What a Law of Nature is

 W. Russ Payne

The title of David Armstrong’s book on the topic asks “What is a Law of Nature?”[1]  The answer I will develop and motivate in this paper is that causal laws are analyses of dispositions.  We describe dispositions in terms of subjunctive conditionals.  For sugar to be soluble in water, for instance, is just for it to be such that if it were submerged in water (under appropriate conditions), it would dissolve.  In general, we can say that for a thing to have a disposition is for it to be such that were certain precipitating conditions to obtain, then a certain manifestation of the disposition would occur.[2]  In the case of solubility, being submerged in water (under appropriate conditions) is the precipitating condition for the manifestation of going into solution.  A careful account of the conditions under which sugar would go into solution in water, that is, an account of the specific nature of its solubility, would be a statement of law.  That statement of law would tell us something about the nature of sugar in terms of the dispositions it grounds. 

The view that laws are necessarily true accounts of the essentially dispositional nature of properties has advocates in Brian Ellis and Caroline Lierse,[3] Alan Chalmers,[4] Sydney Shoemaker[5] and John Bigelow[6] among others.  What distinguishes the account I will offer is that it respects both the intuition that dispositions are relational properties and the intuition that causal powers are grounded in occurent properties that are intrinsic to their instances.  Before I offer the account of causal laws as analyses of dispositions, I will say a few words about the shortcomings the alternative realist account of laws.

The Competition

The view to be developed here is a successor to realist view of laws offered independently by Armstrong,[7] Tooley[8] and Dretske.[9]  Space does not allow for critical remarks directed against other approaches in the philosophy of laws. The realist view takes laws to be nomic relations that hold contingently between universals.  So, for it to be a law of nature that water expands when it freezes is just for the properties of being water, freezing and expanding to stand contingently in the appropriate nomic relation.  There are two objections I find compelling against this view.  One has to do with the modal status of laws in connection with explanation and counterfactual reasoning and the other concerns a proliferation of ways the world could be if nomic relations are contingent.

Armstrong objects to regularity accounts of law on the grounds that mere regularities fail to account for the role of laws in counterfactual reasoning and explanation.  The mere fact that all the Ps are Qs does not account for our intuition that had some non-P been P it would still have been a law that Ps are Qs.  Similarly, the mere fact that all the Ps are Qs does not explain why this P is Q, but a lawful connection between Ps and Qs should explain.  To avoid these defects, the realist’s nomic relations, while contingent, are taken to have some modal force that is lacked by the contingent relation of co-instantiation already recognized on regularity accounts.[10]  Realist laws are taken to be in some sense necessary, but it is denied that nomic relations hold as a matter of metaphysical necessity.  Apparently, however, there is no non-question begging way to say just how necessary contingent nomic relations are supposed to be. This renders the modal status of laws obscure on the contingent nomic relations view.

The second objection to taking nomic relations to be contingent is that doing so opens up the possibility of what Brian Ellis calls “global transubstantiations,”[11] possible worlds just like the actual world except that the basic causal base properties have switched instances and causal powers.  There will be possible worlds where the property that grounds the dispositions associated with charge swaps causal powers and instances with the property that grounds the dispositions associated with gravitational mass.  There will be another such world that is exactly like the actual world except with regard to which properties have which causal powers for every possible assignment of basic properties as causal bases for basic dispositions.  But this conflicts with the feeling that the laws are really the same at global transubstantiations.  We know causal base properties only through the manifestations of the dispositions they ground.  Global transubstantiations of the actual world are empirically indistinguishable from the actual world.  The differences between such worlds have nothing to do with how we understand, confirm, investigate, or express laws.  Worlds that differ only with regard to which properties have which powers will be exactly like the actual world with respect to what (non-nomic) counterfactuals are true, what dispositions things have and which inductive inferences are correct.  For all of these reasons we should like to hold that the laws in each such world are the same.

Laws as Analyses of Dispositions

Ruling out global transubstantiations requires that properties have their causal powers essentially.  And this leads to dispositional essentialism; the general view of laws as characterizing the essentially dispositional nature of properties.  The view on offer here, that causal laws are analyses of dispositions, is a specific version of dispositional essentialism.  The main components of this account include an independently motivated view about the nature of analysis and an account of dispositions as relational properties of instantiating appropriate causal base properties.  Here I will outline these components and illustrate the view with the case of Coulomb’s law.

Analysis

The account of analysis I will employ here is Jeff King’s.[12]  An analysis, according to King, is an account of the nature of a complex property or relation in terms of its structure and simpler component properties and relations.  The object of analysis, the analysandum, is a property or relation that exists independent of the mind or language.  

Proposed analyses of dispositions can be given in what King calls "orthodox form":

(1)   ("x)(Px iff Cx)

In an analysis with this form, the predicate to the left of "iff" will express the object of analysis, the analysandum.  The predicate to the right of "iff" will be a complex expression having only x free which includes predicates expressing properties and relations that are components of the analysandum.  The analyzing predicate to the right of "iff" does not express the same property as the predicate to the left.  But it can be said to "represent" the analysandum by having elements that express properties and relations that are constitutive of the analysandum and by representing those component properties and relations as standing in a complex relation that reveals some of the structure of the property or relation that is the object of analysis.  That structure revealing relation is given in the syntax of the analyzing predicate.  So, for instance, we can analyze the property of being a bachelor as follows:

(2)   x is a bachelor iff x is adult, male, human and unmarried. 

Here we have an account of the complex property of being a bachelor in terms of the component properties of being adult, being male, being human and being unmarried.  The syntax of the analysis reveals that these four properties are structured in the analysandum by a four place conjunctive relation.  In the next section we will consider analyses of dispositions. 

Dispositions

I take a disposition to be a relational property of having some distinct causal base property.  A causal base for a disposition is any property that has the causal power to produce a manifestation of the disposition given the obtaining of the disposition’s precipitating conditions.  At this superficial level, we can offer the following schema for analyses of dispositions.

(3)   Dv iff ($X)(Xv and CX)

This is a second order formulation with the existential quantifier ranging over properties.  In (3), C is the property of being a causal base for the disposition D.   So, for instance, a thing is soluble in water iff it instantiates a causal base property for solubility in water.  (3) tells us that a disposition is a relational property of having some causal base property.  A more complete description of the logical form of an analysis of a disposition will say something about what it is for a property to be a causal base for a disposition. 

A property is a causal base for a disposition if instantiating it in conjunction with the precipitating conditions for the disposition would cause a manifestation of the disposition.  This account of what it is for a property to be a causal base for a disposition involves a relation of counterfactual dependence between properties; call it R*.   R* holds if and only if it is the case that the instantiation of X in conjunction with an instance of P constitutes a sufficient condition for causing an instance of M.  A property X is a causal base for a disposition to produce a manifestation M under precipitating conditions P if and only if R*XPM.  So, on this account, the logical form of a conditional analysis of a single track disposition D to M if P will be. 

(4)        ("v)(Dv iff ($X)(Xv and R*XPM))

Multi-track dispositions are analyzed along the same line with a conjunction of counterfactual dependency relations for the various possible precipitating conditions and manifestations.

Coulomb's law characterizes a fundamental force of mutual attraction or repulsion between two bodies as a function of their electromagnetic charge, the distance between the bodies and a certain property of the medium separating those bodies.  Coulomb's law is expressed mathematically as follows:

(5)        F = KQ1Q2/r2

On the proposed view, we take this force of attraction or repulsion to be the manifestation of a disposition of positive or negative charge.  A specific charge is in part a complex multi-track disposition that includes dispositions to manifest forces in accordance with Coulomb’s law.  A full analysis of charge would take into account interactions with other forces.

It is only analyses of relatively fundamental dispositions that we want to count as laws.  For a disposition to be fundamental in the relevant sense is for it to be the end of an explanatory line.  I take no stance on just what dispositions ought to be regarded as explanatorily fundamental, but the view that laws are analyses of fundamental dispositions should not be taken to beg any questions against the anti-reductionist.

Objections and replies

A variety of potential objections to the proposed view of causal laws as analyses of dispositions will have to be addressed.  I suspect that the contingency of laws is too readily embraced for fear that necessary laws would violate certain intuitions about how things might have been.  In fact I think the modal intuitions commonly thought to be at stake can be nicely accommodated on the proposed view.  I have briefly suggested how previously.  I will say more below.  It is also alleged that dispositions are explanatorily impotent.  I will have to explain how analyses of dispositions can play the explanatory role that laws play in science.  These concerns will be addressed shortly.  But first I will consider the epistemological status of laws as necessarily true analyses.

The Epistemic Status of Laws 

Analytic claims are traditionally characterized as claims that are true in virtue of meaning.  Where linguistic competence is assumed to entail complete understanding of meaning, analytic claims, including analyses, will be generally be regarded as knowable a-priori.  On this view one need only examine the contents of one's mind as a competent speaker to find adequate grounds for the truth of analytic claims.  This is hardly how we discover that a scientific hypothesis is a law.  But we have already rejected the assumptions that lead to this view.  The rough intuition that analyses are known a-priori is typically held in the absence of any specific account of analysis or meaning.  But we have taken positions on these matters.  The meaning of a predicate is just the property or relation it expresses.  Analyses are accounts of the natures of such properties.  Given the mind independent status of properties and relations, our epistemic connection to them is left open.  That we can competently use a word to express a certain property is no guarantee that we fully understand the nature of that property.  We can have acquaintance with properties through their instances and still lack detailed knowledge of their nature.  And we can learn more about the nature of properties instantiated in the world through our experience of the world. 

The Alleged Intuition that the Laws are Contingent 

It seems that gravity might have been a bit stronger or weaker.  This suggests that the actual law of gravity could have been false.  I think the apparent intuition that the laws could have been false is just the correct intuition that things in the world might have instantiated different dispositions.  This intuition is readily accommodated on the proposed view.  The proposed view takes laws to be necessarily true property analyses which have the further property of law-hood contingent upon the analyzed disposition actually being instantiated. 

Let us take Newtonian gravitational mass (NG mass) to be a disposition to manifest an inverse square force in accordance with Newton's law of universal gravitation.  On this supposition, Newton's law of universal gravitation is a necessarily true analysis of NG mass.  It follows that we cannot coherently imagine a world in which Newton's law of universal gravitation is false.  That is, we can not imagine a world in which NG massive bodies fail to exert an inverse square force in accordance with Newton's law.  However, the view here offered does allow that things have properties similar to, but distinct from NG mass.  In fact things do.  This does not render Newton's law false as analysis of NG mass; just false as an analysis of mass, that property of mutual attraction that is in fact instantiated by all bodies.  Newton's law, though we still call it a law, isn't a law of nature; not because it isn't a true analysis of some property similar to mass, but because it is an analysis of a mass like property that is not instantiated by actual bodies.  Conceivability arguments can only support the contingency of laws of nature if they presuppose that laws represent relations between non-dispositional properties.  But this merely begs the question against necessarily true laws.  In fact, our intuitions about how things could have been can be comfortably accommodated on the view that laws are necessarily true analyses of dispositions.

The Alleged Explanatory Impotence of Dispositions 

One might object to the proposed view of laws as analyses of fundamental dispositions on the grounds that dispositions are explanatorily impotent.  We have, for instance, the familiar case of Moliere's joke.  We give no explanation of why ingesting opium causes a person to sleep by attributing to opium the dormative virtue, a disposition to induce sleep when ingested.  How then can laws, conceived of as analyses of dispositions, perform the explanatory work we take laws to perform. 

Appeals to dispositions are explanatorily impotent in certain respects.  That opium has the dormative virtue does not explain why opium causes people to fall asleep.  The question "why does ingesting opium cause people to fall asleep?" presupposes that ingesting opium has the dormative virtue and asks what accounts for its having this disposition.  Attributing the dormative virtue to opium fails to address this question.  But attributing the dormative virtue to a substance does have explanatory value with respect to other questions.  For instance, that Curious George ingested a substance with the dormative virtue can explain why Curious George is asleep.  He might have fallen asleep because he was sleepy.  But appealing to the dormative virtue of a substance Curious George has ingested identifies his being asleep as the manifestation of a particular disposition as opposed to some other possible cause.

The foregoing intuitions about explanatory value accord well with view that charge is a disposition analyzed by Coulomb's law.  Suppose we take charge to be a disposition to behave according to Coulomb's law.  In this case, that electrons have charge will be explanatorily impotent with respect to the question "Why do electrons behave in accordance with Coulomb's law?"  Again, the question presupposes that things have a disposition to behave in accordance with Coulomb's law and asks for some account of why this is the case.  But explanatory impotence in this regard fits our intuitions about the explanatory value of laws quite well.  Science may tell us that electrons have a disposition to behave in accordance with Coulomb's law.  In so doing it tells us that things have charge.  But science does not tell us why electrons have charge.  If we take charge to be a fundamental force, we accept certain facts as basic and reject the relevance of certain questions regarding those basic facts.  In so far as we take charge to be a fundamental force, we accept things having charge as the end of the explanatory line and we reject the question "Why do bodies have charge?"  In taking charge to be a disposition to behave in accordance with Coulomb's law we also reject the question "Why do bodies with charge behave in accordance with Coulomb's law?"  I see no significant cost in accepting this.  That bodies have charge, in conjunction with various other laws, still retains ample explanatory power with respect to questions like "Why does the flashlight light up?" or "Why does the voltmeter register?"

In addressing the foregoing potential objections to the view that causal laws are analyses of dispositions, we have gone some ways towards saying how laws are known, how laws explain, and how to accommodate our seemingly conflicting modal intuitions about laws.  In light of the promising avenues open for addressing these issues, I think we have insufficient grounds for tolerating  the weaknesses of the view that laws are contingent nomic relations between universals.   Therefore, I conclude that nomic relations are necessary, properties have their causal powers essentially, and causal laws are analyses of dispositions.