# Scientific Explanation

Issues concerning scientific explanation have been a focus of philosophical attention from Pre-Socratic times through the modern period. However, modern discussion really begins with the development of the Deductive-Nomological () model. This model has had many advocates (including Popper 1959, Braithwaite 1953, Gardiner, 1959, Nagel 1961) but unquestionably the most detailed and influential statement is due to Carl Hempel (1942, 1965a, and Hempel & Oppenheim 1948). These papers and the reaction to them have structured subsequent discussion concerning scientific explanation to an extraordinary degree. After some general remarks by way of background and orientation (Section 1), this entry describes themodel and its extensions, and then turns to some well-known objections (Section 2). It next describes a variety of subsequent attempts to develop alternative models of explanation, including Wesley Salmonsmodels due to Michael Friedman and Philip Kitcher (Section 5), andtheories found in the work of van Fraassen (Section 6).Section 7provides a summary and discusses directions for future work. This article thus discusses treatments of scientific explanation up to the end of the twentieth century.

2.3 Inductive Statistical Explanation

Model: Nomic Expectability and a Regularity Account of Causation

2.5 Explanatory Understanding and Nomic Expectability: Counterexamples to Sufficiency

3.2 The SR Model and Low Probability Events

3.3 What Do Statistical Theories Explain? What Sorts of Examples are Accounts of Statistical Explanation Intended to Capture?

3.4 Causation and Statistical Relevance Relationships

5. A Unificationist Account of Explanation

5.2 Illustrations of the Unificationist Model

6. Pragmatic Theories of Explanation

6.2 Constructive Empiricism and the Pragmatic Theory of Explanation

7. Conclusions, Open Issues, and Future Directions

As will become apparent, scientific explanation is a topic that raises a number of interrelated issues. Some background orientation will be useful before turning to the details of competing models. A presupposition of most recent discussion has been that science sometimes provides explanations (rather than something that falls short of explanatione.g., mere description) and that the task of a theory or model of scientific explanation is to characterize the structure of such explanations. It is thus assumed that there is (at some suitably abstract and general level of description) a single kind or form of explanation that is scientific. In fact, the notion of scientific explanation suggests at least two contrastsfirst, a contrast between those explanations that are characteristic of science and those explanations that are not, and, second, a contrast between explanation and something else. However, with respect to the first contrast, much of the recent philosophical literature assumes that there is substantial continuity between explanations found in science and some forms of explanation found in ordinary, non-scientific contexts. It is further assumed that it is the task of a theory of explanation to capture what is common to both scientific and some ordinary, non-scientific forms of explanation. These assumptions help to explain (what may otherwise strike the reader as curious) why, as this entry will illustrate, discussions of scientific explanation often move back and forth between examples drawn from bona-fide science (e.g., explanations of the trajectories of the planets that appeal to Newtonian mechanics) and more homey examples (e.g., the tipping over of inkwells).

With respect to the second contrast, most models of explanation assume that it is possible for a set of claims to be true, accurate, supported by evidence, and so on and yet unexplanatory. For example, all of the accounts of scientific explanation described below would agree that an account of the appearance of a particular species of bird of the sort found in a bird guidebook is, however accurate, not an explanation of anything of interest to biologists (such as the development, characteristic features, or behavior of that species). Instead, such an account is merely descriptive. However, different models of explanation provide different accounts of what the contrast between the explanatory and merely descriptive consists in.

A related point is that, while most theorists of scientific explanation have proposed models that are intended to cover at least some cases of explanation that we would not think of as part of science, they have nonetheless assumed some implicit restriction on the kinds of explanation they have sought to reconstruct. It has often been noted that the word explanation is used in a wide variety of ways in ordinary Englishwe speak of explaining the meaning of a word, explaining how to bake a pie, explaining why one made a certain decision (where this is to offer a justification) and so on. Although the various models discussed below have sometimes been criticized for their failure to capture all of these forms of explanation (see, e.g., Scriven 1959), it is clear that they were never intended to do this. Instead, their intendedexplicandumis, very roughly, explanations ofwhythings happen, where the things in question can be either particular events or something more generale.g., regularities or repeatable patterns in nature. Paradigms of this sort of explanation include: the explanation for the advance in the perihelion of mercury provided by General Relativity, the explanation of the extinction of the dinosaurs in terms of the impact of a large asteroid at the end of the Cretaceous period, the explanation provided by the police for why a traffic accident occurred (the driver was speeding and there was ice on the road), and the standard explanation provided in economics textbooks for why monopolies will, in comparison with firms in perfectly competitive markets, raise prices and reduce output.

Finally, a few words about the broader epistemological and methodological background to the models described below. Many philosophers think of concepts like explanation, law, cause, and support for counterfactuals as part of an interrelated family of concepts that are modal in character. For familiar empiricist reasons, Hempel and many other early defenders of theDNmodel regarded these concepts as not well understood, at least prior to analysis. It was assumed that it would be circular to explain one concept from this family in terms of others from the same family and that they must instead be explicated in terms of other concepts from outside the modal familyconcepts that more obviously satisfied (what were taken to be) empiricist standards of intelligibility and testability. For example, in Hempels version of theDNmodel, the notion of a law plays a key role in explicating the concept of explanation, and his assumption is that laws are just regularities that meet certain further conditions that are also acceptable to empiricists. As we shall see, these empiricist standards (and an accompanying unwillingness to employ modal concepts as primitives) have continued to play a central role in the models of explanation developed subsequent to theDNmodel.

A related issue has to do with whether all scientific explanations are causal and if not, what distinguishes causal from non-causal explanations. Hempel recognized both causal and non-causal forms of explanation but held that both were captured by theDNmodel in his view, causal explanations are simplyDNexplanations that cite causal laws (which he regarded as a proper subset of all laws). Many but not all of the accounts discussed below in effect assume that many of the problems with the DN model can be traced to its commitment to an inadequate account of causation; thus that getting clearer about causal notions would lead to more adequate accounts of explanation. By contrast, a substantial amount of recent discussion of explanation has moved away from this focus on causation and instead explores the possibility of non-causal forms of explanation.[1]

Suggested Readings: Salmon (1989) is a superb critical survey of all the models of scientific explanation discussed in this entry. Kitcher and Salmon (1989), Pitt (1988), and Ruben (1993) are anthologies that contain a number of influential articles.

According to the Deductive-Nomological Model, a scientific explanation consists of two major constituents: anexplanandum, which is a sentence describing the phenomenon to be explained and anexplanans, the class of those sentences which are adduced to account for the phenomenon (Hempel & Oppenheim 1948 [1965: 247]). For the explanans to successfully explain the explanandum several conditions must be met. First, the explanandum must be a logical consequence of the explanans and the sentences constituting the explanans must be true (Hempel 1948 [1965: 248]). That is, the explanation should take the form of a sound deductive argument in which the explanandum follows as a conclusion from the premises in the explanans. This is the deductive component of the model. Second, the explanans must contain at least one law of nature and this must be anessentialpremise in the derivation in the sense that the derivation of the explanandum would not be valid if this premise were removed. This is the nomological component of the modelnomological being a philosophical term of art which, suppressing some niceties, means (roughly) lawful. In its most general formulation, theDNmodel is meant to apply both to the explanation of general regularities or laws such as (to use Hempel and Oppenheims examples) why light conforms to the law of refraction and also to the explanation of particular events, conceived as occurring at a particular time and place, such as the bent appearance of the partially submerged oars of a rowboat on a particular occasion of viewing. As an additional illustration of aDNexplanation of a particular event, consider a derivation of the position of Mars at some future time from Newtons laws of motion, the Newtonian inverse square law governing gravity, and information about the mass of the sun, the mass of Mars and the present position and velocity of each. In this derivation the various Newtonian laws figure as essential premises and they are used, in conjunction with appropriate information about initial conditions (the masses of Mars and the sun and so on), to derive the explanandum (the future position of Mars) via a deductively valid argument. TheDNcriteria are thus satisfied.

The notion of a sound deductive argument is (arguably) relatively clear (or at least something that can be regarded as antecedently understood from the point of view of characterizing scientific explanation). But what about the other major component of theDNmodelthat of a law of nature? The basic intuition that guides theDNmodel goes something like this: Within the class of true generalizations, we may distinguish between those that are only accidentally true and those that are laws. To use Hempels examples, the generalization

is, if true, only accidentally so. In contrast,

is a law. Thus, according to theDNmodel, the latter generalization can be used, in conjunction with information that some particular sample of gas has been heated under constant pressure, to explain why it has expanded. By contrast, the former generalization(1)in conjunction with the information that a particular personnis a member of the 1964 Greensbury school board, cannot be used to explain whynis bald.

While this example may seem clear enough, what exactly is it that distinguishes true accidental generalizations from laws? This has been the subject of a great deal of philosophical discussion, most of which must be beyond the scope of this entry.[2]For reasons explained inSection 1, Hempel assumes that an adequate account must explain the notion of law in terms of notions that lie outside the modal family.[3]He considers (1965b) a number of familiar proposals having this character[4]and finds them all wanting, remarking that the problem of characterizing the notion of law has proved highly recalcitrant (1965b: 338). It seems fair to say, however, that his underlying assumption is that, at bottom, laws are just exceptionless generalizations describing regularities that meet certain additional distinguishing conditions that he is not at present able to formulate. In subsequent decades, a variety of criteria for lawhood have been proposed. Of these the so-called best systems analysis (Lewis 1973) is probably the most popular, but no single account has won general acceptance. Finding an adequate characterization of lawhood is thus an ongoing issue for theDNmodel.

One point at which this issue is particularly pressing concerns the explanatory status of the so-called special sciencesbiology, psychology, economics and so on. These sciences are full of generalizations that appear to play an explanatory role and yet fail to satisfy many of the standard criteria for lawfulness. For example, although Mendels law of segregation (M) (which states that in sexually reproducing organisms each of the two alternative forms (alleles) of a gene specifying a trait at a locus in a given organism has 0.5 probability of ending up in a gamete) is widely used in models in evolutionary biology, it has a number of exceptions, such as meiotic drive. A similar point holds for the principles of rational choice theory (such as the generalization that preferences are transitive) which figure centrally in economics. Other widely used generalizations in the special sciences have very narrow scope in comparison with paradigmatic laws, hold only over restricted spatio-temporal regions, and lack explicit theoretical integration.

There is considerable disagreement over whether such generalizations are laws. Some philosophers (e.g., Woodward 2000) suggest that such generalizations satisfy too few of the standard criteria to count as laws but can nevertheless figure in explanations; if so, it apparently follows that we must abandon theDNrequirement that all explanations must appeal to laws. Others (e. g., Mitchell 1997), emphasizing different criteria for lawfulness, conclude instead that generalizations like (M) are laws and hence no threat to the requirement that explanations must invoke laws. In the absence of a more principled account of laws, it is hard to evaluate these competing claims and hence hard to assess the implications of theDNmodel for the special sciences. At the very least, providing such an account is an important item of unfinished business for advocates of theDNmodel.

TheDNmodel is meant to capture explanation via deduction from deterministic laws and this raises the obvious question of the explanatory status of statistical laws. Do such laws explain at all and if so, what do they explain, and under what conditions? Hempel (1965b) distinguishes two varieties of statistical explanation. The first of these,deductive-statistical(DS) explanation, involves the deduction of a narrower statistical uniformity from a more general set of premises, at least one of which involves a more general statistical law. SinceDSexplanation involves deduction of the explanandum from a law, it conforms to the same general pattern as theDNexplanation of regularities. However, in addition toDSexplanation, Hempel also recognizes a distinctive sort of statistical explanation, which he callsinductive-statisticalorISexplanation, involving the subsumption of individual events (like the recovery of a particular person from streptococcus infection) under (what he regards as) statistical laws (such as a law specifying the probability of recovery, given that penicillin has been taken).

While the explanandum of aDNorDSexplanation can be deduced from the explanans, one cannot deduce that some particular individual, John Jones, has recovered from the above statistical law and the information that he has taken penicillin. At most what can be deduced from this information is that recovery is more or less probable. InISexplanation, the relation between explanans and explanandum is, in Hempels words, inductive, rather than deductivehence the name inductive-statistical explanation. The details of Hempels account are complex, but the underlying idea is roughly this: anISexplanation will be good or successful to the extent that its explanans confers high probability on its explanandum outcome.

Thus if it is a statistical law that the probability of recovery from streptococcus, given that one has taken penicillin, is high, and Jones has taken penicillin and recovered, this information can be used to provide anISexplanation of Joness recovery. However if the probability of recovery is low (e.g., less than 0.5), given that Jones has taken penicillin, then, even if Jones recovers, we cannot use this information to provide anISexplanation of his recovery.

Why suppose that all (or even some) explanations have aDNorISstructure? There are two ideas which play a central motivating role in Hempels (1965b) discussion. The first connects the information provided by aDNargument with a certain conception of what it is to achieve understanding of why something happensit appeals to an idea about the object or point of giving an explanation. Hempel writes

aDNexplanation answers the question Whydid the explanandum-phenomenon occur? by showing that the phenomenon resulted from certain particular circumstances, specified in $$C_1,C_2,\ldots,C_k$$, in accordance with the laws $$L_1,L_2,\ldots,L_\gamma$$. By pointing this out, the argument shows that, given the particular circumstances and the laws in question, the occurrence of the phenomenonwas to be expected; and it is in this sense that the explanation enables us tounderstand whythe phenomenon occurred. (1965b: 337, italics in original)

One can think ofISexplanation as involving a natural generalization of this idea. While anISexplanation does not show that the explanandum-phenomenon was to be expected with certainty, it does the next best thing: it shows that the explanandum-phenomenon is at least to be expected with high probability and in this way provides understanding. Stated more generally, both theDNandISmodels, share the common idea that, as Salmon (1989) puts it,

the essence of scientific explanation can be described asnomic expectabilitythat is expectability on the basis of lawful connections. (1989: 57)

The second main motivation for theDN/ISmodel has to do with the role of causal claims in scientific explanation. There is considerable disagreement among philosophers about whether all explanations in science and in ordinary life are causal and also disagreement about what the distinction (if any) between causal and non-causal explanations consists in. Nonetheless, virtually everyone, including Hempel, agrees that many scientific explanations cite information about causes. However, Hempel, along with most other early advocates of theDNmodel, is unwilling to take the notion of causation as primitive in the theory of explanationthat is, he was unwilling to simply say thatXfigures in an explanation ofYif and only ifXcausesY. Instead, adherents of theDNmodel have generally looked for an account of causation that satisfies the empiricist requirements described inSection 1. In particular, advocates of theDNmodel have generally accepted a broadly Humean or regularity theory of causation, according to which (very roughly) all causal claims imply the existence of some corresponding regularity (a law) linking cause to effect. This is then taken to show that all causal explanations imply, perhaps only implicitly, that such a law/regularity exists and hence that laws are involved in all such explanations, just as theDNmodel claims.

To illustrate this line of argument, consider

(3)is a so-called singular causal explanation, advanced by Michael Scriven (1962) as a counterexample to the claim that theDNmodel describes necessary conditions for successful explanation. According to Scriven,(3)explains the tipping over of the inkwell even though no law or generalization figures explicitly in(3)and(3)appears to consist of a single sentence, rather than a deductive argument. Hempels response (1965b: 360ff) is that the occurrence of caused in(3)should not be left unanalyzed or taken as explanatory just as it stands. Instead(3)should be understood as implicitly or tacitly claiming there is a law or regularity linking knee impacts to tipping over of inkwells. According to Hempel, it is the implicit claim that some such law holds that distinguishes(3)from a mere sequential narrative in which the spilling is said to follow the impact but without any claim of causal connectiona narrative that (Hempel thinks) would clearly not be explanatory. This linking law is the nomological premise in theDNargument that, according to Hempel, is implicitly asserted by(3).

The basic idea is thus that a proper explication of the role of causal claims in explanation leads via a Humean or regularity theory of causation, to the conclusion that, at least ideally, explanations should satisfy theDN/ISmodel. Let us call this line of argument the hidden structure argument in recognition of the role it assigns to a hidden (or at least non-explicit)DNstructure that is claimed to be associated with(3).

At this point a comment is in order regarding a feature of this proposal that may seem puzzling. The boundaries of the category scientific explanation are far from clear, but while(3)is arguably an explanation, it is not what one usually thinks of as scienceinstead it is a claim from ordinary life or common sense. This raises the question of why adherents of theDN/ISmodel dont simply respond to the alleged counterexample(3)by denying that it is an instance of the category scientific explanationthat is, by claiming that theDN/ISmodel is not an attempt to reconstruct the structure of explanations like(3)but is rather only meant to apply to explanations that are properly regarded as scientific. The fact that this response is not often adopted by advocates of theDNmodel is an indication of the extent to which, as noted inSection 1, it is implicitly assumed in most discussions of scientific explanation that there are important similarities or continuities in structure between explanations like(3)and explanations that are more obviously scientific and that these similarities that should be captured by some common account that applies to both. Indeed, it is a striking feature not just of Hempel (1965b) but of many other treatments of scientific explanation that much of the discussion in fact focuses on ordinary life singular causal explanations similar to(3), the tacit assumption being that conclusions about the structure of such explanations have fairly direct implications for understanding explanation in science.

As explained above, examples like(3)are potential counterexamples to the claim that theDNmodel providesnecessaryconditions for explanation. There are also a number of well-known counterexamples to the claim that theDNmodel providessufficientconditions for successful scientific explanation. Here are two illustrations.

Explanatory Asymmetries. There are many cases in which a derivation of an explanandumEfrom a lawLand initial conditionsIseems explanatory but a backward derivation ofIfromEand the same lawLdoes not seem explanatory, even though the latter, like the former, appears to meet the criteria for successfulDNexplanation. For example, one can derive the lengthsof the shadow cast by a flagpole from the heighthof the pole and the angle of the sun above the horizon and laws about the rectilinear propagation of light. This derivation meets theDNcriteria and seems explanatory. On the other hand, the following derivation from the same laws also meets theDNcriteria but does not seem explanatory:

Examples like this suggest that at least some explanations possess directional or asymmetric features to which theDNmodel is insensitive.

Explanatory Irrelevancies. A derivation can satisfy theDNcriteria and yet be a defective explanation because it contains irrelevancies besides those associated with the directional features of explanation. Consider an example due to Wesley Salmon (1971a: 34):

All males who take birth control pills regularly fail to get pregnant

John Jones is a male who has been taking birth control pills regularly

It is arguable that (L) meets the criteria for lawfulness imposed by Hempel and many other writers. (If one wants to deny that (L) is a law one needs some principled, generally accepted basis for this judgment and, as explained above, it is unclear what this basis is.) Moreover,(5)is certainly a sound deductive argument in which (L) occurs as an essential premise. Nonetheless, most people judge that (L) and (K) are no explanation of (E). There are many other similar illustrations. For example (Kyburg 1965), it is presumably a law (or at least an exceptionless, counterfactual supporting generalization) that all samples of table salt that have been hexed by being touched with the wand of a witch dissolve when placed in water. One may use this generalization as a premise in aDNderivation which has as its conclusion that some particular hexed sample of salt has dissolved in water. But again the hexing is irrelevant to the dissolving and such a derivation is no explanation.

One obvious diagnosis of the difficulties posed by examples like(4)and(5)focuses on the role of causation in explanation. According to this analysis, to explain an outcome we must cite its causes and(4)and(5)fail to do this. As Salmon (1989a: 47) puts it,

a flagpole of a certain height causes a shadow of a given length and thereby explains the length of the shadow.

the shadow does not cause the flagpole and consequently cannot explain its height.

Similarly, taking birth control pills does not cause Jones failure to get pregnant and this is why(5)fails to be an acceptable explanation. On this analysis, what(4)and(5)show is that a derivation can satisfy theDNcriteria and yet fail to identify the causes of an explanandumwhen this happens the derivation will fail to be explanatory.

As explained above, advocates of theDNmodel would not regard this diagnosis as very illuminating, unless accompanied by some account of causation that does not simply take this notion as primitive. (Salmon in fact provides such an account, which we will consider inSection 4.) We should note, however, that an apparent lesson of(4)and(5)is that the regularity account of causation favored byDNtheorists is at best incomplete: the occurrence ofc,e, and the existence of some regularity or law linking them (orxs having propertyPandxs having propertyQand some law linking these) isnota sufficient condition for the truth of the claim thatccausedorxs havingPis causally or explanatorily relevant toxs havingQ. More generally, if the counterexamples(4)and(5)are accepted, it follows that theDNmodel fails to state sufficient conditions for explanation. Explaining an outcome isntjusta matter of showing that it is nomically expectable.

There are two possible reactions one might have to this observation. One is that the idea that explanation is a matter of nomic expectability is correct as far as it goes, but that something more is required as well. According to this assessment, theDN/ISmodel does state anecessarycondition for successful explanation and, moreover, a condition that is a non-redundant part of a set of conditions that are jointly sufficient for explanation. However, some other, independent feature,X(which will account for the directional features of explanation and insure the kind of explanatory relevance that is apparently missing in the birth control example) must be added to theDNmodel to achieve a successful account of explanation. The idea is thus that Nomic Expectability + X = Explanation. Something like this idea is endorsed, by the unificationist models of explanation developed by Friedman (1974) and Kitcher (1989), which are discussed inSection 5below.

A second, more radical possible conclusion is that theDNaccount of the goal or rationale of explanation is mistaken in some much more fundamental way and that theDNmodel does not even state necessary conditions for successful explanation. As noted above, unless the hidden structure argument is accepted, this conclusion is strongly suggested by examples like(3)(The impact of my knee caused the tipping over of the inkwell) which appear to involve explanation without the explicit citing of a law or a deductive structure.

Suggested Readings. The most authoritative and comprehensive statement of theDNandISmodels is probably Hempel (1965b). This is reprinted in Hempel 1965a, along with a number of other papers that touch on various aspects of the problem of scientific explanation. In addition to the references cited in this section, Salmon (1989: 46ff.) describes a number of well-known counterexamples to theDN/ISmodels and discusses their significance.

Much of the subsequent literature on explanation has been motivated by attempts to capture the features of causal or explanatory relevance that appear to be left out of examples like(4)and(5), typically within the empiricist constraints described above. Wesley Salmons statistical relevance (orSR) model (Salmon 1971a) is a very influential attempt to capture these features in terms of the notion of statistical relevance or conditional dependence relationships. Given some class or population $$A$$, an attribute $$C$$ will bestatistically relevantto another attribute $$B$$ if and only if $$P(B\pmid A.C) \ne P(B\pmid A)$$that is, if and only if t

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