Some Remarks on the Metaphysical Status of Laws of Nature (1997)

WIM CHRISTIAE NS Some Remarks on the Metaphysical Status of Laws of Nature 1. Introduction Armstrong is one of the few analytic philosophers who have constructed a scientific metaphysics. He is a realist with respect to universals: properties, relations, laws of nature and causal relations are repeatables. The confrontation of a world view presupposing some kind of universals and one that only presupposes particulars (nominalism) is very old. I will not go into the confrontation of these two paradigmatic views (see Bigelow et al. 1992). One can present a discussion of the views of Armstrong in different ways: as a confrontation of realism and nominalism, or even a confrontation of realism and antirealism (if you take nominalism to be typical for a contemporary Humean inspired position). I think it is a mistake to make this a confrontation between realism and nominalism. One can be a realist about lots of things. The Regularist (who stays closest to Hume and the received view) is committed to a logical atomism. So he too is a realist. I think it is better to formulate the problem as a confrontation between two kinds of realism: realism with respect to universals and realism with respect to particulars. But both universals and particulars can be interpreted in different ways. For example, universals do not have to be these typically Platonic abstract other wordly entities. I will be concentrating on the relation between laws of nature, causation and universals. Armstrong has interesting things to say about this. With some of it I agree, other things are wrong. In section 2 I discuss some basic ideas about physical laws and causal relations and classify some of the metaphysical theories about laws and causal relations (among them Armstrong’s view). The mechanistic world view is an important determinant. I am in favour of a theory of causation and lawfulness that avoids the basic mechanistic 2 Wim Christiaens ideas. This is the most important determinant for me, and I will use material and reject material from theories of other philosophers (like Armstrong) according to this criterium. Section 3 is a discussion of Armstrong's views on laws and causal relations. Section 4 criticizes the obvious alternative for universals: powers. Section 5 is an exposition of Apostel’s views on causal relations and causal laws. A lot of the ideas of Armstrong can be incorporated in this theory, but I do not agree with the reduction of causal laws and causal relations to higher order universals. Although I tend more toward a powers-andtendencies ontology, my preferred ontology is based on the idea of singular irreducible causal relations and systems. Causal relations should be defined according to intrinsic criteria, and these criteria do not form one clean cut theory but come from different domains (regularity theory, probabilistic causality, logic of time and process, counterfactual analysis, the ontology of powers, tendencies and forces etc.). The concept of system is defined as a structure of structures. Both concepts are important, but I will give most attention to causality. The concept of physical law can then be defined with the help of the concepts of causal relation and system. 2. Physical laws and causality Realism is a complex issue. One can be a realist about lots of things. There are six kinds of realism relevant to our problem: (1) realism about universals and individuals versus anti-realism about universals in conjunction with realism about individuals; (2) realism about dispositional properties versus realism about categorical properties; (3) realism about causal relations (interpreted as internal and irreducibly singular relations) versus realism about causal laws (interpreted as external relations and covering laws). Two remarks. First remark: different combinations lead to different metaphysics. One can for example combine realism about universals, anti-realism about dispositional properties and realism about both causal relations and causal laws. Second remark: I simplified a lot (for example under (3) there is also the position inspired by Hume: anti-realism about causal laws and causal relations). I just wanted to give an impression of the complexity of the matter. In the remainder of this paper I will describe two posi- Some Remark s on the Metaphysical Status of L aws of Nature 3 tions along these dimensions: Armstrong’s views and the views of Leo Apostel. Armstrong (1997, 202) writes: “There really are deep connections between causes and laws. Nevertheless, the beginning of wisdom is to distinguish the two quite sharply”. Let me begin by situating the discussion about universals in the particular context of determining the metaphysical status of (i) laws, (ii) causal relations and (iii) the relation between laws and causal relations. The concept of causal law is a specialization of the concept of physical law. One can distinguish different kinds of physical laws: (a) causal laws, (b) global laws which describe the intrinsic natures of the events and processes which are metaphysically possible in our universe, for example conservation laws (the only events that can occur in our world are those that are conservative of something in some respect), (c) general structural principles, such as those of general relativity (see E llis 2000). The difference is not always clear, and it is not always clear what is meant with a causal laws and which physical laws are causal laws. The intuitive notion of causal law is enough for the discussion here, and it will always be causal laws that I mean, when I use the terms laws of nature or physical laws. Causal relations are specific causal facts. That this pen falls under the influence of the force of gravity generated by this particular planet at this moment in time, is a causal relation: there are purely contextual and unique aspects to the happening. The mathematical relationship known as Newton’s law of gravity, is a causal law because it lacks specificity and can be instantiated by many different entities. How are laws and relations related to each other? There are at least four alternatives: (1) weak reductionism with respect to causal laws: causal laws are logically supervenient on causal relations and non-causal facts; (2) strong reductionism with respect to causal laws: causal laws are logically supervenient on non-causal facts; (3) weak reductionism with respect to causal relations: causal relations are logically supervenient on causal laws and non-causal facts; (4) strong reductionism with respect to causal relations: causal relations are logically supervenient on non-causal facts (cf. Tooley 1993, 173–175). An important idea that determines the discussion about causal laws and causal relations is the dominant world view since the advent of 4 Wim Christiaens Newtonian mechanics: Mechanism. I think most people would agree that two of the most important components of Mechanism are:1 ME CH : (a) Duality property: there is a metaphysical distinction between on the one hand states and on the other hand laws which determine the succession of states. (b) Covering laws: if an entity has a certain behaviour, then this behaviour is determined by a law of nature, i.e., the entity’s behaviour is subsumable under a covering law. Other possible components of mechanicism are determinateness (all variables have determinate values at all times), locality, separability, determinism, continuity, the idea that space is the theater of all physical events and the idea that reality is fundamentally mathematical in nature. Quantum mechanics is one of the biggest challenges for Mechanism (the notions of determinateness, locality, separability and determinism are in some kind of trouble). I will not concern myself with these other components. E very scientist and philosopher makes his own version of ME CH . For example, a lot of philosophers of science in the twentieth century will have combined the above with a broadly Regularist view on the nature of physical laws inspired by Hume. But it is safe to say, I think, that these principles determine most of our ideas about the world. The received view on causality is part of Mechanism. A certain fact is causally connected to another fact if there exists a covering (physical) law which connects them. For example, when you have a physical system with a certain mass, a position and a velocity, then the behaviour of the entity is determined by the laws of Newton. The specific behaviour of the entity is a singular causal fact because it is subsumable under a causal law. Causal relations are supervenient on causal laws and non-causal facts.2 Laws are causal agents, they determine how entities behave. The entities themselves are passive. The world is an aggregate of passive things behaving in ways that are determined (or made probable) by their categorical (i.e., non-dispositional) properties, 1 Other components of mechanicism are determinateness (all variables have determinate values at all times), locality, separability, determinism, continuity and the idea that reality is fundamentally mathematical in nature. 2 Humeans will take the next step and say that causal laws are supervenient on noncausal facts: they are just regularities between events. Some Remark s on the Metaphysical Status of L aws of Nature 5 by the circumstances in which they exist (initial conditions and boundary conditions), and by the laws of nature (see E llis 2000, 330). One could call this prescriptivism. Prescriptivism keeps popping up, even in theories that explicitly try to be an alternative for this, as we will see. A note on the history of Mechanism. The concept of law is a typical Western anthropomorphism with roots going back to the theology of the 17th century.3 In the 17th century it was thought that God created the world (passive things) and also created the laws of nature that regulated or determined the further course of events of the world. These laws are immutable. God is wholly transcendent, he is an ‘absentee God’ (E ncyclopedia of Philosophy) (see Giere 1999, 87). In other words laws are prescriptions laid down by God, determining the behaviour of passive things. The fact that these laws are prescriptions issued by God, implies that they hold for the whole universe. In Mechanism this typical God is not necessary anymore. Descartes and Newton were the main sources for the habit of interpreting reality with concepts of physical law. This secularized version has become the dominant world view: “This is the view of the seventeenth-century mechanical philosophy of Robert Boyle and Robert Hooke. When God wrote the Book of Nature, he inscribed the fundamental laws of mechanics and he laid down the initial distribution of matter in the universe ... But this is not only the view of the seventeenth-century mechanical philosophy. It is a view that lies at the heart of a lot of current-day philosophy of science...” (Cartwright 1983, my italics). Without God the distinction between initial conditions and physical laws (and the prescriptivism.) is a mystery. A situation where no explanation can be given of the distinction between laws and initial conditions is unsatisfactory.4 States seem to be quite concrete things, but laws are not. In fact, the grounds for using the duality property are more methodological than metaphysical. Wigner explains: The world is very complicated and it is clearly impossible for the human mind to understand it completely. Man has therefore devised an artifice 3 See Giere (1999, 86–87); Cartwright (1983, 101) and Bigelow & Pargetter (1990, 266). 4 Many scientists are not satisfied with the duality property (Apostel 1995, 213): see for example Cushing (1985, 455), Penrose (1989), Wheeler (1983) and Wheeler (1989). 6 Wim Christiaens which permits the complicated nature of the world to be blamed on something which is called accidental and thus permits him to abstract a domain in which simple laws can be found. The complications are called initial conditions; the domain of regularities, laws of nature. Unnatural as such a division of the world’s structure may appear from a very detached point of view, and probable though it is that the possibility of such a division has its own limits, the underlying abstraction is probably one of the most fruitful ones the human mind has ever made. It has made the natural sciences possible. (Wigner 1967, 3) The duality property is not something obvious from a metaphysical point of view. It seems to me that it is only because of the prominence of physics in our culture and the early age we confronted with the mathematical description of nature typical for physics, that it has acquired an air of self-evidence. With this in mind, let us look at some theories about the metaphysical status of laws, causal relations and their relation. I will not go over all the particular views on laws of nature and causation. They can be distinguished according to methodological or metaphysical criteria. I look at anti-prescriptivist alternatives. This reduces the many to three positions: (1) Regularity theory: there are no necessary connections or production relations, powers, universals, etc., only contingent regularities in an ontology based on a form of logical atomism. (2) Necessitarianism: laws and causal relations between events, states of affairs, things, ... can be reduced to some kind of metaphysical connection (universals, production relations, powers, etc.), they have a de re modal status (i.e. they express some kind of necessary connections). Necessitarianism A : states of affairs ontology that is also based on a form of logical atomism (all relations are external and all elementary states of affairs are independent, see below), causal laws and causal relations are instances of universals that express necessary connections (which means that these are not independent the way elementary states of affairs are). The best known version is Armstrong’s theory of universals. Some Remark s on the Metaphysical Status of L aws of Nature 7 Necessitarianism B : causal laws and causal relations are the expression of causal powers, capacities, propensities or dispositions of particular entities. E ssentialism is at this moment the best known version of Necessitarianism B. It introduces the concept of natures (Harré & Madden 1975) or essences (E llis 2000). All three views on physical laws try to avoid the prescriptivism inherent in the idea of law and consequently want to be as concrete as possible, i.e. avoid any quantification over abstract entities. (1) According to the regularity theory physical laws express only what does occur.5 The definition of causation draws on extrinsic aspects of the causal relation: spatial contiguity, temporal priority and regularity. On a methodological level the Humean position is rational and acceptable because of the induction problem and the fact that neither powers nor universals can be perceived in a strict empiricist sense. Other broadly speaking Regularist or Humean theses are the following. E vents and states of affairs are logically independent of one another: they adhere to logical atomism in one form or another. Identities of objects are independent of laws of nature that hold for the entities. The dispositional properties of entities depend on what laws of nature hold for these entities and the categorical properties of these entities. Modal characteristics of things are supervenient on non-modal properties. (2) Necessitarianism is either the bottom up approach (Necessitarianism B) or the top down approach (Necessitarianism A) (see Bigelow et al. 1992). According to essentialism, laws of nature are not grounded in empirical regularities, but in the intrinsic causal powers of members of natural kinds of things. The behavioral powers are the identitydetermining properties of natural kinds. All three views are metaphysically reductionistic views (see Lange 2000, ch. 1). A law of nature/causal relation is reduced to a particular aspect of a preferred ontology: in the case of the regularity theory, to regularities, in the case of necessitarianism to either higher order universals (universals between universals) or the exercise of causal powers. I agree with Nancy Cartwright (1989) and Marc Lange (2000) that there 5 For a recent version of the regularity theory, see Swartz (1985). Hume writes (E nquiry, VII): “There are no ideas, which occur in metaphysics, more obscure and uncertain, then those of power, force, energy and necessary connection, of which it is every moment necessary to treat in all our disquisition”. 8 Wim Christiaens are laws without regularities, so I do not take the regularity theory to be a viable alternative. I will not go into this. The point is that regularities are not ubiquitous in nature, they only occur in carefully regulated experimental conditions and theoretical models that are highly idealized. Statistically they occur as tendencies. That leaves necessitarianism. The application of metaphysical reductionism leads to the point of view that takes universals seriously to explain the nature and existence of lawfulness in nature, and the point for view that admits only particular entities with causal powers or capacities and denies the existence of (covering) laws of nature. It is easy enough to discuss the confrontation of a metaphysics of universals and a metaphysics of particulars when they are presented as extremes. When one looks closer, this becomes more and more difficult, because no justice is done to the nuances of each position. On the one hand, Armstrong's universals are not as abstract as one might expect (this will become clear in the next section): he says that universals don't exist outside their instances. On the other hand, anti-universalists use concepts such as essences (E llis) and natures (Harré and Madden) that seem quite abstract objects. The anti-universalists are drawing on ideas coming from Aristotelian metaphysics. But even Armstrong calls his position Aristotelian realism in a broad sense. Furthermore, in a subtle way E llis still adheres to some form of prescriptivism when it comes to the description and metaphysical status of causal relations (see section 4). All the philosophers mentioned claim to be materialists. All of them introduce abstract concepts. I will argue for a third position that avoids as much as possible any metaphysical reductionism to any kind of abstract concepts, but at the same time makes it possible to keep using these abstract concepts. 3. Universals: a case of metaphysical reductionism Although I agree with a lot of what Armstrong says about causation, I disagree on the whole. The reason is his metaphysics. Armstrong proposes three world hypotheses: (1) the world contains nothing but particulars having properties and related to each other; (2) the world is a single spatio-temporal system; (3) the world is completely described in terms of (completed) physics. I concentrate on (1). Armstrong Some Remark s on the Metaphysical Status of L aws of Nature 9 describes his position as anti-Platonic realism, minimal realism and Aristotelian realism in a broad sense (Armstrong 1978, 117). A universal is a property or relation that exists independently of the classifying mind and that is the same in all its instances. It is a repeatable entity. Particulars are non-repeatables, also called tropes. Properties and relations can have properties and stand in relations. These higher order universals explain causal laws and causal relations. Initially according to a top-down metaphysics a lawfull relation is described as an extensional relation between intensions (cf. Bigelow et al. 1992). Which universals exist is determined by science, not by the existence and the use of general terms. (a) Properties. A property is something which is always the same in all its instances. An extensional interpretation of properties will identify a property with the set of objects that have the property. The property red is the set of red things. Instead of interpreting properties of entities extensionally, Armstrong talks about the properties themselves, which is an intensional interpretation of properties. But Armstrong is also a concretist. Two principles ensure this: (1) a property is something which is always instantiated somewhere; (2) there exist no bare particulars, i.e., there exist no entities without properties. (b) Laws. A law is not a statement about the relation between extensions of predicates but a statement about the properties themselves. This means that properties are something over and above the set of objects that correspond with the property. A law is a statement about the intensions of predicates. Dretske (1977, 262-263) calls this “ontological ascent”. Pness implies Qness. Pness is the property P, not the set of objects that have the property P (as is the case in the semantics of classical logic). The same is the case for Q. But there is more to this. A law of nature indicates some kind of necessary connection between phenomena. One can write this in the following way following the traditional notation from modal logic: ฀Pa, ฀( x )Px , ฀( x )(Px Qb), etc. According to Armstrong, a law is a relation of necessity between the properties: ฀(P,Q). The relation between the universals – the relation of necessity ฀(P,Q) – is itself a second order universal. Therefore the extensionality which is characteristic for the nomological relation cannot be reduced 10 Wim Christiaens to a Humean “regular association of events”. E ntities behave according to a law ฀(P,Q) when their properties fall under the properties mentioned in the law: ฀(P,Q)(Pness of a, the Qness of a) is of the form rRs where r = the Pness of a, s = the Qness of a and R = ฀(P,Q). The way it is written one sees the “covering” character of the universals. Laws of nature are explained “top-down”. The nonreducible relations of necessity belong themselves to the realm of universals. Certain regularities are laws of nature, because they are the expression of a universal. Is there a regressus, i.e., do we need third order universals to determine the second order universals? According to Armstrong this is not the case. The universals are facts and are the content of science. They are contingent relations of necessitation. (1) (2) ฀(P,Q) ( x )(Px [ ( x )(Px Qx ) ฀(P,Q)] Qx ) In (1) the implicans is the law. The implicatum is the regularity that follows form that. The second formula indicates that the implication of the first formula is not symmetric. Armstrong (1983, 145) distinguishes derived laws and non-derived laws. Non-derived laws are described by necessity relations between properties. Derived laws are logical consequences of the real laws. Suppose the non-derived laws are given. All true necessities that you can find are derived laws. Derived laws are not the expression of universals. Armstrong (1983, 156–157) gives four properties of the physical necessity, which distinguish this kind of necessity relation from logical necessity: NOM(1) Irreflexivity: the Pness of a cannot cause the Pness of a; NOM(2) Non-transitivity: when ฀(P,Q) and ฀(Q,H ) then it is not always the case that ฀(P,H ). It can be that there is a derived law that combines ฀(P,Q) and ฀(Q,H ). When it is that case that ฀(P,Q), ฀(Q,H ) and ฀(P,H ) then we have overdetermination: both P and Q have a relation of necessity with H . NOM(3) Contraposition is never the case, except maybe for derived laws; NOM(4) Symmetry is violated, except maybe in derived laws. (c) Causal relations. In a causal law a second order universal determines two first order universals. What about a relation of necessity between singular facts? Is this the same nomological relation? Yes. Some Remark s on the Metaphysical Status of L aws of Nature 11 The second order universal (the relation of necessitation between the first order universals) is not different from the relation of necessitation between individuals (Armstrong 1983, 93–97). In the hard version of his theory Armstrong will only admit causal relations that are determined by the same universals that determine causal laws. This is in accordance with the received view on causality: there is a causal law for every causal relation. If this were not the case, the following situation would be possible: ฀(P,Q)(Pness of a, the Qness of a) is not the same as ฀(Pness of a, the Qness of a) because in the latter case it is also possible that ฀(Pness of b, the H ness of b) where a b and H is incompatible with Q (Armstrong 1983, 95–96). In the case of singular facts the relation of necessity exists between “tokens”, in the case of universals it exists between “types”. Lighting a match can result in the match lighting and the match breaking: a causal relation is very contextual. There is no a priori reason for a singular causal relation to fall under a covering law. Armstrong (1978) says that causation logically entails laws. But Armstrong (1983, 95) writes: “I do not see how to exclude the logical possibility of causation without law”. Causation and nomic relationships are higher order universals. Arguably the only higher order universals. Armstrong (1999) argues of singularist causation, but again falls back on his metaphysics of universals, in this way reducing causal relations to causal laws. Causal relations are external relations because he thinks no internal relations exist: all relations are external relations. He is a proponent of the singularist view but holds that the causal relation between two states of affairs is the case because of the relations of necessitation between natural properties of cause and effect. And all of these are (he hopes) universals, i.e. causal laws. This identity thesis is an empirical identity claim. (d) Objections and critiques. (1) The universals have to bring about regularities in their own specific way. An account is necessary of this bringing about. At the same time they cannot exit outside of reality, 12 Wim Christiaens i.e., outside of the particular entities that compose reality. If this were not the case, abstract objects would exist. This problem is solved by denying that the particular part and the properties stand in a relation to each other. Compare the shape and the size of a solid material object. The two fit together neatly and change independently of each other. There is no “tie” necessary between the particular and its properties (Armstrong 1978, 110). Particularity and universality are inseparable: the properties of an individual are not related to that individual. (2) Armstrong has to say that certain relations just are necessitation relations, they are primitive facts that we find in nature. Armstrong does not explain the necessity of the relation, i.e., laws or law statements are nothing more than descriptions of ‘necessary’ relations between universals, but the reason why these relations hold is not given (Bigelow et al. 1992, 377). No explanation is given of the fact that these laws are the case, i.e., no explanation is given of why reality is split up into initial conditions and laws. (3) He has a top down idea of lawfulness and therefore a covering law idea of particular events in nature, in particular about singular causal relations. The argument against covering laws is closely related to the the argument for the modeltheoretic view of theories.6 For some time now, people like Cartwright have challenged the covering law model of causal laws. People like Van Fraassen, Suppe, Suppes, Giere and others challenged the statement view of laws. The two ideas can be combined. Covering laws are typically theoretical and are only true in abstract theoretical models. The ceteris paribus clauses associated with the covering laws indicate the theoretical nature of the model in which the covering laws are true. It is only through the intermediary of more phenomenological models that one can find these laws instantiated in reality. But then they do not nearly resemble the abstract theoretical law you started with in the first place. It is not just that they do not fit the facts only approximately, they only fit the facts in the model. There is no such thing as a direct reference relation of the statement and reality and there is not even a direct reference relation between the model in which the statement is true, except for specially designed experimental situations where all other causal factors are “held fixed”.7 6 See especially Ruttkamp (1999) and Giere (1999). See the discussion about the distinction between idealization and abstraction in Cartwright (1989). 7 Some Remark s on the Metaphysical Status of L aws of Nature 13 To make a long story short: there are not many covering laws around and most of them do not fit the facts. Armstrong holds a statement view of theories; for this reason he wants to find metaphysical counterparts for properties, relations, individuals and the way laws are expressed in this language. For many analytic philosophers language is represented by predicate logic, a very idealized language. E xpressions like Fa, Rab, ... lead naturally to an ontology of states of affairs and a metaphysics of universals. Recent work in the philosophy of science shows that starting from the modeltheoretic approach one arrives at a different conception of metaphysics. I will not go into this here, but only indicate what kind of claims are made. Giere (1999) argues that state spaces lead naturally to de re modalities and causal powers, Apostel argues in his paper “Symmetry and Symmetrybreaking” from 1995 that symmetries of state spaces and models in general lead to a realism of symmetries and invariances (which is a kind of structural realism) and James Ladyman and Stephen French argue for structural realism from considerations about the structural continuity between models in scientific progress. The idea of structural realism also finds support from contemporary theoretical physics (see Castellani 1998). (4) The lack of process in his metaphysics. Contemporary science indicates that process is central to any basic ontology (see Prigogine & Stengers 1984). Process is related to irreversibility and real change. A theory of causation has an intrinsic aspect of process. I do not see how it can be expressed with the very static universals-and-particulars ontology. 4. Powers: another attempt at metaphysical reductionism E ssentialism involves an ontology of entities that posses essential natures, causal powers and belong to natural kinds. Basically they are saying that the necessitation relation between properties is supervenient on the natures of the entities which stand in the relation. A property is indicative of this essential nature. I am not convinced essentialism is a good alternative for Necessitation A, mainly because it is not an alternative at all. There are two objections. (1) With the idea of essential nature the notion of natural kind is introduced, and we find ourselves with a kind of subsumption again. 14 Wim Christiaens The universals have been “sucked in” by the particulars and have become essential natures. Subsumption is brought back in through the back door through the concept of natural kind: when an entity belongs to a natural kind it behaves in a certain way. This needs more careful examination, but I think that essentialism and Necessitation A are related. The fact that Armstrong calls his position Aristotelianism in a broad sense, confirms this. (2) But the most important objection is that the Mechanistic view of causality is as much part of essentialism as it is of Armstrong’s metaphysics of universals. E very instance of a power exerting its activity is a singular causal relation and an instance of a causal law. E llis (2000, 47) writes: No doubt all instances of causation are reducible to elementary causal processes involving elementary events and processes, and all elementary causal processes must be instances of causal laws. The way a causal relation is explained is identical with the way laws applicable to large aggregates of entities are sometimes explained: the law is reduced to (i) the behaviour of every one of the elements in the aggregate and (ii) the fundamental laws that determine the individual behaviour of these elements, i.e., laws at a lower, more fundamental level than the law we want to explain. It is inspired by the relation between thermodynamics and statistical mechanics. Another obvious example is the reduction of the macro-economic laws to the behaviour of individual economic agents. I will not go into all the details (see Weber 200+ ). This kind of explanation is exactly what a singularist denies when it is applied to causality. Let us look at the reasons for this They are related to the fact that I strongly disagree with treating singular causal relations as instantiations of causal laws. The main reason is still the argument from theoretical laws and the models that make them true. Covering causal laws are only true in theoretical models, never in concrete models which are complex and contextual. I think the complexity is irreducible. If it would be reducible to elementary causal processes, then these would all be instances of causal laws and each of these causal laws would be the description of a causal power. That’s a hypothesis. I hold the opposite hypothesis: take the complex causal relation, and treat the simple causal relations that can Some Remark s on the Metaphysical Status of L aws of Nature 15 be described as instances of causal laws as derivation or simplifications of the complex causal relation. It is only the singular complex causal relation that is real. A weak reductionist with respect to causal laws will take specific causal relations as basic and causal laws (even if they are just descriptions of powers) as derived notions. I deny that there is a causal law for every causal relation. The structural complexity of the causal relation (see the next section) is an elementary fact of ontology. This implies that the causal relation can be described but not defined in terms of other things (things like laws, probabilities, universals, powers, etc.). My approach to causality is singularist in the following sense: causality is not to be analyzed with elements extrinsic to the causal context. A causal relation is an internal relation, not an external relation. It is a relation of power, energy or necessary connection holding as a local matter of fact, a local relation holding in singular instances, intrinsic to the relata and the processes connecting them (see Menzies 1999, 313). E llis says that Armstrong’s theory is a further refinement of Mechanism. I think E llis is right. This becomes evident when one looks at Armstrong’s ideas about the relation between laws of nature and singular causation, as we have done in the preceding section. But without a description and analysis of singular causation where the causal relation is intrinsically defined and treated as an internal relation that is always irreducible, E llis (and essentialism with him) is also sliding back into Mechanism. 5. Fixing the reference and finding the root commitments In this section I try to describe the intrinsically complex singular internal causal relation. For this I use material from Armstrong’s metaphysics and from Apostel’s work on causality. 5.1 The general idea According to Armstrong singular causation is conceptually primitive: “We can walk around it, but we cannot analyze it conceptually” (Armstrong 1997, 211). Armstrong (1999) presents us with a different approach: it is possible to fix the reference of the causal relation. Causa- 16 Wim Christiaens tion is a theoretical entity. Causation is not a mysterious and hidden feature that arouses our Humean reflexes. The way to treat causality is analogous with the way David Lewis proposed to treat the causal of mental states (p. 182): collect the platitudes of folk psychology that concern the causal relations of mental states, sensory stimuli and behavioral responses. Call these platitudes when confined to a particular sort of mental state, pain say, the causal role of pain. Pain is a theoretical entity, that entity that plays the causal role of pain. In the case of the causal role of mental states, cause is an undefined notion. Peter Menzies proposes to treat causality in the same way as the mental states: collect the “platitudes” that hold of singular causation (regularity theory, counterfactual theory, probability-raising theory, agency-theories, ...) and say that causation is that relation between singular entities for which these platitudes hold. Armstrong's claim is weaker: regularity theory, counterfactual theory, probability-raising theory, agency-theories, ... contribute their platitude to fixing the reference of the causal relation. (E ach one of these theories is insufficient in themselves to analyze the causal relation or even fix the reference.) This is part of what Apostel has done in the first part of Apostel (1974). Marc Lange has written a book about the laws of nature where he carefully looks at the special relations that laws of nature have with counterfactual conditionals, inductive confirmations and scientific explanations. Any metaphysically reductive explanation should conform to these facts. In contradistinction to Lange I do not think one can understand lawfulness apart from causality. This will become clear in the next section. For the mean time I concentrate on the notion of causality. I would plead (following Lange) to postpone the reduction of causality and lawfulness to a preferred ontology. The regularity theory and Necessitarianism A have a preferred ontology of external relations. E ssentialism tends towards internal relations. I hold an intrinsic conception of causal relations. This is connected to the power concept to be sure. But so are a lot of other concepts, maybe also some kind of universals: the causal relation has a definite structure that is instantiated with every causal relation. I think the analysis should proceed by a careful trade-off between different concepts, languages and theoretical systems, among them metaphysical concepts and Some Remark s on the Metaphysical Status of L aws of Nature 17 theories. When one tries to fit everything within one language, concept or theoretical system from the start, then no justice is done to the content of causality. As I will try to show, we need the power or disposition concept to describe certain aspects of causality, but causality cannot be reduced to this metaphysical concept. The same is true of repeatables and laws. Having described causality from all these perspectives I think there is no need anymore for a metaphysically reductive explanation. Both the concepts of power and universal are needed, but it is the concepts of causality and law as they were analyzed and described (i.e. in all their complexity, as a patchwork of complementing partial theories) that is metaphysically basic. I hope that the patchwork will eventually lead to a unified and coherent theory, but the existence of this unified theory is not necessary to acknowledge the empirical reference of the causal relation and the partial analysis of the causal relation. The causal relation cannot be reduced to one aspect (be it the counterfactual analysis, the probability description, etc.), but only to the patchwork. This is what Apostel attempted in his 1974. This is not the place to give the complete patchwork theory of causality. I will have to confine myself to some basic ideas. Armstrong (1997, 1999) says that we have direct empirical access to singular causal processes, namely from the awareness of forces acting on our bodies and our awareness of the successful operation of our will. Apostel (1974) presented an analysis of causation based on a structural and dynamical analysis of human action. An action has a minimal structure and dynamics, and it is through a conscious anthropomorphism that the causal relations is defined (Apostel 1974, 405): ... notre causalité-production s’emprunte à l’action humaine d’une part ... mais d’autre part prétend décrire cette action comme révélant d’une façon privilégié une structure omniprésente dans l’univers objectif ... More precisely: the platitudes about causation are organized around a central intuition, called production causality. Apostel calls his notion of causality also actomorphic. Actomorphic refers to the singular case: the natural agent which exerts its activity, its powers. 18 Wim Christiaens 5.2 An implicit definition of the causal relation First some remarks on notation. I use the following notation to denote a causal relation between p and q: p q/ q . q is changed into q . Are the relata p, q, r, ... events, processes or things? I retain the metaphysical hypothesis of Necessitation B: “We conceive our world to be an interacting system of powerful particulars” (cf. Harré & Madden 1975, 7). What is a powerful particular? It is best conceived as a causal system or systemic cause. I prefer systems to the rather vague and multiinterpretable things. The concept of system has become popular with the work of Ludwig Von Bertalanffy. There exist many kinds of systems theories: automata theory, linear systems theory, control-theory, network-theory, general Lagrangian dynamics, etc… 8 A system has a definite composition (the set of its components), a definite environment (the set of items with which it is connected), and a definite structure (the relation among its components and the relation with the milieu). The set has an environment and the relations with the environment, the relations in the set and the relations within the environment fall into three distinct categories.9 A school for example, is composed of students and staff members, the milieu is society and the natural environment and the structure consists of teaching and management relations. Causal relations and systems are basic. An event should be analyzable as a set of systems bearing certain relations to each other and a process as a system or set of systems undergoing (radical) changes. In other words: an event is an abbreviation for a causal nexus, a process is an abbreviation for a system seen as entity constituted by causal relations between the components of the system. A system can be seen from a structural point of view and from an causal point of view. From a causal point of view it is constituted by causal relations and implicated in causal relations. I introduce the concept of the causal nexus of an entity: (1) the causal history; (2) the causal influences the entity is undergoing and because of which it changes, (3) the causal processes that constitute the entity at a particular time; (4) the causal acts of the entity, i.e., its own role as cause; (5) the causal actions the entity could perform. A system is at the same time a causal nexus and a structure of structures. 8 9 See Bunge (1977) (appendix A) and Laszlo (1974). See Apostel (1972) and Apostel (1963). Some Remark s on the Metaphysical Status of L aws of Nature 19 I return now to the analysis of the causal relation. One can define the causal relation implicitly or explicitly. An implicit definition takes the causal relation as a primitive connective “ ” and looks at the properties this connective must have and what kind of inferences it allows. Apostel discusses many properties. Among them the four properties of Armstrong’s nomological relation (Apostel 1974, ch. 7). The NOM-properties of the nomological relation can be recast as properties of the undefined causal relation. (A) A causal relation (p p/ p) is never the case. Nothing is the complete cause of itself. (B) Transitivity fails: when (p q) and (q r ) then it is not always the case that (p r ). It can be that there is a causal relation that combines (p q) and (q r ). When it is the case that (p q) and (q r ) and (p r ) then we have overdetermination: both p and q exert a force on r. (C) Also contra-position fails. From (p q) it does not follow that ( q p). Suppose World War I was caused by the murder of prince Ferdinand. The fact that World War I did not occur, does not cause that prince Ferdinand was not murdered. (D) Symmetry is violated, except maybe in derived cases. Apostel adds the following properties (I will not discuss all of them): (E ) E verything event, process or system has a cause and has an effect. (F) There is no first cause and no final effect. (G) A causal relation with a negative antecedent is an abbreviation for a causal relation with a positive antecedent. But an event, process or system can cause an absence. 5.3 An explicit definition of the causal relation I will proceed to give some aspects of an explicit definition of the causal relation. 1. There is a structure that is relatively invariant characterizing something as a causal relation. If you look at an action then you can find the following elements: the actor, the means or instruments, the materials, the goal, the result.10 According to Apostel a similar structural relationship can be found among the conditions and factors in a causal relation and this is one of the defining characteristics of a causal relation. But in the causal relation only the actor, means, materials and 10 See Apostel (1976, 203) and Apostel (1974, 168–170). 20 Wim Christiaens result can be found, there is no goaldirectedness. You can say that they form a hierarchic structure.11 The production causality or actomorphic relation can be defined as follows: a hierarchic structural avalanche of acting forces. I will call this the technomorphic component of the causal relation. A hierarchic structure of acting forces? Do we need vectors? Maybe the forces can be described with a specific kind of vectors. But I will use other concepts. Apostel followed more or less the following procedure. He took the propositions involved in a causal relation: p and q. He analyzed these propositions and discovered that they have a lot of structure, i.e., both relata contain all kinds of temporal and alethic operators and the time and the modal aspects of the relata depend on each other (neither the temporal aspects nor the alethic aspects of the causal relation are extrinsic). (a) The process-implication. If the cause is realized, then the effect will follow soon, i.e., not to late but not to soon either. (The vagueness is intrinsic to the causal relation. It is not something which can be described in terms of more elementary processes and events that can be exactly located on the time line. It is the time line that is a theoretical fiction and the causal relation that is real). The process implication is not reflexive, transitive or symmetric and does not contra-pose. The temporal distance between p and q depends on p and q, but more on p than on q. p, q and the relation between p and q are processes. Although Apostel describes many more properties of the processimplication I will leave it at this. (b) The alethic aspect. The cause is part of a complex network of necessary and sufficient conditions of the effect. Suppose again that q is the material. In “If p would be the case, then q would be the case” p is a sufficient condition (sc). In “If p would not be the case, then q would not be the case” p is a necessary condition (nc) of q. One can make “relative products” of necessary and sufficient conditions: nn/nn, nn/sc, sc/nn, sc/sc, nn/nn/nn, ..., ss/ss/ss, ... One can also 11 E xcept for the use of the universals, the basic idea about causation is well put by Bigelow & Pargetter (1990, 264): “all causation is reducible to the action of forces or to some complex processes involving the action of forces. Basic causation is a structural universal the constituents of which are forces.” E llis (2000, 347) makes the following interesting remark: “... the standard exemplars of causal processes are not elementary. Typically, they involve a great many microlevel processes, occurring in a kind of avalanche ... the causation is direct, and involves the cumulative effect of many different causal actions”. Some Remark s on the Metaphysical Status of L aws of Nature 21 consider relativised necessary and sufficient conditions. A sufficient condition is relative to the extent it depends on other conditions to be a sufficient condition. A necessary condition is relative to the extent it depends on other conditions. These products of relative necessary and sufficient conditions should be described. The possible worlds semantics for graded alethic modalities and for counterfactuals is probably the best tool for this. Apostel 1974, ch. 3) gives several proposals for such analyses. The concepts of power and tendency are also useful. The actomorphic relation is a hierarchisation of sets of time process relation and sets of (necessary/sufficient) conditions leading up to a system, event or process q. The cause of q is the process, event, system that is the maximal element in this hierarchy, the element corresponding to the actor in an action. 2. The second important component of the causal relation is the biomorphic component. A system has more than one structure. The cause will not transmit all structure to the materials. Furthermore the structure that is transmitted will only be transmitted partially.12 The fact that p transmits a structure r to q can be written as: (p r q). Salmon calls this ‘mark transmission’. The concepts of spontaneous preservation or causal process are definitions of the biomorphic relation: the fact that certain properties or structures do not change.13 The other typically Salmonian concept is ‘causal interaction’. A causal interaction is just two related causal relations: when the ball hits the window there is one causal relation, i.e., the ball that breaks the window, and a second causal relation, i.e., the window changing the movement of the ball. E very causal relation is part of a causal interaction. E very material q is the material for more than one causal relation: (p r q/q ), (p r q/q ), (p r q/q ), ... Between p and q there are other entities, processes, events, ... connecting p and q and there is a system p and q are part of, which functions as the structural back12 Apostel proposes to make use of the concepts of symmetry and symmetrybreaking here: the symmetry group of the effect is a subgroup of the symmetrygroup of the cause. See also Stewart & Golubitsky (1992). 13 See Salmon (1984) and Weber (1998). The exact formulation is not that important at this point. The main point is that the biomorphic relation refers to the mark transmission. 22 Wim Christiaens ground of the causal relation. The technomorphic and the biomorphic relations are necessary for each other: the actor transmits the biomorfum through the instruments in the materials. The idea of the actual and the potential is contained in this scheme. For example, in s we have that (p r q/q ). In t we have that (p r q/q ) does not obtain. There are four possible reasons: (1) another structure of part r gets transmitted; (2) another effect q is produced; (3) there is no triggering of any causal power (a formulation with less metaphysical commitments would say: when you look for the q of a causal relation (p r q/q ), then sometimes you cannot find it, because a specific condition for (p r q/q ) is not the case. ); (4) there is a counteracting force. 6. Causality and lawfulness Any entity is both a structure of structures (a system) and a causal nexus. Structure of structures and causal nexus are more or less interdefinable concepts. I explicitly introduce this circularity, because I think only in this way can one avoid all reference to universals. An entity can only be object and subject of causal relations if it has an minimal structure and unity. The causal relation – itself a particular structure, existing between systems and transmitting structure(s) – can only exist “inside” a system. In other words it can only exist against a background of structures. On the other hand, structure is the invariance under specific transformations (i.e. causal relations). A system has a certain structure thanks to the fact that it stays invariant under causal influences. The components of a system hang together because there are stable causal interactions between these subsystems. The duality of system and causal nexus means that the systemic aspect and the causal aspect cannot be separated in reality. They can only be separated conceptually. The concept of system-causal-nexus is the basic concept of my preferred ontology: I refer to as systemic cause or causal system. If an entity is both the causal powers it has and the invariances (or structures) that characterize it, then there is no need to have any concept or term under which to place it to explain why it is a certain way or behaves in a certain way. Concepts like universals or essential natures do not necessarily become superfluous, but they are certainly not fundamental. I propose to take causal sys- Some Remark s on the Metaphysical Status of L aws of Nature 23 tems as the truth-makers of universals, laws, essential natures, properties and many other concepts.14 Let us look at how this could work for laws of nature? What is their status in an ontology of causal systems? Suppose that (p r q/q ) and (p r q/q ) because p, q are subsystems of r and p, q are subsystems of s where q and q are different effects in the same material of the same cause.15 In the context r p has consequence q and in context s (different from r ) p has consequence q . Apostel thinks that causal laws are just very invariant causal relations. Cause, consequence and causal relation can be characterized in terms of invariances. Depending on the strength, number and nature of the invariances of both systems (cause and effect) and of the causal relation a singular and very contextual relation or a strong invariant relation will be the case. When there are r, r , r ,... such that (1) the same p, q are part of r, r , r ... (so that p, q give the impression of being repeatables – lets write them with capitals: P, Q ) (2) and the same causal relation P r Q is the case in all the contexts r, r , r ,... then the causal relation itself will seem to be a universal. Lets write this in Armstrong’s notation: ฀(P,Q). What happens is that the both the relata of a causal relation and the causal relation lose their contextuality. For the causal relation this means it will become more external. There is one major criticism of this idea. In this conceptual scheme there is no strict distinction between physical laws and accidental generalizations. In a strong formulation we could say that there exist no laws of nature. But that would be going to far. In fact there is a gradual transition from unique, irreversible, contextual causal relations to laws of nature, depending on the strength, number and nature of the invariances of the systems involved in the causal relation and the invariances of the causal relation itself. In other words, laws of nature 14 A lot of people (including Armstrong) would like to have properties in their basic ontology. In my ontology the truth-makers of properties are causal systems-systemic causes. Because of this it is probable that every property will have categorical and dispositional aspects. Remember that the reference relation with reality goes through the intermediary of one or more models. I refer to the paper by Rob Vanderbeeken in this volume for a more thorough discussion about dispositional and categorical properties. 15 This is a translation in my ontology of something I described from Armstrong in section 2. 24 Wim Christiaens are not an independent ontological category. When we are confronted with phenomena that appear lawful we know that we should look for the system-causal nexus constituting the law. Methodologically universals exist on a high level of abstraction in knowledge systems, in the austere regions where the theoretical models reside. The closer you get to a concrete situation, the less use you make of properties and laws. Concrete reality has system-causes as basic ingredient. I mention that several philosophers (among them Apostel, Whitehead, Abner Shimony and Yuri Balashov) have entertained the idea that even the most fundamental laws of physics are mutable and are evolving together with the universe and everything else. If one rejects prescriptivism and accepts the contextuality of laws, why not take the next step and make the difference between causal relations and causal laws a matter of degree and not of principle? 7. Final remarks Points of agreement between my conception of causality and Armstrong’s are the following. (1) The properties that I propose as typical for singular causal relations are identical with the properties that Armstrong proposes for the necessitation relation between universals. (2) I agree with Armstrong that we have some kind of direct empirical access to causal relations. My definition of the singular causal relations is in fact based on the analysis of our own role as actors. (3) In a recent paper Armstrong says a real theory about causation should make use of all the intuitions (some of which have grown into full blown philosophical theories: the regularity theories, the counterfactual theories, the probability raising theories, agency theories, ...) to obtain a full theory. This is in fact what Apostel has done in his book Matière et Forme, my main source. (4) Finally, I retained a lot of the ideas and the description of the causal relation and the necessity relation that Armstrong gives, but more or less threw away all of the metaphysics. Instead I used the concept of causal-system/systemiccause, where structure (repeatables) presupposes causality and causality presupposes structure. Nevertheless there are also major differences in our analyses. I side with the modeltheoretic approach, Armstrong holds a statement view about theories. Armstrong believes in external relations and the idea Some Remark s on the Metaphysical Status of L aws of Nature 25 of covering laws is never far off, while I do not believe in these concepts when it comes to the preferred ontology, because I want to get rid of the idea of causal relations as instantiations. The only instantiations that occur are in sentences and in models. Centre for L ogic and Philosophy of Science University of Ghent References Apostel, L. (1963), “Can metaphysics be a science?”, Studia Philosophica Gandensia 1, 7–95, Gent. Apostel, L. (1972), “Systementheorie als instrument ter eenmaking van onze kultuur – een schets”, in L. Apostel (ed.), De E enheid van de Kultuur, Boom, Meppel. Apostel, L. (1974), Matière et Forme, vol 1, Gent, Communication and Cognition. Apostel, L. (1976), “Mereology, Time, Action and Meaning“, Sprache und E rk enntnis, Festschrift für Gerhard Frey, Innsbruck. Apostel, L. (1981), “Some Remarks on Ontology”, in J. Agassi & R. S. Cohen (eds.), Scientific Philosophy Today, Dordrecht, D. Reidel Publishing Company, Dordrecht, pp. 1–44. Apostel, L. (1989), The Philosophy of L eo A postel. V olume 2: The Philosopher Replies, F. Vandamme & R. Pinxten (eds.), Gent, Communication and Cognition. Apostel, L. (1989), The Philosophy of L eo A postel. A L ife History, (with Ingrid Van Dooren), F. Vandamme & R. Pinxten (eds.), Gent, Communication and Cognition. Apostel, L. (1994), “Symmetry and symmetrybreaking: ontology in science (An Outline of a Whole)”, in The Worldviews Group (Aerts D., Apostel L., De Moor B., Hellemans S., Maex E ., Van Belle H., Van der Veken J.) 1995, Perspectives on the World, VUB Press, Brussel. Armstrong, D. M. (1978), A Theory of Universals, 2 volumes, Cambridge University Press, Cambridge. Armstrong, D. M. (1983), What is a L aw of Nature?, Cambridge University Press, Cambridge. Armstrong, D. M. (1997), A World of States of A ffairs, Cambridge University Press, Cambridge. Armstrong, D. M. (1999), “The Open Door: Counterfactual Versus Singularist Theories of Causation”, in Sankey (1999). Batens, D. & P. Burghraeve (1978), “Apostel’s Theory of Causality. Critical Discussion of Leo Apostel’s ‘Matière et Forme. Introduction à une epistémologie réaliste’” , Philosophica, 21, 207–216. Bernet Ruttkamp, E . (1998), A Model-Theoretic Realist Interpretation of Science, Doctoral Dissertation, University of South Africa. 26 Wim Christiaens Bigelow, J. & R. Pargetter (1990), Science and Necessity, Cambridge University Press, Cambridge. Bigelow, J., B. E llis & C. Lierse (1992), “The world as one of a kind: natural necessity and laws of nature”, British Journal for the Philosophy of Science 43, 371–388. Bunge, M. (1977), Treatise on Basic Philosophy, vol. 4, D. Reidel Publishing Company, Dordrecht. Cartwright, N. (1983), How the L aws of Nature L ie, Clarendon Press, Oxford. Cartwright, N. (1989), Nature’s Capacities and their Measurement, Clarendon Press, Oxford. Castellani, E . (ed.) (1998), Interpreting Bodies. Classical and Quantum Objects in Modern Physics, Princeton University Press, Princeton. Cushing, J. T. (1985), “Is there just one possible world? Contingency vs the bootstrap”, Studies in the History and Philosophy of Science, 16, 31–48. Dretske, F. (1977), “Laws of Nature”, Philosophy of Science 44, 248–268. E llis, B. (2000), “Causal Laws and Singular Causation”, Philosophy and Phenomenological Research LXI, 329–351. Giere, R. N. (1999), Science Without L aws, The University of Chicago Press, Chicago and London. Harré, R. & E . H. Madden (1975), Causal Powers: A Theory of Natural Necessity, Basil Blackwell, Oxford. Ladyman, J. (1998), “What is Structural Realism”, Studies in the History and Philosophy of Science, vol. 29A, Nr. 3. Lange, M. (2000), Natural L aws in Scientific Practice, Oxford University Press, Oxford. Laszlo, E . (1974), Introduction to Systems Philosophy. Toward a New Paradigm of Contemporary Thought, Harper Torchbooks. Menzies, P. (1999), “Intrinsic versus E xtrinsic Conceptions of Causation”, in Sankey (1999). Penrose, R. (1989), The E mperor’s New Mind, Oxford University Press, Oxford. Prigogine, I. & I. Stengers (1984), Order out of Chaos. Man’s New Dialogue with Nature, Bantam Books. Salmon, W. (1984), Scientific E xplanation and the Causal Structure of the World, Princeton University Press, Princeton, New Jersey. Sankey, H. (ed.) (1999), Causation and L aws of Nature, Kluwer Academic Publishers, Dordrecht. Stewart, I. & M. Golubitsky, Fearful Symmetry. Is God a Geometer?, Penguin Books. Swartz, N. (1985), The Concept of Physical L aw, Cambridge University Press, Cambridge. Tooley, M. (1993), “Causation: Reductionism versus Realism”, in E . Sosa & M. Tooley (eds.), Causation, Oxford University Press, Oxford. Weber, E . (1998), “The Practical Functions and E pistemology of Causal Beliefs”, Communication and Cognition 31, 297–324. Weber, E . (200+ ), “Explaining Laws by Reduction”, in Philosophical Dimensions of the Unity of Science, 11th International Congress of L ogic and Methodology of Science, to appear. Some Remark s on the Metaphysical Status of L aws of Nature 27 Wheeler, J.A. (1983), “On Recognizing ‘law without law’”, Oersted Medal Response at the Joint APS-AAPT Meeting, New York, 25 January 1983, A merican Journal of Physics, 51, Nr. 5. Wheeler, J. A. (1989), “Information, Physics, Quantum: the Search for Links”, Proceedings of the 3rd International Symposium on the Foundations of Quantum Mechanics, Tokyo, pp. 354–368. Whitehead, A. N. (1929,1978), Process and Reality. A n E ssay in Cosmology, The Free Press, New York, London. Wigner, E . P. (1967), Symmetries and Reflections, Indiana University Press, Bloomington & London.