## 1. Background and Introduction



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 explanation--e.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
contrasts--first, 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 English--we 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 intended
*explicandum* is, very roughly, explanations of *why*
things happen, where the "things" in question can be
either particular events or something more general--e.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 the *DN* model 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
family--concepts that more obviously satisfied (what were taken
to be) empiricist standards of intelligibility and testability. For
example, in Hempel's version of the *DN* model, 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 the *DN* model.



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 the *DN* model
-in his view, causal explanations are simply *DN*
explanations 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.


## 2. The *DN* Model


### 2.1 The Basic Idea



According to the Deductive-Nomological Model, a scientific explanation
consists of two major "constituents": an
*explanandum*, which is a sentence "describing the
phenomenon to be explained" and an *explanans*,
"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
an *essential* premise 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
model--"nomological" being a philosophical term of
art which, suppressing some niceties, means (roughly)
"lawful". In its most general formulation, the *DN*
model is meant to apply both to the explanation of "general
regularities" or "laws" such as (to use Hempel and
Oppenheim's 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 a
*DN* explanation of a particular event, consider a derivation
of the position of Mars at some future time from Newton's 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. The
*DN* criteria are thus satisfied.


### 2.2 The Role of Laws in the *DN* Model



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 the
*DN* model--that of a law of nature? The basic intuition
that guides the *DN* model 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 Hempel's examples, the
generalization



(1)
 All members of the Greensbury School Board for 1964 are bald


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



(2)
 All gases expand when heated under constant pressure


is a law. Thus, according to the *DN* model, 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 person *n*
is a member of the 1964 Greensbury school board, cannot be used to
explain why *n* is 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 in
 Section 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 the *DN* model. 



One point at which this issue is particularly pressing concerns the
explanatory status of the so-called special sciences--biology,
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 Mendel's 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 the *DN* requirement 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 the
*DN* model for the special sciences. At the very least,
providing such an account is an important item of unfinished business
for advocates of the *DN* model.


### 2.3 Inductive Statistical Explanation



The *DN* model 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. Since *DS* explanation involves
deduction of the explanandum from a law, it conforms to the same
general pattern as the *DN* explanation of regularities.
However, in addition to *DS* explanation, Hempel also
recognizes a distinctive sort of statistical explanation, which he
calls *inductive-statistical* or *IS* explanation,
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 a *DN* or *DS* explanation 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. In *IS* explanation, the relation between explanans
and explanandum is, in Hempel's words, "inductive,"
rather than deductive--hence the name inductive-statistical
explanation. The details of Hempel's account are complex, but
the underlying idea is roughly this: an *IS* explanation 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 an *IS* explanation of Jones's 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 an *IS* explanation of
his recovery.


### 2.4 Motivation for the *DN* Model: Nomic Expectability and a Regularity Account of Causation



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



> 
> 
> ... a *DN* explanation answers the question
> "*Why* did 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 phenomenon *was to be
> expected*; and it is in this sense that the explanation enables us
> to *understand why* the phenomenon occurred. (1965b: 337,
> italics in original)
> 
> 
> 



One can think of *IS* explanation as involving a natural
generalization of this idea. While an *IS* explanation 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 the *DN* and *IS* models, share the
common idea that, as Salmon (1989) puts it, 



> 
> 
> the essence of scientific explanation can be described as *nomic
> expectability*--that is expectability on the basis of lawful
> connections. (1989: 57)
> 
> 
> 



The second main motivation for the *DN/IS* model 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 the *DN* model, is unwilling to take the notion of
causation as primitive in the theory of explanation--that is, he
was unwilling to simply say that *X* figures in an explanation of
*Y* if and only if *X* causes *Y*. Instead, adherents
of the *DN* model have generally looked for an account of
causation that satisfies the empiricist requirements described in
 Section 1.
 In particular, advocates of the *DN* model 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 the *DN* model claims.



To illustrate this line of argument, consider



(3)
 The impact of my knee on the desk caused the tipping over of the
inkwell.


(3)
 is a so-called singular causal explanation, advanced by Michael
Scriven (1962) as a counterexample to the claim that the *DN*
model 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. Hempel's 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
connection--a narrative that (Hempel thinks) would clearly not be
explanatory. This linking law is the nomological premise in the
*DN* argument 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 the *DN/IS* model. 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) *DN*
structure 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
"science"--instead it is a claim from "ordinary
life" or "common sense". This raises the question of
why adherents of the *DN/IS* model don't simply respond
to the alleged counterexample
 (3)
 by denying that it is an instance of the category "scientific
explanation"--that is, by claiming that the *DN/IS*
model 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 the *DN* model is an
indication of the extent to which, as noted in
 Section 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.


### 2.5 Explanatory Understanding and Nomic Expectability: Counterexamples to Sufficiency



As explained above, examples like
 (3)
 are potential counterexamples to the claim that the *DN* model
provides *necessary* conditions for explanation. There are also
a number of well-known counterexamples to the claim that the
*DN* model provides *sufficient* conditions for
successful scientific explanation. Here are two illustrations.



**Explanatory Asymmetries**. There are many cases in
which a derivation of an explanandum *E* from a law *L* and
initial conditions *I* seems explanatory but a
"backward" derivation of *I* from *E* and the
same law *L* does not seem explanatory, even though the latter,
like the former, appears to meet the criteria for successful
*DN* explanation. For example, one can derive the length
*s* of the shadow cast by a flagpole from the height *h* of
the pole and the angle th of the sun above the horizon and laws
about the rectilinear propagation of light. This derivation meets the
*DN* criteria and seems explanatory. On the other hand, the
following derivation from the same laws also meets the *DN*
criteria but does not seem explanatory:



(4)
One can derive the height *h* of a flagpole from the length
*s* of its shadow and the angle th of the sun above the
horizon.


Examples like this suggest that at least some explanations possess
directional or asymmetric features to which the *DN* model is
insensitive.



**Explanatory Irrelevancies**. A derivation can satisfy
the *DN* criteria 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):



(5)


(*L*)
All males who take birth control pills regularly fail to get
pregnant
(*K*)
John Jones is a male who has been taking birth control pills
regularly
(*E*)
 John Jones fails to get pregnant



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 a *DN*
derivation 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. 
> 
> 
> 



By contrast, 



> 
> 
> 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 the *DN* criteria and
yet fail to identify the causes of an explanandum--when this
happens the derivation will fail to be explanatory.



As explained above, advocates of the *DN* model 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 in
 Section 4.)
 We should note, however, that an apparent lesson of
 (4)
 and
 (5)
 is that the regularity account of causation favored by *DN*
theorists is at best incomplete: the occurrence of *c*, *e*,
and the existence of some regularity or law linking them (or
*x*'s having property *P* and *x*'s having
property *Q* and some law linking these) is *not* a
sufficient condition for the truth of the claim that *c* caused
 or *x*'s having *P* is causally or
explanatorily relevant to *x*'s having *Q*. More
generally, if the counterexamples
 (4)
 and
 (5)
 are accepted, it follows that the *DN* model fails to state
sufficient conditions for explanation. Explaining an outcome
isn't *just* a 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, the *DN/IS*
model does state a *necessary* condition 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 the *DN* model 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 in
 Section 5
 below.



A second, more radical possible conclusion is that the *DN*
account of the goal or rationale of explanation is mistaken in some
much more fundamental way and that the *DN* model 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 the *DN* and *IS* models 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 the *DN/IS* models and discusses their
significance.


## 3. The SR Model


### 3.1 The Basic Idea



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
Salmon's statistical relevance (or *SR*) 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 be *statistically relevant* to another attribute
\(B\) if and only if \(P(B\pmid A.C) \ne P(B\pmid A)\)--that is,
if and only if the probability of \(B\) conditional on \(A\) and \(C\)
is different from the probability of \(B\) conditional on \(A\) alone.
The intuition underlying the *SR* model is that statistically
relevant properties (or information about statistically relevant
relationships) are explanatory and statistically irrelevant properties
are not. In other words, the notion of a property making a difference
for an explanandum is unpacked in terms of statistical relevance
relationships.



As an illustration, suppose that in the birth control pills example
 (5)
 the original population *T* includes both sexes. Then



\[\begin{align}
P(\text{Pregnancy} \pmid T.&\text{Male.Takes birth control pills})\\
& {} = P(\text{Pregnancy} \pmid T.\text{Male})\\
& {} = 0
\end{align}
\]


while

 

\[
\begin{align}
P(\text{Pregnancy} \pmid T.&\text{Female.Takes birth control pills})\\
&{} \ne P(\text{Pregnancy} \pmid T.\text{Female})
\end{align}
\]


assuming that not all women in the population take birth control
pills. In other words, if you are a male in this population, taking
birth control pills is statistically irrelevant to whether you become
pregnant, while if you are a female it is relevant. Thus taking birth
control pills is explanatorily irrelevant to pregnancy among males but
not among females.



To characterize the *SR* model more precisely we need the
notion of a *homogenous partition.* A homogenous partition of
\(A\) is a set of subclasses or cells \(C\_i\) of \(A\) that are
mutually exclusive and exhaustive, where \(P(B\pmid A.C\_i) \ne
P(B\pmid A.C\_j)\) for all \(C\_i \ne C\_j\) and where no further
statistically relevant partition of any of the cells \(A\), \(C\_i\)
can be made with respect to \(B\)--that is, there are no
additional attributes \(D\_k\) in \(A\) such that 

 

\[P(B\pmid A.C\_i) \ne P(B\pmid A.C\_i.D\_k).\]


On the *SR* model, an explanation of why some member *x*
of the class characterized by attribute \(A\) has attribute \(B\)
consists of the following information:


1. The prior probability of \(B\) within \(A\): \(P(B\pmid A) =
p\).
2. A homogeneous partition of *A* with respect to *B*,
(\(A.C\_1,\ldots ,A.C\_n)\), together with the probability of *B*
within each cell of the partition: \(P(B\pmid A.C\_i) = p\_i\) and
3. The cell of the partition to which *x* belongs.



To employ one of Salmon's examples, suppose we want to construct
an *SR* explanation of why *x* who has a strep infection =
*S*, recovers quickly = *Q*. Let \(T(-T)\) according to
whether *x* is (is not) treated with penicillin, and \(R(-R)\) =
according to whether *x* has a penicillin-resistant strain.
Assume for the sake of argument that no other factors are relevant to
quick recovery. There are four possible combinations of these
properties: \(T.R,\) \(-T.R,\) \(T.{-R},\) \({-T}.{-R},\) but let us
assume that

 

\[
\begin{align}
P(Q\pmid S.T.R) & = P(Q\pmid S.{-T}.R)\\
& = P(Q\pmid S.{-T}.{-R})\\
& \ne P(Q\pmid S.{T}.{-R})\\
\end{align}
\]


That is, the probability of quick recovery, given that one has strep,
is the same for those who have the resistant strain regardless of
whether or not they are treated and also the same for those who have
not been treated. By contrast, the probability of recovery is
different (presumably greater) among those with strep who have been
treated and do not have the resistant strain.



In this case

 

\[[S.(T.R \lor {-T}.R \lor {-R}.{-T})], [S.T.{-R}]\]


is a homogenous partition of *S* with respect to *Q*. The
*SR* explanation of *x*'s recovery will consist of a
statement of the probability of quick recovery among all those with
strep ((i) above), a statement of the probability of recovery in each
of the two cells of the above partition ((ii) above), and the cell to
which *x* belongs, which is \(S.T.R\) ((iii) above). Intuitively,
the idea is that this information tells us about the relevance of each
of the possible combinations of the properties *T* and *R*
to quick recovery among those with strep and is explanatory for just
this reason.


### 3.2 The SR Model and Low Probability Events



The *SR* model has a number of distinctive features that have
generated substantial discussion. First, note that according to the
*SR* model, and in contrast to the *DN/IS* model, an
explanation is *not* an argument--either in the sense of a
deductively valid argument in which the explanandum follows as a
conclusion from the explanans or in the sense of a so-called inductive
argument in which the explanandum follows with high probability from
the explanans, as in the case of *IS* explanation. Instead, an
explanation is an assembly of information that is statistically
relevant to an explanandum. Salmon argues (and takes the birth control
example
 (5)
 to illustrate) that the criteria that a good argument must satisfy
(e.g., criteria that insure deductive soundness or some inductive
analogue) are simply different from those a good explanation must
satisfy. Among other things, as Salmon puts it, "irrelevancies
[are] harmless in arguments but fatal in explanations" (1989:
102). As explained above, in associating successful explanation with
the provision of information about statistical relevance
relationships, the *SR* model attempts to accommodate this
observation.



A second, closely related point is that the *SR* model departs
from the *IS* model in abandoning the idea that a statistical
explanation of an outcome must provide information from which it
follows the outcome occurred with high probability. As the reader may
check, the statement of the *SR* model above imposes no such
high probability requirement; instead, even very unlikely outcomes
will be explained as long as the criteria for *SR* explanation
are met. Suppose that, in the above example, the probability of quick
recovery from strep, given treatment and the presence of a
non-resistant strain, is rather low (e.g., 0.2). Nonetheless, if the
criteria (i)-(iii) above--a homogeneous partition with
correct probability values for each cell in the partition--are
satisfied, we may use this information to explain why *x*, who
had a non-resistant strain of strep and was treated, recovered
quickly. Indeed, according to the *SR* model, we may explain
why some *x* which is *A* is *B*, even if the
conditional probability of *B* given *A* and the cell
\(C\_i\) to which *x* belongs \((p\_i = P(B\pmid A.C\_i))\) is
*less* than the prior probability \((p = P(B\pmid A))\) of
*B* in *A*. For example, if the prior probability of quick
recovery among all those with any form of strep is 0.5 and the
probability of quick recovery of those with a resistant strain who are
untreated is 0.1, we may nonetheless explain why *y*, who meets
these last conditions \(({-T}.R),\) recovered quickly (assuming he
did) by citing the cell to which he belongs, the probability of
recovery given that he falls in this cell, and the other sort of
information described above. More generally, what matters on the
*SR* model is not whether the value of the probability of the
explanandum-outcome is high or low (or even high or low in comparison
with its prior probability) but rather whether the putative explanans
cites all and only statistically relevant factors and whether the
probabilities it invokes are correct. One consequence of this, which
Salmon endorses while acknowledging that many will regard it as
unintuitive, is that on the *SR* model, the same explanans
*E* may explain both an explanandum *M* and explananda that
are inconsistent with *M*, such as \(-M\). For example, the same
explanans will explain both why a subject with strep and certain other
properties (e.g., *T* and \(-R\)) recovers quickly, if he does,
and also why he does not recover if he does not. By contrast, on the
*DN* or *IS* models, if *E* explains *M,*
*E* cannot also explain \(-M\).



This judgment that, contrary to the *IS* model, the value that
a candidate explanans assigns to an explanandum-outcome should not
matter for the goodness of the explanation, is motivated as follows:
When an outcome is the result of a genuinely indeterministic process
we understand both high probability and low probability outcomes (the
latter of which of course will sometimes occur) equally well: in both
cases, once an SR model has been constructed, there are no additional
factors that distinguish the two outcomes.


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



Stepping back from the issues (such as the status of the high
probability requirement) that have dominated discussions of
statistical explanation, there are several more general issues that
deserve mention. One is that these models have been applied to a range
of examples that seem prima-facie to be quite different, including
quantum mechanical examples (e.g., radioactive decay) but also more
ordinary examples such as recovery from disease and (to use an example
of Salmon's) causes of juvenile delinquency. Radioactive decay
is a process that is usually taken to be irreducibly indeterministic
and hence is the sort of thing that Salmon's objective
homogeneity requirement is designed to capture. By contrast, although
the evidence for many models of juvenile delinquency comes from
population level statistics these models do *not* assume that
delinquency is the outcome of an irreducibly indeterministic process
(and the models themselves are very far from satisfying an objective
homogeneity requirement). Indeed, taken literally, standard causal
models assume the opposite: the assumed equations are deterministic
with the stochastic element supplied by an "error term".
This raises the question of whether it is sensible to look for a
single model that captures all of these examples.



A second, more radical assessment focuses on the question of whether
it is appropriate to think of the sorts of statistical theories and
hypotheses on which Hempel and Salmon discuss as explaining individual
events or outcomes at all. For example, why not instead take quantum
mechanics to explain (i) the *probabilities* with which
individual outcomes like decay events occur but not (ii) those
individual outcomes themselves? If we adopt (i) the relationship
between a quantum mechanical model and such explananda will be
deductive and thus subsumable under whatever model of deductive
explanation we favor. This raises the question of what additional work
is accomplished by models of statistical explanation of either the
*IS* or *SR* sort. 


### 3.4 Causation and Statistical Relevance Relationships



Putting aside the issues raised in the previous section, the SR model
embodies several generic assumptions of ongoing philosophical
interest. In particular the model assumes that (i) explanations must
cite causal relationships and that (ii) causal relationships are fully
captured by statistical relevance (or conditional dependence and
independence) relationships. While (i) is a matter of current
controversy, (ii) is clearly false. As a substantial body of
 work[5]
 has made clear, causal relationships are greatly underdetermined by
statistical relevance relationships, even given additional
assumptions. For example, a structure in which *B* is a common
cause of the joint effects *A* and *C* implies (assuming the
Causal Markov assumption which is the appropriate generalization of
Salmon's assumptions connecting causation and probability)
implies the same statistical relevance relations as a chain structure
in which *A* causes *B* which causes *C*. 



**Selected Readings**. Salmon (1971a) provides a detailed
statement and defense of the *SR* model. This essay, as well as
papers by Jeffrey (1969) and Greeno (1970) which defend views broadly
similar to the *SR* model, are collected in Salmon (1971b).
Additional discussion of the model as well as a more recent
characterization of "objective homogeneity" can be found
in Salmon (1984). Cartwright (1979) contains some influential
criticisms of the *SR* model. Theorems specifying the precise
extent of the underdetermination of causal claims by evidence about
statistical relevance relationships can be found in Spirtes, Glymour
and Scheines (1993 [2000: chapter 4]). For additional discussion of
"screening off" and the principle of the common cause, see
the entry on
 Reichenbach's Principle of the Common Cause.


## 4. The Causal Mechanical Model


### 4.1 The Basic Idea



In more recent work (especially, Salmon 1984) Salmon abandoned the
attempt to characterize explanation or causal relationships in purely
statistical terms. Instead, he developed a new account which he called
the Causal Mechanical (*CM*) model of explanation--an
account which is similar in both content and spirit to so-called
*causal* *process* theories of causation of the sort
defended by philosophers like Philip Dowe (2000). We may think of the
*CM* model as an attempt to capture the "something
more" involved in causal and explanatory relationships over and
above facts about statistical relevance, again while attempting to
remain within a broadly Humean framework.



The *CM* model employs several central ideas. A *causal
process* is a physical process, like the movement of a baseball
through space, that is characterized by the ability to transmit a
*mark* in a continuous way. ("Continuous"
generally, although perhaps not always, means "spatio-temporally
continuous".) Intuitively, a mark is some local modification to
the structure of a process--for example, a scuff on the surface
of a baseball or a dent an automobile fender. A process is capable of
transmitting a mark if, once the mark is introduced at one
spatio-temporal location, it will persist to other spatio-temporal
locations even in the absence of any further interaction. In this
sense the baseball will transmit the scuff mark from one location to
another. Similarly, a moving automobile is a causal process because a
mark in the form of a dent in a fender will be transmitted by this
process from one spatio-temporal location to another. Causal processes
contrast with *pseudo-processes* which lack the ability to
transmit marks. An example is the shadow of a moving physical object.
The intuitive idea is that, if we try to mark the shadow by modifying
its shape at one point (for example, by altering a light source or
introducing a second occluding object), this modification will not
persist unless we continually intervene to maintain it as the shadow
occupies successive spatio-temporal positions. In other words, the
modification will not be transmitted by the structure of the shadow
itself, as it would in the case of a genuine causal process.



We should note for future reference that, as characterized by Salmon,
the ability to transmit a mark is clearly a counterfactual notion, in
several senses. To begin with, a process may be a causal process even
if it does not in fact transmit any mark, as long as it is true that
*if* it were appropriately marked, it would transmit the mark.
Moreover, the notion of marking itself involves a counterfactual
contrast--a contrast between how a process behaves when marked
and how it would behave if left unmarked. Although Salmon, like
Hempel, has always been suspicious of counterfactuals, his view at the
time that he first introduced the *CM* model was that the
counterfactuals involved in the characterization of mark transmission
were relatively unproblematic, in part because they seemed
experimentally testable in a fairly direct way. Nonetheless the
reliance of the *CM* model, as originally formulated, on
counterfactuals shows that it does not completely satisfy the Humean
strictures described above. In subsequent work, described in
 Section 4.4
 below, Salmon attempted to construct a version of the *CM*
model that completely avoids reliance on counterfactuals.



The other major element in Salmon's model is the notion of a
*causal interaction*. A causal interaction involves a
spatio-temporal intersection between two causal processes which
modifies the structure of both--each process comes to have
features it would not have had in the absence of the interaction. A
collision between two cars that dents both is a paradigmatic causal
interaction.



According to the *CM* model, an explanation of some event
*E* will trace the causal processes and interactions leading up
to *E* (Salmon calls this the *etiological* aspect of the
explanation), or at least some portion of these, as well as describing
the processes and interactions that make up the event itself (the
*constitutive* aspect of explanation). In this way, the
explanation shows how *E* "fit[s] into a causal
nexus"(1984: 9). For example, when two billiard balls collide
(event *E*), the trajectory of each of the balls is a causal
process (as shown by the fact that if the balls were scratched, such
marks would persist) and their collision is a causal interaction.
Explaining *E* will involve both tracing these trajectories and
noting that *E* involves an interaction.


### 4.2 The *CM* Model and Explanatory Relevance



As the billiard example illustrates, the *CM* model takes as
its paradigms of causal interaction examples such as collisions in
which there is "action by contact" and no spatio-temporal
gaps in the transmission of causal influence. There is little doubt
that explanations in which there are no such gaps (no "action at
a distance") often strike us as particularly satisfying.
However, as Christopher Hitchcock shows in an illuminating paper
(Hitchcock 1995), even here the *CM* model leaves out something
important. Consider the usual elementary textbook "scientific
explanation" of the motion of the balls in the above example
following their collision. This explanation proceeds by deriving that
motion from information about their masses and velocity before the
collision, the assumption that the collision is perfectly elastic, and
the law of the conservation of linear momentum. We usually think of
the information conveyed by this derivation as showing that it is the
mass and velocity of the balls, rather than, say, the scratches on
their surface or chalk that may be transmitted by the cue stick that
is explanatorily relevant to their subsequent motion. However, it is
hard to see what in the *CM* model allows us to pick out the
linear momentum of the balls, as opposed to these other features, as
explanatorily relevant. Part of the difficulty is that to express such
relatively fine-grained judgments of explanatory relevance (that it is
linear momentum rather than chalk marks that matters) we need to talk
about relationships between properties or magnitudes and it is not
clear how to express such judgments purely in terms of facts about
causal processes and interactions. Both the linear momentum and the
chalk mark communicated to the cue ball by the cue stick are marks
transmitted by the spatio-temporally continuous causal process
consisting of the motion of the cue ball.



Ironically, as Hitchcock goes on to note, a similar observation may be
made about the birth control pills example
 (5)
 originally devised by Salmon to illustrate the failure of the
*DN* model to capture the notion of explanatory relevance.
Spatio-temporally continuous causal processes that transmit marks as
well as causal interactions are at work when male Mr. Jones ingests
birth control pills--the pills dissolve, components enter his
bloodstream, are metabolized or processed in some way, and so on.
Similarly, spatio-temporally continuous causal processes (albeit
different processes) are at work when female Ms. Jones takes birth
control pills. However, the pills are irrelevant to Mr. Jones's
non-pregnancy, and relevant to Ms. Jones's non-pregnancy. Again,
it looks as though the relevance or irrelevance of the birth control
pills to Mr. or Ms. Jones's failure to become pregnant cannot be
captured just by asking whether the processes leading up to these
outcomes are causal processes in Salmon's sense. 



A more general way of putting the problem revealed by these examples
is that those features of a process *P* in virtue of which it
qualifies as a causal process (ability to transmit mark *M*) may
not be the features of *P* that are causally or explanatorily
relevant to the outcome *E* that we want to explain (*M* may
be irrelevant to *E* with some other property *R* of
*P* being the property which is causally relevant to *E*).
So while mark transmission may well be a criterion that correctly
distinguishes between *causal processes* and
*pseudo-processes*, it does not, as it stands, provide the
resources for distinguishing those *features* or
*properties* of a causal process that are causally or
explanatorily relevant to an outcome and those features that are
irrelevant.


### 4.3 The *CM* Model and Complex Systems



A second set of worries has to do with the application of the
*CM* model to systems which depart in various respects from
simple physical paradigms such as the collision described above. There
are a number of examples of such systems. First, there are theories
like Newtonian gravitational theory which involve "action at a
distance" in a physically interesting sense. Second, there are a
number of examples from the literature on causation that do not
involve physically interesting forms of action at a distance but which
arguably involve causal interactions without intervening
spatio-temporally continuous processes or transfer of energy and
momentum from cause to effect. These include cases of causation by
omission and causation by "double prevention" or
 "disconnection."[6]
 In all these cases, a literal application of the *CM* model
seems to yield the judgment that no explanation has been
provided--that Newtonian gravitational theory is unexplanatory
and so on. Many philosophers have been reluctant to accept this
assessment.



Yet another class of examples that raise problems for the *CM*
model involves putative explanations of the behavior of complex or
"higher level" systems--explanations that do not
explicitly cite spatio-temporally continuous causal processes
involving transfer of energy and momentum, even though we may think
that such processes are at work at a more "underlying"
level. Most explanations in disciplines like biology, psychology and
economics fall under this description, as do a number of
straightforwardly physical explanations.



As an illustration, suppose that a mole of gas is confined to a
container of volume \(V\_1,\) at pressure \(P\_1,\) and temperature
\(T\_1\). The gas is then allowed to expand isothermally into a larger
container of volume \(V\_2\). One standard way of explaining the
behavior of the gas--its rate of diffusion and its subsequent
equilibrium pressure \(P\_2\)--appeals to the generalizations of
phenomenological thermodynamics--e.g., the ideal gas law,
Graham's law of diffusion, and so on. Salmon appears to regard
putative explanations based on at least the first of these
generalizations as not explanatory because they do not trace
continuous causal processes--he thinks of the individual
molecules as causal processes but not the gas as a
 whole.[7]
 However, it is plainly impossible to trace the causal processes and
interactions represented by each of the \(6 \times 10^{23}\) molecules
making up the gas and the successive interactions (collisions) it
undergoes with every other molecule. Even the usual statistical
mechanical treatment, which Salmon presumably would regard as
explanatory, does not attempt to do this. Instead, it makes certain
general assumptions about the distribution of molecular velocities and
the forces involved in molecular collisions and then uses these, in
conjunction with the laws of mechanics, to derive and solve a
differential equation (the Boltzmann transport equation) describing
the overall behavior of the gas. This treatment abstracts radically
from the details of the causal processes involving particular
individual molecules and instead focuses on identifying higher level
variables that aggregate over many individual causal processes and
that figure in general patterns that govern the behavior of the
gas.



This example raises a number of questions. Just what does the
*CM* model require in the case of complex systems in which we
cannot trace individual causal processes, at least at a fine-grained
level? How exactly does the causal mechanical model avoid the
(disastrous) conclusion that any successful explanation of the
behavior of the gas must trace the trajectories of individual
molecules? Does the statistical mechanical explanation described above
successfully trace causal processes and interactions or specify a
causal mechanism in the sense demanded by the *CM* model, and
if so, what exactly does tracing causal processes and interactions
involve or amount to in connection with such a system? A fully
adequate development of the CM model needs to address such
questions.



There is another aspect of this example that is worthy of comment.
Suppose that a particular sample of gas expands in a way that meets
the conditions described above and that it is somehow possible to
provide an account that traces each of the individual molecular
trajectories of its component molecules. Such an account would
nonetheless leave out information that seems explanatorily relevant.
This information has to do with the fact that there are a large number
of alternative trajectories besides the actual trajectories followed
by the component molecules on this particular occasion that would lead
to the same final pressure \(P\_2\) which is what we want to explain.
Modal information of this sort--both about what would happen if
the molecules followed different trajectories consistent with the
initial conditions \(P\_1\), \(V\_1\) and \(T\_1\) and what would happen if they instead followed initial conditions consistent trajectories consistent with different macroscopic initial conditions is better captured by a treatment in terms of upper level thermodynamic variables.


### 4.4 More Recent Developments



In more recent work (e.g., Salmon 1994), prompted in part by a desire
to avoid certain counterexamples advanced by Philip Kitcher (1989) to
his characterization of mark transmission, Salmon attempted to fashion
a theory of causal explanation that completely avoids any appeal to
counterfactuals. In this new theory which is influenced by the
conserved process theory of causation of Dowe (2000), Salmon defined a
causal process as a process that transmits a non-zero amount of a
*conserved quantity* at each moment in its history. Conserved
quantities are quantities so characterized in physics--linear
momentum, angular momentum, charge, and so on. A causal interaction is
an intersection of world lines associated with causal processes
involving exchange of a conserved quantity. Finally, a process
transmits a conserved quantity from *A* to *B* if it
possesses that quantity at every stage without any interactions that
involve an exchange of that quantity in the half-open interval
 \((A,B]\).[8]



One may doubt that this new theory really avoids reliance on
counterfactuals, but an even more fundamental difficulty is that it
still does not adequately deal with the problem of causal or
explanatory relevance described above. That is, we still face the
problem that the feature that makes a process causal (transmission of
some conserved quantity or other) may tell us little about which
features of the process are causally or explanatorily relevant to the
outcome we want to explain. For example, a moving billiard ball will
transmit many conserved quantities (linear momentum, angular momentum,
charge etc.) and many of these may be exchanged during a collision
with another ball. What is it that entitles us to single out the
linear momentum of the balls, rather than these other conserved
quantities as the property that is causally relevant to their
subsequent motion? In cases in which there appear to be no
conservation laws governing the explanatorily relevant property (i.e.,
cases in which the explanatorily relevant variables are not conserved
quantities) this difficulty seems even more acute. Properties like
"having ingested birth control pills," "being
pregnant", or "being a sample of hexed salt" do not
themselves figure in conservation laws. While one may say that both
birth control pills and hexed salt are causal processes because both
consist, at some underlying level, of processes that unambiguously
involve the transmission of conserved quantities like mass and charge,
this observation does not by itself tell us what, if anything, about
these underlying processes is relevant to pregnancy or dissolution in
water.



In a more recent paper (Salmon 1997), Salmon conceded this point. He
agreed that the notion of a causal process cannot by itself capture
the notion of causal and explanatory relevance. He suggested, however,
that this notion can be adequately captured by appealing to the notion
of a causal process *and* information about statistical
relevance relationships (that is, information about conditional and
unconditional (in)dependence relationships), with the latter capturing
the element of causal or explanatory dependence that was missing from
his previous account:



> 
> 
> I would now say that (1) statistical relevance relations, in the
> absence of information about connecting causal processes, lack
> explanatory import and that (2) connecting causal processes, in the
> absence of statistical relevance relations, also lack explanatory
> import. (1997: 476)
> 
> 
> 



This suggestion is not developed in any detail in Salmon's
paper, and it is not easy to see how it can be made to work. We noted
above that statistical relevance relationships often greatly
underdetermine the causal relationships among a set of variables. What
reason is there to suppose that appealing to the notion of a causal
process, in Salmon's sense, will always or even usually remove
this indeterminacy? We also noted that the notion of a causal process
cannot capture fine-grained notions of relevance between properties,
that there can be causal relevance between properties instances of
which (at least at the level of description at which they are
characterized) are not linked by spatio-temporally continuous or
transference of conserved quantities, and that properties can be so
linked without being causally relevant (recall the chalk mark that is
transmitted from one billiard ball to another). As long as it is
possible (and why should it not be?) for different causal claims to
imply the same facts about statistical relevance relationships and for
these claims to differ in ways that cannot be fully cashed out in
terms of Salmon's notions of causal processes and interactions,
this new proposal will fail as well.



**Selected Readings:** Salmon (1984) provides a detailed
statement of the Causal Mechanical model, as originally formulated.
Salmon (1994 and 1997) provide a restatement of the model and respond
to criticisms. For discussion and criticism of the *CM* model,
see Kitcher (1989, especially pages 461ff), Woodward (1989), and
Hitchcock (1995).


## 5. A Unificationist Account of Explanation


### 5.1 The Basic Idea



In unificationist accounts of explanation developed by philosophers,
scientific explanation is a matter of providing a unified account of a
range of different
 phenomena.[9]
 This idea is unquestionably intuitively appealing. Successful
unification may exhibit connections or relationships between phenomena
previously thought to be unrelated and this seems to be something that
we expect good explanations to do. Moreover, theory unification has
clearly played an important role in science. Paradigmatic examples
include Newton's unification of terrestrial and celestial
theories of motion and Maxwell's unification of electricity and
magnetism. The key question, however, is whether (and which) intuitive
notions of unification can be made more precise in a way that allows
us to recover the features that we think that good explanations should
possess.



Michael Friedman (1974) is an important early attempt to do this.
Friedman's formulation of the unificationist idea was
subsequently shown to suffer from various technical problems (Kitcher
1976) and subsequent development of the unificationist treatment of
explanation has been most closely associated with Philip Kitcher
(especially Kitcher 1989).



Let us begin by introducing some of Kitcher's technical
vocabulary. A *schematic sentence* is a sentence in which some
of the nonlogical vocabulary has been replaced by dummy letters. To
use Kitcher's examples, the sentence "Organisms homozygous
for the sickling allele develop sickle cell anemia" is
associated with a number of schematic sentences including
"Organisms homozygous for *A* develop *P*" and
"For all *X* if *X* is *O* and *A* then
*X* is *P*". *Filling instructions* are
directions that specify how to fill in the dummy letters in schematic
sentences. For example, filling instructions might tell us to replace
*A* with the name of an allele and *P* with the name of a
phenotypic trait in the first of the above schematic sentences.
*Schematic arguments* are sequences of schematic sentences.
*Classifications* describe which sentences in schematic
arguments are premises and conclusions and what rules of inference are
used. An *argument pattern* is an ordered triple consisting of
a schematic argument, a set or sets of filling instructions, one for
each term of the schematic argument, and a classification of the
schematic argument. The more restrictions an argument pattern imposes
on the arguments that instantiate it, the more *stringent* it
is said to be.



Roughly speaking, Kitcher's guiding idea is that explanation is
a matter of deriving descriptions of many different phenomena by using
as few and as stringent argument patterns as possible over and over
again-the fewer the patterns used, the more stringent they are, and
the greater the range of different conclusions derived, the more
unified our explanations. Kitcher summarizes this view as follows:



> 
> 
> Science advances our understanding of nature by showing us how to
> derive descriptions of many phenomena, using the same pattern of
> derivation again and again, and in demonstrating this, it teaches us
> how to reduce the number of facts we have to accept as ultimate.
> (Kitcher 1989: 432)
> 
> 
> 



Kitcher does not propose a completely general theory of how the
various considerations he describes--number of conclusions,
number of patterns and stringency of patterns--are to be
traded-off against one another, but does suggest that it often will be
clear enough what these considerations imply about the evaluation of
particular candidate explanations. His basic strategy is to attempt to
show that the derivations we regard as good or acceptable explanations
are instances of patterns that, taken together, score better according
to the criteria just described than the patterns instantiated by what
we regard as defective explanations. Following Kitcher, let us define
the *explanatory store \(E(K)\)* as the set of argument
patterns that maximally unifies *K*, the set of beliefs accepted
at a particular time in science. Showing that a particular derivation
is a good or acceptable explanation is then a matter of showing that
it belongs to the explanatory store.


### 5.2 Illustrations of the Unificationist Model



As an illustration, consider Kitcher's treatment of the problem
of explanatory asymmetries (recall
 Section 2.5).
 Our present explanatory practices--call these *P*--are
committed to the idea that derivations of a flagpole's height
from the length of its shadow are not explanatory. Kitcher compares
*P* with an alternative systemization in which such derivations
are regarded as explanatory. According to Kitcher, *P* includes
the use of a single "origin and development" (*OD*)
pattern of explanation, according to which the dimensions of
objects-artifacts, mountains, stars, organisms etc. are traced to
"the conditions under which the object originated and the
modifications it has subsequently undergone" (1989: 485). Now
consider the consequences of adding to *P* an additional pattern
*S* (the shadow pattern) which permits the derivation of the
dimensions of objects from facts about their shadows. Since the
*OD* pattern already permits the derivation of all facts about
the dimensions of objects, the addition of the shadow pattern *S*
to *P* will increase the number of argument patterns in *P*
and will not allow us to derive any new conclusions. On the other
hand, if we were to drop *OD* from *P* and replace it with
the shadow pattern, we would have no net change in the number of
patterns in *P*, but would be able to derive far fewer
conclusions than we would with *OD*, since many objects do not
have shadows (or enough shadows) from which to derive all of their
dimensions. Thus *OD* belongs to the explanatory store, and the
shadow pattern does not. Kitcher's treatment of other familiar
problem cases is similar. For example he claims that explanations that
contain irrelevancies (such as Salmon's birth control pills case
are less unifying than competing explanations that do not contain such
irrelevancies. 



Kitcher acknowledges that there is nothing in the unificationist
account *per se* that requires that all explanation be
deductive: "there is no bar in principle to the use of
non-deductive arguments in the systemization of our beliefs".
Nonetheless, "the task of comparing the unifying power of
different systemizations looks even more formidable if non-deductive
arguments are considered" and in part for this reason Kitcher
endorses the view that *"in a certain sense, all explanation
is deductive"* (1989: 448).



What is the role of causation on this account? Kitcher claims that
"the 'because' of causation is always derivative
from the 'because' of explanation." (1989: 477).
That is, our causal judgments simply reflect the explanatory
relationships that fall out of our (or our intellectual
ancestors' ) attempts to construct unified theories of nature.
There is no independent causal order over and above this which our
explanations must capture. Like many other philosophers, Kitcher takes
very seriously (even if in the end he perhaps does not fully endorse)
standard empiricist or Humean worries about the epistemic
accessibility and intelligibility of causal claims. Taking causal,
counterfactual or other notions belonging to the same family as
primitive in the theory of explanation is problematic. Kitcher
believes that it is a virtue of his theory that it does not do this.
Instead, Kitcher proposes to begin with the notion of explanatory
unification, characterized in terms of constraints on deductive
systemizations, where these constraints can be specified in a quite
general way that is independent of causal or counterfactual notions,
and then show how the causal claims we accept derive from our efforts
at unification.


### 5.3 The Illustrations Criticized



As remarked at the beginning of this section, the idea that
explanation is connected in some way to unification is intuitively
appealing. Nonetheless Kitcher's particular way of cashing out
this connection has been subject to criticism. In connection with
Kitcher's treatment of explanatory asymmetries, consider,
following Barnes (1992), a time-symmetric theory like Newtonian
mechanics, applied to a closed system like the solar system. Call
derivations of the state of motion of planets at some future time
*t* from information about their present positions (at time
\(t\_0\)), masses, and velocities, the forces incident on them at
\(t\_0\), and the laws of mechanics *predictive*. Now contrast
such derivations with *retrodictive* derivations in which the
present motions of the planets are derived from information about
their future velocities and positions at *t*, the forces
operative at *t*, and so on. It looks as though there will be
just as many retrodictive derivations as predictive derivations, and
each will require premises of exactly the same general
sort--information about positions, velocities, masses, etc. and
the same laws. Thus the pattern or patterns instantiated by the
retrodictive derivations look(s) exactly as unified as the pattern or
patterns associated with the predictive derivations. However, we
ordinarily think of the predictive derivations and not the
retrodictive derivations as explanatory and the present state of the
planets as the cause of their future state and not vice-versa. 



One possible response to this second example is to bite the bullet and
to argue that from the point of view of fundamental physics, there
really is no difference in the explanatory import of the retrodictive
and predictive derivations, and that it is a virtue, not a defect, of
the unificationist approach that it reproduces this judgment. Whatever
might be said in favor of this response, it is not Kitcher's.
His claim is that our ordinary judgments about causal asymmetries can
be derived from the unificationist account. The example just described
casts doubt on this claim. More generally, it casts doubt on
Kitcher's contention that one can begin with the notion of
explanatory unification, understood in a way that does not presuppose
causal notions, and use it to derive the content of causal
judgments.



**Selected Readings**: The most detailed statement of
Kitcher's position can be found in Kitcher (1989). Salmon (1989:
94ff.) contains a critical discussion of Friedman's version of
the unificationist account of explanation but ends by advocating a
"rapprochement" between unificationist approaches and
Salmon's own causal mechanical model. Woodward (2003) contains
additional criticisms of Kitcher's version of
unificationism.


## 6. Pragmatic Theories of Explanation


### 6.1 Introduction



Despite their many differences, the accounts of Hempel (focusing now
on just the *DN* rather than the *IS* model), Salmon,
Kitcher, and others discussed above, largely share a common overall
conception of what the project of constructing a theory of explanation
should involve and (to a considerable extent) what criteria such a
theory should satisfy if it is to be successful.
"Pragmatic" theories of explanation depart from this
consensus in important respects. Let us say that a theory of
explanation contains "pragmatic" elements if (i) according
to the theory, those elements require irreducible reference to facts
about the interests, beliefs or other features of the psychology of
those providing or receiving the explanation and/or (ii) irreducible
reference to the "context" in which the explanation
occurs. (For what this means, see below.) Although the writers
discussed above agree that pragmatic elements play some role in the
activity of giving and receiving explanations, they assume that there
is a non-pragmatic core to the notion of explanation, which it is the
central task of a theory of explanation to capture. That is, it is
assumed that this core notion can be specified without reference to
psychological features of explainers or their audiences and with
reference to non-contextual features that are sufficiently general,
abstract and "structural," in the sense that they hold
across a range of explanations with different contents and across a
range of different contexts. Relations like deductive entailment or
statistical relevance are examples of candidates for such
"structural" relationships. In addition, these writers see
the goal of a theory of explanation, as capturing the notion of a
*correct* explanation, as opposed to the notion of an
explanation's being considered explanatory by a particular
audience or not, a matter which presumably depends on such
considerations as whether the audience understands the terms in which
the explanation is framed. (In this sense, "correctness"
requires (at least) that the explanans be true or "well-confirmed" and that the explanans stands in the right
relationship to the explanandum.) Finally, as noted in the
Introduction to this entry, writers in this tradition have
*not* had the goal of capturing all the various ways in which
the word "explanation" is used in ordinary English. They
have instead focused on a much more restricted class of examples in
which what is of interest is (something like) explaining
"why" some outcome or general phenomenon occurred, as
opposed to explaining, e.g., the meaning of a word or how to solve a
differential equation. The motivation for this restriction is simply
the judgment that an interesting and non-trivial theory is more likely
to emerge if it is restricted in scope in this way. For ease of
reference, let us call this the "traditional" conception
of the task of a theory of explanation.



Some or all of these assumptions and goals are rejected in pragmatic
accounts of explanation. Early contributors to this approach include
Michael Scriven (e.g., 1962) and Sylvan Bromberger (e.g., 1966), with
more systematic statements, due to van Fraassen (1980) and Achinstein
(1983) appearing in the 1980s. Since it is not always clear just what
the points of disagreement are between pragmatic and traditional
accounts, some orienting remarks about this will be useful before
turning to details. Defenders of pragmatic approaches to explanation
typically stress the point that whether provision of a certain body of
information to some audience produces understanding or is illuminating
for that audience depends on the background knowledge of the audience
members and on other factors having to do with the local context. For
example, an explanation of the deflection of starlight by the sun that
appeals to the field equations of General Relativity may be highly
illuminating to a trained physicist but unintelligible to a layperson
because of their background. Factors of this sort are grouped together
as "pragmatic" and their influence is taken to illustrate
at least one way in which pragmatic considerations enter into the
notion of explanation.



Taken in itself, the observation just described seems completely
uncontroversial and not in conflict with traditional approaches to
explanation. Indeed, as remarked above writers like Hempel and Salmon
explicitly agree that explanation has a pragmatic dimension in the
sense just described--in fact, Hempel invokes the role of
pragmatic factors at a number of points to address prima-facie
counterexamples to the DN model. This suggests that, often at least,
what is distinctive about pragmatic approaches to explanation is not
just the bare idea that explanation has a "pragmatic
dimension" but rather the much stronger claim that the
traditional project of constructing a model of explanation pursued by
Hempel and others has so far been unsuccessful ( and perhaps is
*bound* to be unsuccessful) and that this is so
*because* pragmatic or contextual factors play a central and
ineliminable role in explanation in a way that resists incorporation
into models of the traditional sort. On this view, much of what is
distinctive about pragmatic accounts is their opposition to
traditional accounts and their *diagnosis* of why such accounts
fail--they fail because they omit pragmatic or contextual
elements. It will be important to keep this point in mind in what
follows because there is a certain tendency among advocates of
pragmatic theories to argue as though the superiority of their
approach is established simply by the observation that explanation has
a pragmatic dimension; instead it seems more appropriate to think that
the real issue is whether traditional approaches are inadequate in
principle because of their neglect of the pragmatic dimension of
explanation.



A second issue concerns an important ambiguity in the notion of
"pragmatic". On one natural understanding of this notion,
a pragmatic consideration is one that has to do with utility or
usefulness in the service of some goal connected to human interests,
where these interests are in some relevant sense
"practical". Call this notion
"pragmatic1". On this construal, Hempel's
*DN* model might be correctly characterized as a
pragmatic1 theory since it links explanatory information
closely to the provision of information that is useful for purposes of
prediction and prediction certainly qualifies as a pragmatic goal. For
similar reasons, Woodward's (2003) theory of explanation might
also be counted as a pragmatic1 theory since it connects
explanation with the provision of information that is useful for
manipulation and control--unquestionably useful goals. As these
examples suggest, models of explanation that aspire to traditional
goals can be pragmatic1 theories.



In the context of theories of explanation, however, the label
"pragmatic" is usually intended to suggest a somewhat
different set of associations. In particular, as noted above,
"pragmatic" is typically used to characterize
considerations having to do with facts about the psychology
(interests, beliefs etc.) of those involved in providing or receiving
explanations and/or to characterize considerations involving the local
context, often with the suggestion that both sets of considerations
may vary in complex and idiosyncratic ways that resist incorporation
into the sort of general theory sought by traditional
 models.[10]
 Call this set of associations "pragmatic2". Neither Hempel's nor Woodward's theory is
pragmatic2. In particular, as the example of the
*DN* model illustrates, the fact that a theory is
pragmatic1 in the sense that it appeals to facts about
goals generally shared by human beings (such as prediction) to help to
motivate a model of explanation does *not* preclude attempting
to construct models of explanation satisfying traditional goals and
does not require commitment to the idea that explanation must be
understood as a pragmatic2 notion. We need to be careful to
distinguish these two different ways of thinking about the
"pragmatic" dimension of explanation.



Finally, as emphasized above, a concern with the pragmatics of
explanation naturally connects with an interest in the
"psychology" of explanation and this in turn suggests the
relevance of empirical studies of sorts of information that various
subjects (ordinary folks, scientists) find explanatory, treat as
providing "understanding", the distinctions subjects make
among explanations and so on. Although there is a growing literature
in this area, the most prominent philosophical advocates of pragmatic
approaches to explanation have so far tended not to make use of it. In
this connection, it is worth pointing out that this psychological
literature goes well beyond the truisms found in philosophical
discussion about different people finding different sorts of
information explanatory depending on their interests. In particular,
psychologists have been very interested in exploring general features
or structural patterns present in information that various subjects
find explanatory. For example, Lombrozo (2010) finds evidence that
subjects prefer explanations that appeal to relationships that are
relatively stable (in the sense of continuing to hold across changing
 circumstances)[11]
 and Lien and Cheng (2000) present evidence that in cases in which the
*explanandum* \(E\) has a single candidate cause \(C\),
subjects prefer levels of explanation/causal description that maximize
\(\Delta p = \Pr(E\pmid C) - \Pr(E \pmid \text{not-}C)\).



Notice that in both cases these are relationships or patterns of the
sort that traditional accounts of explanation attempt to capture. As
these examples bring out, there is no necessary incompatibility
between the project of trying to formulate an account of explanation
that satisfies traditional goals and an interest in the psychology of
explanation. It may be that subjects find certain sorts of information
explanatory or understanding-producing *because* certain
structural features of the sort that traditional accounts attempt to
characterize are present in that information--indeed this is what
the Lombrozo and Lien and Cheng papers suggest. Thus, we should
distinguish the project of investigating the empirical psychology of
explanation (which can be pursued with a variety of different
commitments about how to best theorize about explanation) from the
more specific claim that the characterization of what it is for an
explanatory relationship to hold between explanans and explanandum
must be given in "psychologistic" terms, in the sense that
this requires irreducible reference to psychological facts about
particular audiences such as the vagaries of what they happen to be
interested in. 


### 6.2 Constructive Empiricism and the Pragmatic Theory of Explanation



One of the most influential recent pragmatic accounts of explanation
is associated with constructive
 empiricism.[12]
 This is the thesis, defended by Bas van Fraassen in his 1980 book,
*The Scientific Image*, that the aim of science (or at least
"pure" science) is the construction of theories that are
"empirically adequate" (that is, that yield a true or
correct description of observables) and not, as scientific realists
suppose, theories that aim to tell literally true stories about
unobservables. Relatedly, "acceptance" of a theory
involves only the belief that it is empirically adequate (van Fraassen
1980: 12). van Fraassen's account of explanation, which is laid
out in several articles and, most fully, in Chapter Six of his book,
is meant to fit with this overall conception of science: it is a
conception according to which explanation per se is not an epistemic
aim of "pure" science (empirical adequacy is the only such
aim), but rather a "pragmatic" virtue, having to do with
the "application" of science. (Note that the application
of science is arguably a matter of pragmatics1. However,
the idea that explanation has to do with the application of science is
used to motivate the adoption of a pragmatic2 theory of
explanation. We thus have an elision of the two notions of
"pragmatic" distinguished above.) According to van
Fraassen, because explanation is a merely pragmatic virtue, a concern
with explanation is not something that can require scientists to move
beyond belief in the empirical adequacy of their theories to belief in
the literal truth of claims about unobservable entities.



According to van Fraassen, explanations are answers to questions and
getting clear about the logic of questions is central to constructing
a theory of explanation. Questions can take many different forms, but
when the question of interest is a "why" question,
explanatory queries will typically take the following form: a query
about why some explanandum \(P\_k\) rather than any one of the members
of a contrast class \(X\) (a set of possible alternatives to \(P\_k\))
obtained. In addition, some "relevance relation" \(R\) is
assumed by the question. An *answer* \(A\) to this question
will take the form "\(P\_k\) in contrast to (the rest of) \(X\)
because \(A\), where \(A\) bears the relevance relation \(R\) to
\([P\_k,X]\)". To use van Fraassen's example, consider
"Why is this conductor warped?" Depending on the context,
the intended contrast might have to with, e.g., why this particular
conductor is warped in contrast to some other conductor that is
unwarped. Alternatively, it might have to do with why this particular
conductor is warped now when it was previously unwarped. The relevance
relation \(R\) similarly depends on the context and the information
which the questioner is interested in obtaining. For example, \(R\)
might involve causal information (the question might be a request for
what caused the warping) but it also might have to do with information
about function, if the context was one in which it is assumed that the
shape of the conductor plays some functional role in a power station
which the questioner wants to know about. Thus "context"
enters into the explanation both by playing a role in specifying the
contrast class \(X\) and the relevance relation \(R\). van Fraassen
describes various rules for the "evaluation" of answers.
For example, \(P\_k\) and \(A\) must be true, the other members of the
contrast class must not be true, \(A\) must "favor" (raise
the conditional probability of) \(P\_k\) against alternatives, and
\(A\) must compare favorably with other answers to the same question,
a condition which itself has several aspects including, for example,
whether \(A\) favors the topic more than these other answers and
whether \(A\) is screened off by other answers. However, he also makes
it clear (as the example above suggests) that a variety of different
relevance relations may be appropriate depending on context and that
the evaluation of answers also depends on context. Moreover, he
explicitly denies that there is anything distinctive about the
category of scientific explanation that has to do with its structure
or form--instead, a scientific explanation is simply an
explanation that makes use of information that is (or at least, is
treated as) grounded in a "scientific" theory.



Van Fraassen sums up his view of explanation (and gestures at his
grounds for rejecting traditional objectivist approaches) as
follows:



> 
> 
> The discussion of explanation went wrong at the very beginning when
> explanation was conceived of as a relation like description: a
> relation between a theory and a fact. Really, it is a three-term
> relation between theory, fact, and context. No wonder that no single
> relation between theory and fact ever managed to fit more than a few
> examples! Being an explanation is essentially relative for an
> explanation is an *answer*... it is evaluated
> vis-a-vis a question, which is a request for information. But
> exactly... what is requested differs from context to context.
> (1980: 156)
> 
> 
> 



Van Fraassen begins his chapter on explanation with a brief story that
provides a good point of entry into how he intends his account to
work. Recall from
 Section 2.5
 that a well-known counterexample to the *DN* model involves
the claim that one can explain the length *S* of the shadow cast
by a flagpole in terms of the height *H* of the flagpole but that
(supposedly) one cannot explain *H* in terms of *S*, despite
the fact that one can construct a *DN* derivation from *S*
to *H*. This is commonly taken to show that the *DN* model
has left out some factor having to do with the directional or
asymmetric features of explanation--e.g., perhaps an asymmetry in
the relation between cause and effect that ought to be incorporated into
one's model of explanation. In van Fraassen's story, a
straightforward causal explanation of the usual sort of *S* in
terms of *H* (although the object in question is a tower rather
than a flagpole) is first offered. Then a second explanation,
according to which the height of the tower is "explained"
by the fact that it was designed to cast a shadow of a certain length
is advanced. Presumably the moral we are to draw is that as the
context and perhaps the relevance relation *R* are varied,
both

 

\[ H \text{ explains } S\]


and

 

\[ S \text{ explains } H\]


are acceptable (legitimate, appropriate etc.) explanations. Moreover,
since these variations in context and relevance relation turn on
variations in what is of interest to the explainer and his audience,
we are further encouraged to conclude that explanatory asymmetries
have their source in psychological facts about people's
interests and background beliefs, rather than in, say, some asymmetry
that exits in nature independently of these. Pragmatists about
explanation think that a similar conclusion holds for other features
of the explanatory relevance relation that philosophers have tried to
characterize in terms of traditional models of explanation.



One obvious response to this claim, made by several critics (e.g.,
Kitcher & Salmon 1987: 317), is that the example does not really
involve a case in which, depending on context, *H* causally
explains *S* and *S* causally explains *H*. Instead,
although *H* does causally explain *S*, it is (something
like) the *desire* for a shadow of length *S* (rather than
*S* itself) that explains (or at least causally explains) the
height (or the choice of height) for the tower. Or, if one prefers, in
the latter case we are given something like a functional explanation
(but not a causal explanation) for the height of the tower, in the
sense that we are told what the intended function of that choice of
height is. On either of these diagnoses, this will not be a case in
which whether *H* provides a causal explanation of *S* or
whether instead *S* provides a causal explanation of *H*
shifts depending on factors having to do with the interests of the
speaker or audience or other contextual factors. If so, the story
about the tower does not show that the asymmetry present in the
flagpole example must be accounted for in terms of pragmatic factors.
It may be accounted for in some other way. In fact, although
discussion must be beyond the scope of this entry, a number of
possible candidates for such a non-pragmatic account of causal
asymmetries have been proposed, both in philosophy and outside of it
(for example, in the machine learning
 literature[13]).
 



A much more general criticism has been advanced against van
Fraassen's version of a pragmatic theory by Kitcher and Salmon
(1987). Basically, their complaint is that the relevance relation
*R* in van Fraassen's account is completely unconstrained,
with the (in their view, obviously unacceptable) consequence that for
any pair of true propositions *P* and *A*, answer *A*
is relevant to *P* via some relevance relation and thus
"explains" *P*. For example, according to Salmon and
Kitcher, we might define a relationship of "astral
influence" \(R^\*\), meeting van Fraassen's criteria for
being a relevance relation, such that the time *t* of a
person's death is explained in terms of \(R^\*\) and the position
of various heavenly bodies at *t*. Here it may seem that van
Fraassen has a ready response. As noted above, on van Fraassen's
view, background knowledge and, in the case of scientific explanation,
current scientific knowledge, helps to determine which are the
acceptable relevance relations and acceptable answers to the questions
posed in requests for explanation--such knowledge and the
expectations that go along with it are part of the relevant context
when one asks for an explanation of time of death. Obviously, astral
influence is not an acceptable or legitimate relevance relation
according to modern science--hence appeal to such a relation is
not countenanced as explanatory by van Fraassen's theory. More
generally it might be argued that available scientific knowledge will
provide constraints on the relevance relations and answers that
exclude the "anything goes" worry raised by Salmon and
Kitcher--at least insofar as the context is one in which a
"scientific explanation" is sought.



While this response may seem plausible enough as far as it goes, it
does bring out the extent to which much of the work of distinguishing
the explanatory from the non-explanatory in van Fraassen's
account comes from a very general appeal to what is accepted as
legitimate background information in current science. Put differently,
this raises the worry that once one moves beyond van Fraassen's
formal machinery concerning questions and answers (which van Fraassen
himself acknowledges is relatively unconstraining), one is left with
an account according to which a scientific explanation is simply any
explanation employing claims from current science and a currently
scientifically approved relevance relation. Even if otherwise
unexceptionable, this proposal is, if not exactly trivial, at least
rather deflationary--it provides much less than many have hoped
for from a theory of explanation. In particular, in cases (of which
there are many examples) in which there is an ongoing argument or
dispute in some area of science not about whether some proposed theory
or model is true but rather about whether it explains some phenomenon,
it is not easy to see how the proposal even purports to provide
guidance. On the other hand, the obvious rejoinder that might be made
on van Fraassen's behalf is that no more ambitious treatment
that would satisfy the expectations associated with more traditional
accounts of explanation (including a demarcation of candidate
explanations into those that are "correct" and
"incorrect") is possible--a theory like van
Fraassen's is as good as it gets. If there is no defensible
theory of explanation embodying a non-trivially constraining relevance
relation, it cannot be a good criticism of van Fraassen's theory
that he fails to provide this.



A final point that is suggested by van Fraassen's theory is
this: In considering pragmatic theories, it matters a great deal
exactly where the "pragmatic" elements are claimed to
enter into the account of explanation. One point at which such
considerations seem clearly to enter is in the selection or
characterization of what an audience wants explained. This is
reflected in van Fraassen's theory in the choice of a \(P\_k\)
and an associated contrast class \(X\). Obviously, whether we are
looking for an explanation of why, say, this particular conductor is
now bent when it was previously straight or whether instead we want to
know why this conductor is bent while some other conductor is straight
is a matter that depends on our interests. However, this particular
sort of "interest relativity" (and associated phenomena
having to do with the role of contrastive focus in the
characterization of explananda, which really just serve to specify
more exactly which particular explananda we want explained) seems
something that can be readily acknowledged by traditional
 theories.[14]
 After all, it is not a threat to the *DN* or other models with
similar traditional aspirations that one audience may be interested in
an explanation of the photoelectric effect but not the deflection of
starlight by the sun and another audience may have the opposite
interests. What would be a threat to the *DN* and similar
models would be an argument that once some explanandum *E* is
fully specified, whether explanans *M* explains *E* (that
is, whether there is an explanatory relation between *M* and
*E*) is itself "interest-relative". It is natural to
interpret van Fraassen as making this latter claim, both in connection
with explanatory asymmetries and more generally.



**Selected Readings**. van Fraassen (1980, especially
Chapter Six) and Achinstein (1983) are classic statements of pragmatic
approaches to explanation. These pragmatic accounts are discussed and
criticized in Salmon (1989). van Fraassen's account is also
discussed in Kitcher and Salmon (1987). De Regt and Dieks (2005) is a
recent defense of what the authors describe as a
"contextual" account of scientific understanding and which
engages with some of the themes in the "pragmatics of
explanation" literature.


## 7. Conclusions, Open Issues, and Future Directions



What can we conclude from this recounting of some of the more
prominent recent attempts to construct models of scientific
explanation? What important issues remain open and what are the most
promising directions for future work? Of course, any effort at
stock-taking will reflect a particular point of view, but with this
caveat in mind, several observations seem plausible, even if not
completely uncontroversial.


### 7.1 The Role of Causation



One issue concerns the role of causal information in scientific
explanation. All of the traditional models considered above attempt to
capture causal explanations, although some attempt to capture
non-causal explanations as well. It is a natural thought (endorsed by
many) that many of the difficulties faced by the models described
above derive at least in part from their reliance on inadequate
treatments of causation.[15]
 The problems of explanatory asymmetries and explanatory irrelevance
described in
 Section 2.5
 seem to show that the holding of a law between *C* and *E*
is not sufficient for *C* to cause *E*; hence not a
sufficient condition for *C* to figure in an explanation of
*E*. If the argument of
 section 3.3
 is correct, a fundamental problem with the *SR* model is that
statistical relevance information is insufficient to fully capture
causal information in the sense that different causal structures can
be consistent with the same information about statistical relevance
relationships. Similarly, the *CM* model faces the difficulty
that information about causal processes and interactions is also
insufficient to fully capture causal relevance relations and that
there is a range of cases in which causal relationships hold between
*C* and *E* (and hence in which *C* figures in an
explanation of *E*) although there is no connecting causal
process between *C* and *E*. Finally, a fundamental problem
with unificationist models is that the content of our causal judgments
does not seem to fall out of our efforts at unification, at least when
unification is understood along the lines advocated by Kitcher. For
example, as discussed above, considerations having to do with
unification do not by themselves explain why it is appropriate to
explain effects in terms of their causes rather than vice-versa.



These observations suggest that insofar as we are interested in causal
forms of scientific explanation progress may require more attention to
the notion of causation and a more thorough-going integration of
discussions of explanation with the burgeoning literature on
causation, both within and outside of
 philosophy.[16]
 A number of steps in this direction have been taken. (cf. Woodward
2003).



Does this mean that a focus on causation should entirely replace the
project of developing models of explanation or that philosophers
should stop talking about explanation and instead talk just about
causation? Despite the apparent centrality of causation to many
explanations, it is arguable that completely subsuming the latter into
the former loses connections with some important issues. For one
thing, causal claims themselves seem to vary greatly in the extent to
which they are explanatorily deep or illuminating. Causal claims found
in Newtonian mechanics seem deeper or more satisfying from the point
of view of explanation than causal claims of "the rock broke the
window" variety. It is usually supposed that such differences
are connected to other features--for example to how general,
stable, coherent with background knowledge a causal claim is. However,
notions like "generality" are vague and not all forms of
generality seem to be connected to explanatory goodness. So even if
one focuses only on causal explanation, there remains the important
project of trying to understand better what sorts of distinctions
among causal claims matter for goodness in explanation. To the extent
this is so, the kinds of concerns that have animated traditional
treatments of explanation don't seem to be entirely subsumable
into standard accounts of causation, which have tended to focus
largely on the project of distinguishing causal from non-causal
relationships rather than on the features that make causal
relationships "good" for purposes of explanation.



Another important question has to do with whether there are forms of
why-explanation that are non-causal. If so, how important are these
are in science and what is their structure? Hempel seems to have
thought of causal explanations simply as those DN explanations that
appeal to causal laws which he regarded as a proper subset of all
laws. Thus on his view, causal and non-causal explanations share a
common structure. Kitcher's unificationist model was also
intended to apply to both causal and non-causal explanations such as
unifying argument patterns in linguistics. More recently, there has
been a great upsurge of interest in whether there are non-causal forms
of explanation, with some claiming they are ubiquitous in science
(e.g., Lange 2017, Reutlinger & Saatsi 2018). If there are such explanations, this
raises the issue of what distinguishes them from causal explanations
and whether there is some overarching theory that subsumes both causal
and non-causal explanations. 


### 7.2 A Single Model of Explanation?



As noted above, one way in which the attempt to develop a single
general model of explanation might fail is that we might conclude that
there are causal and non-causal forms of explanation that have little
in common. But even putting this possibility aside, another
possibility is that explanation differs across different areas of
science in a way that precludes the development of a single, general
model. It is, after all, uncontroversial that explanatory
practice--what is accepted as an explanation, how explanatory
goals interact with others, what sort of explanatory information is
thought to be achievable, discoverable, testable etc.--varies in
significant ways across different disciplines. Nonetheless, all of the
models of explanation surveyed above are "universalist" in
aspiration--they claim that a single, "one size"
model of explanation fits all areas of inquiry in so far as these have
a legitimate claim to explain. Although the extreme position that
explanation in biology or history has nothing interesting in common
with explanation in physics seems unappealing (and in any case has
attracted little support), it seems reasonable to expect that more
effort will be devoted in the future to developing models of
explanation that are more sensitive to disciplinary differences.
Ideally, such models would reveal commonalities across disciplines but
they should also enable us to see why explanatory practice varies as
it does across different disciplines and the significance of such
variation. For example, as noted above, biologists, in contrast to
physicists, often describe their explanatory goals as the discovery of
mechanisms rather than the discovery of laws. Although it is
conceivable that this difference is purely terminological, it is also
worth exploring the possibility that there is a distinctive story to
be told about what a mechanism is, as this notion is understood by
biologists, and how information about mechanisms contributes to
explanation.



A closely related point is that at least some of the models described
above impose requirements on explanation that may be satisfiable in
some domains of inquiry but are either unachievable (in any
practically interesting sense) in other domains or, to the extent that
they may be achievable, bear no discernible relationship to generally
accepted goals of inquiry in those domains. For example, we noted
above that many scientists and philosophers hold that there are few if
any laws to be discovered in biology and the social and behavioral
sciences. If so, models of explanation that assign a central role to
laws may not be very illuminating regarding how explanation works in
these disciplines. As another example, even if we suppose that the
partition into objectively homogeneous reference classes recommended
by the *SR* model is an achievable goal in connection with
certain quantum mechanical phenomena, it may be that (as suggested
above) it is simply not a goal that can be achieved in a non-trivial
way in economics and sociology, disciplines in which causal inference
from statistics also figures prominently. In such disciplines, it may
be that additional statistically relevant partitions of any population
or subpopulation of interest will virtually always be possible, so
that the activity of finding such partitions is limited only by the
costs of gathering additional information. A similar assessment may
hold for most applications of the *CM* model to the social
sciences.