1. Introduction

Many philosophers accept a nonreductive physicalist view of at least some special sciences, which is to say that while they assert that each particular referent of any special science term is identical to some referent of a physical term, or token physicalism, they deny that special science types are identical to physical types. The most commonly cited reason for this position is Jerry Fodor's (Reference Fodor1975) antireductionist argument based on the fact that many special science terms appear to be multiply physically realizable. I argue that if token physicalism is true, as nonreductive physicalists believe, then this multiple-realization argument fails to preclude reductive physicalism.

2. The Multiple-Realization Argument

Although it is not necessarily inextricably tied to such ideas, Fodor frames his multiple-realization argument in terms of Ernest Nagel's (Reference Nagel1961) model of scientific reduction, which in turn is designed around the covering law model of explanation described by Carl Hempel (Reference Hempel and Colodny1962). Very briefly, according to the covering law model, scientific explanations are arguments, from premises describing (1) relevant laws of nature and (optionally) (2) premises describing initial conditions, to a conclusion asserting the occurrence of the phenomenon to be explained, the explanandum. The covering law explanation provides an explanation by showing that the explanandum could not have failed to obtain unless the world were other than we know it be, either in its laws or in its particulars.

Nagel (Reference Nagel1961) builds on this by modeling the reduction of one theory to another as an argument from premises asserting the laws of the reducing theory to an explanandum asserting the laws of the reduced theory. Essentially, reduction is a matter of providing a covering law explanation of the laws of one science as consequences of the laws of a more basic science. In cases in which the reduced theory contains terms that do not occur in the reducing theory, this explanatory argument requires, for its validity, the addition of bridge laws that at least assert the nomologically necessary coextensivity of each of the novel terms in the reduced theory with some term or logical construction of terms in the reducing theory. Fodor (Reference Fodor1975, 12) assumes the further constraint that the bridge laws should take the form of contingent identities, on the grounds that weaker laws would fail to result in a true reduction.

Although these are certainly not the only models of explanation or reduction, and although there are important criticisms of both models that are not directly related to the multiple-realization argument, I intend to frame my own arguments in similar terms in order to preserve continuity. My own criticisms of Fodor's argument do not, at any rate, depend on these independent criticisms.

Fodor argues that most special science theories are irreducible on the grounds that most special science natural kind terms (i.e., the terms related by the laws of those sciences) are multiply realizable physically. Suppose that some special science explains events of type as the result of events of type . This means that there must be some special science law to serve in covering law explanations. Fodor does not give a precise account of what a law is, but it is safe to say that “→” here represents a nomologically necessary universal generalization, though possibly one modified by ceteris paribus clauses. In order to simplify the following discussion, I will assume that implies until a brief consideration of ceteris paribus clauses at the end of the article. Since is a law, and are natural kind terms of the special science. Now assume that at least one of these special science kinds is multiply realizable physically. For example, the assertion that might be the assertion that is in pain, which can plausibly be physically instantiated in a variety of physiological, and hence a variety of physical, ways (e.g., as different sorts of processes in different sorts of nervous tissue or perhaps as some sort of process in computer circuitry or a totally alien biological process).

As a token physicalist, Fodor is happy to grant that all particular instances of and are instantiated physically and that in each particular instance, there is a physical explanation of the physical realizer of as the result of a physical realizer of . So if is a disjunction of all the nomologically possible physical realizers of and is a disjunction of all the nomologically possible physical realizers of , then for each of the , there is some law of physics, , which allows the explanation of by .

However, Fodor argues that it will rarely be the case that the disjunctions of realizers of the special science predicates will themselves be natural kinds occurring in a physical law

because the different physical realizers will generally be linked by different laws of physics. For example, it seems likely that different physical laws generate the causal properties of biological pain versus robot pain, since these different instantiations of pain would be composed of different kinds of physical stuff. As a result, whereas the argument from the initial condition and the special science law to would constitute an explanation of , the argument from and

to would fail to be an explanation because it contains no law. Furthermore, even if we could assert

as bridge laws, allowing us to derive the special science law from

this would not be a reduction of the special science law because it would not have been derived from a physical law. Finally, even these putative bridge laws will fail to be laws, as their disjunctive physical terms fail to refer to natural kinds.

However, as will be important shortly, it is worth noting that the failure of the disjunctive physical argument to be a covering law explanation does not depend on its being invalid. In fact, it follows from the assumption of token physicalism that it is valid. Token physicalism asserts that there are physical explanations of each of the particular physical realizers of the special science explananda. Each of these explanations will take the form of an argument from one of the initial conditions and one of the laws to one of the . If we knew that one or the other of the (, ) pairs were true, but did not know which one, we could still deduce that one or the other of the were true, without knowing which one. This valid argument fails to be an explanation solely because it lacks a law. Furthermore, although they fail to qualify as bridge laws, if we add and to the argument, we will have an argument from to , which is just as valid as the argument that relies on the special science law , but which fails to be an explanation, again for lack of a law.

3. Partial Explanation and Cursory Explanation

Ultimately then, multiple realization is a problem for reductionism because of missing laws of nature. There is no physical law that relates physical natural kinds corresponding to the special science kinds, and the propositions that state which disjunctions of physical kinds correspond to which special science kinds fail to be bridge laws, much less contingent type identities, because the disjunctions of physical kinds are not themselves kinds.

Philosophers concerned with the related question of special science explanations have also been puzzled by missing laws. There are several reasons why laws seem to be particularly problematic in the special sciences. In some special sciences, scientists seem not to formulate laws at all and yet seem no less successful in generating explanations. Those special sciences that do purportedly contain laws tend to have laws that deviate in one way or another from the paradigm of a law as a nomologically necessary, empirically justified universal generalization by containing ceteris paribus clauses or by being a priori mathematical truths (Sober Reference Sober2000, 72–73). Furthermore, in biology and in any of the special sciences that overlap with it, such as (human and animal) psychology, sociology, anthropology, ecology, and so forth, there is the additional problem that evolutionary theory seems hostile to biological natural kinds. For any biological regularity that one might be tempted to call a biological law will be the result of a contingent process of natural selection, implying that the regularity probably has not held at times in the sufficiently distant past (before natural selection had generated the organisms displaying the regularity) and probably will not hold at times in the sufficiently distant future (at which point changing selective forces are likely to have changed the organisms so that they no longer display the regularity) and at any rate is not nomologically necessary (Rosenberg Reference Rosenberg2001).

In a recent paper devoted to this issue, I argued that a natural extension of the covering law model can explain these features (Press Reference Press2009). The main thesis of that paper is that, whatever its other faults, the covering law model is about as applicable in biology as it is in physics. The crux of the argument is that the covering law model allows for certain kinds of approximation and that once this is fully taken into account, biological explanations that appear not to rely on laws of nature turn out to rely on them after all.

Hempel himself explicitly allows for what he calls partial explanations. His example is an explanation Freud had given for accidentally misdating an appointment in his records. He had written October 20, the correct date, in the slot for September 20, and explained this as the result of his eager anticipation of the arrival of a new patient. Hempel points out that it seems unlikely that Freud meant to claim that any law of psychology would have allowed the deduction of that particular slip of the pen. Instead, Hempel suggests that Freud ought to be interpreted as claiming (at most) merely that his eagerness would be expected to generate some sort of appropriate slip or other. If so, then it would not be possible to model his explanation as a complete covering law explanation, since the initial conditions and laws do not strictly entail the explanandum. However, Hempel suggests that we should still be prepared to model it as a partial explanation of the particular slip. Since the particular slip was one of an identifiable class of possible slips derivable from his eagerness and the relevant psychological laws, we say that it fully explains why he made a slip but only partially explains why he made that slip.

In such partial explanations, it is only possible to deduce the explanandum approximately because the initial conditions are known only approximately. Perhaps if Freud had known more about his psychological state when the slip occurred, he might have been in a position to provide a full explanation of his particular slip. Something similar occurs in other situations where initial conditions are approximated. For example, if a ballistics engineer only approximately knows the mass of the cannonball being launched and the amount of gunpowder used, she may only be able to deduce that it will land between 200 and 220 meters downrange. When it lands 213 meters downrange, she will not have fully explained why it landed there as opposed to, say, 205 or 217 meters, but she will have partially explained this. Since all scientific explanations involve at least some measure of approximation of initial conditions, all covering law explanations will be partial to some extent, and conformity to the covering law model will be a matter of degree.

My suggestion is that if covering law explanations can tolerate approximations in initial conditions, they should also be able to tolerate approximation in their other component, the laws. Suppose, for example, that our ballistics engineer is shooting her cannon in December 1915. She has heard rumors of a new revolution in gravitational theory but knows only enough about it to wonder whether she should change the way she does ballistics. If she happens to be a particularly thoughtful ballistics engineer, her reasoning may go something like this:

The point is that in order to deduce the approximate landing point of her cannonball, the ballistics engineer can rely not only on approximate knowledge of initial conditions but also on approximate knowledge of the laws of nature. She does not need a premise asserting any particular law for her explanation. If instead she replaces that premise with a premise asserting that either Newton's gravitation laws, or Einstein's, or some other law falling within a range consistent with past results is true, she will still be able to deduce the (approximate) landing point of the cannonball from the initial conditions. Furthermore, since each of the possible laws is, if actual, itself a law, then her deduction will be just as counterfactually valid as any covering law explanation. This seems to be a reasonable extension of Hempel's notion of a partial explanation, though since it does go beyond Hempel's explicit use of that term in its approximation, I propose to call explanations that involve this sort of approximation of laws “cursory” covering law explanations.

If we return now to the special sciences, we should be able to see how they might appear to generate scientific explanations without any explicit reference to natural laws. To borrow an example from my previous paper, consider an evolutionary biologist's explanation of the evolution of prehensile tails in monkeys (Press Reference Press2009, 370–74). Presumably, such tails are an adaptation to living in trees, where having a fifth grasping appendage provides a fitness advantage. This explanation will involve many premises describing relevant properties of current and ancestral monkey populations and their environments, the relevant properties being those that provide the advantage, as well as those that determine what is advantageous. For example, one of the things a monkey can do with a prehensile tail is catch itself before it falls out of the tree. That being able to do this is advantageous is determined by properties such as the dispositions these monkeys’ bones have of breaking when the monkeys fall out of sufficiently tall trees. However, none of these premises seem to be statements of biological laws. Rather, they all say something about a particular group of creatures, their ancestors, and how they interact or interacted with the particular environments they inhabit or inhabited.

Now it is not all that hard to figure out that these monkey's bones are disposed to break when the monkeys fall out of tall trees. Biologists can learn this simply by watching the monkeys. Of course, they may know that there is some precise physical explanation of this fact. That explanation will involve the force of gravity that accelerates a falling monkey downward, the electrostatic repulsive force between electrons that rapidly decelerates the monkey when the clouds of electrons surrounding the molecules its body is composed of encounter the clouds of electrons surrounding the molecules of the rocks below, the forces governing the chemical bonds linking the molecules that form the structural components of bone tissue, and so on. But the biologist does not really have to give this a second thought because in knowing the approximate range of fall heights within which the bones are disposed to break, he really knows all he needs to explain the evolution of the monkeys’ tails.

But notice that in knowing about this disposition, the biologist actually knows at least something about some of the laws of nature. He may well know considerably less than the ballistics engineer about gravity. Suppose he has forgotten even his one semester of university physics and is not quite able to remember whether the gravitational force is inversely proportional to the square or the cube of the distance from a center of gravity. Still he does know that there is a gravitational force at the earth's surface sufficient to break monkey bones when these monkeys fall out of tall trees. This knowledge is not much, but it does rule out the possibility of forces of gravity that are much stronger or much weaker than actual, are repulsive at the earth's surface, fluctuate with the seasons, and so forth, and this turns out to be all he really needs to know about gravity to explain the evolution of monkey tails. In a similar way, his knowledge of how monkey bones are disposed to break gives him a little knowledge about the forces responsible for the strength of those bones, though not even necessarily so much knowledge all by itself that he would know that those forces bind molecules, about which he could conceivably be ignorant. Still other dispositional properties referred to in the premises of his explanation, such as the disposition of monkeys to inherit traits from their parents, the disposition of monkeys with healthy bones to outcompete those with broken bones, and so on, will all contribute to constraining the possible ways that natural laws might govern the universe.

So all these dispositional premises about particular populations of monkeys and their environments actually implicitly contain assertions about the laws of nature. They are not, to be sure, about what any of the laws of nature actually are but simply about which laws of nature remain open possibilities. This makes the evolutionary biologist's explanation what I have called a cursory explanation. Just as the ballistics engineer could cursorily explain the landing point by showing that the cannonball ought to have landed approximately where it did whether the law of gravity is Newtonian or Einsteinian, the evolutionary biologist explains the prehensile tails by showing that, whatever the relevant laws of nature happen to actually be, they are apparently such that monkeys, their ancestors, and their environments have the dispositional properties that they are observed to have, which are themselves properties that can be expected to lead to the production of adaptations like prehensile tails. The biologist's explanation is even more cursory than the ballistics engineer's, but this is a matter of degree.

In general then, what this suggests is that the special sciences really have no need for their own natural laws. So long as their explanations contain premises that attribute dispositions, they will assert constraints on the laws of nature, and if the various disposition claims are sufficient to explain the phenomena the special science seeks to explain, it will be because these constraints are strong enough to yield a cursory explanation. So a dearth of laws is, in itself, no reason to abandon the covering law model for the special sciences, since they can simply borrow laws from other sciences by referring to them via claims about particular dispositions.

4. Cursory Reduction

Suppose, then, that we have a cursory explanation of some special science phenomenon as the result of initial conditions , and suppose that in this case there is no special science law linking the two. What will be its logical structure? The previous section suggests that in place of a special science law, we will instead have claims about various dispositional properties, , that place constraints on some of the laws of nature, such that together with implies . For the moment, assume that all these laws are physical laws. This means that the disposition premises imply a disjunction of the physical laws consistent with the existence of those dispositions. It also means that whichever of the physical laws listed in this disjunction happens to be actual, the initial conditions are physically realized in such a way that they and the actual laws imply some physical realizer of the explanandum. In other words, implies .

It is worth noting that a reductionistically inclined scientist stymied by Fodor's (Reference Fodor1975) multiple-realization argument may be in a position to make a considerably stronger claim than this. Fodor's argument does not depend on any ignorance about the kinds of physical realizations a special science predicate might have. We could know the disjunctions describing all the nomologically possible physical realizers and know all the physical laws linking them, but this would not alleviate the fundamental problem that the disjunctions are not themselves physical natural kinds. So for all Fodor has to say about the matter, there is no reason why we could not actually learn that and , as well as which particular and are lawfully related, say that and so on. But if we know all the different possible realizers of the initial conditions, and all the physical laws that lead from each of them to particular realizers of the explanandum, we certainly know that some such physical realizer of the initial conditions and some suitable law does imply some realizer of the explanandum, which is all that is required for a cursory explanation. Consequently, it seems that multiple realization of special science predicates is not a barrier to the formulation of a cursory covering law explanation of special science phenomena. When scientists learn about the various physical ways that special science predicates can be instantiated, and learn how the laws of physics operate on those instantiations, they are filling in physical details that are enlightening in their own right but, strictly speaking, unnecessary to the cursory explanation.

Given all this, what should we say about reductionism? Fodor's argument may force us to conclude that, where special science predicates are multiply realized physically, regularities between special science properties will not map cleanly onto any lawful physical regularities. However, this argument only forces us to conclude that there are irreducible special science laws if there are special science laws relating multiply instantiated special science kinds. Given that there are independent reasons to be suspicious of special science laws, and given the alternative of satisfying the special sciences’ need for scientific explanations with cursory explanations, my suggestion would be to downgrade any such purported special science laws to claims about particular dispositions.

If we take this route, then it will still be impossible to reduce the special sciences to physics according to Nagel's (Reference Nagel1961) model, but for the rather different reason that it is impossible to derive laws that do not exist from the laws of physics. However, the spirit of Nagel's model would seem to remain intact. If the point of reduction is to provide a covering law explanation of all the phenomena of the special sciences in terms of physical events and the laws that govern them, and if those phenomena include only particulars and no special science laws, activity that fills in the missing physical details of cursory covering law explanations of special science phenomena by actually uncovering the physical processes responsible for generating those phenomena would seem to be reductionistic. Cursory special science explanations implicitly assert that there is some covering law explanation of special science phenomena, and scientists engaged in reductionist research programs seek to discover what those implied covering law explanations are. When and if such scientists discover them all, the special science will have been reduced.

At the same time, this analysis preserves what is right about the intuition that special science explanations are autonomous. In a sense, because these cursory explanations imply the existence of physical explanations, the cursory explanations are themselves making claims about physics. However, those claims can often be extremely weak even while producing highly informative special science explanations, like those that invoke the assertion that biological organisms are disposed to inherit traits or that burns are disposed to produce pains or that bones are disposed to break after a fall. This means that one can do a fair amount of biology or psychology or anthropology without knowing a lick of formal physics, although, of course, the more physics one knows, the better chance one has of producing more detailed, less cursory explanations.

Though there is insufficient space to show it here, I think this notion of cursory reduction actually ties in nicely with several recent developments in the reductionism and scientific explanation literature, but perhaps without the same revisionary aspirations (for a useful summary, see Godfrey-Smith Reference Godfrey-Smith, Hohwy and Kallestrup2008). One such development is the tendency to see explanation in terms of modeling or functional analysis. The networks of disposition claims present in cursory explanations are precisely the sort of thing that these views discuss, but whereas these accounts are typically offered as alternative accounts of explanation, the cursory explanation model suggests that they are ultimately related to good old covering law explanations after all. Another development presents reduction as a matter of discovering the mechanisms underlying special science dispositions or regularities. The cursory explanation model would portray this as filling in the details of particular underlying covering law explanations to make cursory explanations less cursory.

5. Loose Ends and Conclusion

Several loose ends remain. I have space to tie up just a few. One is that the availability of cursory explanations does not rule out the possibility that some regularities of some of the special sciences that are sufficiently universal and counterfactual-supporting to themselves be laws of nature. In particular, this will happen when special science terms are not multiply physically realized, since in that case Nagel's (Reference Nagel1961) model simply works.

Given that this is the case, we can relax the assumption of a few paragraphs back that the constraints placed on the natural laws by special science disposition claims are always constraints on physical laws. For example, if there are some laws of physiology that meet the constraint of having physiological kind terms coextensive with physical kind terms, then it is possible that some cursory explanation of psychology could be thought of as placing constraints entirely or partially on physiological laws, rather than physical laws. Of course, since the physiological laws would then be reducible to physical laws, any constraint on the former would place constraints on the latter. However, the point is that this might allow for intermediate levels of reduction between any given special science and physics.

Another loose end involves ceteris paribus special science laws. Special science laws are often supposed to take this form, primarily for the obvious reason that the phenomena of the special sciences are typically multiply realizable, and the entities or processes doing the realizing are messier than the special science law is designed to deal with. For example, burns cause pain, but only ceteris paribus, because the physiological processes responsible for pain are not completely reliable when, say, nerve fibers are damaged, or anesthetic is present. I have suggested that such laws should be downgraded to claims about dispositions, but their raggedy nature remains. This will interfere with the analysis above by introducing stray and into the disjunctions of physical realizers that have no physical lawful connection to any member of the opposite disjunction. But it is not too hard to see what we should say here. Since cursory explanations are, well, cursory, they will generally aim to explain only approximately [and may even tolerate outright failure in outlying cases. As scientists work on reductively filling in the details of these explanations, they will discover lawful physical regularities between most of the and , and they will also discover why the stray and are stray.

Finally, it is worth recalling that we have been operating under the assumption of token physicalism. If there were nonphysical properties, there might be nonphysical laws governing them, and thus when the disposition claims in cursory explanations place constraints on the possible ways that the laws of nature might be, there would be no guarantee that these constraints implied constraints on the laws of physics. Thus, nothing in the forgoing arguments provides, in itself, a reason to reject nonphysicalist accounts of any of the special sciences. The conclusion of this article is simply that the multiple-realization argument provides no reason for a physicalist to accept nonreductive physicalism.