This article originally appeared in Laws of Nature – Essays on the Philosophical, Scientific and Historical Dimensions, edited by Friedel Weinert, pp. 67-91 (New York and Berlin: Walter de Gruyter), 1995. ISBN 3-11-013918-9. © Copyright 1995 by Walter de Gruyter & Co., D-10785 Berlin. Reprinted with permission of the copyright owner.

A Neo-Humean Perspective: Laws as Regularities

Contents Introduction[note 1]

I was seven or eight years old. In Hebrew school we had just learned the Aleph-Bet and were, haltingly, beginning to sound out words. As we spoke the ancient text, our teacher translated: "... And God said: 'Let there be light.' And there was light. ..."[note 2] Here was magic; here was the supernatural; here was the creation of the universe. I resonated to the story. I was filled with wonder, far more than had ever been elicited by any fairy tale my parents had read to me. I pictured in my imagination the majesty of it: God speaks and Nature obeys.

But I did not believe the story that was unfolding.[note 3] I was certainly enraptured by it; but I was not seduced by it. I reveled in the imagery while harboring a conviction, one that would strengthen in the ensuing years, that it was false.

The fable of Genesis is one of the most enduring of Western Civilization. It is so much a part of the fabric of our collective thinking that in its modern-day guises it is all but invisible. But parts of the biblical Creation-myth do persist. The fable survives, even in the thinking of many persons who believe that they have divested themselves of any shred of a theistic or supernatural cosmology, persons who are certain that they have adopted a thoroughgoing materialistic naturalism.

Sometimes ancient mythology is not vanquished: it merely accommodates itself to the prevailing temper of the times and 'goes underground' to form the unarticulated presuppositions of one's metaphysics.[note 4]

What exactly is the 'physics' (so to speak) of the ancient biblical Myth? It is that God's words alone – just His voice, His thoughts, His willing that something occur – are sufficient to bring things (e.g. light, the sun and moon, the creatures of the waters and of the dry land) into existence. And these words – these thoughts, these proclamations – determine the eternal destiny of (some at least of) His creation: "And God set them [the sun and moon] in the firmament of the heaven to give light upon the earth, and to rule over day and over the night, ...".[note 5] It is, in short, the theory of the sovereign power of The Word. God's Words do not describe Nature; God is no Chronicler. God's Words move and shake Nature; God is Creator, God is Prime Mover, and God is Legislator.[note 6]

The myth has been secularized for consumption in the twentieth century. Few scientists ever invoke God in their explanations of events in the world.[note 7] But if God Himself has dropped out of the picture, His Words remain and retain their primeval role. The principal difference is that now those Words are called "physical laws". Just as the background radio hiss in the universe is the remnant of an ancient Big Bang, the theory that physical laws govern the world is the remnant of the ancient supernatural theory that God spake and Nature obeyed.

Here is a typical presentation of the secularized version. This is the introductory paragraph in the section "Looking for Laws: The Scientific Approach to Behavior" in the textbook Psychology: Themes and Variations, by Wayne Weiten:
Whether the object of study is gravitational forces or people's behavior under stress, the scientific approach assumes that events are governed by some lawful order. As scientists, psychologists assume that behavior is governed by discernible laws or principles, just as the movement of the earth around the sun is governed by the laws of gravity. The behavior of living creatures may not seem as lawful and predictable as the "behavior" of the planets. However, the scientific enterprise is based on the belief that there are consistencies or laws that can be uncovered. Fortunately, the plausibility of applying this fundamental assumption to psychology has been supported by the discovery of a great many such consistencies in behavior, some of which provide the subject matter for this text. (Weiten 1992, p. 34)
And the mathematician/physicist P.C.W. Davies writes:
... subatomic physics is not complete anarchy. Many conceivable transmutations and reactions simply do not occur at all. We do not see protons changing into positrons, or electrons into neutrinos. ... Why not? What rules are there that bring at least partial discipline and order to the tangle?

Classical physics has rules governing the interactions of matter [laws of conservation of energy and momentum]. ... When relativity is taken into account, we must include mass with energy because of the equivalence E = mc2. Less familiar is the conservation of angular momentum or spin.

... There is also a universal asymmetrical law which regulates the organization of the activity [the second law of thermodynamics]. (Davies 1980, pp. 155-157. Parenthetical glosses summarize omitted portions.)
The subject matter changes from psychology to physics. But the underlying metaphysical view (we see in these two examples) remains constant. The vocabulary describing the relationship between laws on the one hand and events (/states, /properties, etc.) of the world on the other is the same. Both Weiten and Davies write of laws 'governing' the world; and Davies, note, invokes near-synonyms when he goes on to write of 'rules that bring discipline and order [to Nature]' and of '[laws] regulating the activity [of Nature]'. There is nothing unusual or unfamiliar in these passages. Indeed they were purposely selected just because they are so very ordinary: they express the prevailing view. Indeed it would be a trivial matter to multiply indefinitely examples from other authors in every other scientific field: economics, pharmacology, geography, epidemiology, archaeology, neurophysiology, etc. (And I have recounted in Swartz 1985, p. 120, similar views expressed, not by scientists [as here], but by philosophers as well.)

This standard, or received, view – that physical laws (or Laws of Nature) govern or regulate Nature – is so commonplace, so entrenched, so widely promoted, that it is taken to be truistic. But for all that, this iconic view is challengeable. Indeed – I want to argue – it is misleading, radically unempirical, and overdue for replacement. However, before we turn to that matter, we must pause to make an important distinction.

Physical Laws and Scientific Laws

Physical laws are the 'real' laws of Nature. These laws are true independent of human beings coming to learn their truth. The law of the constancy of the speed of light, for example, has nothing to do with human beings having learned it to be true. It is true – and would have been true – even if human beings had never discovered its truth, indeed even if human beings (or any other sentient creatures for that matter) had never existed in this universe.

Physical laws have at least five properties. They are: (1) true (for all time and all place[note 8]); (2) universal or statistical generalizations; (3) purely descriptive (i.e. free of any terms naming specific items in the universe); (4) conditional; and (5) contingent (i.e. not necessary [logical] truths). Being believed or being known is not a defining property of physical laws. What properties beyond these minimal five properties are necessary for a proposition's being a physical law is the area of contention between the Regularity Theory and its rivals. According to the Regularity Theory these five properties are individually necessary and jointly sufficient for a proposition's being a physical law. Rival theories – which I here wish to reprove – argue that additional properties are necessary for a proposition's being a physical law, that is, these competing theories argue that the list, just given, of five properties is not sufficient.

Scientific laws, in contrast, are human creations. These are statements adopted in our collective effort to explain, predict and control the world. Some of these laws are more-or-less 'read off' nature directly. (Many statistical generalizations are of this sort. Such generalizations may be exceedingly useful tools for prediction. For example, managers of public transportation systems are skillful, using such empirically ascertained generalizations, at hiring the 'right' number of overtime drivers to handle increased demands on New Year's Eve. No sociologist could derive such statistical laws from any extant theory, but the laws are available, standing isolated from any overarching theory, as useful tools. Similarly engineers will determine, through extensive testing, the mean time between failures [MTBF] for various devices – copying machines, fluorescent bulbs, silicon memory chips, etc. – such results being unobtainable from basic theory.) Other laws, we know, are guessed at (hypothesized) and then tested. While still others 'fall out' of higher-order theories.[note 9]

Scientific laws – with few exceptions – are understood (1) to be not literally true, i.e. to be false. Nearly all scientific laws – as pointed out by Scriven and, far more extensively, by Cartwright – are false: not just possibly false, but actually false, and moreover known to be false.[note 10] (Cartwright writes colorfully that the 'laws of physics lie'. Literary license understood, we know that she means that the [scientific] laws of physics are false.) In addition, scientific laws are understood (2) to be approximations to the truth, 'idealized' reconstructions, or instrumental tools; and (3) to be held only tentatively, always subject to the possibility, and in many instances the actuality, of refutation, abandonment, and replacement.

Scientific laws – except for a tiny handful at most – are not physical laws, i.e. they are not the laws of Nature itself, but of human beings trying to understand and subdue Nature. For some proposition (statement) to be regarded as a scientific law, it must satisfy a certain subset of a very complex set of properties. Trying to determine what these properties are – e.g. conferring predictive abilities, providing explanatory premises, being interconnected in a net of theoretical liaisons, being tractable, being testable (even if only very indirectly), etc. – has occupied a very great deal of time among philosophers of science. In pursuing such a philosophical activity one is probably well advised to keep Wittgenstein's model of 'family resemblances' at the fore. There almost certainly is no single set of properties shared by all scientific laws. What it is to be a scientific law is to have a certain subset of a varied mix of 'law-conferring' properties and to have won the approbation "scientific law" from a number of prominent practicing scientists. In short, it is exceedingly difficult to say precisely what a scientific law is, and this for the reason that there is no single defining set of necessary and sufficient conditions for a statement's being a scientific law.

To explicate the concept of scientific law calls upon a great deal of empirical research, specifically concerning how scientists actually use the concept of law and what criteria they use in designating something a scientific law. This philosophical task is as daunting as any. While it has a significant, perhaps preponderant, empirical dimension, it also has a normative one: How – given the empirical data about how scientists actually use the concept of scientific law – ought we to reconstruct (/modify /conceive of) this concept so that it captures actual practice while at the same time can inform that practice and allow us to 'make sense of' (best understand) the scientific enterprise?

In contrast, the question as to what physical laws are, or better, how they are to be conceived, has little, if anything, to do with actual scientific practice. What are to be the defining characteristics of physical laws is ultimately to be decided by our metaphysics, not by our epistemology, and not by an empirical survey of the writings of scientists. (To be sure, metaphysics and epistemology are not wholly distinct disciplines, but in this instance I am talking about relative balance, and on whole, the question of how we are to conceive of physical laws is far more a matter of metaphysics than it is of epistemology or the philosophy of science, especially when the latter is conceived to be a branch of epistemology.)

The terminology we are forced to use is unfortunate. All of the expressions, "physical law", "law of Nature", and "Natural Law", connote – in the first instance at least – the context of physics and chemistry. It would be useful to have a more neutral, more inclusive, terminology, a name for any and all (real) laws whatsoever: those pertaining to the subject matter of physics as well as the subject matter of economics, sociology, geography, sociobiology, anthropology, genetics, etc. Lacking such a term, we will have to make do with "physical law". (The term "Natural Law" carries still other baggage, even more problematic than does "physical law". In some theories in ethics and in theology, the expression "natural law" has been used to denote the warrant in nature or in reason for ethical and moral precepts.[note 11] Thus I eschew the use of "natural law".) In short, I use the term "physical law" broadly: to encompass the laws (i.e. the 'real' laws, not the scientific laws) of all phenomena whatsoever, including, for example, economic laws, sociological laws, etc. Even though it is not usual to regard (the real) laws of economics, or (the real) laws of sociology, as "physical laws", they will here – for lack of any better term – be so regarded.

Throughout this century, much philosophical writing about physical laws (the laws of Nature) has been infected with a serious confusion, or more accurately, a conflation. Many writers fail to take any account whatever of the difference between physical laws on the one hand and scientific laws on the other. (You can detect this conflation in the paragraph by Weiten, quoted a moment ago.) These writers often use the terms "laws of nature" and "scientific laws" interchangeably. John Hospers, for example, in An Introduction to Philosophical Analysis (first edition, 1953) – the text through which doubtless some of the readers of this present volume will have been introduced to analytic philosophy – tacitly treated the two concepts as equivalent: "Scientific laws are generalizations; that is to say, from observing particular examples of nature's uniformities we generalize and assert that these uniformities hold in all cases. ... All laws of nature, then, in what they assert, go beyond the evidence that is available for them at any given time" (p. 168). The confusion remains, and is indeed exacerbated, in the latest (3rd) edition (1988). Writing of laws of nature, Hospers says "An important feature of laws is one that may come as a surprise: no single observation is sufficient to undermine a law" (p. 160). Such a claim may be apt for scientific laws; it is utterly misconceived in the context of physical laws, where the issue of acceptance or rejection cannot intelligibly arise.

In this chapter, I treat the two concepts – physical law and scientific law – as distinct. As I prepare this chapter, having before me only a list of chapter titles and the authors invited to contribute to this volume, it would appear that the majority of the papers in this anthology are given over to examining scientific laws. This chapter may help to even the balance slightly. This chapter will dwell principally on physical laws.

Metaphysics in Science

Many scientists naively believe that they practice a craft free of metaphysics. I have had frequent discussions with scientists who have told me that science – particularly as practiced by them personally – is free of metaphysics that infected science before the modern period, that they themselves carefully and deliberately eschew all metaphysics in their own science.

Such opinions are self-delusional. No science is, or for that matter could be, free of a very substantial component of metaphysical presupposition. (For an extended defense of this latter claim, see Swartz 1991, esp. Chapters 2-8.) The question is not whether our science has metaphysical components, but rather whether we learn to detect those aspects and whether we learn, or want, to examine them critically.[note 12]

What I have been calling the 'standard' or 'received' view of physical laws – viz. that physical laws 'govern' or 'regulate' Nature itself – is so familiar, so widely promoted, that it has taken on the appearance of being an (indubitable) 'fact'. We have been told that this was one of the great discoveries of the sixteenth and seventeenth centuries, that this is one of – and even perhaps the most important of – the cornerstones upon which the edifice of modern science rises (again see the quotation from Weiten above). We have been told that the belief in this claim has proven so successful, and so often confirmed, that it is – now – quite beyond dispute. In short, the standard view is presented as if it were itself a (virtually incontestable) datum of science.

That manner of regarding the epistemic status of the standard view of physical laws is a mistake. The standard view of physical laws is not a scientific datum, but a metaphysical theory, one which needs to be seen as such and to be appraised as such.

No one can reasonably (rationally) claim that there is not considerable order in Nature. There is. Such order occurs in the subatomic through to the galactic; in nonliving through to living matter; in protein fragments through to viruses; and in single-cells through to multi-celled organisms; in small groups, through to complex societies and to entire civilizations; etc. Most, if not all, of Nature 'falls under' physical laws. We know this. It would be irrational to deny this. The (imperfect) laws of science daily add further data pointing to an (underlying) orderliness in Nature itself, that is, pointing to the existence of 'real' (i.e. what I have called 'physical') laws. In challenging the standard view, I do not want to challenge the thesis of the orderliness of Nature or of the existence of 'real' laws. On the contrary, as should be obvious, I want to insist on the existence of such 'real' laws.

What I am intent, however, to challenge are certain metaphysical claims made about the nature of these underlying (or 'real' or 'physical') laws. In particular, I want to challenge the theory (i) which portrays physical laws as governing the world and (ii) which attributes to physical laws a special property of 'lawfulness', usually called by philosophers "nomicity" and taken to be a kind of 'physical necessity'.

Truth Reported versus Truth Imposed

It is only in the Twentieth Century, more exactly since the 1930s, that philosophy can finally claim to have the makings of a viable theory of truth. (In Tarski's theory, the vehicles of truth and falsity were sentences. Here I will assume that the vehicles of truth and falsity are propositions[note 13] and will adapt his theory accordingly.) On Tarski's semantic theory of truth (modified as just explained), the proposition expressed by the sentence "Snow is white" is true if and only if snow is white. (The theory says nothing about our being able to find out whether a given proposition is true, but that is not the intent of his theory. Tarski's theory is meant to explain, or at least remove some of the historical seeming mystery surrounding, the nature of truth itself, i.e. it sets out to explicate the semantic concept of truth. The theory does not even address, let alone answer, how to discern actual truths from actual falsities. Indeed one of the great merits of his theory is that it thoroughly dissociates questions of semantics from questions of epistemology.)

Propositions do not 'become' true. A person may become the treasurer of a company; her becoming so is an event which is datable. The truth of a proposition is not a datable event or occurrence; propositions bear their truth omnitemporally. "John F. Kennedy is (/was /will be) assassinated on November 22, 1963" is true, has always been true, and will always be true. It did not 'become' true on November 22, 1963. The proposition's having been true for all time prior to November 22, 1963 was not the cause of Kennedy's death. (So-called 'logical determinism' is a crass confusion.) The cause of Kennedy's death was an occurrence (event) in Dallas, Texas, on the fateful day; it was not a proposition or its truth.

More generally, and perhaps somewhat colloquially but at the same time more perspicuously, the Tarskian theory of truth has it that propositions (originally "sentences") 'take their truth from the way the world is'. The semantic 'truth-making' relation – if I may be permitted to put it that way – proceeds from the world to propositions (or sentences).[note 14] If the world is a certain way, then any proposition which says (reports) that the world is that way is true; and any proposition which says that the world is otherwise is false. The way the world is, was and will be, accounts for certain propositions being true (and of course for others being false). (The technical details are, to be sure, formidable; but enough has been said for current purposes.)

In a bizarre quirk of history, the received account of physical laws, deriving from a medieval view that physical laws were dictates of God – the account which has it that the world is governed by physical laws – turns the Tarskian account of truth precisely 'on its head'.

On a Tarskian theory of truth, the proposition expressed by the sentence "The charge on each electron is  –1.6 × 10–19 coulombs" is true if and only if the charge on each electron is  –1.6 × 10–19 coulombs.[note 15] However, according to the 'standard' account of the nature of physical laws, electrons bear the charge they do because they are governed by the 'law' "The charge on each electron is  –1.6 × 10–19 coulombs". The Moon and the Earth dance (to first approximation) in elliptical orbits around a common focus because they are governed by the Einsteinian laws of Space-time (General Relativity). Cats learning to escape from puzzle boxes do so in accord with (what Thorndike called) 'the law of effect': "If a response in the presence of a stimulus leads to satisfying effects, the association between the stimulus and the response is strengthened".[note 16] And, acting in accord with the laws of sociobiology, a person is more likely to come to the aid of a grandchild than of a cousin. In other words, on the standard account, there are certain, special, propositions, viz. physical laws, which do not take their truth from the way the world is, but instead 'dictate' to Nature, forcing it, governing it, regulating it, to 'behave' in certain ways and not in others.

There are, then, in the 'standard' account two radically different kinds of propositions: ordinary, garden variety ones (such as expressed by "Snow is white" and "Kennedy was assassinated on November 22, 1963") which 'take their truth' from the way the world is; and 'lawful' propositions (e.g. the second law of thermodynamics) which 'reverse the truth-making semantic relationship', which do not take their truth from the way the world is, but rather 'govern', 'regulate', 'discipline', 'rule', and 'impose order on' Nature itself. These latter propositions are said to be nomologically (or nomically [occasionally physically, onticly, or contingently]) necessary. Philosophers who plump for the existence of nomological necessity are called "Necessitarians".

It is a mark of just how peculiar the Necessitarian account of physical laws is that the theory of truth it presupposes has been so little examined in the philosophical literature that it does not even bear an accepted name. In the Concept of Physical Law, I tried to fill this void by dubbing that theory of truth 'the Autonomy Theory', the idea being that nomological propositions bear their truth 'autonomously': their truth does not arise out of the way the world is but rather occurs 'primitively' or 'independently' (or more aptly, sui generis).[note 17]

In greater detail: on the standard, Necessitarian, account, physical laws bear their truth, not indicatively, but subjunctively (or counterfactually). Physical laws are not only true, they would remain true (and their contraries would remain false) even if the world were different, in particular, even if those laws had no actual instances. Nomological laws do not bear their truth on the basis of correctly reporting (perhaps future) states of the world. For example, nomological laws of economics, of psychology, of biology, of sociology, etc., are regarded as being true from time immemorial even if life had never appeared in the universe. On the Necessitarian view, the way the universe unfolds depends on two 'factors': on the 'initial state' of the universe and on the nomological laws of the universe.[note 18]

This latter view of physical laws – that they bear their truth subjunctively and autonomously and that they function like inviolable prescriptions – is the single most important difference between the Standard (i.e. Necessitarian) Account of physical laws and the Regularity Theory. On the Regularity Theory, physical laws are descriptions, nothing more. They do not govern Nature; they do not bear their truth subjunctively or autonomously. On the Regularity Theory, there is but a single theory of truth.

The Regularity Theory, or, Being More Humean than Hume

Until fairly recently, the received reconstruction of Hume's theory of physical laws had it that Hume advanced a regularity theory, that for Hume, physical laws were nothing more or less than 'constant conjunctions'. Hume was alleged to have argued that physical laws are simply (a proper subset of) universally true generalizations and, more especially, were not 'necessary' – neither logically necessary nor physically (i.e. nomologically) necessary.

Thus, for example, in the first edition (1952) of his widely-read and respected A History of Western Philosophy, we find W.T. Jones offering this reconstruction of Hume's theory:
Like identity [through time], necessary connection is something in us, not something in the object; like identity, it is grounded in a custom or habit of the imagination rather than in a rationale in the universe. (Jones 1952, p. 780)
Or again, a few years later, we find Ernest Nagel writing in The Structure of Science:
... Hume proposed an analysis of causal statements in terms of constant conjunctions and de facto uniformities. Ignoring important details in Hume's account of the spatiotemporal relations of events which are said to be causally connected, the substance of the Humean position is briefly as follows. The objective content of the statement that a given event c is the cause of another event e, is simply that c is an instance of a property C, e is an instance of a property E (these properties may be quite complex), and any C is as a matter of fact also E. On this analysis, the "necessity" allegedly characterizing the relation of c to e does not reside in the objective relations of the events themselves. The necessity has its locus elsewhere -- according to Hume, in certain habits of expectation that have been developed as a consequence of the uniform but de facto conjunctions of C and E. (Nagel 1961, pp. 55-56)
It is not clear that either Jones or Nagel subscribed to the reconstructions they offered of Hume's theory of physical laws, indeed they probably did not. But the point, for our purposes, is that they believed that they had accurately reported Hume's view.

More recent scholarship refutes this earlier 'standard' reconstruction of Hume.[note 19] What Hume denied was that there was any empirical evidence for necessity. His so-called skepticism concerned our finding out that physical laws are nomological. But his skepticism about our ability to find evidence did not carry over to a skepticism about the existence of such necessity. He had a belief in such necessity; his problem was to justify that belief rationally and he found it difficult to do so.

The regularity and the necessitarian theories of physical laws seesaw. For much of this century, the regularity theory – the supposedly Humean theory – was, I think, predominant in the thinking and writing of many, perhaps most, philosophers. But in recent years a number of developments have reversed that balance. Certainly the concept of modality is far more familiar and attractive than it had been in the first half of the century – possible-world semantics and related techniques have made various concepts of necessity respectable. Philosophers have turned to a number of new, related, problems, e.g. the investigation of the truth-conditions for counterfactuals. And modern scholarship has, as I have said, substantially revised the received view of the historical Hume. The latter reversal is sometimes summed-up in the aphorism "Hume was no Humean" (i.e. the actual, historical, Hume did not advance the theories traditionally attributed to him).

I am heir to some of Hume's skepticism.[note 20] But where his own worry about physical necessity was only epistemological and was not mirrored in counterpart metaphysical beliefs, my own is far more corrosive and pervasive. For my own skepticism about physical necessity permeates both my epistemology and my metaphysics. While I agree with Hume that there is no empirical evidence for such a thing, I do not share his belief that metaphysics, nonetheless, requires the positing of physical necessity. It is possible to advance a cogent metaphysics free of the concept of physical necessity.

The Nomicity of Scientific Laws and the Nomicity of Physical Laws

There are two, wholly different, accounts of nomicity.

As I have said, philosophers of science have expended much effort in trying to uncover (better 'reconstruct') by what criteria scientists distinguish between 'mere accidentally true generalizations' and those which are designated as scientific laws. Many philosophers have come to regard the crucial difference under the label of "nomicity", i.e. on this account of nomicity, physical necessity is a property accruing to scientific laws out of the praxis of actual science. (An analogy may be helpful: the distinction is not terribly unlike the difference between a musical performance's being judged prize-winning while another is deemed merely competent.) The nomicity of scientific laws is strictly a human artifact.

This first kind of nomicity is entirely innocuous, one to which I have no objection whatsoever. (It is, of course, a gross confusion – to which many have succumbed – to ascribe or transfer this sort of nomicity to physical laws.)

Of far more, indeed central, concern to this chapter is the 'deeper' necessity conceived to attach – quite independent of human knowledge or scientific practice – to the real, i.e. physical, laws of nature. Is there, or could there be, any empirical evidence for such a thing?

Hume believed that there could not be, and I think he was right. However, a number of philosophers, particularly in recent years, have tried to argue that there can be such evidence. Elsewhere I have reviewed and tried to rebut (in Swartz 1985 and Swartz 1988) some of these attempts. On this occasion, I will have to content myself with a single later example. Martin Gerwin has written (in what I would describe to be 'a Lockean fashion'):
It is my contention that, contrary to what Hume has claimed, there is a very familiar type of experience which perfectly well could, and most probably does, give rise to the idea of necessary connection between phenomena. It is the experience of trying to do something and failing, so that one concludes, "I can't do it". Such an experience is quite fundamental to our awareness of ourselves as agents, and in the most intimate way. This, it seems to me, is what Hume was searching for, and he did overlook it. (Gerwin 1987, p. 7)
Gerwin and I have corresponded about this paragraph. Here is an edited version of my reply:
I doubt that 'trying and failing' will do the trick. After all, many times we try to do something, fail at it, and yet – for whatever reasons – do not conclude "I can't do it." (It happened to me recently. I was trying to install a new pump on a dishwasher and was having no success, indeed I was failing miserably. I stopped for a while, tried again, and succeeded.) I am absolutely convinced that there is no phenomenological, introspective, felt (call it what you will) difference whatsoever between failing to do something which is possible (e.g. installing a dishwasher pump) and failing to do something which necessitarians call 'nomically impossible', e.g. flapping my arms and flying.

What do I feel when I find that I repeatedly fail to do something? Disappointment, remorse, anger, sadness, annoyance, irritability, fury, etc. Do I experience (physical or nomological) impossibility? Not that I can tell. I would not know how to recognize it if I did. I can experience that I have not done what I wanted; that I have tried especially hard; etc. But I do not see that I have experienced that I cannot do it. I may say, "I can't do it." But I have not experienced anything more than failure. (personal correspondence, March 1, 1989)
In short, I have never found any good argument to the effect that there is empirical evidence for the existence of nomicity (physical necessity).

The Need for a 'Gestalt Switch'

The standard, necessitarian, account of physical laws is so much a part of the contemporary metaphysics in which modern science is pursued that it is difficult to discern its existence and perhaps even more difficult to imagine abandoning that view.

To do so requires the philosophical equivalent of a 'gestalt switch': believing that the world unfolds, certain patterns emerge, certain 'orderliness' prevails, but that none of this is 'governed'; it simply occurs.

To abandon necessitarianism means to elevate – and to live with – contingency: the world does not have to be the way it is; it just is. The charge on the electron does not have to be  –1.6 × 10–19 coulombs; it just is. Light does not have to have a constant, finite, velocity; it just does. To invoke nomological necessities to 'account' for such constancies (order, etc.) is to engage in explanatory hand-waving. Is it really any more informative to be told that light has a constant velocity because there is a law of nature to that effect than to be told that opium is sleep-inducing because it has a 'dormative power'? The form of an explanation has been given, but the content is chimerical.

There is orderliness is Nature. That's the way Nature is. There are no secret, sublime, mystical laws forcing Nature to be that way. Or at least, there is no good rational reason to believe that there are such queer entities. Physical laws are descriptions, they neither are, nor function like, prescriptions.

Advantages of the Regularity Theory

There are three advantages the Regularity Theory has over the Necessitarian Theory.

First of all, the Regularity Theory falls within the Empiricist worldview which has managed to discard a significant amount of historical baggage now regarded as explanatorily superfluous. No scientists in the late twentieth century invoke such metaphysical concepts as substance, vital forces, or natural places. These metaphysical arcana have fallen out of use because we have come to reject the kind of explanations offered which utilized them. Such concepts are not like the empirical concepts of phlogiston, caloric, and electric fluids, for example. These latter concepts came to be rejected because the theories in which they occurred were superseded by better empirical theories. But no empirical theory, no scientific theory, competed with the theory of substance, for example. The theory of substance fell into disuse because philosophers and scientists came to believe that its putative explanatory power was illusory: there was no empirical test possible for the existence of substance, and positing its existence merely deferred, without genuinely solving, the very problems it was invoked to explain.[note 21] Similarly, there is no empirical test for nomicity, in spite of claims to the contrary by some Necessitarians. Nomological necessity is purely a metaphysical posit, an anachronism that has outlived its usefulness. It is not that we must regard the theory as false, only as superfluous. Speaking of God, Laplace is alleged to have said to Napoleon "I have no need of such an hypothesis." Speaking now of nomicity, I would echo Laplace's words.

Second, the Regularity theory provides a metaphysical underpinning to a philosophy of science which legitimizes the social sciences as readily as it does the so-called more basic sciences of physics and chemistry. One infrequently articulated, but clearly central, cluster of presuppositions of the Necessitarian theory is that there are only a finite number of bona fide physical laws, that these laws are in fact relatively few in number, that they concern the subject matter of physics and chemistry, and that all 'other' laws are supposed to be consequences (or implications) of these basic laws. The trouble with this latter view is that it promotes the idea that the social sciences are, in some sense, 'second-class' sciences: that the scientific laws of the latter are less 'authentic' than the scientific laws of physics and chemistry which are 'closer to' the real laws of Nature. No such attitude is warranted in the Regularity Theory. For the Regularity Theory rejects all of the presuppositions just mentioned. On the Regularity Theory, there is no warranted claim that the number of physical laws is small (or even finite for that matter) and there is no claim – for there are no good grounds upon which to make such a claim – that the laws of physics are more basic than those of, let's say, economics (see again note 9). Furthermore, the Regularity Theory is more congenial to the existence of statistical laws. Accommodating the existence of statistical laws was an historical wrench for the Necessitarian theory and remains an awkwardness in a theory which sees laws as governing nature and as bearing their truth autonomously: "How could statistical truths be laws? What sort of underlying 'mechanism' could one imagine that would account for the permanency and constancy of certain statistical truths (not only those of quantum mechanics, but of economics, psychology, sociology, etc.)? How, more precisely, could a 'necessity' which 'drives' Nature operate stochastically? Is there 'partial' nomological necessity?" There are no counterpart worries in the Regularity Theory. Inasmuch as physical laws, in the latter theory, 'take their truth from the way the world is', i.e. are descriptions, there can be no problem about statistical laws. If there are certain stochastic regularities in Nature, then there are true (probabilistic) descriptions of those regularities. The metaphysical conundrum concerning 'partial necessities' does not arise.

Third, adopting the Regularity Theory solves one of the perennial problems, not just of academic philosophy, but of the wider Western worldview. For generations, thinkers have struggled with 'the problem of determinism and free will'. "How could human beings possibly have, and exercise, free will in a world governed (in every detail) by physical laws?" The number of attempted solutions fills volumes, but few of these solutions manage to wring much conviction from their readers. The very persistence, the obduracy, of the problem suggests that there is something seriously wrong with its presuppositions. (It is not unlike the puzzle "What is the last digit in the decimal expansion of ?" None of the answers "0", "1", ... "9" is acceptable: instead one must reject one of the presuppositions of the question itself, viz. one must argue that there is no last digit in the decimal expansion of .) The solution to the perdurable problem of determinism and free will lies ready at hand if one adopts the Regularity Theory. For one is then in a position to reject the principal presupposition of the puzzle, namely the belief that the world is 'governed' by physical law. Give up that belief – more exactly, continue to believe that there are physical laws, but abandon the Necessitarian account of physical laws which makes them nomologically necessary, regard physical laws simply as true descriptions of what occurs in the world – and the problem of free will and determinism is solved so completely that it cannot even coherently be stated so as to appear to be a problem. (The argument in its full comprises chapters 10-11 in Swartz 1985.)

Technical Appendix – The 'Paradox' of Regularity

This anthology is expressly designed for an interdisciplinary audience. I have, therefore, tried above to keep technical details to a minimum. But there is one technical aspect of the Regularity Theory which has attracted attention and deserves discussion here.

Consider any omnitemporally false existential statement. George Molnar's example (1963) was "There is a river of Coca Cola" [in symbols "(x)(Rx & Cx)"]. Each such statement is the logical contradictory of (and hence inconsistent with) a true negative universal statement [e.g., in the case at issue, "(x)(Rx  ~Cx)"]. On the Regularity Theory, the latter (true [negative] universal) statement turns out to be a physical law. Add now the usual definition of "physical impossibility", viz. that anything logically inconsistent with a physical law is physically impossible, and one can generate an unanticipated 'paradox': Every omnitemporally false existential statement (e.g. that there is a river of Coca Cola) is not just false but is physically impossible.

Many writers have taken the conclusion of the argument in the preceding paragraph to be the reductio ad absurdum of the Regularity Theory. The Regularity Theory cannot possibility be a correct account of physical laws – it is alleged by these critics – inasmuch as it has egregiously counterintuitive consequences: it would make every omnitemporally false existential statement a physical impossibility.

To this I would reply that the critics' objection is guilty of an unwitting equivocation. What it does is to carry over the baggage associated with the concept of "physical impossibility" in the Necessitarian account and to use it (illicitly) to tar the Regularity Theory.[note 22] On the Necessitarian account – i.e. on the received theory – for something to be 'physically impossible' means (roughly) that it is 'disallowed' or 'forbidden' by the nomological laws of nature. On the Necessitarian account, being 'physically impossible' is to have encountered an insurmountable metaphysical obstacle.

On the Regularity Theory, an existential proposition's "being physically impossible" connotes something far more benign: simply that proposition's being omnitemporally false. If (ex hypothesi) there never is (past, present, or future) a river of Coca Cola, then it is a universal truth (physical law) that no rivers are (constituted of) Coca Cola. Accordingly, in the sense in which "physical impossibility" is understood in the Regularity Theory, it is physically impossible for there to be a river of Coca Cola. Physical impossibility in this latter theory is simply omnitemporal falsity: it is not the confronting of an insurmountable metaphysical obstacle. Rather than being a fatal flaw in the theory, the physical impossibility of all omnitemporally false existential propositions rightly ought to be seen to be nothing more than an innocuous logical triviality.


1. It has been ten years since I wrote The Concept of Physical Law. In the meantime I have been working on other research. Friedel Weinert's kind invitation to me to contribute this paper affords me a welcome opportunity to produce what is really a Postscript to that book. The principal arguments for the Regularity Theory, developed more leisurely and in greater detail, are to be found therein. Here I will try to present the theory briefly, using the occasion to air some new arguments and (without mentioning their names explicitly) reply to some of my critics. [Resume]

2. Genesis 1:3, The Holy Scriptures According to the Masoretic Text, 1955. (Philadelphia: The Jewish Publication Society of America) [Resume]

3. Our Hebrew school teachers – throughout a formal religious training that lasted another eight years or so – never once asked me or my classmates whether we believed what we read in the Bible. The goal was always understanding the text, not believing it (which, of course, is not to say that we were expected to disbelieve it); in short, it was never an issue whether or not we believed what we were reading. (It comes as something of a shock for some Christians to learn that Judaism is a religion whose criteria for membership and standing do not mandate theological beliefs.) [Resume]

4. See Swartz 1993b. [Resume]

5. Genesis 1:17-18 [Resume]

6. It was, we do well to recall, fewer than 250 years ago, well within the Modern Period, that Montesquieu in his influential The Spirit of the Laws (1748) devoted several paragraphs of Chapter 1, Book 1, to explaining that the Laws of Nature (what we would call physical laws) are the handiwork of God. [Resume]

7. By "world" I mean the entire universe, not just the planet Earth. [Resume]

8. This latter feature – viz. being true for all time and place – is the central theme of James Trefil's Reading the Mind of God: In Search of the Principle of Universality, 1989. [Resume]

9. I use the imprecise term "fall out" because I am loath to describe the process as that of their being 'deduced'. The deriving of Kepler's Laws from Newton's, or specific heats [of particular elements] from statistical thermodynamics, when actually examined in the writings of physicists, is nothing like the mathematical proofs or derivations in logic textbooks – these 'derivations' by physicists are far more natural-language prose than they are symbol manipulation in accord with deductively valid inference rules. [Resume]

10. Although Scriven adopts the term "physical laws", it is clear from his discussion that he is referring to what I am here calling "scientific laws". [Resume]

11. See, for example, Wollheim 1967.

The concept of natural law features prominently and frequently in Pope John Paul II's encyclical Veritatis Splendor, 1993, where he writes (quoting Aquinas): "the natural law 'is nothing other than the light of understanding infused in us by God, whereby we understand what must be done and what must be avoided. God gave this light and this law to man at creation'" (section 40).

In the 1993 federal election in Canada, the Natural Law Party fielded a candidate in every riding (constituency). Their 44-page advertising brochure includes these explanations: "The most fundamental level of Natural Law is the Unified Field of Natural Law, the Constitution of the Universe. Both modern science and ancient Vedic Science locate the source of Nature's perfect order in a single self-interacting Unified Field of pure intelligence. This field sequentially creates, from within itself, all the diverse Laws of Nature governing life at every level of the manifest universe" and "The technology to enliven the Unified Field of Natural Law is the group practice of Maharishi's Transcendental Meditation and TM-Sidhi program, including Yogic Flying" (p. 5). [Resume]

12. Here are just a very few examples (taken from a virtually inexhaustible list): (1) that there is (/is not) a real external world; (2) that there is (/is not) such a thing as 'the' causal relation; (3) that truth is (/is not) manifest; (4) that there are (/are not) purposes in Nature; (5) that material objects are (/are not) 'amalgams' of instances of properties in an underlying substance; (6) that matter 'preserves' (/does not preserve) itself in existence; (7) that all aspects of the world are (/are not) quantifiable [measurable]; (8) that relations are (/are not) 'real'; etc. (On the last-mentioned topic, viz. whether relations are 'real', I have recently corresponded at length with an American sociologist who has conveyed to me an ongoing dispute he has had with professional colleagues on the issue of the reality of 'social' relationships.) [Resume]

13. See Bradley and Swartz 1979, pp. 65-86. [Resume]

14. Tarski, himself, put it this way: "The truth of a sentence consists in its agreement with (or correspondence to) reality" (Tarski 1949, p. 54). [Resume]

15. More exactly:  –1.6021892 × 10–19 coulombs, with an uncertainty of 2.9 parts per million. See Taylor 1983. [Resume]

16. Weiten 1992, p. 201. [Resume]

17. Necessitarianism comes in a variety of 'flavors'. In recent years, some philosophers have argued that physical necessity is not imposed on nature by laws but instead arises (or is grounded) directly in nature itself. For example, Armstrong – along with some others – argues that nomological necessity is a relation between universals. However, he admits "... the following complaint [against any such theory] may be made. At the end of all of our explanations, this factor of necessitation remains unexplained. This reproach is just, I think, but the inexplicability of necessitation just has to be accepted. Necessitation, the way that one Form (universal) brings another along with it as Plato puts it in the Phaedo (104d-105), is a primitive, or near primitive, which we are forced to postulate. ... We must admit it in the spirit of natural piety, to adopt Samuel Alexander's phrase" (Armstrong 1983, p. 92). Some of my objections below are not appropriate for this particular version of necessitarianism; however, most of them – e.g. concerning the lack of an empirical test; the dispensability of the notion; its mischievousness; etc. – remain intact. [Resume]

18. For an even more extravagant view of nomicity, see Rescher 1984. For a critique, see Swartz 1993a. [Resume]

19. See, e.g., Wright 1983, esp. pp. 143-144; Beauchamp and Rosenberg 1981; and Strawson 1989. [Resume]

20. But only to some. For example, I do not share Hume's skepticism, or even strong worries, about the existence of the external world or of the endurance of unperceived objects. [Resume]

21. See Swartz 1991, chapters 10-12. [Resume]

22. The mistake is not unlike that many persons make when they invoke 'intuitions', arising out of acquaintance with finite mathematics, to reject as paradoxical the theses of transfinite mathematics. If one is to consider a new theory, one must adopt (even if only tentatively) all its unique contextual definitions, and not selectively import or retain key concepts from earlier or competing theories. [Resume]


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