that is alien to us. Regularity in the course of the world follows thereof. To sum up, the dispositionalist can avoid horizontal underdetermination and multiple realisation in only postulating single-track dispositions. We have seen earlier that all fundamental dispositions had better be permanently manifested in order to avoid humility and quidditism situations (see chapter 2.1.3). Taken together, these two postulates guarantee a regular and transparantly knowable behaviour of the world. They exclude sceptical scenarios. As such, the two postulates represent for the dispositionalist what the Humean calls natural kindness, namely that only few types of properties are instantiated in the world and that the types of observable structure are also the types under which unobservable structure can be subsumed (this is, of course, only the case for horizontal inference). Therefore, insofar as the license of horizontal inference is concerned the Humean and the dispositionalist are on a par. They both simply postulate the validity of the inference. Insofar as the dispositionalist recognises worlds where her postulates are invalid the kindness of nature is a contingent fact for both of them. Nature could not have been kind in both cases such that our inferences are not valid outside our empirically accessible area of observation. To the extent that the natural necessity the dispositionalist vindicates

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is insufficient by itself to license horizontal inference the argument from antirealism is not an anti-Humean argument. The licence for vertical inference is closely linked with the metaphysical justification of reductionism. As we have seen before (in chapter 3.2.2.2) Humeanism is generally compatible with any kind of reductionism. In this sense, Humeanism can be combined with the idea that unobservable less complex structure composes to more complex observable structure, thus satisfying the scientific realist demand that the unobservable must have the potential to reconstruct what is directly observable for us. There is no difference in the argumentative resources the Humean and the dispositionalist can make use of if it comes to a metaphysical justification of reductionism (except for the seeming incompatibility of radical structural realism and reductionism, as mentioned before). The licence of vertical inference is independent of the metaphysics of causation that one likes to adopt. Vertical inference concerns synchronic instances of properties and their subsumption under types. More precisely, the realist requirement of necessary connections between the unobservable and the observable structures cannot be satisfied by the existence of a disposition of the unobservable structure. In particular, the relation of composition that is featured in reductionist accounts is metaphysically necessary, but does not reduce to a disposition of the composing entities to bring about the composed entity. Therefore, the existence of dispositions is neither necessary nor sufficient to license vertical inference and in this sense the argument from anti-realism is not an anti-Humean argument. To conclude, the previous section has made the following points. Epistemic structural realism is insufficient to vindicate scientific realism. Ontic structural realism in its radical form at least needs primitive modality in order to be a scientific realist position. Still, there are problems to license vertical inference from the observable to the unobservable stemming from its compatibility problems with reductionism. The question whether ontic structural realism in its moderate version is a scientific realist position is independent of the metaphysics of causation that one adopts. Given that for unorthodox Humeanism (that is the Humean version of moderate structural realism) it is possible to distinguish fundamental first order property types it requires an additional metaphysical postulate to vindicate scientific realism. Unorthodox dispositionalism is also in need of an additional (and much similar) metaphysical postulate

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in order to qualify as a scientific realist position. Therefore, the unorthodox Humean has no qualitative disadvantage compared to the unorthodox dispositionalist when it comes to the question of scientific realism. So far we have not encountered any knockdown argument in favour of primitive modality. More precisely, we have not encountered any decisive advantage for the dispositionalist from considerations internal to the metaphysics of nature or science, or from the epistemology of science. One anti-Humean argument stemming from the philosophy of mind is still pertinent: the argument from the veracity of human agency. Independently from the question whether she defends an orthodox or an unorthodox ontology the Humean subscribes to the thesis that causation supervenes globally on the entire distribution of fundamental property instances. Insofar as mental causation is reducible to physical causation, causal statements including mental predicates have truthmakers. Hence, the Humean can account for mental causation. What she cannot account for, however, is the fact that when our mental states cause other mental states or physical behaviour, we have a feeling of being individually responsible for our actions in the sense that it is something about us (and us alone) that brings about the relevant effects. In other words, we have a feeling of individual agency. Individual agency includes the idea of singular causation. Only if our mental states are ontologically sufficient by themselves to bring about effects can we consider our feeling of agency as veridical. Therefore, the veracity of our self-assigned role as agents implies dispositionalism (according to our definition). The Humean cannot hold the first without the latter. Thus, the Humean project of reducing causation to regularities comes along with a project to challenge the assumption that the idea of mental causation is tied to the idea of individual agency. This project is not going to be addressed here, because our primordial focus lies on the metaphysics and epistemology of science and nature. Let us therefore come back to the main hypotheses and conclusions that we want to set out in this context.

Humean metaphysics of causation as informed of contemporary science One of the central debates in the metaphysics of science nowadays is about which metaphysics of causation should be adopted. Two opposite points of view are defensible: the position that causation is fundamental in nature (dispositionalism) and the position that causation is reducible to merely regular sequences of events (Humeanism). They are distinct insofar as they posit different sets of ontological primitives. Dispositionalism regards a proper subset of the distribution of fundamental properties and their instantiation of irreducible natural modality as primitive. Humeanism regards the entire distribution of fundamental properties without natural modality as primitive. Both positions exist as orthodox versions in combination with ontological atomism. Contemporary fundamental physics suggests that atomism is false. It suggests that fundamental objects do not instantiate fundamental intrinsic properties, but only fundamental relational properties. This is ontological holism. In order to be in accordance with contemporary fundamental physics unorthodox versions of both Humeanism and dispositionalism can be developed. However, an important metaphysical assumption comes with the shift from an orthodox to an unorthodox ontology: that the difference in the metaphysics of causation that distinguishes Humeanism from dispositionalism is still meaningful. There is room for interpretation of the concept of meaningfulness here. Actual fundamental physics admits of the interpretation that whole states of the world at a given time are holistically related through relations of quantum entanglement. If this interpretation proves to be true, then more or less local causal processes as we experience them on the macroscopic level are impossible. In particular our experience of such processes cannot be veridical in such a case. The lack of veracity of our experience of causal relations affects both the Humean and the dispositionalist account. Note that in such a case the argument against Humeanism that puts forward the veracity of our experience as agents also loses its point. Therefore, it makes sense to postulate the existence of

212

Humean metaphysics of causation as informed of contemporary science

physical dynamics that reduce entangled states to localised physical states with properties having definite numerical values. The meaningfulness of the debate on the metaphysics of causation is certainly guaranteed in the presence of such a dynamics. In the extreme case, however, in which the world is physically conceived as one maximally holistic state both ontologies are not distinguishable anymore. In such a world there is no physical time and therefore no initial state of the world (which constitutes the set of ontological primitives for the dispositionalist). The discussion about the fundamental nature of causation loses its object and arguments in favour of one or the other cannot be traded off. The main arguments in favour of dispositionalism are: the argument from the dynamic world, the argument from explanatory advantage, the argument from conservative reductionism, the ungrounded argument, the argument from humility, the argument from quidditism and the argument from scientific realism. None of these arguments have been shown to be robust anti-Humean arguments. Some of them, however, (notably the arguments from humility and quidditism) give us metaphysical reasons at hand (in addition to the physical considerations) to adopt an unorthodox version of Humeanism. The project to defend an unorthodox version of Humeanism is therefore well corroborated. With these motivations in mind the mission of the present work consists in making explicit unorthodox Humeanism. If successful then it is reasonable to believe in the possibility of an ontology of nature that pays tribute to the Humean spirit – the reluctance to accept primitive natural necessity and subsequently the reducibility of modal notions – and that is competitive as an overall attempt to unify the different aspects of the world such as they are presented to us through our scientific theorising and experiencing. With the reference to the competitiveness of unorthodox Humeanism one has to keep in mind that the final word of the debate has not been spoken yet. Neither the lists of pro- nor of anti-Humean arguments shall be regarded as exhaustive and even within the arguments presently discussed substantial further development is likely. In this light any contribution of this work to the project of propagating clarity and the understanding of the concepts involved in our particular debate aligns with the fundamental purpose of analytic philosophy.

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Index actualism, 25 Albert, David, 157, 159 anti-realism, 13, 82, 87, 153, 193– 209 anti-reductionism, 85, 86 Armstrong, David, 17, 27, 53, 72, 73, 82, 97, 107, 123, 128, 152 atomism, 11, 12, 74, 114, 151, 153, 170–172, 191, 192, 211 backwards causation, 70 Baumgartner, Michael, 34 Beebee, Helen, 107, 118–120 Bell, John, 158, 159 Bennett, Jonathan, 39 Big Bang, 37, 56, 107 Bird, Alexander, 70, 72, 79, 81, 88, 89, 101, 102, 108, 144–146, 168, 197 Black, Robert, 144, 145 Blackburn, Simon, 84, 120 Block, Ned, 132 Bohm, David, 159, 203 Bohmian mechanics, 203 Carnap, Rudolf, 85, 87, 95 categorialism, 11, 70–74, 107, 152, 196 Chakravartty, Anjan, 199 Chalmers, David, 132

Chisholm, Roderick, 64, 146 Choi, Sungho, 89, 130, 138 Churchland, Paul, 86 Cleland, Carol, 162, 163 Coulomb’s law, 9, 108, 127 Coulomb, Charles, 9, 108, 127 Cross, Troy, 89, 91, 130, 138 Demopoulos, William, 199 determinism, 38–40, 68, 70, 71, 97, 104, 169, 170, 180, 181 Dieks, Dennis, 140, 176, 178 Dorato, Mauro, 172 Dowe, Phil, 35, 42, 44 Dretske, Fred, 107, 152 Earman, John, 152 Eleatic Principle, 73, 74 eliminativism, 85, 86, 94, 95, 116, 130–134, 136, 164 Ellis, Brian, 72, 121 empiricism, 153 constructive, 193, 195, 200 epiphenomenalism, 47, 61, 74 Esfeld, Michael, 53, 106, 122, 123, 130, 136, 157, 161, 163, 165, 167, 168, 171, 172, 184, 191, 194, 197, 199, 200, 203 externalism, 137 Fine, Kit, 39

224

Fodor, Jerry, 129 Frankfurt, Harry, 7 Freland, Laurent, 80 French, Steven, 163, 164, 168, 172, 194, 195 Friedman, Michael, 28, 126, 199 general relativity, 8, 53, 103, 121– 123, 184 Ghirardi, GianCarlo, 105, 121, 123, 171, 173, 184 Gnassounou, Bruno, 79 Goodman, Nelson, 87 Gundersen, Lars, 28, 89, 93, 95, 130, 138 haecceitism, 64, 65, 70 haecceity, 64 Handfield, Toby, 119 Harr´e, Rom, 79 Hauska, Jan, 91 Heil, John, 17, 19, 23, 67, 78–80, 165 Heisenberg, Werner, 157 holism, 12, 167, 170, 172, 181, 211, 212 Hume, David, 10, 32, 35, 53, 115, 121, 123 humility, 141–144, 147, 148, 153– 155, 185, 190–193, 198, 200, 207, 212 indeterminism, see probabilism Jackson, Frank, 16, 74, 128, 132 Kim, Jaegwon, 61, 63, 65, 74, 128, 165

Index

Kistler, Max, 35, 79 Ladyman, James, 162–168, 172, 194, 195 Lam, Vincent, 163, 165, 167, 172, 184, 194 Langton, Rae, 26, 44, 74, 147 Laurence, Stephen, 132 Lewis, David, 10, 16–18, 20–31, 33– 47, 49, 51–58, 60, 61, 63, 64, 67, 72, 74, 77, 86, 88, 92, 95, 106, 110, 113, 114, 116, 121, 130, 132, 138, 142–147, 151, 152, 154, 162, 172, 175, 176, 178–183, 185, 188, 189, 191, 196, 197, 202, 205 Lierse, Caroline, 121 Loewer, Barry, 28, 30, 31, 61, 63– 65, 107 Mackie, John, 32–34 Madden, Edward, 79 Malzkorn, Wolfgang, 86, 88, 94, 95 Manley, David, 88, 89 Margolis, Eric, 132 Martin, Charles, 67, 75, 78–80, 85, 87–89, 91, 93, 99 Maudlin, Tim, 151, 152, 154, 157, 158, 181 McKitrick, Jennifer, 83, 84 Mellor, Hugh, 79, 93–95 miracle argument, 142 miracles, 36–39, 97–99, 179–182 asymmetry of, 39 quasi-, 39, 180–182

Index

Mumford, Stephen, 79, 85, 91, 93, 94, 121, 137, 138, 140, 141

225

Occam’s razor, 115, 126 Occam, William, 115, 126 overdetermination, 40, 42, 61–63 asymmetry of, 39

quantum entanglement, 105, 121–123, 158–164, 168–173, 181–185, 187, 192, 197–199, 201, 211, 212 quantum mechanics, 8, 103, 121, 156, 157, 159–161, 175–178, 183, 184, 203 quidditism, 70, 144–149, 153–155, 185–191, 193, 198, 200, 207, 212 quiddity, 189 Quine, Willard, 203

Papineau, David, 61 Pargetter, Robert, 74 physicalism, 16, 60, 61, 63, 71, 127, 128, 132, 152 a posteriori, 132 a priori, 132 non-reductive, 128 picture theory, 23, 79, 80 Platonism, 165, 167, 168, 194, 196 Poincar´e, Henri, 162 Popper, Karl, 105 positivism, 85, 87 preemption, 41–48, 51, 52 early, 41, 42, 44, 46 late, 41–44, 46 Principal Principle, 107 Prior, Elizabeth, 74 probabilism, 11, 38, 39, 104–108, 169, 177–181, 184 propensity, 105–107, 177, 178 Psillos, Stathis, 82, 83, 138, 140 Putnam, Hilary, 142

Ramsey sentence, 95, 199 Ramsey, Frank, 20, 23–25, 63, 95, 199 realism, 21, 23, 80, 191–196, 202, 205, 206, 208 about laws and causation, 10, 40, 60, 96, 174 about possible worlds, see modal about universals, 17, 18 dispositional, 80, 85, 94, 96 modal, 56, 58, 77, 114, 177, 178, 189 qualitative, 80 scientific, 23, 138, 139, 141, 165, 190, 194, 208, 209, 212 structural, 12, 143, 153, 162, 163, 167, 169, 171, 172, 188, 193, 196 dispositionalist, 169–174, 193, 195, 196 epistemic, 162, 191, 194, 208 Humean, 153, 169–174, 193

Newman, Max, 191, 194, 198, 199 Newton, Isaac, 154 Ney, Alyssa, 142, 198 non-separability, 154, 159, 160

226

modal, see dispositionalist moderate, 163, 167–173, 175, 181, 184, 188, 189, 195, 196, 204, 208 non-modal, see Humean ontic, 162, 194, 208 radical, 163–165, 167, 168, 194– 196, 208 Redhead, Michael, 168 reductionism, 10, 12, 195, 196, 208 a posteriori, 94 a priori, 94, 132, 136 conservative, 94, 128–137, 212 epistemological, 129–131, 134, 136, 166, 167 ontological, 60, 61, 63, 94, 129, 136, 166, 167 semantic, 11, 85–96 token, 131 Rimini, Alberto, 105, 123, 173 Rosenthal, Jacob, 106, 107 Ross, Don, 163–168, 172, 194, 195 Sachse, Christian, 129, 167 Salmon, Wesley, 35 Saunders, Simon, 165, 168 Schaffer, Jonathan, 38, 47–52, 97, 99, 141, 165, 180 Schr¨odinger equation, 171, 173, 176, 183, 184 Schr¨odinger, Erwin, 171, 173, 176, 183, 184 separability, 151, 154–157, 160 Shoemaker, Sydney, 67, 79, 81 special relativity, 159

Index

Stalnaker, Robert, 132 Strawson, Galen, 117–120 Su´arez, Mauricio, 105, 178 superposition, 157–161, 169, 170, 177, 198 Teller, Paul, 160 tropes, 17, 18 trumping, 41, 44–46, 91 truthmaker principle, 19 uncertainty relation, 157 universals, 17, 18, 72, 73, 123, 152, 164, 195 Van Fraassen, Bas, 26, 31, 95, 193– 195 Wasserman, Ryan, 88, 89 Weber, Tullio, 105, 123, 173 Williams, Neil, 137 Worrall, John, 162, 191

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