Laws and Lawmakers: Science, Metaphysics, and the Laws of Nature

In recent years a resurgence of interest in the laws of nature has led to a number of new books on the topic, articulating a variety of perspectives from neo-empiricism to neo-Aristotelianism, and from primitivism to eliminativism. Of these new works, in my view, the most original and intriguing is Marc Lange's Laws and Lawmakers. It has long been noted that laws support counterfactual and subjunctive conditionals. Generally those who have thought this an important relationship have held, as would seem natural, that laws are prior to the conditionals. Nonetheless, Nelson Goodman pointed out the difficulty of straightforwardly deriving the conditionals from laws plus categorical facts. David Lewis's metaphysics has the conditionals fixed by the proximity structure of possible worlds, which is itself in turn fixed in part by the laws—similarity of laws trumps similarity of nonnomic facts in making worlds close. But it is not clear what metaphysical reason there is for supposing regularities, which is what Lewis's laws are, should have this trumping power. So, despite the fact that consensus gives long odds to the view that the conditionals are fundamental, the smart money might be on that option. Hence the prima facie ground for taking seriously Lange's proposal that subjunctive facts are primitive and that we can explain which facts are the laws in terms of the subjunctive and counterfactual conditionals (I will henceforth use ‘subjunctives’ for both).We take laws as held fixed, as far as possible, when considering subjunctives. The consensus view holds that this is because the subjunctives are determined by the laws (and nonsubjunctive facts). But maybe it is just that the nomic facts are especially stable under subjunctive considerations. Some facts are more stable than others under hypothetical subjunctive circumstances. If the temperature in Bristol were to remain below 0oC for a couple of days, then the water in the pond would freeze. But it would still be colder in Calgary than in Bristol (this being written in January). If it were to be colder in Bristol than in Calgary, it would still be the case that water freezes at 0oC. Perhaps laws remain true under any subjunctive circumstance: L is a law if for any F, F ▪ → L. That cannot be quite right, for the following looks to be true: if gravity were an inverse cube law, then the strength of gravitational attraction would fall off even faster with distance. But note that in this case, the antecedent is inconsistent with the actual laws. So perhaps the laws remain fixed under subjunctive conditions consistent with the laws, unlike the nonnomic facts. This is the essence of Lange's account of the laws of nature.Consider all the facts not including those articulated using phrases such as ‘it is a law that…’ (that is, including ‘gravitational force is inversely proportional to the square of distance’, but excluding ‘it is a law that gravitational force is inversely proportional to the square of distance’). These are the ‘sub-nomic facts’ in Lange's terminology. A subset of this set is ‘sub-nomically stable’ if every subjunctive supposition consistent with that set leaves members of the set unchanged (as in: ‘if the Earth were twice its current size, gravitational force would [still] be inversely proportional to the square of distance’). Lange proves (very nicely) that the subnomically stable sets form a hierarchy of nested sets. The set of all subnomic facts forms the largest (and trivially) subnomic set. The next subnomically stable set is one containing the laws, plus mathematical, conceptual, and logical truths—it excludes all the accidental truths. A set containing the mathematical, conceptual, and logical truths but not the laws is a subnomically stable subset of this set and so forth. This hierarchy is a hierarchy of degrees of necessity. Compared to the accidental truths, the laws of nature are necessary. But the mathematical truths are even more necessary because they are part of a set that is stable under counterlegal suppositions: even if gravitational force were inversely proportional to the cube of distance, two squared would still be four.It is this hierarchy of sets of necessities that gives Lange's view an advantage over competing views, in particular the view that lawmakers are powers. That view makes the laws necessary also, but gives them full-on metaphysical necessity. That view does not allow for degrees of necessity—metaphysical necessity is the only real necessity, and either a fact is necessary or it is not. So the powers view squashes Lange's hierarchy, preserving only the distinction between the accidents and the laws. Lange regards it as an advantage that his view neatly accommodates the appearance that mathematical truths are more necessary than nomological truths. Furthermore, it allows for a distinction within the laws, for some laws seem to be more resilient under counterfactual suppositions than others: the symmetry and conservation laws seem stable under counterfactual changes to the force laws: if gravitational force were inversely proportional to the cube of distance, then energy would still have been conserved.There is a great deal in this book. Lange discusses, for example, how his account handles (better than other views) the “lawmaker's regress” (a regress in accounting for the necessity of laws), the relationship between laws and objective chances, and the nature of instantaneous velocity and acceleration. The latter, argues Lange, are best understood in terms of certain subjunctive facts. This, in turn, is one advantage of what might otherwise seem to be a disadvantage, the fact that his ontology rests on a basis of subjunctive facts, with laws as derivative—whereas almost every other metaphysician wants to make subjunctives derivative. While Lange makes an excellent case for his preference, it does nonetheless leave us with a quantitative profligacy. There are lots of (very specific) subjunctive facts. If laws are basic, then we can (hope to) explain the subjunctive facts with a handful of fundamental laws. I need to be told more about how subjunctive facts organize themselves if I am to be comfortable with so many of them.Lange writes with restrained elegance, but this does not disguise the fact that his book is in many places hard intellectual work. That reflects the fact that this is a work of highest intellectual caliber, not unlike important advances in mathematics, that happens to deal with difficult material. It is to Lange's credit both that his cleverness produced such ideas and that he makes it as easy as he can for the reader to follow them. The reader's effort will be amply repaid. This book is a must for anyone interested in laws, but I would recommend it to any metaphysician also since Lange's view has ramifications well beyond the realm of laws and his book is exemplary of how we should approach our work.

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