In What is a Law of Nature? (1983) David Armstrong promotes a theory of laws according to which laws of nature are contingent relations of necessitation between universals. The metaphysics Armstrong develops uses deterministic causal laws as paradigmatic cases of laws, but he thinks his metaphysics explicates other sorts of laws too, including probabilistic laws, like that of the half-life of radium being 1602 years. Bas van Fraassen (1987) gives seven arguments for why Armstrong’s theory of laws is incapable of explicating probabilistic laws. The main thrust of the arguments is that Armstrong’s metaphysical apparatus serves to drive up the initial probability values stated by probabilistic laws. Armstrong replies to van Fraassen in his (1988) and (1997) by appealing to limiting relative frequencies. Remarkably little has since been written about Armstrong’s theory of probabilistic laws1 and I wish to revive interest in the debate here by assessing Armstrong’s response. I will argue that his response fails because the principle of instantiation puts the limiting relative frequencies that he requires out of reach. I further argue that Armstrongians should give up their account of [End Page 1] probabilistic laws for a metaphysics of irreducible propensities, since propensity theory employs many of the assumptions that undergird Armstrong’s metaphysics of laws.
I Metaphysical Assumptions
We begin with a brief review of the assumptions stated in What is a Law of Nature? that are methodologically important for Armstrong’s metaphysics of laws.
Naturalism is the view that nothing exists except the single, spatio-temporal world studied by science. The assumption gives Armstrong an Aristotelian account of universals, so that if universals exist, we must consider them to be features of our world.
Realism about laws takes laws to exist independently of the minds that attempt to grasp them. Armstrong thinks that we posit the existence of a law as an inference to the best explanation: independently existing laws that underlie and are distinct from phenomena explain the existence of regularities that we find in nature.
Realism about universals takes universal properties to exist independently of anyone who knows of them. As a consequence of his naturalism, Armstrong adopts the Aristotelian view by which properties and relations are universals existing in re. Armstrong’s realism about universals requires the principle of instantiation. To exist, a universal must have been instantiated in some particular in the past, present, or future. We will soon see that the principle of instantiation also requires laws to have been instantiated at some time or other. There is no place in Armstrong’s ontology for uninstantiated universals or uninstantiated laws.
Actualism is the thesis that ‘we should not postulate any particulars except actual particulars, nor any properties and relations (universals) save actual, or categorical, properties and relations’ (Armstrong, 1983, 8–9). One consequence of assuming the truth of actualism is that it debars the merely physically possible, including dispositions and powers, where these are conceived of as properties that cannot be reduced to categorical properties of objects. Armstrong doesn’t deny that there are statements that attribute dispositions and powers to objects, but the truth-makers for these statements are not objective dispositional properties, but actual, categorical properties.
II Laws of Nature
For Armstrong, the statement ‘All Fs are Gs’ expresses a deterministic law of nature if and only if a relation of necessitation relates the universals F and G. Accordingly, a law is symbolized by the letters ‘N(F,G),’ [End Page 2] which may be read as ‘it is a law that being an F necessitates being a G.’ N directly relates universal properties, not objects or propositions. The necessity that relates objects is in virtue of the properties objects instantiate and the laws relating the properties. Thus object a being F necessitates a being G in virtue of the fact that there is a law that N(F,G), such that a is necessarily G because a is F.
Armstrong integrates probabilistic laws into his schema by arguing that probabilistic laws are probabilities of necessitation. By taking them to be probabilities of necessitation, Armstrong thinks that probabilistic laws involve...