This joint review appeared in History of European Ideas, vol. 8, no. 1 pp. 97-99 (1987).

What is a Law of Nature?, D.M. Armstrong (Cambridge University Press, 1983), 180 pp.

The Concept of a Physical Law, Norman Swartz (Cambridge University Press, 1985), 220 pp., $29.95, £22.50.


Looking backwards, one can locate in the mid-1960s a crisis, that is to say, a turning point in western conceptions of science. The last twenty years have witnessed a flood tide of social-historical, antiobjectivist and increasingly subjectivist interpretations of science, climaxing (?) in the current 'strong programme' in the sociology of science and technology (Barnes, Collins, Knorr-Cetina, McKenzie, Mulkay, Pinch, Restivo and Shapin, among many others), defending the thesis that even the most technical details of artifacts and theories are social constructions burdened with parochial ideologies.

This characterisation is only partly accurate, however, for alongside the rejection of objectivism there has grown an increasingly insistent defence of objective knowledge. As early as 1966, Israel Scheffler, in his Science and Subjectivity, attempted to undo the subjectivisation of knowledge that he, correctly, foresaw following from the work of Polanyi, Kuhn and Hanson. Scheffler attempted a reformulation of the objectivity of the given that was widely perceived at the time not only as unsuccessful, but as reactionary: refusing the liberation of science from the clutches of logical positivism and analytical philosophy promised by the new subjectivists. (Ironically, Kuhn's Structure of Scientific Revolutions was published by the Encyclopaedia of the Unified Sciences!)

Subsequently, the accelerating radicalisation of knowledge has elicited responses from a wide range of philosophers, historians and social scientists who have suddenly confronted the anarchic implications for their own work of ceding objectivity and embracing the ubiquity of ideology. The result has been a spring tide (not yet of flood proportions) of realist interpretations of science and scientific knowledge. Three recent contributions to this literature are R. Tuomela's Science, Action and Reality, D.M. Armstrong's What is a Law of Nature? and N. Swartz's The Concept of Physical Law.

Swartz's and Armstrong's books bear to one another something of the relationship of yin and yang in the well-known visual symbol called the t'ai chi: superficially antipodal, each bears within it a seed of its opposite. Armstrong argues a philosophical realist position in which universals are both logically and ontologically prior to particular events in the world, and in which particular events are the necessary instantiations of their universals. Swartz argues a nominalist position in which particular events, in virtue of being all there is to reality, are both logically and ontologically prior to universals. Swartz sharply distinguishes his conception of physical law from what are called 'laws' in the practice of science, to the detriment of the latter, while Armstrong identifies science with knowledge. Where Armstrong dismisses with barely concealed contempt the Regularity Theory of laws of nature and embraces a Prescriptivist view in which laws are more real than, and in some sense dictate, their empirical instantiations, Swartz dismisses Prescriptivism as secular Providentialism and embraces a version of the Regularity Theory in which what are called 'laws' are no more than summative expressions of the particular events that actually occur in the world (although strictly speaking, for Swartz, events are themselves nonunique constructions woven out of particular facts).

What binds Swartz and Armstrong in complex reciprocal opposition is that both offer scholastic propositional interpretations of truth and cognate metaphysical interpretations of propositions from which their characterisations of science and knowledge follow; both defend versions of realism and objectivism; and both resort to rhetorical devices (repetition, dogmatic insistence) when argument flags.

Armstrong's monograph, its title notwithstanding, is not an inquiry into the nature of what are called 'laws of nature', but an application of the author's earlier (1978) Universals and Scientific Realism. Armstrong here assumes the truth of the following propositions: that 'laws exist independently of the minds which attempt to grasp them' (p.7); that a Regularity Theory underlies all anti-Realist views of laws of nature; that universals have a real existence such that 'any satisfactory account of laws of nature must involve universals and irreducible relations between them' (p.10); that 'we should not postulate any particulars except actual particulars' (pp.8-9); and that 'science plays the vanguard role in gaining knowledge and/or reasonable beliefs about the world' (p.4).

Part One of What is a Law of Nature? is a tendentious 'destructive critique' of non-Realist views of the regularities we 'discover' in phenomena. Armstrong simply finds unintelligible any other interpretation of phenomenal regularities than a noumenal architectonic of which both phenomena and their genuine correlations are necessary instantiations. Any other view inevitably falls prey to inductive scepticism which, to Armstrong, is fundamentally irrational because it entails scepticism of the rationality of inferences to the best possible explanation. Armstrong insists that rationality ultimately means inference to the best possible explanation, that nothing else can be called 'rational' if inference to the best possible explanation is not rational, and so any basis for science that is vulnerable to inductive scepticism is eo ipso fatally flawed.

Part Two argues Armstrong's 'positive theses': that laws of nature are 'dyadic relations of necessitation (or probabilification) holding between universals' (p.172); that all genuine laws of nature are instantiated laws, so that functional laws, which necessarily entail uninstantiated cases, are higher-order laws from which lower-order instantiations are derived by substituting particular values for independent variables; that irreducibly probabilistic laws (as in quantum mechanics), of which deterministic laws are limiting cases, are also relations between universals, relations 'constituted by a certain objective probability' that instances of the antecedent universal will necessitate instances of the consequent universal; that 'all laws [of nature] link a state of affairs where a particular has a property with a state of affairs where that same particular has a further property' (p.173).

The argument in Swartz's book also rests on an earlier work for its full comprehension, in his case on the 1979 book Possible Worlds, coauthored with R. Bradley, in which they offer an ontology of propositions. This is a necessary complement to Swartz's thesis in this monograph because for Swartz physical laws are propositions of a certain sort, namely, 'contingently true conditionals, of universal or statistical form all of whose non-logical and mathematical terms are purely descriptive predicates' (p.33). (A predicate will be 'purely descriptive' if it does not refer in a spatio-temporally specific way to its subject term.) Physical laws are thus always true, but have no epistemic properties. Scientific laws, on the other hand, are calculating algorithms expressive always of sets of simplifying assumptions and approximations that give scientific laws explanatory power, but guarantee that virtually all scientific laws are false! True propositions, of which physical laws are a subset, are abstract objects and for Swartz, in direct opposition to Armstrong on this very same point, 'abstract objects are just not the right sorts of things – ontologically speaking – to ground, account for, or constitute the truth conditions of, physical possibilities' (p.99).

Physical laws are reducible to singular propositions about the world and owe their truth to singular facts of the world (p. 107). But even our particular descriptions of the world, out of which physical laws are spun, are not and cannot be unique inventories of atomic events in the manner of Wittgenstein-of-the-Tractatus (p.38). Only events under descriptions can 'fall under a physical law, but descriptions are necessarily non-unique. This implies that there are a virtual infinity of physical laws, reflecting not an infinity of events in the world, but the limitless ways in which events can be created out of what actually transpires in the world.

From the vast number of physical laws that must exist, that is, from the vast number of true propositions describing, in the manifold ways compatible with the definition of a physical law-type of proposition, what actually has transpired in the world, Swartz derives the mutual compatibility of freedom and determinism. (His resolution of this problem is strikingly similar to a popular treatment by Raymond Smullyan in the essay 'Is God a Taoist?', in his The Tao is Silent, Harper & Row, New York, 1977.) Swartz argues that the Laplacean version of determinism is simply wrong, independent of quantum mechanics and its notorious uncertainty relations, because it rests on the erroneous suppositions that there are only a finite, indeed only a manageably small, number of physical laws each of which have already been instanced.

For Swartz, determinism is both true and non-prescriptive because physical laws only describe what does happen in the world, not what must happen. Thus, humans are free 'to the extent that the truths describing what we do derive solely from what we do' and this freedom is possible because of the complexity of the world, a complexity that is in no way reduced simply by describing every event that transpires as the second member of a sequence falling under a universal physical law (p.32). Following Bar-Hillel, Swartz identifies this complexity with the infinite number of state descriptions – here, the infinite number of descriptions defining the events that then are made to fall under physical laws – characteristic even of systems vastly less complicated than the world of our experience.

There is much more in this rich little book which, seemingly the antithesis of Armstrong's book in so many particulars, nevertheless shares with the latter a number of central commitments. It is not too arch to say that if a reader were to choose one book reflecting current notions of the status of laws of nature, these two books would be one good book to choose.

STEVEN LOUIS GOLDMAN