3000

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MSc Global Affairs Dissertation:
Research methods
Notions of Causation
Sunil Mitra Kumar
1/12
Today
In the context of dissertation projects
1. Identifying when claims are causal, what might be some
non-causal claims?
2. What does “A causes B” mean?
3. Challenges to posing causal claims
2/12
Are dissertations ubiquitously causal?
Dissertation arguments can be
1. Causal claims: how/why/whether one or more A shapes one or
more B
1.1 What explains B?
1.2 Does A cause B? To what extent?
1.3 Under what circumstances can A cause B?
2. Non-causal arguments or descriptions
2.1 a detailed description of some phenomenon without suggesting
what explains A
2.2 Proving a mathematical theorem
My claim: You will write a causal dissertation!
3/12
https://www.tandfonline.com/doi/abs/10.1080/03014468800009821?casa_token=rEPExKiAubUAAAAA:BYV-tyCtOuWsX1BhPDaVXTZSdogBQVjXKT-09H-F1ha9J2VtUqysxMXY64qBmm5rgw9snxUELw
Some recent dissertation titles
Safe Third Country? An analysis of the US-Guatemala Asylum
Cooperation Agreement (2019) and the principle of
non-refoulement in international refugee law
Does a consumption based approach to emission accountability
minimise climate colonialism in a post-2015 climate change
governance? A comparative study of India and the USA
To what extent to India’s strides towards modernisation and
expansion of its nuclear arsenal directly challenge the posture of
‘Credible Minimum Deterrance’ enshrined in its official nuclear
doctrine?
4/12
Enquiries into causation
“Causes of effects”
“Effects of causes”
5/12
Hang on…
What does it mean to say “A causes B”?
1. Necessity?
2. Likelihood
⇒ More specifically, a shift in the probability
distribution of outcomes
6/12
Hang on…
What does it mean to say “A causes B”?
1. Necessity?
2. Likelihood ⇒ More specifically, a shift in the probability
distribution of outcomes
6/12
J.L. Mackie’s INUS conditions
An electric short circuit caused a fire in a house. This short circuit
was an “INUS condition” for the fire:
1. The short circuit was IN:
I On its own it was insufficient to have caused the fire
I But it was necessary in this case to have caused the fire ⇔
the fire wouldn’t have happened without it
2. …and, the short circuit was part of another enabling
condition(s) that were US:
I The presence of flammable material was on its own
unnecessary, but in this case proved
I sufficient to lead to a fire once the short circuit provided the
spark
7/12
J.L. Mackie’s INUS conditions
An electric short circuit caused a fire in a house. This short circuit
was an “INUS condition” for the fire:
1. The short circuit was IN:
I On its own it was insufficient to have caused the fire
I But it was necessary in this case to have caused the fire ⇔
the fire wouldn’t have happened without it
2. …and, the short circuit was part of another enabling
condition(s) that were US:
I The presence of flammable material was on its own
unnecessary, but in this case proved
I sufficient to lead to a fire once the short circuit provided the
spark
7/12
INUS!
An electric short circuit caused a fire in a house. This short circuit
was an “INUS condition” for the fire:
1. The short circuit was IN:
I insufficient: other enabling conditions were required to be
present to cause the fire
I necessary: at that moment in time and with other conditions
as they stood, the fire wouldn’t have happened without it
2. …and, the short circuit was part of another enabling
condition(s) that were US:
I unnecessary: there exist many alternative conditions that
would cause fire; this particular one wasn’t necessary, but…
I sufficient: but in this case, this specific enabling condition
combined with the short circuit was sufficient for the fire ⇔ we
need not search for other explanations
8/12
Problems with constructing causal arguments
1. We wrongly infer “A causes B” when in fact there exists a C
such that “C causes B” or “C causes A and B”
2. We wrongly infer “A causes B” when in fact “B causes A”
9/12
Problems of the first type
A: School B: Learning achievement
C: Socioeconomic status
10/12
Problems of the first type
A: School B: Learning achievement
C: Socioeconomic status
10/12
Problems of the first type
A: School B: Learning achievement
C: Socioeconomic status
10/12
Problems of the second type
The Colonial Origins of Comparative Development:
An Empirical Investigation
By DARON ACEMOGLU, SIMON JOHNSON, AND JAMES A. ROBINSON*
We exploit differences in European mortality rates to estimate the effect of institu-
tions on economic performance. Europeans adopted very different colonization
policies in different colonies, with different associated institutions. In places where
Europeans faced high mortality rates, they could not settle and were more likely to
set up extractive institutions. These institutions persisted to the present. Exploiting
differences in European mortality rates as an instrument for current institutions, we
estimate large effects of institutions on income per capita. Once the effect of
institutions is controlledfor, countries in Africa or those closer to the equator do not
have lower incomes. (JEL 011, P16, P51)
What are the fundamental causes of the
large differences in income per capita across
countries? Although there is still little con-
sensus on the answer to this question, differ-
ences in institutions and property rights have
received considerable attention in recent
years. Countries with better “institutions,”
more secure property rights, and less distor-
tionary policies will invest more in physical
and human capital, and will use these factors
more efficiently to achieve a greater level of
income (e.g., Douglass C. North and Robert
P. Thomas, 1973; Eric L. Jones, 1981; North,
1981). This view receives some support from
cross-country correlations between measures
of property rights and economic development
(e.g., Stephen Knack and Philip Keefer, 1995;
Paulo Mauro, 1995; Robert E. Hall and
Charles I. Jones, 1999; Dani Rodrik, 1999),
and from a few micro studies that investigate
the relationship between property rights and
investment or output (e.g., Timothy Besley,
1995; Christopher Mazingo, 1999; Johnson et
al., 1999).
At some level it is obvious that institutions
matter. Witness, for example, the divergent
paths of North and South Korea, or East and
West Germany, where one part of the country
stagnated under central planning and collec-
tive ownership, while the other prospered
with private property and a market economy.
Nevertheless, we lack reliable estimates of
the effect of institutions on economic perfor-
mance. It is quite likely that rich economies
choose or can afford better institutions. Per-
haps more important, economies that are dif-
ferent for a variety of reasons will differ both
* Acemoglu: Department of Economics, E52-380b,
Massachusetts Institute of Technology, Cambridge, MA
02319, and Canadian Institute for Advanced Research
(e-mail: daron@mit.edu); Johnson: Sloan School of Man-
agement, Massachusetts Institute of Technology, Cam-
bridge, MA 02319 (e-mail: sjohnson@mit.edu); Robinson:
Department of Political Science and Department of Eco-
nomics, 210 Barrows Hall, University of California, Berke-
ley, CA 94720 (e-mail: jamesar@socrates.berkeley.edu).
We thank Joshua Angrist, Abhijit Banerjee, Esther Duflo,
Stan Engerman, John Gallup, Claudia Goldin, Robert
Hall, Chad Jones, Larry Katz, Richard Locke, Andrei
Shleifer, Ken Sokoloff, Judith Tendler, three anonymous
referees, and seminar participants at the University of
California-Berkeley, Brown University, Canadian Insti-
tute for Advanced Research, Columbia University, Har-
vard University, Massachusetts Institute of Technology,
National Bureau of Economic Research, Northwestern
University, New York University, Princeton University,
University of Rochester, Stanford University, Toulouse
University, University of California-Los Angeles, and the
World Bank for useful comments. We also thank Robert
McCaa for guiding us to the data on bishops’ mortality.
1369
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11/12
A third problem: Cartwright on extrapolation
Nancy Cartwright’s chapter Predicting “it will work for us”: (Way)
beyond statistics
1. Policy evidence, especially statistical, and especially
randomised experiments: something worked, somewhere, at
some time
2. something, somewhere, some time: will it work in a different
context at a future date?
⇐ an inferential leap
3. The concern is with, therefore, “external validity”
12/12
A third problem: Cartwright on extrapolation
Nancy Cartwright’s chapter Predicting “it will work for us”: (Way)
beyond statistics
1. Policy evidence, especially statistical, and especially
randomised experiments: something worked, somewhere, at
some time
2. something, somewhere, some time: will it work in a different
context at a future date? ⇐ an inferential leap
3. The concern is with, therefore, “external validity”
12/12
Causes and Conditions
Author(s): J. L. Mackie
Source: American Philosophical Quarterly , Oct., 1965, Vol. 2, No. 4 (Oct., 1965), pp. 245-
264
Published by: University of Illinois Press on behalf of the North American
Philosophical Publications
Stable URL: https://www.jstor.org/stable/20009173
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https://www.jstor.org/stable/20009173
American Philosophical Quarterly
Volume 2, Number 4, October 1965
I. CAUSES AND CONDITIONS
J. L. MACKIE
ASKED what a cause is, we may be tempted to say that it is an event which precedes the
event of which it is the cause, and is both necessary
and sufficient for the latter’s occurrence; briefly,
that a cause is a necessary and sufficient preceding
condition. There are, however, many difficulties in
this account. I shall try to show that what we
often speak of as a cause is a condition not of this
sort, but of a sort related to this. That is to say,
this account needs modification, and can be modi?
fied, and when it is modified we can explain much
more satisfactorily how we can arrive at much of
what we ordinarily take to be causal knowledge;
the claims implicit within our causal assertions can
be related to the forms of the evidence on which
we are often relying when we assert a causal
connection.
? i. Singular Causal Statements
Suppose that a fire has broken out in a certain
house, but has been extinguished before the house
has been completely destroyed. Experts investigate
the cause of the fire, and they conclude that it was
caused by an electrical short-circuit at a certain
place. What is the exact force of their statement
that this short-circuit caused this fire? Clearly the
experts are not saying that the short-circuit was a
necessary condition for this house’s catching fire
at this time; they know perfectly well that a short
circuit somewhere else, or the overturning of a
lighted oil stove, or any one of a number of other
things might, if it had occurred, have set the house
on fire. Equally, they are not saying that the
short-circuit was a sufficient condition for this
house’s catching fire; for if the short-circuit had
occurred, but there had been no inflammable
material nearby, the fire would not have broken
out, and even given both the short-circuit and the
inflammable material, the fire would not have
occurred if, say, there had been an efficient auto?
matic sprinkler at just the right spot. Far from
being a condition both necessary and sufficient for
the fire, the short-circuit was, and is known to the
experts to have been, neither necessary nor
sufficient for it. In what sense, then, is it said to
have caused the fire?
At least part of the answer is that there is a set
of conditions (of which some are positive and some
are negative), including the presence of inflam?
mable material, the absence of a suitably placed
sprinkler, and no doubt quite a number of others,
which combined with the short-circuit constituted
a complex condition that was sufficient for the
house’s catching fire?sufficient, but not necessary,
for the fire could have started in other ways. Also,
of this complex condition, the short-circuit was an
indispensable part: the other parts of this con?
dition, conjoined with one another in the absence
of the short-circuit, would not have produced the
fire. The short-circuit which is said to have caused
the fire is thus an indispensable part of a complex
sufficient (but not necessary) condition of the fire.
In this case, then, the so-called cause is, and is
known to be, an insufficient but necessary part of a
condition which is itself unnecessary but sufficient for
the result. The experts are saying, in effect, that
the short-circuit is a condition of this sort, that it
occurred, that the other conditions which con?
joined with it form a sufficient condition were also
present, and that no other sufficient condition of
the house’s catching fire was present on this
occasion. I suggest that when we speak of the
cause of some particular event, it is often a con?
dition of this sort that we have in mind. In view
of the importance of conditions of this sort in our
knowledge of and talk about causation, it will be
convenient to have a short name for them: let us
call such a condition (from the initial letters of
the words italicized above), an inus condi?
tion.1
This account of the force of the experts’ state?
ment about the cause of the fire may be confirmed
by reflecting on the way in which they will have
reached this conclusion, and the way in which
anyone who disagreed with it would have to
1 This term was suggested by D. G. Stove who has also given me a great deal of help by criticizing earlier versions of this
article.
A 245
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246 AMERICAN PHILOSOPHICAL QUARTERLY
challenge it. An important part of the investigation
will have consisted in tracing the actual course of
the fire; the experts will have ascertained that no
other condition sufficient for a fire’s breaking out
and taking this course was present, but that the
short-circuit did occur and that conditions were
present which in conjunction with it were sufficient
for the fire’s breaking out and taking the course
that it did. Provided that there is some necessary
and sufficient condition of the fire?and this is an
assumption that we commonly make in such con?
texts?anyone who wanted to deny the experts’
conclusion would have to challenge one or another
of these points.
We can give a more formal analysis of the
statement that something is an inus condition. Let
6 A9 stand for the inus condition?in our example,
the occurrence of a short-circuit at that place?and
let ‘?’ and ‘C (that is, ‘not-C, or the absence of C)
stand for the other conditions, positive and nega?
tive, which were needed along with A to form a
sufficient condition of the fire?in our example,
B might be the presence of inflammable material,
C the absence of a suitably placed sprinkler. Then
the conjunction ‘ABC represents a sufficient con?
dition of the fire, and one that contains no re?
dundant factors ; that is, ABC is a minimaljufficient
condition for the fire.2 Similarly, let DEF, GHI,
etc., be all the other minimal sufficient conditions of
this result. Now provided that there is some
necessary and sufficient condition for this result,
the disjunction of all the minimal sufficient con?
ditions for it constitutes a necessary and sufficient
condition.3 That is, the formula “ABC or DEF or
GHI or . . .” represents a necessary and sufficient
condition for the fire, each of its disjuncts, such
as ‘ABC9, represents a minimal sufficient condition,
and each conjunct in each minimal sufficient con
dition, such as lA\ represents an inus condition. To
simplify and generalize this, we can replace the
conjunction of terms conjoined with ‘A’ (here ‘BC’)
by the single term ‘X\ and the formula representing
the disjunction of alljthe other minimal sufficient
conditions?here “DEF or GHI or . . .”?by the
single term QT\ Then an inus condition is defined
as follows:
A is an inus condition of a result P if and only if,
for some X and for some T, (AX or T) is a necessary
and sufficient condition of P, but A is not a sufficient
condition of P and X is not a sufficient condition
of P.
We can indicate this type of relation more
briefly if we take the provisos for granted and
replace the existentially quantified variables ‘X*
and 6T9 by dots. That is, we can say that A is an
inus condition of P when (A . . . or . . .) is a
necessary and sufficient condition of P.
(To forestall possible misunderstandings, I
would fill out this definition as follows.4 First, there
could be a set of minimal sufficient conditions of
P, but no necessary conditions, not even a complex
one ; in such a case, A might be what Marc-Wogau
calls a moment in a minimal sufficient condition,
but I shall not call it an inus condition. I shall
speak of an inus condition only where the dis?
junction of all the minimal sufficient conditions is
also a necessary condition. Secondly, the definition
leaves it open that the inus condition A might be
a conjunct in each of the minimal sufficient con?
ditions. If so, A would be itself a necessary condition
of the result. I shall still call A an inus condition in
these circumstances : it is not part of the definition
of an inus condition that it should not be necessary,
although in the standard cases, such as that
2 The phrase “minimal sufficient condition” is borrowed from Konrad Marc-Wogau, “On Historical Explanation,”
Theoria, vol. 28 (1962), pp. 213-233. This article gives an analysis of singular causal statements, with special reference to
their use by historians, which is substantially equivalent to the account I am suggesting. Many further references are made
to this article, especially in n. 9 below.
3 Gf. n. 8 on p. 227 of Marc-Wogau’s article, where it is pointed out that in order to infer that the disjunction of all the
minimal sufficient conditions will be a necessary condition, “it is necessary to presuppose that an arbitrary event C, if it
occurs, must have sufficient reason to occur.” This presupposition is equivalent to the presupposition that there is some
(possibly complex) condition that is both necessary and sufficient for C.
It is of some interest that some common turns of speech embody this presupposition. To say “Nothing but X will do,” or
“Either lor f will do, but nothing else will,” is a natural way of saying that X, or the disjunction (X or T), is a necessary
condition for whatever result we have in mind. But taken literally these remarks say only that there is no sufficient condition
for this result other than X, or other than (X or T). That is, we use to mean “a necessary condition” phrases whose literal
meanings would be “the only sufficient condition,” or “the disjunction of all sufficient conditions.” Similarly, to say that Z
is “all that’s needed” is a natural way of saying that ? is a sufficient condition, but taken literally this remark says that Z *s
the only necessary condition. But, once again, that the only necessary condition will also be a sufficient one follows only if
we presuppose that some condition is both necessary and sufficient.
4 I am indebted to the referees for the suggestion that these points should be clarified.
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CAUSES AND CONDITIONS 247
sketched above, it is not in fact necessary.5 Thirdly,
the requirement that X by itself should not be
sufficient for P insures that A is a nonredundant
part of the sufficient condition AX; but there is a
sense in which it may not be strictly necessary or
indispensable even as a part of this condition, for
it may be replaceable : for example KX might be
another minimal sufficient condition of P.6 Fourthly,
it is part of the definition that the minimal sufficient
condition, AX, of which A is a nonredundant part,
is not also a necessary condition, that there is
another sufficient condition T (which may itself be
a disjunction of sufficient conditions). Fifthly, and
similarly, it is part of the definition that A is not
by itself sufficient for P. The fourth and fifth of
these points amount to this : I shall call A an inus
condition only if there are terms which actually
occupy the places occupied by (X’ and CT9 in the
formula for the necessary and sufficient condition.
However, there may be cases where there is only
one minimal sufficient condition, say AX. Again,
there may be cases where A is itself a minimal
sufficient condition, the disjunction of all minimal
sufficient conditions being (A or T); again, there
may be cases where A itself is the only minimal
sufficient condition, and is itself both necessary
and sufficient for P. In any of these cases, as well
as in cases where A is an inus condition, I shall
say that A is at least an inus condition. As we shall
see, we often have evidence which supports the
conclusion that something is at least an inus con?
dition; we may or may not have other evidence
which shows that it is no more than an inus con?
dition.)
I suggest that a statement which asserts a
singular causal sequence, of such a form as “A
caused F,” often makes, implicitly, the following
claims :
(i) A is at least an inus condition of P?that is,
there is a necessary and sufficient condition of P
which has one of these forms: {AX or T), (A or T),
AX, A.
(ii) A was present on the occasion in question.
(iii) The factors represented by the 6X9, if any,
in the formula for the necessary and sufficient
condition were present on the occasion in question.
(iv) Every disjunct in ‘T9 which does not con?
tain iAi as a conjunct was absent on the occasion
in question. (As a rule, this means that whatever
T’ represents was absent on this occasion. If *T9
represents a single conjunction of factors, then it
was absent if at least one of its conjuncts was
absent; if it represents a disjunction, then it was
absent if each of its disjuncts was absent. But we
do not wish to exclude the possibility that ‘T9
should be, or contain as a disjunct, a conjunction
one of whose conjuncts is A, or to require that
this conjunction should have been absent.7)
I do not suggest that this is the whole of what
is meant by “A caused P” on any occasion, or even
that it is a part of what is meant on every occasion :
some additional and alternative parts of the mean?
ing of such statements are indicated below.8 But
I am suggesting that this is an important part of
the concept of causation; the proof of this sugges?
tion would be that in many cases the falsifying of
any one of the above-mentioned claims would
rebut the assertion that A caused P.
This account is in fairly close agreement, in
substance if not in terminology, with at least two
accounts recently offered of the cause of a single
event.
Konrad Marc-Wogau sums up his account thus:
when historians in singular causal statements speak of
a cause or the cause of a certain individual event ?,
then what they are referring to is another individual
event a which is a moment in a minimal sufficient and
at the same time necessary condition post factum ?.9
5 Special cases where an inus condition is also a necessary one are mentioned at the end of ? 3.
6 This point, and the term “nonredundant,” are taken from Michael Scriven’s review of NagePs The Structure of Science, in
Review of Metaphysics, 1964. See especially the passage on p. 408 quoted below.
7 See example of the wicket-keeper discussed below.
8 See ?? 7) 8.
9 See pp. 226-227 of the article referred to in n. 2 above. Marc-Wogau’s full formulation is as follows:
“Let ‘msc’ stand for minimal sufficient condition and *nc’ for necessary condition. Then suppose we have a class K of
individual events a1} a2, . . . an. (It seems reasonable to assume that K is finite; however even if K were infinite the reasoning
below would not be affected.) My analysis of the singular causal statement: a is the cause of ?, where a and ? stand for
individual events, can be summarily expressed in the following statements:
(1) (EK) (K = {a1} a2, . . ., an}); (4) (x) ( (* c Kx ^ a?) => x is not fulfilled when a occurs);
(2) (x) (x K = x msc ?) ; (5) a is a moment in ax.
(3) Ui v a2 v . . . an) nc ?;
(3) and (4) say that ax is a necessary condition post factum for ?. If a? is a necessary condition post factum for ?, then every
moment in a? is a necessary condition post factum for ?, and therefore also a. As has been mentioned before (note 6) there is
assumed to be a temporal sequence between a and ?; ? is not itself an element in K”
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248 AMERICAN PHILOSOPHICAL QUARTERLY
He explained his phrase “necessary condition
postfactum” by saying that he will call an event ax
a necessary condition post factum for x if the dis?
junction “?j or a2 or a3 . . . or an” represents a
necessary condition for x, and of these disjuncts
only a1 was present on the particular occasion
when x occurred.
Similarly Michael Scriven has said:
Causes are not necessary, even contingently so, they
are not sufficient?but they are, to talk that language,
contingently sufficient. . . . They are part of a set of
conditions that does guarantee the outcome, and they
are non-redundant in that the rest of this set (which
does not include all the other conditions present) is
not alone sufficient for the outcome. It is not even
true that they are relatively necessary, i.e., necessary
with regard to that set of conditions rather than the
total circumstances of their occurrence, for there may
be several possible replacements for them which
happen not to be present. There remains a ghost of
necessity; a cause is a factor from a set of possible
factors the presence of one of which (any one) is
necessary in order that a set of conditions actually
present be sufficient for the effect.10
There are only slight differences between these
two accounts, or between each of them and that
offered above. Scriven seems to speak too strongly
when he says that causes are not necessary: it is,
indeed, not part of the definition of a cause of this
sort that it should be necessary, but, as noted
above, a cause, or an inus condition, may be
necessary, either because there is only one minimal
sufficient condition or because the cause is a
moment in each of the minimal sufficient con?
ditions. On the other hand, Marc-Wogau’s account
of a minimal sufficient condition seems too strong.
He says that a minimal sufficient condition con?
tains “only those moments relevant to the effect”
and that a moment is relevant to an effect if “it
is a necessary condition for ?: ? would not have
occurred if this moment had not been present.”
This is less accurate than Scriven’s statement that
the cause only needs to be nonredundant.11 Also,
Marc-Wogau’s requirement, in his account of a
necessary condition post factum, that only one
minimal sufficient condition (the one containing a)
should be present on the particular occasion, seems
a little too strong. If two or more minimal sufficient
conditions (say a1 and a2) were present, but a was
a moment in each of them, then though neither
ax nor a2 was necessary post factum, a would be so.
I shall use this phrase “necessary post factum” to
include cases of this sort : that is, a is a necessary
condition post factum if it is a moment in every
minimal sufficient condition that was present. For
example, in a cricket team the wicket-keeper is
also a good batsman. He is injured during a match,
and does not bat in the second innings, and the
substitute wicket-keeper drops a vital catch that
the original wicket-keeper would have taken. The
team loses the match, but it would have won if
the wicket-keeper had both batted and taken that
catch. His injury was a moment in two minimal
sufficient conditions for the loss of the match;
either his not batting, or the catch’s not being
taken, would on its own have insured the loss of
the match. But we can certainly say that his
injury caused the loss of the match, and that it
was a necessary condition post factum.
This account may be summed up, briefly and
approximately, by saying that the statement “A
caused P” often claims that A was necessary and
sufficient for P in the circumstances. This de?
scription applies in the standard cases, but we have
already noted that a cause is nonredundant rather
than necessary even in the circumstances, and we
shall see that there are special cases in which it
may be neither necessary nor nonredundant.
? 2. Difficulties and Refinements12
Both Scriven and Marc-Wogau are concerned
not only with this basic account, but with certain
difficulties and with the refinements and complica?
tions that are needed to overcome them. Before
dealing with these I shall introduce, as a refine?
ment of my own account, the notion of a causal
field.13
10 Op. cit., p. 408.
11 However, in n. 7 on pp. 222-233, Marc-Wogau draws attention to the difficulty of giving an accurate definition of
“a moment in a sufficient condition.” Further complications are involved in the account given in ? 5 below of “clusters” of
factors and the progressive localization of a cause. A condition which is minimally sufficient in relation to one degree of
analysis of factors may not be so in relation to another degree of analysis.
12 This section is something of an aside: the main argument is resumed in ? 3.
13 This notion of a causal field was introduced by John Anderson. He used it, e.g., in “The Problem of Causality,” first
published in the Australasian Journal of Psychology and Philosophy, vol. 16 (1938), and reprinted in Studies in Empirical Philosophy
(Sydney, 1962), pp. 126-136, to overcome certain difficulties and paradoxes in Mill’s account of causation. I have also used
this notion to deal with problems of legal and moral responsibility, in “Responsibility and Language,” Australasian Journal of
Philosophy, vol. 33 (i955)> PP- 143-?59
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CAUSES AND CONDITIONS 249
This notion is most easily explained if we leave,
for a time, singular causal statements and consider
general ones. The question “What causes influ?
enza?” is incomplete and partially indeterminate.
It may mean “What causes influenza in human
beings in general?” If so, the (full) cause that is
being sought is a difference that will mark off cases
in which human beings contract influenza from
cases in which they do not; the causal field is then
the region that is to be thus divided, human beings
in general. But the question may mean, “Given that
influenza viruses are present, what makes some
people contract the disease whereas others do
not?” Here the causal field is human beings in con?
ditions where influenza viruses are present. In all such
cases, the cause is required to differentiate, within
a wider region in which the effect sometimes
occurs and sometimes does not, the sub-region in
which it occurs: this wider region is the causal
field. This notion can now be applied to singular
causal questions and statements. “What caused
this man’s skin cancer?”14 may mean “Why did
this man develop skin cancer now when he did
not develop it before?” Here the causal field is the
career of this man: it is within this that we are
seeking a difference between the time when skin
cancer developed and times when it did not. But
the same question may mean “Why did this man
develop skin cancer, whereas other men who were
also exposed to radiation did not?” Here the
causal field is the class of men thus exposed to
radiation. And what is the cause in relation to one
field may not be the cause in relation to another.
Exposure to a certain dose of radiation may be the
cause in relation to the former field: it cannot be
the cause in relation to the latter field since it is
part of the description of that field, and being
present throughout that field it cannot differen?
tiate one sub-region of it from another. In relation
to the latter field, the cause may be, in Scriven’s
terms, “Some as-yet-unidentified constitutional
factor.”
In our first example of the house which caught
fire, the history of this house is the field in relation
to which the experts were looking for the cause of
the fire: their question was “Why did this house
catch fire on this occasion, and not on others?”
However, there may still be some indeterminacy
in this choice of a causal field. Does this house,
considered as the causal field, include all its
features, or all its relatively permanent features,
or only some of these ? If we take all its features,
or even all of its relatively permanent ones, as
constituting the field, then some of the things that
we have treated as conditions?for example the
presence of inflammable material near the place
where the short-circuit occurred?would have to
be regarded as parts of the field, and we could not
then take them also as conditions which in relation
to this field, as additions to it or intrusions into it,
are necessary or sufficient for something else. We
must therefore take the house, in so far as it con?
stitutes the causal field, as determined only in a
fairly general way, by only some of its relatively
permanent features, and we shall then be free to
treat its other features as conditions which do not
constitute the field, and are not parts of it, but
which may occur within it or be added to it. It
is in general an arbitrary matter whether a par?
ticular feature is regarded as a condition (that is,
as a possible causal factor) or as part of the field,
but it cannot be treated in both ways at once. If
we are to say that something happened to this
house because of, or partly because of, a certain
feature, we are implying that it would still have
been this house, the house in relation to which we
are seeking the cause of this happening, even if it
had not had this particular feature.
I now propose to modify the account given
above of the claims often made by singular causal
statements. A statement of such a form as “A
caused P” is usually elliptical, and is to be ex?
panded into “A caused P in relation to the field F.”
And then in place of the claim stated in (i) above,
we require this:
(ia) A is at least an inus condition of P in the
field F?that is, there is a condition which, given
the presence of whatever features characterize F
throughout, is necessary and sufficient for P, and
which is of one of these forms: (AX or T), (A or T),
AX, A.
In analyzing our ordinary causal statements,
we must admit that the field is often taken for
granted or only roughly indicated, rather than
specified precisely. Nevertheless, the field in re?
lation to which we are looking for a cause of this
effect, or saying that such-and-such is a cause,
may be definite enough for us to be able to say
14 These examples are borrowed from Scriven, op. cit., pp. 409-410. Scriven discusses them with reference to what he calls
a “contrast class,” the class of cases where the effect did not occur with which the case where it did occur is being contrasted.
What I call the causal field is the logical sum of the case (or cases) in which the effect is being said to be caused with what
Scriven calls the contrast class.
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25O AMERICAN PHILOSOPHICAL QUARTERLY
that certain facts or possibilities are irrelevant to
the particular causal problem under consideration,
because they would constitute a shift from the
intended field to a different one. Thus if we are
looking for the cause, or causes, of influenza, mean?
ing its cause (s) in relation to the field human beings,
we may dismiss, as not directly relevant, evidence
which shows that some proposed cause fails to
produce influenza in rats. If we are looking for
the cause of the fire in this house, we may similarly
dismiss as irrelevant the fact that a proposed cause
would not have produced a fire if the house had
been radically different, or had been set in a
radically different environment.
This modification enables us to deal with the
well-known difficulty that it is impossible, without
including in the cause the whole environment, the
whole prior state of the universe (and so excluding
any likelihood of repetition), to find a genuinely
sufficient condition, one which is “by itself, ade?
quate to secure the effect.”15 It may be hard to
find even a complex condition which was abso?
lutely sufficient for this fire because we should
have to include, as one of the negative conjuncts,
such an item as the earth’s not being destroyed by
a nuclear explosion just after the occurrence of the
suggested inus condition ; but it is easy and reason?
able to say simply that such an explosion would,
in more senses than one, take us outside the field
in which we are considering this effect. That is to
say, it may be not so difficult to find a condition
which is sufficient in relation to the intended field.
No doubt this means that causal statements may
be vague, in so far as the specification of the field
is vague, but this is not a serious obstacle to
establishing or using them, either in science or in
everyday contexts.16
It is a vital feature of the account I am suggest?
ing that we can say that A caused P, in the sense
described, without being able to specify exactly
the terms represented by tXi and ‘Y9 in our
formula. In saying that A is at least an inus con?
dition for P in F, one is not saying what other
factors, along with A, were both present and
nonredundant, and one is not saying what other
minimal sufficient conditions there may be for P
in F. One is not even claiming to be able to say
what they are. This is in no way a difficulty: it is
a readily recognizable fact about our ordinary
causal statements, and one which this account
explicitly and correctly reflects.17 It will be shown
(in ? 5 below) that this elliptical or indeterminate
character of our causal statements is closely con?
nected with some of our characteristic ways of
discovering and confirming causal relationships:
it is precisely for statements that are thus “gappy”
or indeterminate that we can obtain fairly direct
evidence from quite modest ranges of observation.
On this analysis, causal statements implicitly con?
tain existential quantifications; one can assert an
existentially quantified statement without asserting
any instantiation of it, and one can also have good
reason for asserting an existentially quantified
statement without having the information needed
to support any precise instantiation of it. I can
know that there is someone at the door even if
the question “Who is he?” would floor me
Marc-Wogau is concerned especially with cases
where “there are two events, each of which in?
dependently of the other is a sufficient condition
for another event.” There are, that is to say, two
minimal sufficient conditions, both of which
actually occurred. For example, lightning strikes
a barn in which straw is stored, and a tramp throws
a burning cigarette butt into the straw at the same
place and at the same time. Likewise for an
historical event there may be more than one
“cause,” and each of them may, on its own, be
15 Cf. Bertrand Russell, “On the Notion of Cause,” Afysticism and Logic (London, 1917), p. 187. Cf. also Scriven’s first
difficulty, op. cit., p. 409: “First, there are virtually no known sufficient conditions, literally speaking, since human or accidental
interference is almost inexhaustibly possible, and hard to exclude by specific qualification without tautology.” The intro?
duction of the causal field also automatically covers Scriven’s third difficulty and third refinement, that of the contrast class
and the relativity of causal statements to contexts.
16 J. R. Lucas, “Causation,” Analytical Philosophy, ed. R. J. Butler (Oxford, 1962), pp. 57-59, resolves this kind of difficulty
by an informal appeal to what amounts to this notion of a causal field: “. . . these circumstances [cosmic cataclysms, etc.]
. . . destroy the whole causal situation in which we had been looking for Z to appear . . . predictions are not expected to
come true when quite unforeseen emergencies arise.”
17 This is related to Scriven’s second difficulty, op. cit., p. 409: “there still remains the problem of saying what the other
factors are which, with the cause, make up the sufficient condition. If they can be stated, causal explanation is then simply
a special case of subsumption under a law. If they cannot, the analysis is surely mythological.” Scriven correctly replies that
“a combination of the thesis of macro-determinism . . . and observation-plus-theory frequently gives us the very best of
reasons for saying that a certain factor combines with an unknown sub-set of the conditions present into a sufficient condition
for a particular effect.” He gives a statistical example of such evidence, but the whole of my account of typical sorts of evidence
for causal relationships in ?? 5 and 7 below is an expanded defence of a reply of this sort.
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CAUSES AND CONDITIONS 25I
sufficient.18 Similarly Scriven considers a case
where
. . . conditions (perhaps unusual excitement plus con?
stitutional inadequacies) [are] present at 4.0 p.m. that
guarantee a stroke at 4.55 p.m. and consequent death
at 5.0 p.m. ; but an entirely unrelated heart attack at
4.50 p.m. is still correctly called the cause of death,
which, as it happens, does occur at 5.0. p.m.19
Before we try to resolve these difficulties let us
consider another of Marc-Wogau’s problems:
Smith and Jones commit a crime, but if they had
not done so the head of the criminal organization
would have sent other members to perform it in
their stead, and so it would have been committed
anyway.20 Now in this case, if 6A9 stands for the
actions of Smith and Jones, what we have is that
AX is one minimal sufficient condition of the result
(the crime), but AZ is another, and both X and
Z are present. A combines with one set of the
standing conditions to produce the result by one
route : but the absence of A would have combined
with another set of the standing conditions to
produce the same result by another route. In this
case we can say that A was a necessary condition
post factum. This sample satisfies the requirements
of Marc-Wogau’s analysis, and of mine, of the
statement that A caused this result; and this agrees
with what we would ordinarily say in such a case.
(We might indeed add that there was also a deeper
cause?the existence of the criminal organization,
perhaps?but this does not matter: our formal
analyses do not insure that a particular result will
have a unique cause, nor does our ordinary causal
talk require this.) It is true that in this case we
cannot say what will usually serve as an informal
substitute for the formal account, that the cause,
here A, was necessary (as well as sufficient) in the
circumstances; for A would have done just as well.
We cannot even say that A was nonredundant.
But this shows merely that a formal analysis may
be superior to its less formal counterparts.
Now in Scriven’s example, we might take it
that the heart attack prevented the stroke from
occurring. If so, then the heart attack is a necessary
condition post factum : it is a moment in the only
minimal sufficient condition that was present in
full, for the heart attack itself removed some factor
that was a necessary part of the minimal sufficient
condition which has the excitement as one of its
moments. This is strictly parallel to the Smith and
Jones case. Again it is odd to say that the heart
attack was in any way necessary, since the absence
of the heart attack would have done just as well :
this absence would have been a moment in that
other minimal sufficient condition, one of whose
other moments was the excitement. Nevertheless,
the heart attack was necessary post factum, and the
excitement was not. Scriven draws the distinction,
quite correctly, in terms of continuity and dis?
continuity of causal chains: “the heart attack was,
and the excitement was not the cause of death
because the ‘causal chain’ between the latter and
death was interrupted, while the former’s ‘went to
completion’.” But it is worth noting that a break
in the causal chain corresponds to a failure to
satisfy the logical requirements of a moment in a
minimal sufficient condition that is also necessary
post factum.
Alternatively, if the heart attack did not prevent
the stroke, then we have a case parallel to that of
the straw in the barn, or of the man who is shot
by a firing squad, and two bullets go through his
heart simultaneously. In such cases the require?
ments of my analysis, or of Marc-Wogau’s, or of
Scriven’s, are not met: each proposed cause is
redundant and not even necessary post factum,
though the disjunction of them is necessary post
factum and nonredundant. But this agrees very well
with the fact that we would ordinarily hesitate to
say, of either bullet, that it caused the man’s death,
or of either the lightning or the cigarette butt that
it caused the fire, or of either the excitement or
the heart attack that it was the cause of death.
As Marc-Wogau says, “in such a situation as this
we are unsure also how to use the word ’cause’.”
Our ordinary concept of cause does not deal clearly
with cases of this sort, and we are free to decide
whether or not to add to our ordinary use, and to
the various more or less formal descriptions of it,
rules which allow us to say that where more than
one at-least-iNUS-condition, and its conjunct con?
ditions, are present, each of them caused the
result.21
The account thus far developed of singular
causal statements has been expressed in terms of
18 Op. cit., pp. 228-233.
19 Op. cit., pp. 410-411 : this is Scriven’s fourth difficulty and refinement.
20 Op. cit., p. 232: the example is taken from P. Gardiner, The Nature of Historical Explanation (Oxford, 1952), p. 101.
21 Scriven’s fifth difficulty and refinement are concerned with the direction of causation. This is considered briefly in ? 8
below.
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252 AMERICAN PHILOSOPHICAL QUARTERLY
Statements about necessity and sufficiency; it is
therefore incomplete until we have added an
account of necessity and sufficiency themselves.
This question is considered in ? 4 below. But the
present account is independent of any particular
analysis of necessity and sufficiency. Whatever
analysis of these we finally adopt, we shall use it
to complete the account of what it is to be an
inus condition, or to be at least an inus condition.
But in whatever way this account is completed,
we can retain the general principle that at least
part of what is often done by a singular causal
statement is to pick out, as the cause, something
that is claimed to be at least an inus condition.
? 3. General Causal Statements
Many general causal statements are to be under?
stood in a corresponding way. Suppose, for
example, that an economist says that the restriction
of credit causes (or produces) unemployment.
Again, he will no doubt be speaking with reference
to some causal field; this is now not an individual
object, but a class, presumably economies of a
certain general kind; perhaps their specification
will include the feature that each economy of the
kind in question contains a large private enterprise
sector with free wage-earning employees. The
result, unemployment, is something which some?
times occurs and sometimes does not occur within
this field, and the same is true of the alleged cause,
the restriction of credit. But the economist is not
saying that (even in relation to this field) credit
restriction is either necessary or sufficient for unem?
ployment, let alone both necessary and sufficient.
There may well be other circumstances which must
be present along with credit restriction, in an
economy of the kind referred to, if unemployment
is to result; these other circumstances will no
doubt include various negative ones, the absence
of various counteracting causal factors which, if
they were present, would prevent this result. Also,
the economist will probably be quite prepared to
admit that in an economy of this kind unemploy?
ment could be brought about by other combina?
tions of circumstances in which the restriction of
credit plays no part. So once again the claim that
he is making is merely that the restriction of credit
is, in economies of this kind, a nonredundant part
of one sufficient condition for unemployment : that
is, an inus condition. The economist is probably
assuming that there is some condition, no doubt
a complex one, which is both necessary and
sufficient for unemployment in this field. This
being assumed, what he is asserting is that, for
some X and for some Y, (AX or Y) is a necessary
and sufficient condition for P in F, but neither A
nor X is sufficient on its own, where ‘A9 stands
for the restriction of credit, ‘P’ for unemployment,
and ‘F’ for the field, economies of such-and-such
a sort. In a developed economic theory the field F
may be specified quite exactly, and so may the
relevant combinations of factors represented here
by CX9 and T5. (Indeed, the theory may go beyond
statements in terms of necessity and sufficiency to
ones of functional dependence, but this is a com?
plication which I am leaving aside for the present.)
In a preliminary or popular statement, on the
other hand, the combinations of factors may either
be only roughly indicated or be left quite un?
determined. At one extreme we have the statement
that (AX or Y) is a necessary and sufficient con?
dition, where X9 and T’ are given definite mean?
ings; at the other extreme we have the merely
existentially quantified statement that this holds
for some pair X and Y. Our knowledge in such
cases ordinarily falls somewhere between these two
extremes. We can use the same convention as
before, deliberately allowing it to be ambiguous
between these different interpretations, and say
that in any of these cases, where A is an inus
condition of P in F, (A … or …) is a necessary
and sufficient condition of P in F.
A great deal of our ordinary causal knowledge
is of this form. We know that the eating of sweets
causes dental decay. Here the field is human beings
who have some of their own teeth. We do not
know, indeed it is not true, that the eating of
sweets by any such person is a sufficient condition
for dental decay: some people have peculiarly
resistant teeth, and there are probably measures
which, if taken along with the eating of sweets,
would protect the eater’s teeth from decay. All we
know is that sweet-eating combined with a set of
positive and negative factors which we can specify,
if at all, only roughly and incompletely, constitutes
a minimal sufficient condition for dental decay?
but not a necessary one, for there are other com?
binations of factors, which do not include sweet
eating, which would also make teeth decay, but
which we can specify, if at all, only roughly and
incompletely. That is, if ‘A9 now represents sweet
eating, CP’ dental decay, and ‘F9 the class of human
beings with some of their own teeth, we can say
that, for some X and Y, (AX or Y) is necessary
and sufficient for P in F, and we may be able to
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causes and conditions 253
go beyond this merely existentially quantified
statement to at least a partial specification of the
X and T in question. That is, we can say that
(A … or …) is a necessary and sufficient con?
dition, but that A itself is only an inus condition.
And the same holds for many general causal
statements of the form “A causes (or produces) P.”
It is in this sense that the application of a potential
difference to the ends of a copper wire produces
an electric current in the wire; that a rise in the
temperature of a piece of metal makes it expand ;
that moisture rusts steel; that exposure to various
kinds of radiation causes cancer, and so on.
However, it is true that not all ordinary general
causal statements are of this sort. Some of them
are implicit statements of functional dependence.
Functional dependence is a more complicated
relationship of which necessity and sufficiency can
be regarded as special cases. (It is briefly discussed
in ? 7 below.) Here too what we commonly single
out as causing some result is only one of a number
of factors which jointly affect the result. Again,
some causal statements pick out something that is
not only an inus condition, but also a necessary
condition. Thus we may say that the yellow fever
virus is the cause of yellow fever. (This statement
is not, as it might appear to be, tautologous, for
the yellow fever virus and the disease itself can be
independently specified.) In the field in question?
human beings?the injection of this virus is not
by itself a sufficient condition for this disease, for
persons who have once recovered from yellow
fever are thereafter immune to it, and other
persons can be immunized against it. The injection
of the virus, combined with the absence of im?
munity (natural or artificial), and perhaps com?
bined with some other factors, constitutes a
sufficient condition for the disease. Beside this, the
injection of the virus is a necessary condition of
the disease. If there is more than one complex
sufficient condition for yellow fever, the injection
of the virus into the patient’s bloodstream (either
by a mosquito or in some other way) is a factor
included in every such sufficient condition. If ‘A9
stands for this factor, the necessary and sufficient
condition has the form (A … or A … etc.),
where A occurs in every disjunct. We sometimes
note the difference between this and the standard
case by using the phrase “the cause.” We may
say not merely that this virus causes yellow fever,
but that it is the cause of yellow fever; but we would
say only that sweet-eating causes dental decay, not
that it is the cause of dental decay. But about an
individual case we could say that sweet-eating was
the cause of the decay of this person’s teeth, meaning
(as in ? i above) that the only sufficient condition
present here was the one of which sweet-eating is
a nonredundant part. Nevertheless, there will not
in general be any one item which has a unique
claim to be regarded as the cause even of an in?
dividual event, and even after the causal field has
been determined. Each of the moments in the
minimal sufficient condition, or in each minimal
sufficient condition, that was present can equally
be regarded as the cause. They may be distin?
guished as predisposing causes, triggering causes,
and so on, but it is quite arbitrary to pick out as
“main” and “secondary,” different moments which
are equally nonredundant items in a minimal
sufficient condition, or which are moments in two
minimal sufficient conditions each of which makes
the other redundant.22
? 4. Necessity and Sufficiency
One possible account of general statements of
the forms “? is a necessary condition of T” and
“5 is a sufficient condition of T”?where c<5" and ' T9 are general terms?is that they are equivalent to simple universal propositions. That is, the former is equivalent to "All Tare S9i and the latter to "All S are T." Similarly, "S is necessary for T in the field F" would be equivalent to "All FT are S," and "S is sufficient for T in the field F" to "All FS are 7V' Whether an account of this sort is adequate is, of course, a matter of dispute; but it is not disputed that these statements about necessary and sufficient conditions at least entail the corresponding universals. I shall work on the assumption that this account is adequate, that general statements of necessity and sufficiency are equivalent to universals: it will be worth while to see how far this account will take us, how far we are able, in terms of it, to understand how we use, support, and criticize these statements of necessity and sufficiency. A directly analogous account of the correspond? ing singular statements is not satisfactory. Thus it will not do to say that "A short-circuit here was a necessary condition of a fire in this house" is equivalent to "All cases of this house's catching fire are cases of a short-circuit occurring here," because the latter is automatically true if this house has caught fire only once and a short-circuit has 22 Cf. Marc-Wogau's concluding remarks, op. cit., pp. 232-233. This content downloaded from ������������165.154.227.98 on Wed, 27 Apr 2022 13:55:35 UTC������������� All use subject to https://about.jstor.org/terms 254 AMERICAN PHILOSOPHICAL QUARTERLY occurred on that occasion, but this is not enough to establish the statement that the short-circuit was a necessary condition of the fire; and there would be an exactly parallel objection to a similar statement about a sufficient condition. It is much more plausible to relate singular statements about necessity and sufficiency to certain kinds of non-material conditionals. Thus "A short-circuit here was a necessary condition of a fire in this house" is closely related to the counter factual conditional "If a short-circuit had not occurred here this house would not have caught fire," and "A short-circuit here was a sufficient condition of a fire in this house" is closely related to what Goodman has called the factual con? ditional, "Since a short-circuit occurred here, this house caught fire." However, a further account would still have to be given of these non-material conditionals themselves. I have argued elsewhere23 that they are best considered as condensed or telescoped arguments, but that the statements used as premisses in these arguments are no more than simple factual uni versais. To use the above-quoted counterfactual conditional is, in effect, to run through an in? complete argument: "Suppose that a short-circuit did not occur here, then the house did not catch fire." To use the factual conditional is, in effect, to run through a similar incomplete argument, "A short-circuit occurred here; therefore the house caught fire." In each case the argument might in principle be completed by the insertion of other premisses which, together with the stated premiss, would entail the stated conclusion. Such additional premisses may be said to sustain the non-material conditional. It is an important point that someone can use a non-material conditional without com? pleting or being able to complete the argument, without being prepared explicitly to assert pre? misses that would sustain it, and similarly that we can understand such a conditional without knowing exactly how the argument would or could be completed. But to say that a short-circuit here was a necessary condition of a fire in this house is to say that there is some set of true propositions which would sustain the above-stated counterfactual, and to say that it was a sufficient condition is to say that there is some set of true propositions which would sustain the above-stated factual conditional. If this is conceded, then the relating of singular statements about necessity and sufficiency to non material conditionals leads back to the view that they refer indirectly to certain simple universal propositions. Thus if we said that a short-circuit here was a necessary condition for a fire in this house, we should be saying that there are true universal propositions from which, together with true statements about the characteristics of this house, and together with the supposition that a short-circuit did not occur here, it would follow that the house did not catch fire. From this we could infer the universal proposition which is the more obvious, but unsatisfactory, candidate for the analysis of this statement of necessity, "All cases of this house's catching fire are cases of a short circuit occurring here," or, in our symbols, "All FP are A.99 We can use this to represent approx? imately the statement of necessity, on the under? standing that it is to be a consequence of some set of wider universal propositions, and is not to be automatically true merely because there is only this one case of an FP, of this house's catching fire.24 A statement that A was a sufficient condition may be similarly represented by "All FA are P." Correspondingly, if all that we want to say is that (A... or ...) was necessary and sufficient for P in F, this will be represented approximately by the pair of universals "All FP are (A... or ...) and all F (A... or ...) are P," and more accurately by the statement that there is some set of wider universal propositions from which, together with true state? ments about the features of F, this pair of universals follows. This, therefore, is the fuller analysis of the claim that in a particular case A is an inus con? dition of P in F, and hence of the singular state? ment that A caused P. (The statement that A is at least an inus condition includes other alternatives, corresponding to cases where the necessary and sufficient condition is (A or ...), A..., or A.) Let us go back now to general statements of necessity and sufficiency and take F as a class, not as an individual. On the view that I am adopting, at least provisionally, the statement that ? is a necessary and sufficient condition for P in F is 23 "Counterfactuals and Causal Laws," Analytical Philosophy, ed. R. J. Butler (Oxford, 1962), pp. 66-80. 24 This restriction may be compared with one which Nagel imposes on laws of nature : "the vacuous truth of an unrestricted universal is not sufficient for counting it a law; it counts as a law only if there is a set of other assumed laws from which the universal is logically derivable" (The Structure of Science [New York, 1961], p. 60). It might have been better if he had added "or if there is some other way in which it is supported (ultimately) by empirical evidence." Cf. my remarks in "Counterfactuals and Causal Laws," op. cit., pp. 72-74, 78-80. This content downloaded from ������������165.154.227.98 on Wed, 27 Apr 2022 13:55:35 UTC������������� All use subject to https://about.jstor.org/terms CAUSES AND CONDITIONS 255 equivalent to "All FP are Z and a11 FZ are p" Similarly, if we cannot completely specify a necessary and sufficient condition for P in F, but can only say that the formula "(A... or ...)" re? presents such a condition, this is equivalent to the pair of incomplete universals, "All FP are (A... or ...) and all F (A... or ...) are P." In saying that our general causal statements often do no more than specify an inus condition, I am therefore saying that much of our ordinary causal knowledge is knowledge of such pairs of incomplete universals, of what we may call elliptical or gappy causal laws. ? 5. Evidence for Causal Connections If we assume that the general causal statement that A causes P, or the singular causal statement that A caused P, often makes the claims set out in ?? 1, 2, 3, and 4, including the claim that A is at least an inus condition of P, then we can give an account of a combination of reasoning and observation which constitutes evidence for these causal statements. This account is based on what von Wright calls a complex case25 of the Method of Difference. Like any other method of eliminative induction, this can be formulated in terms of an assumption, an observation, and a conclusion which follows by a deductively valid argument from the assumption and the observation together. To get any positive conclusion by a process of elimination, we must assume that the result (the phenomenon a cause of which we are going to discover) has some cause in the sense that there is some condition the occurrence of which is both necessary and sufficient for the occurrence (as a rule, shortly afterwards) of the result. Also, if we are to get anywhere by elimination, we must assume that the range of possibly relevant causal factors, the items that might in some way constitute this necessary and sufficient condition, is restricted in some way. On the other hand, even if we had specified some such set of possibly relevant factors, it would in most cases be quite implausible to assume that the supposed necessary and sufficient condition is identical with just one of these factors on its own, and fortunately we have no need to do so. If we represent each possibly relevant factor as a single term, the natural assumption to make is merely that the supposed necessary and sufficient con? dition will be represented by a formula which is constructed in some way out of some selection of these single terms, by means of negation, con? junction, and disjunction. However, any formula so constructed is equivalent to some formula in disjunctive normal form?that is, one in which negation, if it occurs, is applied only to single terms, and conjunction, if it occurs, only to single terms and/or negations of single terms. So we can assume without loss of generality that the formula of the supposed necessary and sufficient condition is in disjunctive normal form, that it is at most a disjunction of conjunctions in which each conjunct is a single term or the negation of one, that is, a formula such as "(ABC or G H or J)." Summing this up, the assumption that we require will have this form : For some ?, Z 1S a necessary and sufficient con? dition for the phenomenon P in the field F, that is, all FP are Z and all FZ are P, and ? is a condition represented by some formula in disjunctive normal form all of whose constituents are taken from the range of possibly relevant factors A, B, C, D, E, etc. Along with this assumption, we need an observa? tion which has the form of the classical difference observation described by Mill. This we can for? mulate as follows: There is an instance Ix, in which P occurs, and there is a negative case JVl5 in which P does not occur, such that one of the possibly relevant factors (or the negation of one), say A, is present in Ix and absent from JVl5 but each of the other possibly relevant factors is either present in both Ix and Nx or absent both from Ix and from JVX. We can set out an example of such an observa? tion as follows, using V and (p9 to stand for "absent" and "present." P A B C D E ] I? p p p a a p > etc.
JS/\ a a p a a p J
Given the above-stated assumption, we can
reason in the following way about any such
observation :
25 A Treatise on Induction and Probability (New York, 1951), pp. 90 ff. The account that I am here giving of the Method of
Difference, and that I would give of the eliminative methods of induction in general, differs, however, in several respects
from that of von Wright. An article on “Eliminative Methods of Induction,” which sets out my account, is to appear in the
Encyclopedia of Philosophy, edited by Paul Edwards, to be published by the Free Press of Glencoe, Collier-Macmillan.
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256 AMERICAN PHILOSOPHICAL QUARTERLY
Since P is absent from N?, every sufficient con?
dition for P is absent from jV15 and therefore every
disjunct in Z 1S absent from Nt. Every disjunct in
Z which does not contain A is therefore also absent
from Ix. But since P is present in 7l5 and ? is a
necessary condition for P, Z 1S present in Ix.
Therefore at least one disjunct in Z 1S present in
Iv Therefore at least one disjunct in Z contains A.
What this shows is that Z>tne supposed necessary
and sufficient condition for P in F, is either A
itself, or a conjunction containing A, or a dis?
junction containing as a disjunct either A itself or
a conjunction containing A. That is, Z nas one ?f
these four forms: A; A…; (A or …); (A., or …).
We can sum these up by saying that Z nas tne
form (A-or-), where the dashes indicate
that these parts of the formula may or may not
be filled in. This represents briefly the statement
that A is at least an inus condition. It follows also
that if there are in the (unknown) formula which
represents the complete necessary and sufficient
condition any disjuncts not containing A, none of
them was present as a whole in JV”X (but of course
some of their component terms may have been
present there), and also that in at least one of the
disjuncts that contains A, the terms, if any, con?
joined with A stand for factors (or negations of
factors) that were present in Iv This is all that
follows from this single observation. But in general
other observations will show that the dotted spaces
do need to be filled in, and that A alone is neither
sufficient nor necessary for P in F. We can then
infer that the necessary and sufficient condition
actually has the form (A… or …), and that A
itself is only an inus condition.
This analysis is so far merely formal, and we
have still to consider whether such a method can
be, or is, actually used, whether an assumption of
the sort required can be justified and whether an
observation of the sort required can ever be made.
Even at this stage, however, it is worth noting that
the Method of Difference does not require the
utterly unrealistic sort of assumption used in what
von Wright calls the simple case?namely, that
the supposed necessary and sufficient condition is
some single factor on its own?but that the much
less restrictive assumption used here will still yield
information when it is combined with nothing more
than the classical difference observation. It is worth
noting also that the information thus obtained,
though it falls far short of what von Wright calls
absolutely perfect analogy, that is, of a full speci?
fication of a necessary and sufficient condition, is
information of exactly the form that is implicit in
our ordinary causal assertions, both singular and
general.26
But can observations of the kind required be
made? A preliminary answer is that the typical
controlled experiment is an attempt to approximate
to an observation of this sort. The experimental
case corresponds to our 7l5 the control case to our
jVl5 and the experimenter tries to insure that there
will be no possibly relevant difference between these
two except the one whose effect he is trying to
determine, our A. Any differential outcome, present
in the experimental case but not in the control
case, is what he takes to be this effect, correspond?
ing to our P.
The before-and-after observation is a par?
ticularly important variety of this kind. Suppose,
for example, that we take a piece of blue litmus
paper and dip it in a certain liquid, and it turns
red. The situation before it is dipped provides the
negative case JV^; the situation after it is dipped
provides the instance Iv As far as we can see, no
other possibly relevant feature of the situation has
changed, so that I? and JVX are alike with regard
to all possibly relevant factors except A, the paper’s
being dipped in a liquid of this sort, but the result
P, the paper’s turning red, is present in Ix but not
in JVV We can take this in either of two ways.
First, we may take the field F to be pieces of blue
litmus paper, and if we assume that in this field
there is some necessary and sufficient condition
for P, made up in some way from some selection
from the factors we are considering as possibly
relevant, we can conclude that (A? or ?) is
necessary and sufficient for P in F. Other observa?
tions may show that A alone is neither necessary
nor sufficient, and hence that the necessary and
sufficient condition is (A… or …). Thus wre can
establish the gappy causal law, “All FP are (A…
or …) and all F(A… or …) are P.” This amounts
to the assertion that in some circumstances being
dipped in a liquid of this sort turns blue litmus
paper red. Secondly, we can take the field (which
we shall here call Fx) to be this particular piece of
paper, and what the experiment then establishes
26 What is established by the present method may be compared with the four claims listed in ? i above, that A is at least
an inus condition, that A was present on the occasion in question, that the factors represented by ‘J?’?that is, the other
moments in at least one minimal sufficient condition in which A is a moment?were present, and that every disjunct in Y
which does not contain A?that is, every minimal sufficient condition which does not contain A?was absent.
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CAUSES AND CONDITIONS 257
is the singular causal statement that on this par?
ticular occasion the dipping in this liquid turned
this piece of paper red. This is established in
accordance with the analysis of singular causal
statements completed in ? 4. For the experiment,
together with the assumption, has established the
wider universals indicated by the above-stated
gappy causal law. It has shown that for some X
and Y all FP are (AX or Y) and allF^Z or Y) are
P, and from these, since Fx is an F (that is, this
piece of paper is a piece of blue litmus paper), it
follows that for some X and Tall FXP are (AXor Y)
and all FX(AX or Y) are P. Also, ‘X9 represents
circumstances which were present on this occasion,
and T’ circumstances which were not present in
Nl9 the “before” situation. That is to say, the
observation, together with the appropriate assump?
tion, entails that there are true propositions which
sustain the counterfactual and factual conditionals,
“If, in the circumstances, this paper had not been
dipped in this liquid it would not have turned red,
but since it was dipped it did turn red”; but it
does not fully determine what these propositions
are, it does not fill in the gaps in the causal laws
which sustain these conditionals. The importance
of this is that it shows how an observation can
reveal not merely a sequence but a causal sequence :
what we discover is not merely that the litmus
paper was dipped and then turned red, but that
the dipping made it turn red.
It is worth noting that despite the stress tradition?
ally laid, in accounts of the Method of Difference,
on the requirement that there should be only one
point of difference between Ix and jVl5 very little
really turns upon this. For suppose that two of our
possibly relevant factors, say A and B, were both
present in Ix and both absent from jV*1? but that
each of the other possibly relevant factors was
either present in both or absent from both. Then
reasoning parallel to that given above will show
that at least one of the disjuncts in Z either con”
tains A or contains B (and may contain both). That
is, this observation still serves to show that the
cluster of factors (A, B) contains something that is
at least an inus condition of P in F, whether this
condition turns out in the end to be A alone, or
B alone, or the conjunction AB, or the disjunction
(A or B). And similar considerations apply if there
are more than two points of difference between Ix
and JVj. However many there are, an observation
of this form, coupled with our assumption, shows
that a cause in our sense (in general an inus con?
dition) lies somewhere within the cluster of terms,
positive or negative, in respect of which Ix differs
from Nv (Note that it does not show that the other
terms, those common to Ix and Nx, are causally
irrelevant; our reasoning does not exclude factors
as irrelevant, but positively locates some of the
relevant factors within the differentiating cluster.)
This fact rebuts the criticism sometimes leveled
against the eliminative methods that they pre?
suppose and require a finally satisfactory analysis
of causal factors into their simple components,
which we never actually achieve. On the contrary,
any distinction of factors, however rough, enables
us to start using such a method. We can proceed,
and there is no doubt that discovery has often
proceeded, by what we may call the progressive
localization of a cause. Using the Method of Differ?
ence in a very rough way, we can discover first,
say, that the drinking of wine causes intoxication.
That is, the cluster of factors which is crudely
summed up in the single term “the drinking of
wine” contains somewhere within it an inus con?
dition of intoxication ; and we can subsequently go
on to distinguish various possibly relevant factors
within this cluster, and by further observations of
the same sort locate a cause of intoxication more
precisely. In a context in which this cluster is either
introduced or excluded as a whole, it is correct to
say that the introduction of this cluster was non
redundant or necessary post factum, and experiments
can establish this, even if, in a different context,
in which distinct items in the cluster are introduced
or excluded separately, it would be correct to say
that only one item, the alcohol, was nonredundant
or necessary post factum, and this could be estab?
lished by more exact experimentation.
One merit of this formal analysis is that it shows
in what sense a method of eliminative induction,
such as the Method of Difference, rests upon a
deterministic principle or presupposes the uni?
formity of nature. In fact, each application of this
method requires an assumption which in one
respect says much less than this, in another a little
more. No sweeping general assumption is needed:
we need not assume that every event has a cause,
but merely that for events of the kind in question,
P, in the field in question, F, there is some necessary
and sufficient condition. But?and this is where we
need something more than determinism or uni?
formity in general?we must also assume that this
condition is constituted in some way by some
selection from a restricted range of possibly relevant
factors.
It is this further assumption that raises a doubt
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258 AMERICAN PHILOSOPHICAL QUARTERLY
about the use of this method to make causal
discoveries. As for the mere deterministic assump?
tion that the phenomenon in question has some
necessary and sufficient condition, we may be
content to say that this is one which we simply do
make in all inquiries of this kind, and leave its
justification to be provided by whatever solution
we can eventually find for the general problem of
induction. But the choice of a range of possibly
relevant factors cannot be brushed aside so easily.
Also, the wider a range of possibly relevant factors
we admit, the harder it will be to defend the claim
that Ix and Nx are observed to be alike with respect
to all the possibly relevant factors except the one,
or the indicated cluster of factors, in which they
are observed to differ. Alternatively, the more
narrowly the range of possibly relevant factors is
restricted, the easier it will be to defend the claim
that we have made an observation of the required
form, but at the same time the less plausible will
our assumption be.
However, this difficulty becomes less formidable
if we consider the assumption and the observation
together. We want to be able to say that there is
no possibly relevant difference, other than the one
(or ones) noted, between Ix and Nv We need not
draw up a complete list of possibly relevant factors
before we make the observation. In practice we
usually assume that a causally relevant factor will
be in the spatial neighborhood of the instance of
the field in or to which the effect occurs in Il9 or
fails to occur in Nl9 and it will either occur shortly
before or persist throughout the time at which the
effect occurs in Il9 or might have occurred, but
did not, in jV2. No doubt in a more advanced
application of the Method of Difference within an
already-developed body of causal knowledge we
can restrict the range of possibly relevant factors
much more narrowly and can take deliberate steps
to exclude interferences from our experiments ; but
I am suggesting that even our most elementary
and primitive causal knowledge rests upon implicit
applications of this method, and the spatio-tem?
poral method of restricting possibly relevant factors
is the only one initially available. And perhaps it
is all we need. Certainly in terms of it the observer
could say, about the litmus paper, for example,
“I cannot see any difference, other than the dipping
into this liquid, between the situation in which
the paper turned red and that in which it did not,
that might be relevant to this change.”
It may be instructive to compare the Method
of Difference as a logical ideal with any actual
application of it. If the assumption and the
observation were known to be true, then the causal
conclusion would be established. Consequently,
anything that tells in favor of both the assumption
and the observation tells equally in favor of the
causal conclusion. No doubt we are never in a
position to say that they are known to be true,
and therefore that the conclusion is established;
but we are often in a position to say that, given
the deterministic part of the assumption, we cannot
see any respect in which they are not true (since
we cannot see any difference that might be relevant
between Ix and jVx), and consequently that we
cannot see any escape from the causal conclusion.
In this sense at least we can say that an application
of this method confirms a causal conclusion: the
observer has looked for but failed to find an escape
from this conclusion.27
In practice we do not rely as much on single
observations as this account might suggest. We
assure ourselves that it was the dipping in this
27 An account of how eliminative inductive reasoning supports causal conclusions is given by J. R. Lucas in the article
cited in n. 16 above. His account differs from mine in many details, but agrees with it in general outline. Contrast with this
the remarks of von Wright, op. cit., p. 135: “. . . in normal scientific practice we have to reckon with plurality rather than
singularity, and with complexity rather than simplicity of conditions. This means that the weaker form of the Deterministic
Postulate, or the form which may be viewed as a reasonable approximation to what is commonly known as the Law of
Universal Causation, is practically useless as a supplementary premiss or ‘presupposition’ of induction.” I hope I have shown
that this last remark is misleading.
It has been argued by A. Michotte (La perception de la causalit? [Louvain, 1946], translated by T. R. and E. Miles as The
Perception of Causality [London, 1963] ) that we have in certain cases an immediate perception or impression of causation.
His two basic experimental cases are these. In one, an object A approaches another object B; on reaching B, A stops and B
begins to move off in the same direction; here the observer gets the impression that A has “launched” B, has set B in motion.
In the other case, A continues to move on reaching B, and B moves at the same speed and in the same direction; here the
observer gets the impression that A is carrying B with it. In both cases observers typically report that A has caused the
movement of B. Michotte argues that it is an essential feature of observations that give rise to this causal impression that
there should be two distinguishable movements, that of the “agent” A and that of the “patient” B, but also that it is essential
that the movement of the patient should in some degree copy or duplicate that of the agent.
This would appear to be a radically different account of the way in which we can detect causation by observing a single
sequence, for on Michotte’s view our awareness of causation can be direct, perceptual, and non-inferential. It must be con?
ceded that not only spatio-temporal continuity, but also qualitative continuity between cause and effect (^ampliation du
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CAUSES AND CONDITIONS 259
liquid that turned the litmus paper red by dipping
other pieces of litmus paper and seeing them, too,
turn red just after they are dipped. This repetition
is effective because it serves as a check on the
possibility that some other relevant change might
have occurred, unnoticed, just at the moment
when the first piece of litmus paper was dipped in
the liquid. After a few trials it will be most unlikely
that any other relevant change has kept on occur?
ring just as each piece was dipped (or even that
there has been a succession of different relevant
changes at the right times). Of course, it may be
that there is some other relevant change (or set of
relevant changes) which keeps on occurring just
as each paper is dipped because it is linked with
the dipping by what Mill calls “some fact of
causation.”28 If so, then this other relevant change
may be regarded as part of a cluster of factors
which can be grouped together under the title
“the dipping of the paper in this liquid,” taking
this in a broad sense, as possibly including items
other than the actual entry of the paper into the
liquid. But if this is not so, then it would be a sheer
coincidence if this other relevant change kept on
occurring just as each piece of paper was dipped,
or if there was a succession of relevant changes at
the right times. The hypothesis that such co?
incidences have continued will soon become
implausible, even if it cannot be conclusively
falsified.29 It is an important point that it is not
the repetition as such that supports the conclusion
that the dipping causes the turning red, but the
repetition of a sequence which, on each single
occasion, is already prima facie a causal one. The
repetition tends to disconfirm the set of hypotheses
each of which explains a single sequence of a
dipping followed by a turning red as a mere
coincidence, and by contrast it confirms the hypo?
thesis that in each such single sequence the dipping
is causally connected with the change of color.
The analysis offered here of the Method of
Difference has this curious consequence : in employ?
ing this method we are liable to use the word
“cause” in different senses at different stages. In
the assumption, it is said that the phenomenon P
has some “cause,” meaning some necessary and
sufficient condition; but the “cause” actually
found?A in our formal example?may be only
an inus condition. But we do need to assume that
something is both necessary and sufficient for P in
F to be able to conclude that A is at least an inus
condition, that it is a moment in a minimal
sufficient condition that was present, and that it
was necessary post factum.
? 6. Falsification of Incomplete Statements
A possible objection to this account is that the
gappy laws and singular statements used here are
so incomplete that they are internally guaranteed
against falsification and are therefore not genuine
scientific statements at all. However, it is not a
satisfactory criterion of a scientific statement that
it should be exposed to conclusive falsification:
what is important is that to treat a statement as a
scientific hypothesis involves handling it in such
a way that evidence would be allowed to tell
against it. And there are ways in which evidence
can be, and is, allowed to tell against a statement
which asserts that something is an inus condition.
Suppose, for example, that by using the Ix and
Nx set out in ? 5 above we have concluded that A
is at least an inus condition of P?taking this both
as a singular causal statement about an individual
mouvement), are important ingredients in the primitive concept of causation; they may contribute to the notion of causal
“necessity”; and both these continuities can sometimes be directly perceived. But it is equally clear that these continuities
are not in general required either as observed or as postulated features of a causal sequence, and that a sequence which has
these continuities may fail to be causal. What is perceived in Michotte’s examples is neither necessary nor sufficient for causal
relationship as we now understand it, though it may have played an important part in the genesis of the causal concept.
It is worth noting that these examples also exhibit the features stressed in my account. They present the observer with an
apparently simple and isolated causal field, within which there occurs a maiked change, i?’s beginning to move. The approach
of A is the only observed possibly relevant difference between the times when B is stationary and when B begins to move. If
B’s beginning to move has a cause, then ^4’s approach is a suitable candidate, and nothing else that the observer is allowed
to see or encouraged to suspect is so. Thus these examples could also give rise to an inferential awareness of causation, though
it is true that other examples which would do this equally well would fail, and in Michotte’s experiments do fail, to produce
a direct impression of causation.
28 E.g., in the Fifth Canon, A System of Logic, Book III, Chapter VIII, ? 6.
29 Cf. J. R. Lucas, op. cit., p. 53: “It might be that two quite independent processes were going on, and we were getting
constant concomitance for no reason except the chance fact that the two processes happened to keep in step. If this be so, an
arbitrary disturbance in one will reveal the independence of the other. If an arbitrary disturbance in the one is followed by
a corresponding alteration in the other, it always could be that it was a genuine coincidence. . . . But to argue this per?
sistently is to make the same illicit extension of Coincidence’ as some phenomenalists do of ‘illusion’. … It is no longer a
practical possibility that we are eliminating but a Cartesian doubt.”
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2?0 AMERICAN PHILOSOPHICAL QUARTERLY
field Fj and as an incomplete law about the general
field F. Now suppose that closer examination shows
that some other factor, previously unnoticed, say
K, was present in Ix and absent from jVl5 and that
we also discover (or construct experimentally)
further cases 72 and jV2, such that the observational
evidence is now of this form :
P ABCDE …K …
Ix p p p a a p …p …
Ni a a p a a p …a …
12 p a p a a p …p …
No a p p a a p …a …
Here N2 shows that for any X which does not
contain K, AX is not sufficient : so X must contain
K. But any X that contains K is present in I2, and
may therefore be sufficient for P on its own, without
A. This evidence does not conclusively falsify the
hypothesis that A is an inus condition as stated
above, but it takes away all the reason that the
previous evidence gave us for this conclusion.
Observations of this pattern would tell against this
conclusion, and would lead us to replace the view
that A causes P, and caused P in Iu with the view
that K causes P, and caused P both in I2 and in Il9
with A not even forming an indispensable part of
the sufficient condition which was present in Iv
(A fuller treatment of this kind of additional
evidence would require accounts of the Method of
Agreement and of the Joint Method, parallel to
that of the Method of Difference given in ? 5.)
It remains true that some of the claims made
by singular causal statements and by causal laws
as here analyzed?that is, claims that some factor
is at least an inus condition of the effect?are not
conclusively falsifiable. But ordinary causal laws
and singular causal statements are not conclusively
falsifiable, as direct consideration will show. It is
a merit of the account offered here, not a difficulty
for it, that it reproduces this feature of ordinary
causal knowledge.30
? 7. Functional Dependence and
Concomitant Variation
As I mentioned in ? 3, causal statements some?
times refer not to relations of necessity and suffi?
ciency, nor to any more complex relations based
on these, like that of being an inus condition, but
to relations of functional dependence. That is, the
effect and the possible causal factors are things
which can vary in magnitude, and the cause of
some effect P is that on whose magnitude the
magnitude of P functionally depends. But causal
statements of this sort can be expanded and
analyzed in an account parallel to that which we
have given of causal statements of the previous
kinds. Again we speak of a field, individual or
general, in relation to which a certain functional
dependence holds. Also, we can speak of the total
cause, the complete set of factors on whose magni?
tude the magnitude of P, given the field F, wholly
depends: that is, variations of P in F are com?
pletely covered by a formula which is a function
of the magnitudes of all of the factors in this “com?
plete set,” and of these alone. This total cause is
analogous to a necessary and sufficient condition.
It can be distinguished from each of the factors that
compose it, each of which is causally relevant to
the effect, but it is not the whole cause of its varia?
tions : each of these partial causes is analogous to an
inus condition.
The problem of finding a cause in this new
sense would require, for its full solution, the com?
pletion of two tasks. We should have both to
identify all the factors in this total cause, and also
to discover in what way the effect depends upon
them?that is, to discover the law of functional
dependence of the effect on the total cause, or the
partial differential equations relating it to each of
the partial causes. The first?but only the first?of
these two tasks can be performed by what is really
the Method of Concomitant Variation, developed
in a style analogous to that in which the Method
of Difference was developed in ? 5. That is, we
assume that there is something on which the
magnitude of P in F functionally depends, and
that there is a restricted set of possibly relevant
factors; then if while all other possibly relevant
factors are held constant one factor, say A, varies
and P also varies, it follows that A is at least a
partial cause, that it is one of the actually relevant
factors. It is this relationship that is commonly
asserted by statements of such forms as “A affects
P” and “On this occasion A affected P.” Some of
our causal statements, singular or general, have
just this force, and all that I am trying to show
here is that these statements can be supported by
reasoning along the lines of the Method of Con?
comitant Variation, developed analogously with
the development in ? 5 of the Method of Difference.
Just as we there assumed that there was some
necessary and sufficient condition, and by com?
bining this assumption with our observations dis
30 This was pointed out by D. C. Stove.
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causes and conditions 261
covered something which is at least an inus
condition, so we here assume that there is some
total cause and so discover something which is at
least a partial cause. However, a complete account
of the Method of Concomitant Variation would
involve the examination of several other cases
besides the one sketched here.31 For our present
purpose, we need note only that there is this
functional dependence part of the concept of
causation as well as the presence-or-absence part,
indeed that the latter can be considered as a special
limiting case of the former,32 but that the two
parts are systematically analogous to one another,
and that our knowledge of both singular and
general causal relationships of these two kinds can
be accounted for on corresponding principles.
? 8. The Direction of Causation
This account of causation is still incomplete, in
that nothing has yet been said about the direction
of causation, about what distinguishes A causing
P from P causing A. This is a difficult question,
and it is linked with the equally difficult question
of the direction of time. I cannot hope to resolve
it completely here, but I shall state some of the
relevant considerations.33
First, it seems that there is a relation which may
be called causal priority, and that part of what is
meant by “A caused P” is that this relation holds
in one direction between A and P, not the other.
Secondly, this relation is not identical with temporal
priority; it is conceivable that there should be
evidence for a case of backward causation, for A
being causally prior to P whereas P was temporally
prior to A. Most of us believe, and I think with
good reason, that backward causation does not
occur, so that we can and do normally use temporal
order to limit the possibilities about causal order;
but the connection between the two is synthetic.
Thirdly, it could be objected to the analysis of
“necessary” and “sufficient” offered in ? 4 above
that it omits any reference to causal order, whereas
our most common use of “necessary” and “suffi?
cient” in causal contexts includes such a reference.
Thus “A is (causally) sufficient for B99 says “If A,
then B, and A is causally prior to B,99 but “B is
(causally) necessary for A99 is not equivalent to
this: it says “If A, then B, and B is causally prior
to A.” However, it is simpler to use “necessary”
and “sufficient” in senses which exclude this causal
priority, and to introduce the assertion of priority
separately into our accounts of “A caused P” and
A causes P.” Fourthly, although “A is (at least) an
inus condition of P” is not synonymous with “P is
(at least) an inus condition of A,” this difference
of meaning cannot exhaust the relation of causal
priority. If it did exhaust it, the direction of
causation would be a trivial matter, for, given that
there is some necessary and sufficient condition of
A in the field, it can be proved that if A is (at
least) an inus condition of P, then P is also (at least)
an inus condition of A : we can construct a minimal
sufficient condition of A in which P is a moment.34
Fifthly, it is often suggested that the direction of
causation is linked with controllability. If there is
a causal relation between A and B, and we can
control A without making use of B to do so, and
the relation between A and B still holds, then we
decide that B is not causally prior to A and, in
general, that A is causally prior to B. But this
means only that if one case of causal priority is
known, we can use it to determine others: our
rejection of the possibility that B is causally prior
to A rests on our knowledge that our action is
causally prior to A, and the question how we know
the latter, and even the question of what causal
priority is, have still to be answered. Similarly, if
one of the causally related kinds of event, say A,
can be randomized, so that occurrences of A are
either not caused at all, or are caused by some?
thing which enters this causal field only in this way,
by causing A, we can reject both the possibility
that B is causally prior to A and the possibility that
some common cause is prior both to A and separ?
ately to B, and we can again conclude that A is
causally prior to B. But this still means only that
we can infer causal priority in one place if we
first know that it is absent from another place. It
is true that our knowledge of the direction of
causation in ordinary cases is thus based on what
we find to be controllable, and on what we either
find to be random or find that we can randomize ;
but this cannot without circularity be taken as
providing a full account either of what we mean
31 I have given a fuller account of this method in the article cited in n. 25.
32 Cf. J. R. Lucas, op. cit., p. 65.
33 As was mentioned in n. 21, Scriven’s fifth difficulty and refinement are concerned with this point (op. cit., pp. 411-412),
but his answer seems to me inadequate. Lucas touches on it (op. cit., pp. 51-53). The problem of temporal asymmetry is
discussed, e.g., by J. J. C. Smart, Philosophy and Scientific Realism (London, 1963), pp. 142-148, and by A. Gr?nbaum in the
article cited in n. 36 below.
24 I am indebted to one of the referees for correcting an inaccurate statement on this point in an earlier version.
B
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2?2 AMERICAN PHILOSOPHICAL QUARTERLY
by causal priority or of how we know about it.
A suggestion put forward by Popper about the
direction of time seems to be relevant here.35 If a
stone is dropped into a pool, the entry of the stone
will explain the expanding circular waves. But the
reverse process, with contracting circular waves,
“would demand a vast number of distant coherent
generators of waves the coherence of which, to
be explicable, would have to be shown … as
originating from one centre.” That is, if B is an
occurrence which involves a certain sort of “co?
herence” between a large number of separated
items, whereas A is a single event, and A and B
are causally connected, A will explain B in a way
in which B will not explain A unless some other
single event, say C, first explains the coherence in
B. Such examples give us a direction of explanation,
and it may be that this is the basis, or part of the
basis, of the relation I have called causal priority.
? 9. Conclusions
Even if Mill was wrong in thinking that science
consists mainly of causal knowledge, it can hardly
be denied that such knowledge is an indispensable
element in science, and that it is worth while to
investigate the meaning of causal statements and
the ways in which we can arrive at causal know?
ledge. General causal relationships are among the
items which a more advanced kind of scientific
theory explains, and is confirmed by its success in
explaining. Singular causal assertions are involved
in almost every report of an experiment: doing
such and such produced such and such an effect.
Materials are commonly identified by their causal
properties : to recognize something as a piece of a
certain material, therefore, we must establish
singular causal assertions about it, that this object
affected that other one, or was affected by it, in
such and such a way. Causal assertions are
embedded in both the results and the procedures
of scientific investigation.
The account that I have offered of the force of
various kinds of causal statements agrees both with
our informal understanding of them and with
accounts put forward by other writers : at the same
time it is formal enough to show how such state?
ments can be supported by observations and
experiments, and thus to throw a new light on
philosophical questions about the nature of causa?
tion and causal explanation and the status of
causal knowledge.
One important point is that, leaving aside the
question of the direction of causation, the analysis
has been given entirely within the limits of what
can still be called a regularity theory of causation,
in that the causal laws involved in it are no more
than straightforward universal propositions,
although their terms may be complex and perhaps
incompletely specified. Despite this limitation, I
have been able to give an account of the meaning
of statements about singular causal sequences,
regardless of whether such a sequence is or is not
of a kind that frequently recurs : repetition is not
essential for causal relation, and regularity does
not here disappear into the mere fact that this
single sequence has occurred. It has, indeed, often
been recognized that the regularity theory could
cope with single sequences if, say, a unique
sequence could be explained as the resultant of a
number of laws each of which was exemplified in
many other sequences ; but my account shows how
a singular causal statement can be interpreted,
and how the corresponding sequence can be shown
to be causal, even if the corresponding complete
laws are not known. It shows how even a unique
sequence can be directly recognized as causal.
One consequence of this is that it now becomes
possible to reconcile what have appeared to be
conflicting views about the nature of historical
explanation. We are accustomed to contrast the
“covering-law” theory adopted by Hempel, Pop?
per, and others with the views of such critics as
Dray and Scriven who have argued that explana?
tions and causal statements in history cannot be
thus assimilated to the patterns accepted in the
physical sciences.36 But while my basic analysis of
singular causal statements in ?? i and 2 agrees
closely with Scriven’s, I have argued in ? 4 that
this analysis can be developed in terms of complex
35 “The Arrow of Time,” Nature, vol. 177 (1956), p. 538; also vol. 178, p. 382 and vol. 179, p. 1297.
36 See, for example, G. G. Hempel, “The Function of General Laws in History,” Journal of Philosophy, vol. 39 (1942),
reprinted in Readings in Philosophical Analysis, ed. by H. Feigl and W. Sellars (New York, 1949), pp. 459-471; G. G. Hempel
and P. Oppenheim, “Studies in the Logic of Explanation,” Philosophy of Science, vol. 15 (1948), reprinted in Readings in the
Philosophy of Science, ed. by H. Feigl and M. Brodbeck (New York, 1953), pp. 319-352; K. R. Popper, Logik der Forschung
(Vienna, 1934), translation The Logic of Scientific Discovery (London, 1959), pp. 59-60, also The Open Society (London, 1952),
vol. II, p. 262; W. Dray, Laws and Explanation in History (Oxford, 1957); N. Rescher, “On Prediction and Explanation,”
British Journal for the Philosophy of Science, vol. 9 (1958), pp. 281-290; various papers in Minnesota Studies in the Philosophy of
Science, vol. Ill, ed. by H. Feigl and G. Maxwell (Minneapolis, 1962); A. Gr?nbaum, “Temporally-asymmetric Principles,
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CAUSES and conditions263
and elliptical universal propositions, and this means
that wherever we have a singular causal statement
we shall still have a covering law, albeit a complex
and perhaps elliptical one. Also, I have shown in
? 5, and indicated briefly, for the functional de?
pendence variants, in ? 7, that the evidence which
supports singular causal statements also supports
general causal statements or covering laws, though
again only complex and elliptical ones. Hempel
recognized long ago that historical accounts can
be interpreted as giving incomplete “explanation
sketches,” rather than what he would regard as
full explanations, which would require fully-stated
covering laws, and that such sketches are also
common outside history. But in these terms what
I am saying is that explanation sketches and the
related elliptical laws are often all that we can
discover, that they play a part in all sciences, that
they can be supported and even established without
being completed, and do not serve merely as
preliminaries to or summaries of complete deduc?
tive explanations. If we modify the notion of a
covering law to admit laws which not only are
complex but also are known only in an elliptical
form, the covering-law theory can accommodate
many of the points that have been made in
criticism of it, while preserving the structural
similarity of explanation in history and in the
physical sciences. In this controversy, one point
at issue has been the symmetry of explanation and
prediction, and my account may help to resolve
this dispute. It shows, in agreement with what
Scriven has argued, how the actual occurrence of
an event in the observed circumstances?the Ix of
my formal account in ? 5?may be a vital part of
the evidence which supports an explanation of
that event, which shows that it was A that caused
P on this occasion. A prediction on the other hand
cannot rest on observation of the event predicted.
Also, the gappy law which is sufficient for an
explanation will not suffice for a prediction (or for
a retrodiction) : a statement of initial conditions
together with a gappy law will not entail the
assertion that a specific result v/ill occur, though
of course such a law may be, and often is, used to
make tentative predictions the failure of which will
not necessarily tell against the law. But the recog?
nition of these differences between prediction and
explanation does not affect the covering-law theory
as modified by the recognition of elliptical laws.
Although what I have given is primarily an
account of physical causation, it may be indirectly
relevant to the understanding of human action
and mental causation. It is sometimes suggested
that our ability to recognize a single occurrence as
an instance of mental causation is a feature which
distinguishes mental causation from physical or
“Humean” causation.37 But this suggestion arises
Parity between Explanation and Prediction, and Mechanism versus Teleology,” Philosophy of Science, vol. 29 (1962), pp. 146-170.
Dray’s criticisms of the covering-law theory include the following : we cannot state the law used in an historical explanation
without making it so vague as to be vacuous (op. cit., especially pp. 24-37) or so complex that it covers only a single case
and is trivial on that account (p. 39) ; the historian does not come to the task of explaining an event with a sufficient stock
of laws already formulated and empirically validated (pp. 42-43) ; historians do not need to replace judgment about particular
cases with deduction from empirically validated laws (pp. 51-52). It will be clear that my account resolves each of these
difficulties. Gr?nbaum draws an important distinction between (1) an asymmetry between explanation and prediction with
regard to the grounds on which we claim to know that the explanandum is true, and (2) an asymmetry with respect to the
logical relation between the explanans and the explanandum; he thinks that only the former sort of asymmetry obtains.
I suggest that my account of the use of gappy laws will clarify both the sense in which Gr?nbaum is right (since an explana?
tion and a tentative prediction can use similarly gappy laws which are similarly related to the known initial conditions and
the result) and the sense in which, in such a case, we may contrast an entirely satisfactory explanation with a merely
tentative prediction. Scriven (in his most recent statement, the review cited in n. 10 above) says that “we often pin down
a factor as a cause by excluding other possible causes. Simple?but disastrous for the covering-law theory of explanation,
because we can eliminate causes only for something we know has occurred. And if the grounds for our explanation of an event
have to include knowledge of that event’s occurrence, they cannot be used (without circularity) to predict the occurrence of
that event” (p. 414). That is, the observation of this event in these circumstances may be a vital part of the evidence that
justifies the particular causal explanation that we give of this event : it may itself go a long way toward establishing the
elliptical law in relation to which we explain it (as I have shown in ? 5), whereas a law used for prediction cannot thus rest
on the observation of the event predicted. But as my account also shows, this does not introduce an asymmetry of Gr?nbaum’s
second sort, and is therefore not disastrous for the covering-law theory.
37 See, for example, G. E. M. Anscombe, Intention (Oxford, 1957), especially p. 16; J. Teichmann, “Mental Cause and
Effect,” Mind, vol. 70 (1961), pp. 36-52. Teichmann speaks (p. 36) of “the difference between them and ordinary (or
‘Humian’) sequences of cause and effect” and says (p. 37) “it is sometimes in order for the person who blinks to say absolutely
dogmatically that the cause is such-and-such, and to say this independently of his knowledge of any previously established
correlations,” and again “if the noise is a cause it seems to be one which is known to be such in a special way. It seems that
while it is necessary for an observer to have knowledge of a previously established correlation between noises and Smith’s
jumpings, before he can assert that one causes the other, it is not necessary for Smith himself to have such knowledge.”
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264 AMERICAN PHILOSOPHICAL QUARTERLY
from the use of too simple a regularity account of
physical causation. If we first see clearly what we
mean by singular causal statements in general, and
how we can support such a statement by observa?
tion of the single sequence itself, even in a physical
case, we shall be better able to contrast with
this our awareness of mental causes, and to see
whether the latter has any really distinctive
features.
This account also throws light on both the form
and the status of the “causal principle,” the de?
terministic assumption which is used in any
application of the methods of eliminative induction.
These methods need not presuppose determinism
in general, but only that each specific phenomenon
investigated by such a method is deterministic.
Moreover, they require not only that the pheno?
menon should have some cause, but that there
should be some restriction of the range of possibly
relevant factors (at least to spatio-temporally
neighboring ones, as explained in ? 5). Now the
general causal principle, that every event has some
cause, is so general that it is peculiarly difficult
either to confirm or to disconfirm, and we might
be tempted either to claim for it some a priori
status, to turn it into a metaphysical absolute
presupposition, or to dismiss it as vacuous. But
the specific assumption that this phenomenon has
some cause based somehow on factors drawn from
this range, or even that this phenomenon has some
neighboring cause, is much more open to empirical
confirmation and disconfirmation: indeed the
former can be conclusively falsified by the observa?
tion of a positive instance Ix of P, and a negative
case Mx in which P does not occur, but where
each of the factors in the given range is either
present in both Ix and Nx or absent from both.
This account, then, encourages us to regard the
assumption as something to be empirically con?
firmed or disconfirmed. At the same time it shows
that there must be some principle of the confirma?
tion of hypotheses other than the eliminative
methods themselves, since each such method rests
on an empirical assumption.
University of York
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Contents
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
Issue Table of Contents
American Philosophical Quarterly, Vol. 2, No. 4 (Oct., 1965), pp. 245-326
Causes and Conditions [pp. 245-264]
Symposium on Inductive Evidence
The Concept of Inductive Evidence [pp. 265-270]
Discussion: Is There a Problem of Induction? [pp. 271-273]
Comments on Salmon’s “Inductive Evidence” [pp. 274-276]
Rejoinder to Barker and Kyburg [pp. 277-280]
Operationalism and Ordinary Language: A Critique of Wittgenstein [pp. 281-295]
A Vindication of Scientific Inductive Practices [pp. 296-304]
Propositions as Answers [pp. 305-311]
Seeming to See [pp. 312-318]
Can a Smell or a Taste or a Touch Be Beautiful? [pp. 319-324]
Corrigenda to Medlin, Rankin and Spiegelberg [p. 325-325]
Choose a journal article, book chapter, or book from one of the core readings from any of the modules you have taken which applies one of the methods listed below, or in the case of “notions of causation” or “ethics and positionality”, that touches directly upon either issue.
Write a critical review (see word limits below) of the way in which this method has been applied or how questions of causality or of ethics have been navigated. As part of building this critique, your review can also consider the limitations or shortcomings of relying on a single or given method. Equally, if the source you have chosen uses more than one method (e.g. a case study and discourse analysis), then your review can critique both parts of this.
As part of building your critique, you are strongly encouraged to refer to the literature from the module reading list and to add to this by searching for additional relevant references.
(Ensure that you provide a full reference for the article/chapter/book you have chosen, as well as the module reading list to which it belongs)
List of topics:
· Notions of causation
· Ethics and Positionality
· Interviews, ethnography and participatory methods
· Case studies and comparative methods
· Discourse analysis
· Archival methods
· Intro to uses of quant data
· Visualising data 1
· Surveys and sampling
Word limits:
1. For those who began their course in 2021: 3000 words.

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