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1
PHYSICAL THEORY
Method and Interpretation
Edited by Lawrence Sklar

1
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Library of Congress Cataloging-in-Publication Data
Physical theory : method and interpretation / edited by Lawrence Sklar.
pages cm
Includes index.
ISBN 978–0–19–514564–9 (hardback : alk. paper) 1. Science—
-Methodology. 2. Science—Philosophy. I. Sklar, Lawrence, editor of compilation.
Q175.P514 2014
501—dc23
2013010048
1 3 5 7 9 8 6 4 2
Printed in the United States of America
on acid-free paper

CONTENTS
List of Contributors vii
Introduction 1
PART ONE
SCI ENTIFIC M ETHOD
1. Scientific Explanation 9
James Woodward
2. Probabilistic Explanation 40
Michael Strevens
3. Laws of Nature 63
Marc Lange

C o n t e n t s
vi
4. Reading Nature: Realist, Instrumentalist, and
Quietist Interpretations of Scientific Theories 94
P. Kyle Stanford
5. Structure and Logic 127
Simon Saunders and Kerry McKenzie
6. Evolution and Revolution in Science 163
Jarrett Leplin
PART TWO
FOU NDATIONS OF PH YSICS
7. What Can We Learn about the Ontology of Space
and Time from the Theory of Relativity? 185
John D. Norton
8. QM∞
229
Laura Ruetsche
9. Statistical Mechanics in Physical Theory 269
Lawrence Sklar
Index 285

LIST OF CONTRIBUTORS
Marc Lange University of North Carolina at Chapel Hill
Jarrett Leplin University of North Carolina at Greensboro
Kerry McKenzie University of Calgary
John D. Norton University of Pittsburgh
Laura Ruetsche University of Michigan
Simon Saunders Oxford University
Lawrence Sklar University of Michigan
P. Kyle Stanford University of California, Irvine
Michael Strevens New York University
James Woodward University of Pittsburgh

1
Introduction
The contributions to this volume provide a survey of two aspects of
contemporary philosophy of science. The pieces in the first part of the
volume give the reader a rich sampling of current work in the general
methodology of science. The pieces in the second part of the volume
offer a sample of the current work exploring the foundations of our most
general and basic science, contemporary physics.
1. SCIENTIFIC METHOD
Three general problem areas have dominated discussion about the
methods of the sciences. How do scientists answer “why?” questions—
that is, what kinds of explanations do the sciences offer of the phenom-
ena in their domains? What is the nature of the broad structures we call
“theories”—how do theories unify science and provide a context for
particular explanations? Finally, what is our rationale for believing or
disbelieving in the explanations and theories proffered by our current,
best available science? These problem areas are explored by the contrib-
utors to part 1 of the volume.
In “Scientific Explanation,” James Woodward explores what the
structure of an explanatory answer to a “why?” question might be in
science. He outlines the important idea that to explain is to place what
occurs under a generalization, exceptionless or statistical, about what
kinds of things occur. Then he notes a number of objections to that
simple notion of explanation. Woodward then explores some propos-
als to supplement this subsumption model of explanation, including the
proposal to demand that explanations in science be unifying and the
proposal that a basic notion of causation is essential to our concept of
explanation.

I n t r o d u c t i o n
2
In “Probabilistic Explanation,” Michael Strevens pursues the struc-
ture of explanations that are statistical or probabilistic further. The
subsumption model of statistical explanation along with some of its
demands (such as maximal specificity) and results (such as the epis-
temic relativity of explanations) are explored. Proposals that causation
is essential even to statistical explanation and that statistical explana-
tions are founded on irreducible stochastic dispositions are explored, as
is the issue of whether or not one can have genuine statistical explana-
tions in a deterministic world. Finally, Strevens suggests that a notion of
“robustness” is a requirement of a probabilistic explanation.
When scientists proffer explanations, they refer us to relevant gen-
eralizations, exceptionless or statistical, that they call “laws of nature.”
But what is a law of nature? This is the subject of Marc Lange’s “Laws of
Nature.” Lange takes up the problems of the distinction between “genu-
ine laws” and “mere accidental generalizations” and of the relation of a
law to the counterfactual conditionals it supports. The notion of “natu-
ral necessities” is discussed, as is the idea that what makes us consider a
generalization a law is the place of that generalization in our scientific
hierarchy of principles. Finally, the role of laws in the “inexact sciences”
is discussed.
Scientists do not stop at the level of laws, however. The laws are fit-
ted into that larger structure of science we call “theories.” One aspect of
theories is that they often posit new entities and properties, and often
these entities and properties are not within the realm of the “observ-
able” as that is naively understood. How should we understand what the
scientist is really claiming when some such theory is proposed? These
are the issues taken up by P. Kyle Stanford in “Reading Nature: Realist,
Instrumentalist, and Quietist Interpretations of Scientific Theories.”
Should we understand the theories to be telling us of the real existence
of a world beyond our powers of observation, a world that explains why
the observable things behave the way they do, or should we rather think
of theories as useful “instruments” for predicting correlations among
the observables but not as positing brand new realms of being? Can we
even make such a distinction in a legitimate way? The epistemological,
semantic, and ontological aspects of those questions are taken up in this
contribution.

3
The nature of theories is taken up from a different perspective by
Simon Saunders and Kerry McKenzie in “Structure and Logic.” One
proposal for understanding how theories work takes the theory to con-
sist of an observational base with a theoretical “structure” imposed on it.
A deep understanding of what this might mean was suggested by Frank
Ramsey many years ago. But how are we to understand the “Ramsey
sentence” reconstruction of a theory? Does the theoretical structure
guide us to real things and features in the world or only to a structural
“embedding” for the genuine, observational structure. Claims concern-
ing the “underdetermination” of the referential structure of the theory
are often taken as conclusive arguments against a realist reading of the
theory. But is this correct? These are some of the issues discussed in this
contribution.
Finally, in this methodological part of this volume there are the
issues of the grounds on which we are justified in accepting or rejecting a
scientific theory. Some crucial issues here are discussed by Jarrett Leplin
in “Evolution and Revolution in Science.” A profound problem that has
been much discussed is whether the changes in science are gradual and
“progressive” or whether instead they are “revolutionary,” with no clear
conceptual path from theory to later theory that we can think of as tak-
ing us ever closer to some final truth. Here Leplin takes the notions of
“evolution” versus “revolution” seriously as they are applied outside
philosophy of science to explore how adequate these terms can be in
describing scientific change.
2. FOUNDATIONS OF PHYSICS
Science comes in a wide variety of forms, and each particular science
raises its own philosophical questions. In the social sciences we find
concepts and explanations that look quite different from the mathemati-
cal specifications of states and formal presentations of laws that we find
in physics. In biology we find the idiosyncratic concepts and explana-
tions that frame the theory of evolution.
One particularly important and philosophically puzzling branch of
scienceisfundamentalphysics.Herewefindthetheoriesthatarealleged

4
to be the broadest and in many ways the deepest in all the sciences. It is
often claimed as well that our assurance of the “correctness” of these
theories is much less controversial than is our epistemic certitude in
other science. Despite this, these theories of foundational physics give
rise to the most intractable and long-lived philosophical quandaries in
all philosophy of science. These foundational theories introduce novel
concepts and ontologies remote from those of everyday language and
experience. The explanations these theories offer are frequently deeply
puzzling as well. Special kinds of probabilistic explanation are intro-
duced. The theories seem to posit “actions at a distance” that are hard
to reconcile with our ideas that causality is local. Many explanations
indeed do not seem “causal” in any ordinary sense at all. It is to these
special problems arising out of the curious nature of these fundamental
physical theories that the contributions in the second part of this vol-
ume are directed.
In “What Can We Learn about the Ontology of Space and Time
from the Theory of Relativity?” John D. Norton takes up the issue of just
what exactly the theories of special and general relativity tell us about
space and time that forces us to revise the ideas we had about these two
“frameworks” of all phenomena in our common sense and in prerelativ-
istic physics. What are the features that are genuinely novel, that follow
from the new theories, that are part and parcel of a literal understanding
of the theories, and that are robust in the sense of not being faced with
contradictory “morals” that can also be drawn from these new theories?
Quantum mechanics notoriously introduced deep puzzles about
what it was telling us about the world. Quantum field theory, the gener-
alization of quantum mechanics developed to deal with the creation and
destruction of elementary particles, introduced its own new interpre-
tative difficulties. These are explored by Laura Ruetsche in “QM∞
.” In
quantum mechanics the so-called commutation operators on the basic
descriptive operators fix the descriptive realm of the theory. How are we
to understand this theory that seems to allow for distinct, incompatible
ways of representing the basic features of the world? Ruetsche explores
some of the answers given to this deep problem.
The first theory of physics in which probabilistic notions played
a constitutive role was statistical mechanics, the attempt to ground

5
the macroscopic theory of heat and temperature on the underlying
atomic constitution of matter. This theory is explored in Lawrence
Sklar’s “Statistical Mechanics in Physical Theory.” Here such issues
as the need for and structure of the basic probabilistic posits of the
theory, the justification of these posits, and the issues concerning
how a time-asymmetrical theory of heat could be consistent with a
time-symmetrical underlying dynamics of the constituents of matter
are discussed. The claim that our very idea that time is asymmetrical
rests on these physical asymmetries is also explored.

9
Chapter 1
Scientific Explanation
JA M ES WOODWA R D
1. INTRODUCTION
Accounts of scientific explanation have been a major focus of discussion
in philosophy of science for many decades. It is a presupposition of such
accounts that science aims at (and sometimes succeeds in) providing
“explanations” and that this activity contrasts in a nontrivial way with
other aspects of the scientific enterprise that are not explanatory (“mere
description” is one obvious candidate for such an alternative). If this
were not true, there would be no distinctive topic of scientific explana-
tion. Further, as a normative matter the philosophical literature assumes
that (at least usually or other things being equal) it is a desirable feature
in a theory that it provide successful explanations—explanation is seen
as a goal of scientific inquiry.
Of course the notion of explanation, as it occurs in ordinary speech,
encompasses many different possibilities (one speaks of explaining the
meaning or a word, how to solve a differential equation, and so on).
However, with some conspicuous exceptions (e.g., Scriven 1962), the
literature on scientific explanation has tended to assume a narrower
focus: very roughly, the task is conceived as providing an account or
“model” of the notion of explanation that is in play when one speaks
of explaining why some particular event or regular pattern of events
occurs. Examples include the explanation of Kepler’s laws in terms of
Newtonian mechanics, the explanation of phenomena like refraction
and diffraction in terms of the wave theory of light, the explanation of

Sci e n t ific M e t h o d
10
the distribution of phenotypic characters in subsequent generations
in terms of the genotypes of parents and the principles of Mendelian
genetics, and the explanation of why some particular person or group of
people developed a certain disease.
In addition, most of the influential accounts of explanation tend to
assume that there is some common abstract structure shared by success-
ful explanations in all areas of science—physics, biology, psychology—
and perhaps in common sense as well. The task of a model of explanation
is to characterize this common structure in a way that abstracts from the
specific content of (or the specific empirical assumptions that underlie)
the different scientific disciplines. Relatedly, advocates of the various
competing models discussed below have also tended to assume that
explanation in the sense they are trying to capture is a relatively “objec-
tive,” audience-independent matter—that is, that the right account of
explanation is not just the banality that different people will find dif-
ferent pieces of information explanatory, depending on their interests
and background beliefs. This assumption is of course closely connected
to the idea that successful explanation is a normatively appealing goal
of science—it is commonly supposed that a highly contextual and
audience-dependent account of explanation is not a good candidate for
this normative role.
2. THE DN MODEL
Contemporary discussion of scientific explanation in philoso-
phy of science has been greatly shaped by the formulation of the
deductive-nomological (DN) model in the middle part of the twentieth
century. Although there are many anticipations and alternative state-
ments of the basic idea, the most detailed and influential version is that
of Carl Hempel (1965b). Assume that we are dealing with a domain in
which the available laws are deterministic. Then, according to the DN
model, scientific explanation has the form of a valid deductive argument
in which the fact to be explained (the explanandum in Hempel’s ter-
minology) is deduced from other premises that do the explaining (the
explanans). (This is the deductive part of the DN model.) These premises

11
Sci e n t ific E x pla n a t i o n
must be true and must include at least one “law of nature” that figures
in the deduction in a nonredundant way in the sense that the deduction
would no longer be valid if this premise were removed. The law premise
is the nomological part of the model, “nomological” being a philosophi-
cal term of art for “lawful.” Commonly, the explanans will include other,
nonlawful premises as well—for example, these may include state-
ments about “initial conditions” and other matters of particular fact.
The explanandum may be either a generalization or itself a claim about
a particular matter of fact, although Hempel tended to focus largely on
the latter possibility.
As an illustration, consider the derivation of the position of a planet
at some future time t from (a) information about its earlier position and
momentum and the position, velocity, and mass of other gravitating
bodies (other planets, the sun) and (b) Newton’s laws of motion and
the Newtonian gravitational inverse square law. The information in
(a) represents initial conditions, and in (b) are laws of nature that figure
nonredundantly in the deduction. The resulting derivation is a sound,
deductively valid argument that constitutes a DN explanation of the
position of the planet.
3. THE IS MODEL
Hempel recognized that in many areas of science generalizations are
statistical rather than deterministic in form. When such generaliza-
tions take the form of statistical “laws,” Hempel (1965a, 376–412)
suggested that we may think of them as providing explanations of
individual outcomes in accordance with a distinctive form of explana-
tion that he calls inductive-statistical (IS) explanation. Formulating
an adequate model of statistical explanation turned out to be a com-
plicated matter and gave rise to a substantial literature, but Hempel’s
underlying idea is straightforward: statistical laws explain individual
outcomes to the extent that they show that, given the prevailing initial
conditions, those outcomes are highly probable. For example, if it is a
statistical law that a particular radium atom has a probability of 0.9 of
decaying within a certain time interval ∆t and the atom does decay in

12
this time interval, then we can provide an IS explanation of the decay
by citing these facts. Similarly, if it is a statistical law that those with
staph infection have a probability of 0.8 of recovering when penicillin
is administered (and certain other conditions are met), we can use this
law to provide an IS explanation of why some particular patient, Jones,
recovers from such an infection.
4. THE ROLE OF LAWS
The requirement that DN explanations be deductively valid seems
clear and straightforward, but how exactly should we understand the
requirement that the deduction contains a law of nature? Hempel
thought of laws as (a proper subset of those) generalizations describ-
ing “regularities” or uniform patterns of occurrence in nature. In the
canonical case, these generalizations have the form of universally quan-
tified conditionals (for any object x, if x is an F, then x is also a G—that
is, all Fs are Gs). A DN explanation of why a is G thus will appeal to this
nomological premise and to the claim that a is F. However, as Hempel
and other defenders of the DN model recognized, not all true general-
izations having this form are naturally regarded as laws; instead some
appear to be only “accidentally” true. To use Hempel’s (1965a) exam-
ple, the generalization “All members of the Greenbury schoolboard for
1964 are bald” (339) seems intuitively to be, even if true, accidentally
so rather than a law. If so, this generalization cannot be used to pro-
vide a DN explanation of why some individual member of that board is
bald—an assessment that certainly conforms to our intuitive judgment
about this case.
As Hempel recognized, it would be desirable not to leave judgments
about whether a true generalization counts as a law or not at an intui-
tive level but instead to provide clear, noncircular criteria that allow us
to distinguish laws and nonlaws in a more principled manner. Various
candidates for these distinguishing criteria are considered by Hempel
(1965a, 335ff.): for example, the suggestions that laws (as opposed
to true generalizations) must contain purely qualitative predicates,
that they must contain “projectable” predicates, and that they must

13
support counterfactuals. Hempel argues, however, that these candi-
dates either fail to distinguish between laws and accidental regulari-
ties or are in other respects unsatisfactory. Although there has been a
great deal of subsequent discussion in the intervening decades and an
approach to the problem that enjoys considerable support (the so-called
Mill-Ramsey-Lewis [MRL] theory, discussed briefly in section 11),
philosophers are still far from a consensus regarding the law-nonlaw
distinction. Indeed there is considerable disagreement even about the
role laws play in science, both in general and in the various particular
sciences, with some philosophers defending a “no-law” view, according
to which there is nothing corresponding to the philosophical notion of
a law of nature in any area of science, including physics and chemistry,
and others claiming that even if there are laws in physics and chemistry,
there are few or no laws in disciplines like biology and psychology.1
The
development of a more adequate account that allows us to distinguish
between laws and other true generalizations (and which gives us some
insight into the role laws play in explanation) thus remains an impor-
tant project for defenders of the DN and other law-based models of
explanation.
In practice, defenders of the DN model have often assumed an infor-
malandverypermissivenotionoflaw,accordingtowhich“laws”include
not just such fundamental physical principles as the Schrödinger equa-
tion but far more local and exception-ridden generalizations from the
special sciences (e.g., Mendel’s “laws” of segregation and independent
assortment) as well as garden-variety causal generalizations, such as
“Aspirin cures headaches” and “If a rock strikes a window hard enough,
the window will shatter.” Thus even this last generalization is often
regarded as capable of serving as a nomological premise in a DN expla-
nation of some particular episode of window shattering. This permissive
conception of law in turn is connected to the close connection between
the DN model and Humean or regularity-based accounts of causation,
which is discussed below.
1. For general disagreements about the role played by laws in science, compare Hempel
1965a and Earman 1993 with van Fraassen 1989 and Giere 1999.

14
5. THE DN/IS MODEL IN CONTEXT
Many interesting historical questions about the DN/IS model remain
largely unexplored. Why did “scientific explanation” emerge when it
did as a major topic for philosophical discussion? Why were the “logi-
cal empiricist” philosophers of science who defended the DN model so
willing to accept the idea that science provides “explanations,” given
the tendency of many earlier writers in the positivist tradition to think
of “explanation” as a rather subjective or “metaphysical” matter and to
contrast it unfavorably with “description” (or “simple and economical
description”), which they regarded as a more legitimate goal for empiri-
cal science? And why was discussion, at least initially, organized around
“explanation” rather than “causation,” since (as we shall observe) it is
often the latter notion that seems to be of central interest in subsequent
debates and since the former notion seems (to contemporary sensibili-
ties) somewhat squishy and ill-defined?
At least part of the answer to this last question seems to be that
Hempel and other defenders of the DN model inherited standard empir-
icist or Humean scruples about the notion of causation. They assumed
that causal notions are only (scientifically or metaphysically) acceptable
to the extent that it is possible to paraphrase or redescribe them in ways
that satisfied empiricist criteria for meaningfulness and legitimacy. One
obvious way of doing this was to take causal claims to be tantamount to
claims about the obtaining of regularities, and it is just this idea that is
captured by the DN/IS model (see below). Part of the initial appeal of
the topic of “scientific explanation” was thus that it functioned as a more
respectable surrogate for (or entry point into) the problematic topic of
causation.2
Another motivation was the interest of Hempel and other
early defenders of the DN model in forms of explanation, such as “func-
tional explanation” (thought to be employed in such special sciences as
biology and anthropology), that were not obviously causal. This also
2. See Cartwright 2004 for a similar diagnosis and for another survey of some of the issues
described here. Sklar 1999 is a very interesting discussion of the historical background
and motivation for the DN model.

15
made it natural to frame discussion around a broad category of explana-
tion (see Hempel 1965c).
6. MOTIVATION FOR THE DN/IS MODELS
Why think that successful explanation must have a DN or an IS struc-
ture? Hempel appeals to two interrelated ideas. The first has to do with
the point or goal of explanation. A DN/IS explanation shows that the
phenomenon to be explained “was to be expected” on the basis of a law,
and “it is in this sense that the explanation enables us to understand
why the phenomenon occurred” (Hempel 1965a, 337). This connection
between explanation and law-based (or “nomological”) expectability
has considerable intuitive appeal; one thing we might hope for from an
explanation is that it diminish our feeling that the explanandum phe-
nomenon is surprising, arbitrary, or unexpected, and showing that the
explanandum follows from a law and other conditions, either for certain
or with high probability, contributes to accomplishing this. In addition,
it is widely (although not universally, see footnote 1) believed that in
some fundamental areas of science, like physics, the discovery of laws
of nature is centrally important. The DN/IS model resonates with this
observation by assigning laws a central role in explanation. We should
note, however, that these remarks leave some obvious questions unad-
dressed. What is so special, from the point of view of explanation, about
nomological expectability? After all, there are other ways, including
appealing to true accidental generalizations, of showing that an out-
come “was to be expected.” Why are not some of these also sufficient for
explanation? What exactly is it that citing a law contributes to successful
explanation? And even if a demonstration of nomological expectability
is necessary for explanation, how do we know that there are not other
requirements that a successful explanation must meet as well?
A second and closely related idea that motivates the DN/IS
model has to do with an assumed connection between causation
and the instantiation of laws or regularities—what we might call
the assumption of the nomological (which in this context means
regularity-based) character of causation. Hempel is of course aware

16
that we often think of explaining an outcome as a matter of providing
information about its causes. However, for the reasons alluded to in
section 5, he is unwilling to take the notion of causation as primitive
or unanalyzed in the theory of explanation. Instead he insists that
causal claims always “implicitly claim” or “presuppose” the existence
of some associated law or laws, according to which the candidate for
cause is part of some larger complex of “antecedent conditions” that
are linked via a regularity to the explanandum phenomenon. The
correct account of causation is thus assumed to be broadly Humean
in the sense that causal claims are to be explicated in terms of the
obtaining of regularities. Generalizations describing these regulari-
ties in turn serve as nomological premises in a DN (or perhaps an IS)
explanation of the effect that we wish to explain, so that all causal
explanation turns out to be, at least implicitly, DN or IS explanation.
The role assigned to nomic expectability thus fits naturally with David
Hume’s story about how experience of the regular association leads to
our learning to expect or anticipate the effect when we observe the
cause (cf. Cartwright 2004).
7. COUNTEREXAMPLES TO THE
DN/IS MODEL
A number of well-known “counterexamples” have been advanced
against both the sufficiency (counterexamples [7.1] and [7.2] below)
and the necessity (counterexample [7.3] below) of the DN/IS require-
ments on explanation. These are commonly presented as examples in
which our “intuitive” or “preanalytic” judgments about whether expla-
nations have been provided seem to differ from the judgments dictated
by the DN/IS model. The common thread running through these coun-
terexamples has to do with the apparent failure of the DN/IS model to
adequately capture how causal notions enter into our judgments about
explanation—that is, the counterexamples appear to be a reflection of
the inadequacy of the simple version of a regularity theory of causation
assumed in the DN/IS model.

17
7.1. Counterexample (7.1)
Many explanations exhibit “directional” or asymmetrical features that
do not seem to be captured by the DN/IS model. From information
about the length l of a simple pendulum and the value of the accelera-
tion g produced by gravity, one may derive its period T by employing
the “law” T l g
= 2π / . This derivation satisfies the DN requirements
and seems intuitively to be explanatory. However, by running the deri-
vation in the “opposite” direction, one may deduce the length l from the
values of T and g and the generalization l gT
= 2 2
4
/ π . This derivation
again satisfies the DN requirements assuming that l gT
= 2 2
4
/ π is also
a law but seems intuitively to be no explanation of why the pendulum
has the length that it does (cf. Bromberger 1966). Other illustrations of
the same basic point are readily produced. From the mass and accelera-
tion of a test particle and the law Ft
= ma, one can deduce the total force
Ft
incident on the particle, but intuitively this is no explanation of why
the particle experiences the force Ft
. Instead the explanation for this is
to be sought in the various component forces that sum to produce Ft
, the
specialized force laws governing these, and so on.
The presence of certain kinds of irrelevant information seems to
undermine the goodness of explanations, even if these satisfy the DN
requirements. To employ a famous example (Salmon 1971), from the
generalization (M) “All males who take birth control pills fail to get
pregnant” and the additional premise that Jones is a male who takes
birth control pills, one can deduce that Jones fails to get pregnant.
Arguably (M) counts as a law according to the usual philosophical crite-
ria employed by philosophers. However, the resulting derivation seems
not to explain why Jones fails to get pregnant. Intuitively, this is because,
given that Jones is male, his taking birth control pills is irrelevant to
whether he gets pregnant. As this example illustrates, a condition that
is nomologically sufficient for an outcome need not be explanatorily rel-
evant to the outcome. Successful explanation seems to require the citing
of relevant conditions (cf. Salmon 1971).

18
Suppose that only those who have latent syphilis (s) develop paresis (p)
but that the probability of p, given s, is low, say, 0.3 (cf. Scriven 1959). If
Jones develops paresis, it seems (again intuitively) explanatory to cite
the fact that he has s. But in doing so we have not (at least explicitly)
cited laws and conditions that make p certain or even highly probable,
which is what the DN/IS model demands.
The reaction of many philosophers to these counterexamples has
been that they show that the DN/IS model fails to adequately capture
the role of distinctively causal information in explanation.3
Thus the
directional features that seem to be omitted from the DN/IS model
appear to be closely connected to (if not identical with) the asymmetry
of causation: the length of the pendulum is one of the causes of it having
the period that it does and not vice versa. It is because it is legitimate to
explain effects in terms of their causes but not vice versa that it is appro-
priate to explain the period in terms of the length and not vice versa.
Counterexample (7.2) seems to trade on the fact point that (barring
complications having to do with causal preemption and overdetermina-
tion) causes must make a difference to their effects. Taking birth con-
trol pills does not make a difference to whether males become pregnant
(they will not become pregnant whether or not they take birth control
pills) and in consequence does not explain this outcome. More gener-
ally, counterexample (7.2) shows that a factor can be (or can be part of)
a nomologically sufficient condition for an outcome and yet not cause
it. With respect to counterexample (7.3), we seem willing to accept it as
explanatory (to the extent that we do), because it is natural to think of
latent syphilis as a cause of paresis. Counterexample (7.3) suggests that
a factor can cause an outcome (and hence, arguably, explain it) without
being nomologically sufficient for it (or even rendering it probable).
Assuming this analysis is correct, it appears that the way forward (or
at least a large part of the way forward) is to focus more directly on the
role of causal considerations in explanation and on the development of
3. See Salmon 1989; Woodward 2003; and Cartwright 2004, among others, for this
diagnosis.

19
a more adequate theory of causation. To a large extent (although by no
means entirely) this is the path taken in subsequent philosophical dis-
cussion—particularly by Wesley Salmon in his statistical relevance and
(subsequently) causal mechanical models of explanation.
8. THE SR MODEL
Salmon’s (1971) statistical relevance (SR) model departed from the
DN/IS model in a number of major respects. Most fundamentally, the
SR model employed a very different formal/mathematical framework—
probabilitytheoryratherthanthefirstorderlogiconwhichDNtheorists
relied. In this respect it followed a general trend in philosophy of sci-
ence, which had become manifest by the late sixties and early seventies,
of employing ideas from probability theory (rather than logic) to expli-
cate important concepts—evidence, confirmation, cause, explanation,
and so on. The SR model also drew on a very different guiding idea about
explanationfromtheideaonwhichDNtheoristsrelied—thisbeingthat
explanation requires furnishing causal or explanatorily relevant infor-
mation about the explanandum and that (as counterexamples [7.1] and
[7.2] above illustrate) this is not just a matter of exhibiting a condition
that is nomologically sufficient for (or that probabilifies) the explanan-
dum. Probability-related notions, such as independence/dependence
and correlation, turn out to be more successful (even if not entirely sat-
isfactory) at capturing the notion of relevance than logic-based notions.
The details of the SR model are complex (and, in any case, available
elsewhere),4
but the underlying strategy is to assume that the variables
that figure in the explanation are random variables with a well-defined
joint probability distribution given by a probability function P and then
to try to capture the relevance relationships that are essential to expla-
nation by means of so-called statistical relevance and screening off (condi-
tional independence and dependence) relationships. A factor A is said
to be statistically relevant to another factor B in circumstances C if and
4. In addition to Salmon 1971, see Salmon 1984 and 1989 for exposition of the SR model.

20
only if either P(B/A.C) ≠ P(B/C) or P(B/-A.C) ≠ P(B/C). D screens off A
from B if and only if P B A C D P B D C
/ . . / .
( )= ( ). Very roughly, the intu-
ition underlying the SR model is that we explain an outcome by assem-
bling information about factors that remain statistically relevant to it as
we conditionalize on other suitable factors,5
together with the statistical
relevance relationships themselves, as reflected in the underlying prob-
ability distribution. We do not include statistically irrelevant factors.6
Moreover, according to Salmon, such information about statistical rel-
evance relationships tells us about the causes of phenomena we wish to
explain. Thus although the SR model presented as a theory of explana-
tion, it in effect assumes a theory of causation according to which causal
relationships can be fully captured by or reduced to facts about rela-
tionships between conditional probabilities. In this respect Salmon’s
assumed theory of causation continues to satisfy broadly Humean con-
straints, even though it is different from the account of causation tacitly
assumed in the DN model.
To illustrate, return to the birth control pills of counterexample (7.2).
On Salmon’s analysis, whether or not Jones takes birth control pills is
not statistically relevant to (and hence, according to the SR model, does
not explain) whether he becomes pregnant, because P(Fails to Become
Pregnant / Is Male. Takes Birth Control Pills) = P(Fails to Become Pregnant
/ Is Male) and P(Fails to Become Pregnant / Is Male. Does Not Take Birth
Control Pills) = P(Fails to Become Pregnant / Is Male). These statistical
relationships capture or correspond to the fact that taking birth control
pills does not cause failure to become pregnant in males. By contrast,
P Paresis LatentSyphilis P Paresis
/ ( )
( )≠ , and this would presumably
remain true as we conditionalize on other appropriate factors W; hence
latent syphilis remains relevant to (and causes and explains) paresis. In the
SR model, in contrast to the DN/IS model, it is thus possible to explain
low probability events by exhibiting factors that are statistically relevant to
their occurrence.
5. For an attempt to characterize what “suitable” means, see Salmon 1984.
6. The full details of the SR model are considerably more complex. See Salmon 1984,
36–37.

21
The SR model contains a number of important insights about
explanation, including an appreciation of the central importance
of the notion of causal/explanatory relevance. However, there is an
important respect in which the model is inadequate: as philosophers
(including Salmon himself) soon recognized, it is not possible to fully
capture causal relationships in terms of statistical relevance relation-
ships. Instead the causal relationships among a set of variables are
greatly underdetermined even by full information about the statisti-
cal relevance relationships among them. To the extent that it is true, as
the SR model assumes, that explaining an outcome involves providing
information about its causes, the model rests on an inadequate theory
of causation.
The failure of statistical relevance relations to fully capture causal
relationships is reflected in the familiar adage that “correlation is not
causation.” As an illustration, consider the following three (different)
causal structures: in (8.1) C is a common cause of both A and B, with
no other causal connections present; in (8.2) A causes C, which in turn
causes B; in (8.3) B causes C, which causes A. (Here A, B, and C are ran-
dom variables rather than names for factors or properties.) If we make
assumptions like Salmon’s about the relationship between causation
and screening off relations, then all three structures imply exactly the
same independence and dependence relationships. In all three struc-
tures A and B are unconditionally dependent but become independent
conditional on C, A and C and B and C are dependent, and so forth. In
some cases, it may be possible to appeal to some other considerations
(e.g., temporal order) to distinguish among (8.1), (8.2), and (8.3),
but statistical relevance relationships alone will not accomplish this.7
Moreover, there are good reasons to think that even when statistical
relevance relationships are supplemented by temporal considerations,
they will not always allow us to distinguish among alternative causal
structures.
7. For additional relevant discussion in the context of probabilistic theories of causation,
see Cartwright 1983. Nancy Cartwright was one of the first philosophers to explicitly
recognize the underdetermination of causal facts by statistical information. Formal
results about the extent of this underdetermination are in Spirtes et al. 2000.

22
9. THE CM MODEL
In later work Salmon (e.g., 1984) in effect recognized this and devised
a new account of explanation—the causal/mechanical (CM) model—
that attempts to capture the “something more” that is involved in cau-
sation besides mere statistical relevance relationships. One of the key
components of the CM model is the notion of a causal process. This is a
physical process, such as the movement of a billiard ball or light wave
through space, that has the ability to “transmit a mark.” This means
that if the process is altered in some appropriate way (e.g., white light
is passed through a red filter), this alteration will persist in the absence
an additional external interference. More generally, causal processes
have the ability to propagate their own structures from place to place
and over time, in a spatiotemporally continuous way, without the need
for further outside interactions. Typically, if not always, this involves
the transfer of energy and momentum between successive stages of
the process. Causal processes contrast with pseudoprocesses, which
lack these characteristics. The successive positions of a spot of light on
the surface of a dome that is cast by a rotating search light represent a
pseudoprocess. If we “mark” the light at one position by temporarily
interposing a red-colored filter between the light source and the sur-
face, the spot of light will be colored at that point, but this mark will
not persist for successive positions of the light spot unless we continu-
ously move the filter in the appropriate way. The spot thus lacks the
ability to transmit its own structure without outside supplementation.
One distinguishing feature of causal processes is that they are sub-
ject to an upper limit on their velocity of propagation—c, the speed
of light. By contrast, pseudoprocesses may move at arbitrarily high
velocities.
A causal interaction occurs when two causal processes (spatiotempo-
rally) intersect and modify each other, as when a collision between two
billiard balls results in a change in momentum of both. In general causal
processes but not pseudoprocesses are the carriers of causal influence.
For the CM model, the difference among the structures (8.1), (8.2), and
(8.3) is thus that they involve different causal processes, something that
might be revealed in their different implications for the persistence of

23
marks or in different patterns of spatiotemporal connectedness, despite
their satisfying the same statistical relevance relationships. It is in this
waythattheCMmodelattemptstocapturethe“somethingmore”thatis
involved in causation, over and above statistical relevance relationships.
According to the CM model, an explanation of some phenomenon
E involves tracing the causal processes and interactions (or some por-
tion of these) that lead up to E. In still more recent work Salmon (e.g.,
1994, 1997) retained this basic picture but attempted to characterize
the notion of a causal process in terms of conservation laws rather than
in terms of markability, an approach to causation that has been extended
by others working in the physical process view of causation, such as
Philip Dowe (2000).
The CM model represents an attempt to characterize causation in,
as it were, physical or material (or as Salmon says, “ontic”) terms rather
than in terms of the more formal or mathematical relations emphasized
in the DN/IS and SR models. It purports to be a model of causation as it
exists and operates in our world rather than a model that aims to char-
acterize what causation must involve in all logically possible worlds.
(Perhaps in some logically possible worlds causation does not involve
spatiotemporally continuous processes and the transfer of energy and
momentum, but it does in ours.) The paradigmatic application of the
CM model is simple mechanical systems, like colliding billiard balls,
in which causal influence is transmitted by spatiotemporal contact and
which involve the transfer of quantities like momentum and energy that
are locally conserved. The model nicely captures the sense that many
people have that there is something especially intelligible or explana-
torily satisfying about such mechanical interactions (and the theories
that describe them) and something fundamentally unsatisfying from
the point of view of explanation about theories that postulate action at
a spatiotemporal distance, nonlocal causal influences, and so on. (On
the other hand, as we note below, it is also arguably a limitation of the
model that its application appears to be limited to theories that pos-
tulate causal relations that do not explicitly involve spatio-temporally
continuous processes.) Moreover, regardless of what one thinks about
the adequacy of Salmon’s various characterizations of causal processes,
it also seems uncontroversial that the contrast between causal and

24
pseudoprocesses is a real one, that it has considerable scientific impor-
tance, and that when the notion of tracing causal processes is appli-
cable (see below), these have, in comparison with pseudoprocesses, a
privileged role in explanation. Finally, the CM model deserves credit
for drawing attention to the importance of the notion of “mechanism”
in explanation—a notion that until recently has been unexplored by
philosophers of science, despite the fact that in many areas of science,
including in particular the biomedical sciences, explaining a phenom-
enon is often seen as a matter of elucidating the operation of the mecha-
nisms that produce that outcome.8
(It is of course a further question
whether the CM model provides a useful account of what a mechanism
is in contexts outside physics.)
Despite these attractions, the CM model, like its predecessors, suf-
fers from some serious limitations. First and rather ironically, given that
it was Salmon who first emphasized the importance of this notion, the
CM model fails to adequately capture the role of causal relevance in
explanation. The reader is referred to Hitchcock 1995 and Woodward
2003 for details, but the basic point is quite simple: information about
the presence of a connecting process between C and E need not tell us
anything about how, if at all, changes in C would affect changes in E, and
it is this latter information that is crucial to assessments of relevance. For
example,whenanordinaryrubberballisthrownagainstabrickwalland
then bounces off, there is a connecting causal process from the thrower
to the wall, but the existence of this process is not (in ordinary circum-
stances) causally or explanatorily relevant to whether the wall continues
to stand up (Hausman 2002). This is because (again in ordinary circum-
stances) a thrown ball will not transfer enough momentum to the wall
to knock it down, so whether or not it is thrown makes no difference to
this feature of the wall. In other words, whether or not the wall remains
standing depends on the magnitude of the momentum transferred, as
becomes apparent if we think instead of the impact of a high-velocity
cannonball. The information that the trajectory of the ball is a causal
process does not convey this.
8. For recent discussions of the notion of a mechanism, see Machamer et al. 2000 and
Bechtel and Abrahamsen 2005.

25
A second issue concerns the scope of the CM model. As we have
noted, the most straightforward application of the CM model is to sim-
ple mechanical systems involving macroscopic or classically behaved
objects. The implications of the model for other sorts of systems,
those studied both in physics and elsewhere, are less straightforward
and arguably less intuitive. Consider an action at a distance theory like
Newtonian gravitational theory as originally formulated by Newton.
This theory does not trace continuous causal processes and interac-
tions. A literal reading of the CM model thus seems to imply that this
theory is entirely unexplanatory, despite its many other virtues. Or
consider standard (nonrelativistic) quantum mechanical treatments of
such phenomena as nonclassical electron tunneling through a poten-
tial barrier. When one writes down and solves the Schrödinger equa-
tion for such a system, finding a nonzero probability that the electron
may be found on the other side of the barrier and thus (one might sup-
pose) “explaining” barrier penetration (or at least its possibility), this
does not seem to involve tracing spatiotemporally continuous causal
processes. Again, what does the notion of assembling information
about causal processes and interactions amount to when one is deal-
ing with systems with many interacting parts, such as a gas containing
1023
molecules or complex systems of the sort studied in neurobiology
or economics? Whatever understanding the behavior of such systems
involves, it must consist in more than just recording information about
individual episodes of energy/momentum transfer via spatiotemporal
contact (between, e.g., individual molecules in the case of the gas);
instead it must involve finding tractable modes of representation that
abstract from such details and represent (the relevant aspects of) their
aggregative or cumulative impact. Such models may provide mechani-
cal explanations in some broad sense that involve showing how the
behavior of aggregates depends on features of local interactions among
their parts, but this will usually involve going well beyond the very
specific constraints on mechanical explanation imposed by Salmon’s
theory. Providing an account of explanation that remains in the broad
spirit of the CM model but applies to such complex systems should be
an important item on the agenda of those who wish to extend Salmon’s
work.

26
10. UNIFICATIONIST MODELS
These models draw their inspiration from the idea that there is a close
connection between the extent to which a theory is explanatory and the
extent to which it provides a unified treatment of a range of superficially
different phenomena. This is a very intuitively attractive idea—unification
is often regarded as an important scientific achievement or goal of inquiry.
(Consider Newton’s unification of terrestrial and celestial mechanics, the
unification of electricity and magnetism begun by James Clerk Maxwell
and perfected in the special theory of relativity, the unification of the elec-
tromagnetic and weak forces by Steven Weinberg and Abdus Salam, and
so on.) Of course in developing this idea in a more systematic way, much
will turn on exactly how the notion of unification is cashed out. In philoso-
phy of science one of the earliest influential formulations of this approach,
that of Michael Friedman (1974), understood unification as a matter of
deriving a wide range of different explananda from a much “smaller” set of
independently acceptable assumptions. Friedman’s proposal was shown
to suffer from various technical difficulties by Philip Kitcher (1976), who
went on to develop his own version of the unificationist account in a series
of influential essays (see especially Kitcher 1989).
Kitcher’s basic idea is that successful unification is a matter of repeat-
edly using the same small number of argument patterns (that is, abstract
patterns that can be instantiated by different particular arguments) over
and over again to derive a large number of different conclusions—the
fewer the number of patterns required, the more stringent they are in the
sense of the restrictions they impose on the particular arguments that
instantiate them, and the larger the number of conclusions derivable via
them, the more unified the associated explanation. Thus Kitcher’s model
resembles the DN model in taking explanation to be deductive in struc-
ture but adds the further constraint that we should choose the deductive
systemization of our knowledge that is most unifying among competing
systemizations—it is the derivations provided by this systemization that
are the explanatory ones.
Kitcher further claims that this additional constraint about unifica-
tion allows us to avoid the standard counterexamples to the DN model,
such as those described in section 7 above. Very roughly, this is because

27
the unexplanatory derivations associated with the counterexamples turn
out to use argument patterns that are less unified than the competing
argument patterns that license derivations corresponding to our usual
explanatory judgments. For example, according to Kitcher, derivations of
factsaboutcauses(thelengthofapendulum)fromfactsabouteffects(the
period of the pendulum) involve argument patterns and systemizations
that are less unified than derivations that proceed in the opposite direc-
tion, and for this reason the latter are explanatory and the former are not.
More generally, Kitcher (1989, 477) claims that “the ‘because’ of cau-
sationisalwaysderivativefromthe‘because’ofexplanation.”Thatis,unifi-
cationiswhatisprimary;thecausaljudgmentthat,forexample,thelength
of a pendulum causes its period is simply a consequence or reflection of
oureffortsatunification.Therearenoindependentfactsaboutcausalrela-
tionships in nature to which our efforts at explanatory unification must be
adequate. In this respect Kitcher returns to the original DN idea that the
notion of explanation is more fundamental than the notion of causation.
Despite the intuitive appeal of the idea that there is a close connec-
tion between explanation and unification, providing a characterization of
unification that captures our intuitive explanatory judgments has turned
out to be far from straightforward. Part of the problem is that there are
many different possible kinds of unification and only some of these seem
to be connected to explanation—that is, there are nonexplanatory as well
as explanatory unifications.9
For example, one sort of “unification” con-
sists in the use of the same mathematical structures and techniques to
represent very different physical phenomena, as when both mechanical
systems and electrical circuits are represented by means of Hamilton’s or
Lagrange’s equations. This unified representation allows for the derivation
of the behavior of both kinds of systems, but it would not be regarded
by physicists as giving a common unified explanation of both kinds of
systems or as an explanatory unification of mechanics and electromagne-
tism. Exactly what the latter involves is not entirely clear, but arguably it
requires a demonstration that the same physical mechanisms or principles
(perhaps more specifically the same forces) are at work in producing both
9. For a systematic development of this point and a far more detailed exploration of the
relationship between explanation and unification, see Morrison 2000.

28
kinds of phenomena. (This after all is what is achieved by the Newtonian
unification of terrestrial and celestial gravitational phenomena and by the
unification of electricity and magnetism.) A closely related observation
is that the Friedman/Kitcher conception of unification seems at bottom
to be simply a notion of data compression or economical description—
of finding a characterization of a set of phenomena or observations that
allows one to derive features of them from a minimal number of assump-
tions. Many systems of classification (of biological species, diseases,
personality types, etc.) seem to accomplish this without providing what
seems intuitively to be explanations. Or to put the matter more cautiously,
if they do provide explanations in some sense, these have a very different
feel from the sorts of unifications provided by Newton and Maxwell.
A closely related observation, developed by several authors, is that it
simply does not seem to be true that considerations of comparative uni-
fication always yield familiar judgments about causal asymmetries and
causal irrelevancies—these seem to have (at least in part) an independent
source.10
Consider a theory, such as Newtonian mechanics, that is deter-
ministic in both the past to future and the future to past directions and
that contains time-symmetrical laws. It is far from obvious that derivations
in such a theory that run from the future to the past—for example, from
information about the future positions of the planets to their positions in
the past—are any more or less unified than derivations that run from the
past to the future, even though our intuitive judgments about preferred
explanatory direction favor the latter explanations (cf. Barnes 1992).
Considerations such as these suggest a possible alternative view about the
role of unification in explanation: judgments about causal or explanatory
dependence and about whether the same sort of dependence relationship
is at work in different situations have some other source besides our efforts
at unification. However, once we make such judgments, we can then go
on to ask about the extent to which different phenomena are the result of
the operation of the same mechanisms or dependency relations—to the
extent that this is so, we have a unified explanation. Something like this
“bottom up” picture of the role of unification in explanation is suggested
10. For details, see Barnes 1992 and Woodward 2003.

29
by Salmon (1989) and seems to fit at least some historical examples of
successful unification.11
Even with this picture, however, there are puzzles.12
Biological
researchers originally worked out the mechanism of long-term potentia-
tion or LTP (thought to be centrally involved in many forms of learning)
intheseasnail,Aplysia.Itwasthenfoundthatthesamemechanismunder-
lies learning in many other biological species, including humans. Is this
an example of explanatory unification? It certainly seems to conform to
Kitcher’s intuitive picture of unification—different phenomena (aspects
of learning in many different biological species) are shown to result from
the operation of the same fundamental mechanism.
On the other hand, how exactly should we understand the explana-
tory advance (if that was what it was) that was achieved? There is a nat-
ural thought that how well or badly the original account explains LTP
in Aplysia should not depend on whether or not the same account also
applies to other species. (Finding that this explanans applies to other spe-
cies does not after all alter its content in any way. And if, contrary to actual
fact, we were to find that the account applied only to Aplysia, with the
explanation of long-term potentiation in other species taking a rather dif-
ferent form, why does this show that the account is any less good as an
explanation of LTP in Aplysia.) Of course when we find that the account
applies more widely, there is an obvious sense in which there is an explana-
tory advance—we now know the explanation of LTP in other species as
well. But this seems to be a matter of being in a position to explain new
explananda rather than (as Kitcher’s discussion seems to suggest) having a
better explanation of our original explanandum.13
We also learn about new
connections and relationships that were not previously understood, but
11. For an argument that this is the case for Newton, see Ducheyne 2005.
12. For related observations and additional discussion of some of the points that follow, see
Woodward 2003 and Strevens 2007.
13. Suppose the explanatory improvement that takes place under unification consists
just in our being able to explain new phenomena. Someone who is a skeptic about the
explanatory virtue of unification could then argue that a theory that is not unified with
our original theory could equally well explain these new phenomena. The moral seems
to be that for Kitcher’s story to work, the virtue of a more unified theory cannot be just
that it enables us to explain things that were not previously explained. It must be that
the unified theory explains things better than the disunified competitor.

30
again it is not entirely clear that this is an additional explanatory achieve-
ment rather than something else.
In this last connection it is worth noting that often one advantage
or virtue of a relatively unified theory over less unified rivals is eviden-
tial: when a theory explains a range of different phenomena in terms of
a single (or small set) of mechanisms or principles, there is, other things
being equal, less room for “overfitting” in comparison with a theory that
is allowed to resort to many disparate mechanisms. The requirement that
a theory explain many different phenomena by reference to the same
assumptions allows us to use those phenomena to sharply constrain the
features of the postulated explanans and to bring evidence from many
different sources to bear on it. This advantage is lost if each phenomenon
is explained in a different way by reference to different assumptions. This
observation prompts the thought that while it indeed may be a virtue or
a good feature in a theory that it is unified, the virtue in question may
have more to do with evidential support than with explanation.14
On the
other hand, the explanatory and evidential virtues may not be as sharply
separable as this last remark assumes, especially given the rather elastic
character of the notion of explanation. My rather inconclusive assess-
ment is thus that although it is very plausible that explanation and uni-
fication are interconnected in important ways, more work needs to be
done to characterize the kind of unification that is important for expla-
nation and to spell out just what it is that unification gives us.
11. CONCLUSION
I conclude with some more general remarks about the current status of
the topic of scientific explanation and possible directions for future work.
11.1. The Fate of the DN Model
The counterexamples to the DN model surveyed in section 7. are
decades old and very widely known. Nonetheless, this model has shown
14. See Sober 2002 for an argument to this effect.

31
remarkable staying power. Although I know of no systematic surveys
on the matter, my impression is that many philosophers (particularly
in philosophy of physics and in areas of philosophy outside philosophy
of science, including metaphysics) continue to believe that there must
be something broadly right about the underlying idea of the DN model,
even if the details may need to be tweaked in various ways. By contrast,
philosophers of science who focus primarily on scientific disciplines
other than physics, such as biology and the social sciences, tend to be
more skeptical of the DN model.
Why is this? I conjecture that several factors are at work. First, it
seems undeniable that in physics many paradigmatic textbook examples
(examples that it seems natural to regard as cases of explanation) involve
writing down a set of equations taken to describe some system of inter-
est (where these equations are plausibly regarded as describing laws of
nature), making assumptions about initial and boundary conditions,
and then exhibiting a solution to the equations that corresponds to some
behavior of the system one wants to understand. Illustrations include
derivations of expressions for the fields set up by charged conductors
of various shapes from the laws of classical electromagnetism and then
derivations of the motions of charged particles within these fields;
the various solutions to the field equations of general relativity (that
is, derivations of features of the metrical structure of space-time from
information about the mass-energy distribution within some region of
space, various choices of boundary conditions, and the field equations
themselves), such as the Schwarzschild solution, the Kerr solution, and
so on; and the use of the Schrödinger equation to model various proto-
typical examples in elementary quantum mechanics (charged particle
in a potential well, charged particle penetrating a potential barrier, and
so on).
Each of these exercises seems to involve deriving a description of the
behavior we are trying to understand from premises that include laws of
nature—that is, it looks as though they use just the ingredients that fig-
ure in a DN explanation. Of course it is a jump to move from this obser-
vation to the conclusion that the DN model is the full story about why we
find such derivations explanatory—that is, that such explanations work
just by showing that their explananda are nomologically expectable and

32
that nothing else about these derivations contributes to their explana-
tory import. Nonetheless, the ubiquity of deductive structures involv-
ing laws as premises contributes to many people’s sense that the DN
model corresponds to something real in scientific practice, at least in
physics and perhaps in other areas of science where similar structures
seem to play a role. By contrast, mathematical derivations from highly
general principles seem to play a far less central role in disciplines like
molecular biology and neurobiology (at least in their present stage of
development). It is thus not surprising that the DN model seems less
obviously applicable in such disciplines.
11.2. The Role of Causation
A second set of considerations bearing on the status of the DN model
and the assessment of the various competing accounts of explanation
has to do with the role of causal considerations in explanation. As we
have seen, many of the standard counterexamples to the DN model
seem to show that the model fails to incorporate certain commonsense
causal distinctions (having to do with, e.g., the direction of causation).
It is important to emphasize that this is not just a matter of the DN model
failing to generate judgments that are in accord with our so-called intu-
itions. In many areas of inquiry (biomedicine, psychology, economics)
the correct identification of causal direction and of relations of causal
relevance is a central methodological concern. Assuming, for example,
that there is a correlation between changes in the money supply M
and economic output O, it is very important from the point of view of
economics whether this correlation arises (i) because M causes O, (ii)
because O causes M, or (iii) for some other reason. Among other con-
siderations, this matters because these different claims about causal
direction have very different implications, manipulation, and control. If
(i) is correct, the Federal Reserve should be able, at least in principle, to
manipulate O by intervening with the money supply; not so if (ii) is the
correct analysis. From the perspective of a discipline like economics, it
is hard to take seriously the idea that the difference between (i) and (ii)
is somehow unreal or unimportant. So an account of explanation that is
insensitive to the difference between (i) and (ii) will seem inadequate to

33
economists and philosophers of economics and similarly for researchers
in such other disciplines as biology and psychology. This is another rea-
son philosophers who focus primarily on these disciplines often find it
most natural to think of explanation as having to do with the identifica-
tion of causal relationships and causal mechanisms rather than with the
instantiation of DN-like structures.
It is arguable that these issues about the role of causal considerations
in explanation look rather different if one takes the paradigmatic sci-
ence to be fundamental physics. Although the topic deserves a far more
detailedtreatmentthanIcangiveithere,thereisawidespread(although
by no means universal) belief among philosophers of physics that a rich
and thick notion of causation of the sort found in common sense (or at
least important features of this notion) fail to apply in a straightforward
or unproblematic way in certain fundamental physics contexts or at
least that this causal notion is not “grounded” simply in facts about fun-
damental physical laws. (For various views of this character although
they differ among themselves in important ways see, e.g., Russell 1913;
Field 2003; Norton 2007, and for additional discussion, see Woodward
2007.) I take no stand here on whether this belief is correct but merely
observe that to the extent that one regards it as correct, the failure of the
DN model to fully incorporate commonsense causal distinctions may
look like a virtue of that model or at least not a serious defect.
One of the clearest illustrations of this point is provided by the asym-
metry of the causal relationship. I have suggested that in disciplines
like biology and economics causal claims that reflect this asymmetry
are pervasive and, to the extent that they can be tied to asymmetries of
manipulation and control, are often taken to be unproblematic. Both the
ultimate physical origin(s) of such asymmetries (and whether indeed
there is a unified story to be told about their origin) and the possibility
that their range of application may be limited in some way are not issues
thatfallwithinthepurviewofthesedisciplines.Bycontrast,issuesofthis
sort do of course arise in fundamental physics and seem to have implica-
tions for how we should think about fundamental physical explanation
and the role of causal considerations in such explanation. To take only
one of the most obvious possibilities, suppose that the causal asymme-
tries have their origin in thermodynamic asymmetries in some way (cf.

34
Albert 2000; Kutach 2007). Then one might well wonder whether causal
asymmetries have any application to sufficiently simple microscopic sys-
tems governed by time-symmetrical laws that lack a well-defined direc-
tion of entropy increase. Perhaps for such systems there are symmetrical
relations of dependence, grounded in physical law, but no objective basis
for picking out one event as asymmetrically related to another as cause to
effect. If so, a model of explanation that applies to such systems presum-
ably should not incorporate directional features. My point is not that we
should regard this last claim as uncontroversially correct but rather that
if one takes it to be correct (or at least takes it to be a serious possibility),
then the failure of a model of physical explanation to incorporate com-
monsense considerations about causal asymmetries need not automati-
cally be regarded as a fundamental defect. One might well take the view
that until we have a better understanding of the physical basis and sig-
nificance of the causal asymmetries we see in everyday life (and relatedly
therangeofsystemsinwhichtheappropriatephysicalbasisfortheasym-
metries is present), it is premature to insist that these asymmetries must
be incorporated into a model of explanation that is applicable to funda-
mental physics. Similarly for other features of commonsense causal rea-
soning. Thus one development that would contribute to further progress
in connection with the topic of scientific explanation is a better under-
standing of the legitimate role (if any) that causal considerations play in
fundamental physics. Relatedly, those who are skeptical about the role of
causal considerations in fundamental physics should spell out the impli-
cations of their views for physical explanation.
11.3. Laws Revisited
We noted above that there is considerable disagreement about the crite-
ria that distinguish laws from other true generalizations and about the
role of laws in the various scientific disciplines. This in turn raises some
obvious and still unresolved questions for the DN and other law-based
models of explanation. Putting aside the view that the whole notion of a
law of nature rests on a confusion, it might appear that in physics at least
there often will be agreement in particular cases about whether gener-
alizations count as laws, even if we lack an adequate general theory of

35
lawfulness: the Schrödinger equation and the Klein-Gordon equation
count as laws if anything does, and Bode’s “law” does not. However, in
the absence of a more adequate general theory, a nontrivial difficulty
arises when one tries to apply the DN and other law-based models to
sciences like biology, psychology, and economics. Virtually everyone
agrees that these disciplines contain true causal generalizations that
can figure in explanations, but there is a great deal of controversy about
whether these generalizations should be regarded as laws. For example,
the “laws” of segregation and independent assortment in Mendelian
genetics have well-known exceptions and appear to be contingent on
the course of evolution in the sense that these generalizations would not
apply to biological organisms even to the extent that they do had those
organisms been subject to sufficiently different selective pressures (cf.
Beatty 1997). Does this mean that we should not think of these general-
izations as laws? Philosophers of biology have been sharply divided on
this question, and one finds a parallel debate concerning the status of
the generalizations that figure in the other special sciences.15
Taken literally and strictly, the DN and other nomothetic models
seem to imply that scientific disciplines that do not contain laws do
not provide explanations. If this conclusion is unacceptable, then there
seem to be two remaining possibilities: (i) either there are laws in the
special sciences after all (and we need to provide an account that iden-
tifies such laws and explains how to distinguish them from nonlaws),
or else (ii) we need to formulate an alternative to law-based models of
explanation that allows the special sciences to furnish explanations and
causal knowledge even though they do not contain laws. With respect
to (i), the challenge, in my opinion, is to provide an account that both
(a) includes in the category of laws those generalizations that are plau-
sibly regarded as explanatory and (b) at the same time does not include
nonexplanatory generalizations. Most current proposals seem to fail
along dimension (b).16
15. For biology, see, for example, Beatty 1997; Brandon 1997; Sober 1997; Mitchell 2000.
For the social sciences, see Kincaid 1989.
16. For example, it is arguable that this is true of current attempts to show that the gener-
alizations of the special sciences are “ceteris paribus” laws. See Earman et al. 2002 and
Woodward 2002.

36
I noted above that to the extent that we lack a compelling account of
what laws are we will also lack insight into whether (and, if so, why) laws
are required for explanation. In this connection it is worth considering
the account of laws that is currently regarded as the most promising by
many philosophers, the MRL theory. According to this theory, laws are
those generalizations that figure as axioms or theorems in the deductive
systemization of our empirical knowledge that achieves the best com-
bination of simplicity and strength (where strength has to do with the
range of empirical truths that are deducible).17
If we ask about the model
of explanation with which this treatment of laws most naturally fits, the
answer seems to be unificationist approaches: if laws are generalizations
that play a central role in the achievement of simple (and presumably
unified) deductive systemizations, then by appealing to laws in expla-
nation we achieve explanatory unification—this makes it intelligible
why it is desirable that explanations invoke laws.18
If an account along
these lines could be made to work (that is, if we had a good defense of
the MRL theory and of the idea that explanation involves unification),
then we would have the sort of integrated story about laws and expla-
nation that I claimed was largely lacking in the DN account—a story
about what laws are that is directly connected to a story about the point
of explanation. I do not claim that the story just sketched is unproblem-
atic—we have already noted that there are difficulties with the unifica-
tionist model, and there are also problems with the MRL theory of laws
as well19
—but it does represent an exemplar of the sort of integrated
story that advocates of law-based models should be attempting to tell.
In this connection it is also worth asking what the implications of the
MRL account are for the lawfulness of the generalizations of the special
sciences. In my view, it is far from obvious that the MRL account yields
17. For a statement of the basic idea, see Lewis 1973.
18. Notice, though, that although this rationale yields an account of why it is desirable to
construct explanations appealing to laws (when this is possible), it is not clear that it
yields the result that explanation always requires laws. Perhaps there are generalizations
that unify sufficiently to qualify as explanatory, according to the unificationist account,
but do not count as laws according to the MRL account. In this connection it is interest-
ing that Kitcher’s version of the unficationist model explicitly does not require laws.
19. See Woodward 2003, 288–295, 358–373.

37
the result that laws are common in the special sciences, but it would be
very useful to have a more systematic exploration of this issue.
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40
Chapter 2
Probabilistic Explanation
M ICH A EL STR EV ENS
1. VARIETIES OF PROBABILISTIC
EXPLANATION
Science turns to probabilistic, as opposed to deterministic, explanation
for three reasons. Most obviously, the process that produces the phe-
nomenon to be explained may be irreducibly indeterministic, in which
case no deterministic explanation of the phenomenon will be possible,
even in principle. If, for example, the laws of quantum mechanics are
both probabilistic and fundamental—as most scientists believe—then
any explanation of, say, an episode of radioactive decay can at best cite
a very high probability for the event (there being a minuscule probabil-
ity that no atom will ever decay). The decay, then, must be explained
probabilistically.
Because all the world’s constituents conform to quantum dictates,
it might seem that, for the very same reason, everything must be given
a probabilistic explanation. For many phenomena involving large num-
bers of particles, however, the relevant probabilities tend to be so close
to zero and one that the processes producing the phenomena take on a
deterministic aspect. It is traditional in the philosophy of explanation to
treat the corresponding explanations as deterministic.
Thus, you might think, there will be a simple division of labor
between probabilistic and deterministic explanation: probabilistic
explanation for phenomena involving or depending on the behavior
of only a few fundamental-level particles, due to the indeterministic

41
P r o babili s t ic E x pla n a t i o n
aspect of quantum mechanical laws, and deterministic explanation
for higher-level phenomena where quantum probabilities effectively
disappear. However, even high-level phenomena are routinely given
probabilistic explanations—for reasons that have nothing to do with
metaphysical fundamentals.
In some cases, the recourse to probability is for epistemic rather
than metaphysical reasons. Although the phenomenon to be explained
is produced in an effectively deterministic way, science’s best model of
the process may be missing some pieces and so may not predict the phe-
nomenon for sure. In such a case, the explanation is typically given a
probabilistic form. Whatever the model says about the phenomenon is
put in statistical terms—perhaps as a probability of the phenomenon’s
occurrence or as a change in the probability of the phenomenon’s occur-
rence brought about by certain factors—and these statistical facts are
offered as a partial explanation of what has occurred.
There are many examples to be found in medicine. If a heavy
smoker contracts emphysema, his or her smoking is typically cited as
a part of the explanation of the disease. Smoking probabilifies emphy-
sema, but we do not know enough about its etiology to see for sure
whether any particular heavy smoker will become emphysemic. Thus
our best explanation of a heavy smoker’s emphysema must be proba-
bilistic. Though we will perhaps one day be able to do better, we find
the present-day probabilistic explanation enlightening: if it is not the
best possible explanation of emphysema, it is certainly a fairly good
explanation.
A third occasion for probabilistic explanation arises in certain cases
where the process producing the phenomenon to be explained is rather
complex and could have produced that very phenomenon in a number
of different ways. In such cases, there appears to be explanatory value
in a description of the process that abstracts away from the details that
determine that the phenomenon occurred in the particular way that it
did and that presents only predisposing factors that make it highly likely
that some such process would occur.
Perhaps the best examples are to be found in statistical physics.
To explain why a gas rushes into a vacuum so as to equalize its density
everywhere, you might recount the deterministic details in virtue of

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land on the Ile de Puteaux. I promptly extinguished the flame with
my Panama hat ... without other incident.
No. 9 CATCHES FIRE OVER THE ILE DE PUTEAUX
For reasons like these I went up on my first air-ship trip without
fear of fire, but not without doubt of a possible explosion due to
insufficient working of my balloon's escape valves. Should such a
cold explosion occur, the flame-spitting motor would probably
ignite the mass of mixed hydrogen and air that would surround me;
but it would have no decisive influence on the result. The cold
explosion itself would doubtless be sufficient....
Now, after five years of experience, and in spite of the retour de
flamme above the Ile de Puteaux, I continue to regard the danger
from fire as practically nil; but the possibility of a cold explosion
remains always with me, and I must continue to purchase immunity
from it at the cost of vigilant attention to my gas escape valves.
Indeed, the possibility of the thing is greater technically now than in
the early days which I describe. My first air-ship was not built for

speed—consequently, it needed very little interior pressure to
preserve the shape of its balloon. Now that I have great speed, as in
my No. 7, I must have enormous interior pressure to withstand the
exterior pressure of the atmosphere in front of the balloon as I drive
against it.

CHAPTER X
I GO IN FOR AIRSHIP BUILDING
In the early spring of 1899 I built another air-ship, which the
Paris public at once called The Santos-Dumont No. 2. It had the
same length and, at first sight, the same form as the No. 1; but its
greater diameter brought its volume up to 200 cubic metres—over
7000 cubic feet—and gave me 20 kilogrammes (44 lbs.) more
ascensional force. I had taken account of the insufficiency of the air
pump that had all but killed me, and had added a little aluminium
ventilator to make sure of permanency in the form of the balloon.

ACCIDENT TO No. 2, MAY 11, 1899
(FIRST PHASE)
This ventilator was a rotary fan, worked by the motor, to send air
into the little interior air balloon, which was sewed inside to the
bottom of the great balloon like a kind of closed pocket. In Fig. 5, G
is the great balloon filled with hydrogen gas, A the interior air
balloon, VV the automatic gas valves, AV the latter's air valve, and
TV the tube by which the rotary ventilator fed the interior air
balloon.
Fig. 5
The air valve AV was an exhaust valve similar to the two gas
valves VV in the great balloon, with the one exception that it was
weaker. In this way, when there happened to be too much fluid (i.e.
gas or air, or both) distending the great balloon, all the air would
leave the interior balloon before any of the gas would leave the
great balloon.
The first trial of my No. 2 was set for 11th May 1899.
Unfortunately, the weather, which had been fine in the morning,
grew steadily rainy in the afternoon. In those days I had no balloon
house of my own. All the morning the balloon had been slowly filling
with hydrogen gas at the captive balloon station of the Jardin
d'Acclimatation. As there was no shed there for me the work had to
be done in the open, and it was done vexatiously, with a hundred
delays, surprises, and excuses.
When the rain came on, it wetted the balloon. What was to be
done? I must either empty it and lose the hydrogen and all my time

and trouble, or go on under the disadvantage of a rain-soaked
balloon envelope, heavier than it ought to be.
I chose to go up in the rain. No sooner had I risen than the
weather caused a great contraction of the hydrogen, so that the
long cylindrical balloon shrunk visibly. Then before the air pump
could remedy the fault, a strong wind gust of the rainstorm doubled
it up worse than the No. 1, and tossed it into the neighbouring
trees.
My friends began at me again, saying:
This time you have learned your lesson. You must understand
that it is impossible to keep the shape of your cylindrical balloon
rigid. You must not again risk your life by taking a petroleum motor
up beneath it.
I said to myself:
What has the rigidity of the balloon's form to do with danger
from a petroleum motor? Errors do not count. I have learned my
lesson, but it is not that lesson.

ACCIDENT TO No. 2, MAY 11,
1899
(SECOND PHASE)
Accordingly I immediately set to work on a No. 3, with a
shorter and very much thicker balloon, 20 metres (66 feet) long and
7·50 metres (25 feet) at its greatest diameter (Fig. 6). Its much
greater gas capacity—500 cubic metres (17,650 cubic feet)—would
give it, with hydrogen, three times the lifting power of my first, and
twice that of my second air-ship. This permitted me to use common
illuminating gas, whose lifting power is about half that of hydrogen.
The hydrogen plant of the Jardin d'Acclimatation had always served
me badly. With illuminating gas I should be free to start from the
establishment of my balloon constructor or elsewhere as I desired.

Fig. 6
It will be seen that I was getting far away from the cylindrical
shapes of my first two balloons. In the future I told myself that I
would at least avoid doubling up. The rounder form of this balloon
also made it possible to dispense with the interior air balloon and its
feeding air pump that had twice refused to work adequately at the
critical moment. Should this shorter and thicker balloon need aid to
keep its form rigid I relied on the stiffening effect of a 10-metre (33-
foot) bamboo pole (Fig. 6) fixed lengthwise to the suspension cords
above my head and directly beneath the balloon.
While not yet a true keel, this pole keel supported basket and
guide rope and brought my shifting weights into much more
effectual play.
On November 13th, 1899, I started in the Santos-Dumont No.
3, from the establishment of Vaugirard, on the most successful
flight that I had yet made.

1899
(THIRD PHASE)
From Vaugirard I went directly to the Champ de Mars, which I
had chosen for its clear, open space. There I was able to practise
aerial navigation to my heart's content—circling, driving ahead in
straight courses, forcing the air-ship diagonally onward and upward,
and shooting diagonally downward, by propeller force, and thus
acquiring mastery of my shifting weights. These, because of the
greater distance they were now set apart at the extremities of the
pole keel (Fig. 6), worked with an effectiveness that astonished even
myself. This proved my greatest triumph, for it was already clear to
me that the central truth of dirigible ballooning must be ever: To

descend without sacrificing gas and to mount without sacrificing
ballast.
During these first evolutions over the Champ de Mars I had no
particular thought of the Eiffel Tower. At most it seemed a
monument worth going round, and so I circled round it at a prudent
distance again and again. Then—still without any dream of what the
future had in store for me—I made a straight course for the Parc des
Princes, over almost the exact line that, two years later, was to mark
the Deutsch prize route.
I steered to the Parc des Princes because it was another fine
open space. Once there, however, I was loth to descend, so, making
a hook, I navigated to the manœuvre grounds of Bagatelle, where I
finally landed, in souvenir of my fall of the year previous. It was
almost at the exact spot where the kite-flying boys had pulled on my
guide rope and saved me from a bad shaking-up. At this time,
remember, neither the Aéro Club nor myself possessed a balloon
park or shed from which to start and to which to return.
On this trip I considered that had the air been calm my speed in
relation to the ground would have been as much as 25 kilometres
(15 miles) per hour. In other words, I went at that rate through the
air, the wind being strong though not violent. Therefore, even had
not sentimental reasons led me to land at Bagatelle, I should have
hesitated to return with the wind to the Vaugirard balloon house—
itself of small size, and difficult of access, and surrounded by all the
houses of a busy quarter. Landing in Paris, in general, is dangerous
for any kind of balloon, amid chimney-pots that threaten to pierce its
belly, and tiles that are always ready to be knocked down on the
heads of passers-by. When in the future air-ships become as
common as automobiles are at present, spacious public and private
landing-stages will have to be built for them in every part of the
capital. Already they have been foretold by Mr Wells in his strange
book, When the Sleeper Wakes.

1899
(FINALE)
Considerations of this order made it desirable for me to have a
plant of my own. I needed a building for the housing of my air-ship
between trips. Heretofore I had emptied the balloon of all its gas at
the end of each trip, as one is bound to do with spherical balloons.
Now I saw very different possibilities for dirigibles. The significant
thing was the fact that my No. 3 had lost so little gas (or, perhaps,
none at all) at the end of its first long trip that I could well have
housed it overnight and gone out again in it the next day.

I had no longer the slightest doubt of the success of my
invention. I foresaw that I was going into air-ship construction as a
sort of life work. I should need my own workshop, my own balloon
house, hydrogen plant, and connection with the illuminating gas
mains.
The Aéro Club had just acquired some land on the newly-opened
Côteaux de Longchamps at St Cloud, and I concluded to build on it a
great shed, long and high enough to house my air-ship with its
balloon fully inflated, and furnished with all the facilities mentioned.
This aerodrome, which I built at my own expense, was 30
metres long (100 feet), 7 metres (25 feet) wide, and 11 metres (36
feet) high. Even here I had to contend with the conceit and
prejudice of artisans which had already given me so much trouble at
the Jardin d'Acclimatation. It was declared that the sliding doors of
my aerodrome could not be made to slide on account of their great
size. I had to insist. Follow my directions, I said, and do not
concern yourselves with their practicability! Although the men had
named their own pay, it was a long time before I could get the
better of this vainglorious stubbornness of theirs. When finished the
doors worked, naturally. Three years later the aerodrome built for
me by the Prince of Monaco on my plans had still greater sliding
doors.
While this first of my balloon houses was under construction, I
made a number of other successful trips in the No. 3, the last time
losing my rudder and luckily landing on the plain at Ivry. I did not
repair the No. 3. Its balloon was too clumsy in form and its motor
was too weak. I had now my own aerodrome and gas plant. I would
build a new air-ship, and with it I would be able to experiment for
longer periods and with more method.

START OF No. 3, NOVEMBER 13,
1899

CHAPTER XI
THE EXPOSITION SUMMER
The Exposition of 1900, with its learned congresses, was now
approaching. Its International Congress of Aeronautics being set for
the month of September I resolved that the new air-ship should be
ready to be shown to it.
This was my No. 4, finished 1st August 1900, and by far the
most familiar to the world at large of all my air-ships. This is due to
the fact that when I won the Deutsch prize, nearly eighteen months
later and in quite a different construction, the newspapers of the
world came out with old cuts of this No. 4, which they had kept on
file.
It was the air-ship with the bicycle saddle. In it the 10-metre
(33-foot) bamboo pole of my No. 3 came nearer to being a real
keel in that it no longer hung above my head, but, amplified by
vertical and horizontal cross pieces and a system of tightly-stretched
cords, sustained within itself motor, propeller, and connecting
machinery, petroleum reservoir, ballast, and navigator in a kind of
spider web without a basket (see photograph, page 135).
I was obliged to sit in the midst of the spider web below the
balloon on the saddle of a bicycle frame which I had incorporated
into it. Thus the absence of the traditional balloon basket appeared
to leave me astride a pole in the midst of a confusion of ropes,
tubes, and machinery. Nevertheless, the device was very handy,
because round this bicycle frame I had united cords for controlling
the shifting weights, for striking the motor's electric spark, for

opening and shutting the balloon's valves, for turning on and off the
water-ballast spigots and certain other functions of the air-ship.
Under my feet I had the starting pedals of a new 7 horse-power
petroleum motor, driving a propeller with two wings 4 metres (13
feet) across each. They were of silk, stretched over steel plates, and
very strong. For steering, my hands reposed on the bicycle handle-
bars connected with my rudder.
SANTOS-DUMONT No. 4
Above all this there stretched the balloon, 39 metres (129 feet)
long, with a middle diameter of 5·10 metres (17 feet) and a gas
capacity of 420 cubic metres (nearly 15,000 cubic feet). In form it
was a compromise between the slender cylinders of my first
constructions and the clumsy compactness of the No. 3. (See Fig.
7.) For this reason I thought it prudent to give it an interior
compensating air balloon fed by a rotary ventilator like that of the
No. 2, and as the balloon was smaller than its predecessor I was
obliged to return again to hydrogen to get sufficient lifting power.

For that matter, there was no longer any reason why I should not
employ hydrogen. I now had my own hydrogen gas generator, and
my No. 4, safely housed in the aerodrome, might be kept inflated
during weeks.
Fig. 7
In the Santos-Dumont, No. 4, I also tried the experiment of
placing the propeller at the stem instead of the stern of the air-ship.
So, attached to the pole keel in front, the screw pulled, instead of
pushing it through the air. The new 7 horse-power motor with two
cylinders turned it with a velocity of 100 revolutions per minute, and
produced, from a fixed point, a traction effort of some 30
kilogrammes (66 lbs.).
The pole keel with its cross pieces, bicycle frame, and
mechanism weighed heavy. Therefore, although the balloon was
filled with hydrogen, I could not take up more than 50 kilogrammes
(110 lbs.) of ballast.
I made almost daily experiments with this new air-ship during
August and September 1900 at the Aéro Club's grounds at St Cloud,
but my most memorable trial with it took place on 19th September
in presence of the members of the International Congress of
Aeronautics. Although an accident to my rudder at the last moment
prevented me from making a free ascent before these men of
science I, nevertheless, held my own against a very strong wind that
was blowing at the time, and gave what they were good enough to
proclaim a satisfying demonstration of the effectiveness of an aerial
propeller driven by a petroleum motor.

MOTOR OF No. 4
A distinguished member of the Congress, Professor Langley,
desired to be present a few days later at one of my usual trials, and
from him I received the heartiest kind of encouragement.
The result of these trials was, nevertheless, to decide me to
double the propeller's power by the adoption of the four-cylinder
type of petroleum motor without water jacket—that is to say, the
system of cooling à ailettes. The new motor was delivered to me
very promptly, and I immediately set about adapting the air-ship to
it. Its extra weight demanded either that I should construct a new
balloon or else enlarge the old one. I tried the latter course. Cutting
the balloon in half I had a piece put in it, as one puts a leaf in an
extension table. This brought the balloon's length to 33 metres (109
feet). Then I found that the aerodrome was too short by 3 metres
(10 feet) to receive it. In prevision of future needs I added 4 metres
(13 feet) to its length.
Motor, balloon, and shed were all transformed in fifteen days.
The Exposition was still open, but the autumn rains had set in. After
waiting, with the balloon filled with hydrogen, through two weeks of
the worst possible weather I let out the gas and began
experimenting with the motor and propeller. It was not lost time, for,

bringing the speed of the propeller up to 140 revolutions per minute,
I realised, from a fixed point, a traction effort of 55 kilogrammes
(120 lbs.). Indeed, the propeller turned with such force that I took
pneumonia in its current of cold air.
I betook myself to Nice for the pneumonia, and there, while
convalescing, an idea came to me.
This new idea took the form of my first true air-ship keel.
In a small carpenter shop at Nice I worked it out with my own
hands—a long, triangular-sectioned pine framework of great
lightness and rigidity. Though 18 metres (59½ feet) in length it
weighed only 41 kilogrammes (90 lbs.). Its joints were in aluminium,
and, to secure its lightness and rigidity, to cause it to offer less
resistance to the air and make it less subject to hygrometric
variations, it occurred to me to reinforce it with tightly-drawn piano
wires instead of cords.
VISIT OF PROFESSOR LANGLEY

Then what turned out to be an utterly new idea in aeronautics
followed. I asked myself why I should not use this same piano wire
for all my dirigible balloon suspensions in place of the cords and
ropes used in all kinds of balloons up to this time. I did it, and the
innovation turned out to be peculiarly valuable. These piano wires,
8/10ths of a millimetre (0·032 inch) in diameter, possess a high
coefficient of rupture and a surface so slight that their substitution
for the ordinary cord suspensions constitutes a greater progress than
many a more showy device. Indeed, it has been calculated that the
cord suspensions offered almost as much resistance to the air as did
the balloon itself.
Fig. 8
At the stern of this air-ship keel I again established my propeller.
I had found no advantage result from placing it in front of the No.
4, where it was an actual hindrance to the free working of the guide
rope. The propeller was now driven by a new 12 horse-power four-
cylinder motor without water jacket, through the intermediary of a
long, hollow steel shaft. Placing this motor in the centre of the keel I
balanced its weight by taking my position in my basket well to the
front, while the guide rope hung suspended from a point still farther
forward (Fig. 8). To it, some distance down its length, I fastened the
end of a lighter cord run up to a pulley fixed in the after part of the
keel, and thence to my basket, where I fastened it convenient to my
hand. Thus I made the guide rope do the work of shifting weights.

Imagine, for example, that going on a straight horizontal course (as
in Fig. 8) I should desire to rise. I would have but to pull in the
guide rope shifter. It would pull the guide rope itself back (Fig. 9),
and thus shift back the centre of gravity of the whole system that
much. The stem of the air-ship would rise (as in Fig. 9), and,
consequently, my propeller force would push me up along the new
diagonal line.
No. 4. FLIGHT BEFORE
PROFESSOR LANGLEY
The rudder was fixed at the stern as usual, and water-ballast
cylinders, accessory shifting weights, petroleum reservoir, and the
other parts of the machinery, were disposed in the new keel, well
balanced. For the first time in these experiments, as well as the first

time in aeronautics, I used liquid ballast. Two brass reservoirs, very
thin, and holding altogether 54 litres (12 gallons), were filled with
water and fixed in the keel, as above stated, between motor and
propeller, and their two spigots were so arranged that they could be
opened and shut from my basket by means of two steel wires.
Fig. 9
Before this new keel was fitted to the enlarged balloon of my
No. 5, and in acknowledgment of the work I had done in 1900, the
Scientific Commission of the Paris Aéro Club had awarded me its
Encouragement prize, founded by M. Deutsch (de la Meurthe), and
consisting of the yearly interest on 100,000 francs. To induce others
to follow up the difficult and expensive problem of dirigible
ballooning I left this 4000 francs at the disposition of the Aéro Club
to found a new prize. I made the conditions of winning it very
simple:
The Santos-Dumont prize shall be awarded to the aeronaut, a
member of the Paris Aéro Club, and not the founder of this prize,
who between 1st May and 1st October 1901, starting from the Parc
d'Aerostation of St Cloud, shall turn round the Eiffel Tower and come
back to the starting-point, at the end of whatever time, without

having touched ground, and by his self-contained means on board
alone.
If the Santos-Dumont prize is not won in 1901 it shall remain
open the following year, always from 1st May to 1st October, and so
on, until it be won.
The Aéro Club signified the importance of such a trial by
deciding to give its highest reward, a gold medal, to the winner of
the Santos-Dumont prize, as may be seen by its minutes of the time.
Since then the 4000 francs have remained in the treasury of the
Club.
SANTOS-DUMONT No. 5

CHAPTER XII
THE DEUTSCH PRIZE AND ITS PROBLEMS
This brings me to the Deutsch prize of aerial navigation, offered
in the spring of 1900, while I was navigating my No. 3, and after I
had on at least one occasion—all unknowing—steered over what was
to be its exact course from the Eiffel Tower to the Seine at Bagatelle
(see page 127).
This prize of 100,000 francs, founded by M. Deutsch (de la
Meurthe), a member of the Paris Aéro Club, was to be awarded by
the Scientific Commission of that organisation to the first dirigible
balloon or air-ship that between 1st May and 1st October 1900,
1901, 1902, 1903, and 1904 should rise from the Parc d'Aerostation
of the Aéro Club at St Cloud and, without touching ground and by its
own self-contained means on board alone, describe a closed curve in
such a way that the axis of the Eiffel Tower should be within the
interior of the circuit, and return to the point of departure in the
maximum time of half-an-hour. Should more than one accomplish
the task in the same year the 100,000 francs were to be divided in
proportion to the respective times.
The Aéro Club's Scientific Commission had been named
expressly for the purpose of formulating these and such other
conditions of the foundation as it might deem proper, and by reason
of certain of them I had made no attempt to win the prize with my
Santos-Dumont, No. 4. The course from the Aéro Club's Parc
d'Aerostation to the Eiffel Tower and return was 11 kilometres
(nearly 7 miles), and this distance, plus the turning round the Tower,

must be accomplished in thirty minutes. This meant in a perfect calm
a necessary speed of 25 kilometres (15½ miles) per hour for the
straight stretches—a speed I could not be sure to maintain all the
way in my No. 4.
Another condition formulated by the Scientific Commission was
that its members, who were to be the judges of all trials, must be
notified twenty-four hours in advance of each attempt. Naturally, the
operation of such a condition would be to nullify as much as possible
all minute time calculations based either on a given rate of speed
through perfect calm or such air current as might be prevailing
twenty-four hours previous to the hour of trial. Though Paris is
situated in a basin, surrounded on all sides by hills, its air currents
are peculiarly variable, and brusque meteorological changes are
extremely common.
I foresaw also that when a competitor had once committed the
formal act of assembling a Scientific Commission on a slope of the
River Seine so far away from Paris as St Cloud he would be under a
kind of moral pressure to go on with his trial, no matter how the air
currents might have increased, and no matter in what kind of
weather—wet, dry, or simply humid—he might find himself.
Again, this moral pressure to go on with the trial against the
aeronaut's better judgment must extend even to the event of an
unlucky change in the state of the air-ship itself. One does not
convoke a body of prominent personages to a distant riverside for
nothing, yet in the twenty-four hours between notification and trial
even a well-watched elongated balloon might well lose a little of its
tautness unperceived. A previous day's preliminary trial might easily
derange so uncertain an engine as the petroleum motor of the year
1900. And, finally, I saw that the competitor would be barred by
common courtesy from convoking the Commission at the very hour
most favourable for dirigible balloon experiments over Paris—the
calm of the dawn. The duellist may call out his friends at that sacred
hour, but not the air-ship captain.

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