A Powerful Theory of Causation

Abstract and Figures

Hume thought that if you believed in powers, you believed in necessary connections in nature. He was then able to argue that there were none such because anything could follow anything else. But Hume wrong-footed his opponents. A power does not necessitate its manifestations: rather, it disposes towards them in a way that is less than necessary but more than purely contingent. In this paper a dispositional theory of causation is offered. Causes dispose towards their effects and often produce them. But a set of causes, even though they may succeed in producing an effect, cannot necessitate it since the effect could have been counteracted by some additional power. This would require a separation of our concepts of causal production and causal necessitation. The most conspicuous cases of causation are those where powers accumulate and pass a requisite threshold for an effect to occur.
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Printed in Anna Marmodoro (ed.) The Metaphysics of Powers, Routledge 2010: 143-59
A Powerful Theory of Causation
Rani Lill Anjum
Department of Philosophy, University of Tromsø and Nottingham
Stephen Mumford
Department of Philosophy, University of Nottingham
Hume thought that if you believed in powers, you believed in necessary connections in nature.
He was then able to argue that there were none such because anything could follow anything
else. But Hume wrong-footed his opponents. A power does not necessitate its manifestations:
rather, it disposes towards them in a way that is less than necessary but more than purely
In this paper a dispositional theory of causation is offered. Causes dispose towards their
effects and often produce them. But a set of causes, even though they may succeed in
producing an effect, cannot necessitate it since the effect could have been counteracted by
some additional power. This would require a separation of our concepts of causal production
and causal necessitation. The most conspicuous cases of causation are those where powers
accumulate and pass a requisite threshold for an effect to occur.
We develop a model for representing powers as constituent vectors within an n-dimensional
quality space, where composition of causes appears as vector addition. Even our resultant
vector, however, has to be understood as having dispositional force only. This model throws
new light on causal modality and cases of prevention, causation by absence and probabilistic
1. The dispositionality of causation
When it comes to causation, we should think less of necessity and more of dispositionality.
Others have already suggested that it should be possible to get a theory of causation from an
ontology of real dispositions or powers (Harré and Madden 1975, Bhaskar 1975, Cartwright
1989, Ellis 2001, Molnar 2003: ch. 12, Martin 2007: ch. 5). Such a project is far from
complete but even here we find that the key point of a dispositional theory of causation has
been lacking. One of the key attractions of a dispositional theory of causation should be the
claim that causes dispose towards their effects. This offers us something stronger than
Humeanism, in which everything is loose and separate. Unlike many opponents of the old
Hume, however, we do not want dispositionality to be reduced to necessity either for that too
would be to overlook what is most important about dispositionalism. Causes do not
necessitate their effects: they produce them but in an irreducibly dispositional way.
Many theories of causation assume that it must involve some kind of necessity, or that the
cause must be entirely sufficient for the effect.1 It is, however, not always clear what necessity
means in this context. It is often accepted that causal processes can be prevented or
interrupted and thus that any such necessity cannot be strict. In that case it is not clear what
the alleged necessity adds to the notion of causation, nor how it deserves the name.
There is, though, already an older tradition that acknowledges the dispositional nature of
causation. Aquinas‟s philosophy of nature, according to Geach (1961), is one in which causes
only tend towards their effects rather than necessitating them and the view presented in this
paper is on that account neo-Aquinian.2 Many contemporary treatments of causation follow
from Hume, however, as he was traditionally understood prior to the „New Hume‟ debate.
Constant conjunction is there depicted as a necessary condition for causation having occurred.
Dispositionalists have highlighted the weakness of constant conjunction, pointing out that
there can be accidental cases that were not genuinely causal, and instead saw real dispositions
as somehow imposing natural necessity on top of constant conjunction. We argue that a true
dispositionalism, in contrast, is one in which a cause only tends towards its effect. For a
general causal claim to be true, such as that smoking causes cancer, there need be no constant
conjunction. And in particular causal claims, even if one cause indeed produced its effect, that
doesn‟t mean it necessitated it. Something could have got in the way of the effect, even if it
did not as a matter of fact.
2. Causal production
How, one might wonder, can there be causal production unless there is necessitation? Isn‟t
necessitation required for causation because a cause has to be sufficient for its effect; in other
words, it must necessitate it? On the contrary, we maintain that the most natural account of
causation is one that does not require necessitation. The issue of causal production should be
seen as independent from the issue of causal necessitation for, as Collins, Hall and Paul
(2004: 18) say, that would be „simply to confuse guaranteeing an outcome with causing that
outcome‟. Perhaps some things can be guaranteed but, if that is the case, it is not causation
alone that makes the guarantee: it is something more. A cause should be understood,
therefore, as something that disposes towards a certain effect or manifestation. That will
suffice for general causal claims. In many particular causal claims, however, there is typically
also a factive element, which states that the effect actually did/does/will occur. The
dispositional theory thus says in the case of particular causal claims that a cause is something
that disposes towards an effect and succeeds in producing it (at least partially).
1 Examples are too numerous to list in full but for one contemporary instance see Sosa: „What there is in
common to all forms of causation is, it appears, necessitation‟ (Sosa: 1980: 241). Historical examples are to be
found in Aristotle, Metaphysics 5: 264, Spinoza 1677 I, ax. iii: 46, Kant 1781 book II, ch. II, sec iii, second
analogy, Mill 1843: III, V, sec 6, Russell 1913: 2, Ducasse 1924: 55, Davidson 1967: 698, Popper 1972: 91 and
Mackie 1980: 62.
2 Aquinas uses the terms inclinatio and appetitus. See Geach 1961: 101.
How, then, would causal production work? We offer what can be called a threshold account
in which an effect occurs when its causes have accumulated to reach the requisite threshold.
Our preference is to outline this account in terms of powers, which we believe to be the most
plausible truthmakers of causal claims, but we note that other views of the truthmakers may
be able to make use of the same idea. A threshold account is consistent with causes being
events or facts though we think that causation has an essentially powerful nature that sits
especially well with it being understood in terms of thresholds rather than necessity.3
Causation typically involves complexity. As Molnar says (2003: 194-8), different powers
accumulate polygenically and pleiotropically to produce what we would recognize as the
effect of a causal process (see Mumford 2009). That these effects are polygenic means that
they are typically produced by more than one power acting together. That powers are
pleiotropic means that they make the same contribution to any effect of which they are a
cause. The same power always makes the same contribution, when it manifests, even though
the final effect may vary according to what other powers it is operating with. Among other
things, this would allow us to understand the composition of powers along the lines of vector
addition, as shown in figure 1. Powers can be plotted as vectors on a one-dimensional quality
space with F and G as two possible effects of the accumulated powers. F could be the
property of being cold and G the property of being hot, for instance. Vectors are a useful way
of modeling powers because, like powers, they have a direction the possible manifestation
the power is „for‟ – and they have a strength or intensity, indicated by the length of the vector.
Figure 1: Powers modeled as vectors.
The threshold account of causal production states that an effect is produced when some local
aggregation of operative powers reaches the requisite threshold for that effect. In other words,
an effect is caused when powers have accumulated to reach the point at which that effect is
triggered. However, in reaching that point, we cannot consider simply the addition of
operative powers. Other powers might be subtracting from the accumulation and tending
away from the requisite threshold. In striking a match, for instance, and aiming to light it, I
am doing what I think needs doing for the threshold for lighting to be met. I am using a match
3 Empiricists tend to prefer events as the relata of causal relations while Mellor (1995) argues that the relata are
facts. Either view is consistent with a threshold account.
that I already judge to be suitably empowered, with its flammable tip intact. I am trying to
strike it in the right way, against a suitable surface and in the presence of oxygen. But I will
also be conscious of the powers that could subtract from those I have accumulated. I will try,
for example, to keep out of the wind precisely because I know that the wind could tend away
from the match igniting. Powers compose additively and subtractively in the sort of way we
would have to consider when calculating vectors. To calculate a final effect, we have to
consider the strength and direction of each individual vector. The resultant vector R will be
constituted by all the component vectors along the lines of vector addition (figure 2).4
Figure 2: A resultant vector R that meets a threshold.
What, though, are these causal thresholds and how do they relate to effects? The threshold is
not a real thing at all; it is only a way of understanding the point at which an effect occurs.
Often thresholds are marked as particular points that interest us because they involve some
significant or dramatic change. Water can become hotter and hotter, for instance, because of a
variety of factors at work. There is, however, a significant threshold that can be passed when
the water gets to 100C because at that point the water turns from liquid to steam. In another
case, pressure can be exerted on a vase and at some point the factors taken as a whole are
enough to make the vase shatter. An effect need not be quite so dramatic, however. I may
require simply that the water in my radiators reaches some point short of 100 but enough to
keep my living room warm. The desired effect in this case is simply a comfortable room
The threshold idea of production, mixed with the idea of causes as polygenic, shows us why
causal production does not require necessitation. Geach (1961: 102) provides a nice example
that we can use in which the same room contains both a heating unit A, which can raise the
room‟s temperature to 25 in an hour, but also a refrigerator unit B that can lower the room‟s
temperature to 10 in an hour. On its own, the heater A would have enough power to raise the
room temperature to 25, and sometimes does so. But it doesn‟t necessitate it. It won‟t reach
4 The understanding of causation along the lines of vector addition appears in Cartwright (1983: 59 & 1989:
163), though she rejects it on various grounds. She does not think that forces in the world, for instance, literally
add. She thinks that only resultant forces are real because they can be measured. In contrast, she thinks that
component forces have no separate existence because if they did there would be a systematic overdetermination.
Cartwright‟s view, applied directly to powers, is rejected in Mumford and Anjum (forthcoming).
that temperature won‟t reach the threshold – if the refrigerator is also on. If A alone is on,
the room reaches 25 in an hour. But if A and B are both operating, the room reaches, let us
suppose, only 15. So even though the heater A in one context would have enough power for
a certain effect, in another situation there is not overall enough for that same effect. Even
though the unit A appears sufficient for this effect, because it actually succeeds in producing
it in one situation, it cannot be the standard sufficiency as understood by philosophers because
we can have another situation in which A operates but does not produce that effect. The
example shows the way in which dispositionality, accumulation and subtraction are all in play
when it comes to whether or not an effect is actually produced. The bare notions of necessity
and causal sufficiency cannot do this justice.
3. Causes do not necessitate their effects
What is the argument for the claim that, in general, causes do not necessitate their effects? In
this section, the argument against necessity is advanced.
Let us call a group of polygenic causes C1, … Cn and assume that there is a case in which
together they produce the effect E, the match lights. Nevertheless, it can be claimed, had all of
C1, … Cn occurred but also some interfering condition I been present, such as a gust of wind,
then E might not have occurred. We are taking I to be a real natural or physical possibility,
rather than a mere logical one. This shows that C1, … Cn, although they caused E, were
nevertheless consistent with E not occurring. Therefore, C1, … Cn do not necessitate E, even
if as a matter of fact they do cause E.5
It should be noted that the argument applies whether we are talking about the causes of an
event as particulars or we are talking about type causal claims. We cannot say that causes of
the types C1, … Cn necessitate E if there are some instances of those types that fail to produce
E. But also we cannot say that particular tokens of C1, … Cn necessitated their token effect E
if something could have prevented it.
The argument against necessity might immediately provoke objections. We anticipate four of
Objection 1
The first objection to the argument against necessity is that it works only by changing the
original causal situation which, had it indeed been fully present, would after all have
guaranteed the effect. Suppose, for instance, a simple case where we have just four causes of
E, namely A, B, C and D. A might be that a particular match is dry, B that it is flammable, C
that there is oxygen present, and D that the match is struck. In this case A D do in fact cause
5 A precedent for the argument is to be found in Schrenk (2008). It is also deployed by Hume (1739: 161) against
the powers view, though we argue in §7 that it works against powers only when they are misconceived. The
argument also bears similarities to Bird‟s (1998) antidote case, where we could call I an antidote to the
disposition(s) that would produce E.
E: the match lights. But suppose I now allege that A D might have occurred without E
because, in some other situation, there is also the interference I that the humidity is too high
which prevents E. An objection to this claim would be that this new factor, I, is really just
the taking away of A because the match is no longer sufficiently dry when there is high
humidity. We do not then, in this second situation, have all of A to D present because I is
effectively just not-A by another name and we have thus failed to show that A to D are
consistent with E not occurring.6
This could indeed be true in this particular instance but it does not establish that all such
alleged cases of prevention are equally spurious, which is what would be needed for this
objection to be successful. The genuine exception cases are those where all of the causes A to
D, which in some cases succeed in producing E, are indeed present but E fails. Instead of high
humidity, for instance, a strong wind might prevent the match from lightning. The wind is not
a factor that is incompatible with A - D, that stops any of them happening or being the case,
but still it interferes with A - D such that they fail to produce E. Another case that we think is
clearly of this kind is that of a lumberjack felling a tree by cutting a wedge out of one side and
then letting gravity take hold of it. Do the wedge and the gravity necessitate that the tree falls?
Evidently not. The gravitational attraction to the Earth could still have been there, and the
wedge cut out of the tree, but these are consistent with a cyclone appearing above the tree and
sucking it off into the air.
Using the vector model, we can see that there is a clear distinction to be drawn between what
we may call subtractive and additive interference (figures 3 and 4). The argument against
necessity is premised on the possibility of additive interference, which it seems hard to deny
outright as a real possibility.
Figure 3: Subtractive interference (dotted vector is removed).
6 Our thanks to Maria Jose Encinas for developing this line of objection.
Figure 4: Additive interference (broken vector is added).
Objection 2
A second objection to the argument against necessity is that, as a matter of fact, there are
some cases of causation where it is just absolutely impossible that there be any prevention
because an effect follows a particular cause with absolute uniformity. Hume alleged a couple
of causal examples of inviolable constant conjunction for instance.7 One was that a flame
would cause us to withdraw our hand. No man could put his hand into the fire, and hold it
there, till it be consumed. Another case he cites is that A man who at noon leaves his purse
full of gold on the pavement at Charing-Cross, may as well expect that it will fly away like a
feather, as that he will find it untouched after an hour‟ (both examples 1748: VIII, 20).
Contrary to Hume‟s claims, however, both these cases could be prevented. Some people have
a condition in which they can feel no pain and would be capable of holding their hand in the
flame. And even if, as a matter of fact, there were no such condition, its very possibility is
enough for us to allow that such a causal claim admits the possibility of an exception. Again
in the second case, there is at least the possibility that all those who pass by Charing Cross
leave alone the purse for its owner‟s return.
An example from physics might be the case of gravitational attraction, which seems to be a
universal phenomenon whose operation can never be prevented. Suppose one thought that
gravity always resulted in a tendency to attract bodies. Gravity and this tendency are always
conjoined with no possibility of prevention. Is this a counterexample to the claim that causes
do not necessitate their effects? We argue not. It would be a misapprehension to think of
gravity and the tendency as standing in a causal relation. On the contrary, gravity just is the
tendency to attract bodies. What gravity, understood as such a tendency, actually causes
(when it does) is the movement of bodies towards each other and whether it actually does so
is obviously something that can be prevented by other powers and attractions. In the case of
gravity, the constant conjunction between gravity and the tendency to attract is not indicative
of causation at all but, it seems more plausible, identity.
7 Both these examples occur when Hume tries to show that we (people) are as much subject to causation as
inanimate matter. If constant conjunction could be shown for the most difficult case of persons, even with their
apparent free will to resist it, then it would seem also established for inanimate matter.
In answer to objection 2, therefore, we argue that when we consider the world, it is clear that
most causal cases admit the possibility of prevention. If there is a causal process for which
there is no preventer, it seems the exception rather than the rule. And even then, it seems that
we can countenance a possible preventer even if there is no actual one. To allow that is to
accept that even this process does not involve necessity.
Objection 3
Might one be able to ensure the necessity of the effect by just including more? Might it be that
as well as all the positive factors in the effect, all of C1, … Cn, part of the cause is also that all
the possible interfering factors are ruled out? Burks made this move in defending the
sufficiency of the cause for the effect, for example, stating that „By “sufficient conditions” we
mean a set of conditions, complete with respect to negative properties as well as positive ones
(i.e., counteracting causes must be explicitly mentioned) (1951: 368). Hence, the cause, as
well as C1, … Cn, includes ¬I1, ¬I2, and so on. Let us call this complete set of circumstances,
both positive and negative, the set . Is it the case, as Burks supposed, that necessitates the
effect in question, E? We can see immediately that it does not. The problem is that precisely
the same argument can be applied to . Although it may perfectly well produce E on any
number of occasions, that does not mean that it necessitated E. There could have been plus
one other counteracting power, I, that prevents E. There is no reason to think that the
possible interfering factors are of finite extent such that they could all be listed. And even if,
as a matter of fact, interferers are of finite extent in actuality, to prove that necessitates E
requires that there is not even some physically possible I that can prevent E. There seems to
be no plausible reason to rule out some such thing (though we will consider an attempt under
the next objection). Rather, we should conclude from this that there is no that could serve as
a „sufficient condition for E even though does indeed produce E.
It can also be noted here that if strictly there are no sufficient conditions for an effect then
there are no INUS conditions either. Mackie famously characterized a cause as an insufficient
but necessary part of a condition which is itself unnecessary but sufficient for the result‟
(1965: 34). No matter how big and complex the total cause is, it would never be sufficient for
its effect in the sense that it is impossible to have without E.
Objection 4
Could it be said that attempting to mention all the causes of E in a finite list such as is both
misguided and not what we actually do when we pick out a cause of an effect? Isn‟t it the case
that when we identify a cause of some effect, we automatically rule out any additional factors
that might interfere with it?
There are a number of mechanisms for doing so. One would be idealized models where we
abstract away from interfering factors and consider the causal process in isolation. But this, of
course, can be no more than an abstraction and should not be mistaken for the actual causal
scenarios as they play out in the world. There is, however, a real world correlate to
abstraction, which is the case of screening off‟ (Cartwright 1999: ch. 3), where in some
carefully controlled experiment we put up barriers to possible interferers. Armstrong‟s totality
facts (2004: 57f.) would also serve this purpose as they are the higher-order facts that there
are no more first-order facts. These could be used to stop the addition of anything further to .
Another suggestion might be that because we are surrounded by successful cases, where some
particular set of causes does indeed produce an effect, we are able to refer to that cause,
complex though it may be, ostensively. Employing externalist semantics, we might then
always have this kind of causal situation in mind and thus as the reference of future causal
attributions.8 Finally, there would be a Lewisian kind of constraint (Lewis 1973, 1986) that in
assessing causal claims we should consider only the closest possible worlds, which are worlds
in which interferers such as I are ruled out as gratuitous differences from the actual world. All
these solutions would purportedly work by picking out an exact kind of total circumstance, to
which nothing could be added, that is successful for the production of E and thus, it would
seem, sufficient for E. Let us call such a total circumstance, *.
If this kind of proposal is to add any more to those already discussed and dismissed, it is
because it would have some automatic exclusion of any further preventers such as I. But then
would the proposal really have established that * necessitates E? We should be skeptical of
that. How would we know that circumstances of type * necessitate E? That would have to
mean at least that every case of *, both actual and possible, is followed by E. How would we
know that E always does follow? To say so is to assume the very thesis that we deny, that *
necessitates E, and would thus be begging the question. * thus has no power to defeat the
argument against necessity. It merely denies it.
The major reason this approach ultimately fails is that it works by excluding one of the few
things that could convince us of the presence of necessity. The „solution‟ tries to
automatically rule out anything being added to the successful causal set up of that might
block E. But then it automatically excludes one of the most reliable, this-worldly tests we
have of necessity, namely, antecedent strengthening. When we want to know whether A
necessitates B, where B on its own is not already necessary, one plausible test is to consider
whether B would still be the case, given A, no matter what else happens. So if A is followed
by B, even if C, D, and no matter what else, then that is a good reason to believe that A
necessitates B. For example, we might think it necessary that „if x is human, then x is mortal
because we could strengthen the antecedent in any way we wanted and we would still get a
true conditional. „If x is human and , then x is mortal‟ remains true for any . Therefore, it
would only be non-question begging to say that * necessitates E if we could add something
else, I*, to * and still get E. But this is the very move that is supposed to be ruled out by this
strategy as a way of avoiding the argument that this I* could prevent E.
4. What if determinism is true?
8 Such a suggestion has been made to us by Matthew Tugby, following an idea of Alexander Bird‟s.
It may be objected to the account that we are assuming too much in an essentially a priori
consideration of causation. In particular, are we assuming in our theory that causal
determinism is false and thereby deciding a priori on a thesis that may be an a posteriori
matter? What, for instance, if physics were to tell us eventually that the whole history of the
universe was determined? If the truth or falsity of determinism is an a posteriori matter, then
no philosophical account of causation should rule it out.9 How should we respond?
In the first place, it should be noted that causal necessitarianism the thesis that causes
necessitate their effects is not the same thing as determinism. One could accept that all
causes necessitated their effects without being a determinist simply if one accepted that some
events are uncaused. Determinism would require, therefore, that not only do all causes
necessitate their effects but also that all events are caused. This shows that causal
necessitarianism does not entail determinism.
But does determinism entail causal necessitarianism? We have argued that causes should be
understood as disposing towards their effects and that because dispositions can be prevented
from manifesting, they should therefore be understood as not necessitating their effects. If
causal determinism is true, however, everything that happens is causally fixed by what has
happened earlier. But this would still be consistent with the possibility that any individual
causal process can be prevented, and in that sense the argument against the necessity of
effects stands. There is still a very real sense in which any causal process can be naturally
prevented. The determinist, however, would then have to say that where an individual, token
causal process is prevented, it was determined that it was so prevented. What did the
preventing, according to the powers theorist, will always be a countervailing power. What has
been said of necessity applies also to this countervailing power. Although its actual effect is to
prevent a certain process, our countervailing power could itself have been prevented from
operating and in that sense did not necessitate its effect. The causal determinist again will say
that whether or not it does so whether or not something else prevents it is an entirely
determined matter.
If this kind of determinism is true, then everything that happens naturally is fixed, including
which causal processes are prevented and which are not. This brings necessity in the sense
that nothing could have been different. It is a very strong claim, however. There would be no
probabilistic causation at all. Were we to be told on a posteriori grounds that the world is
indeed this way, we would beat a tactical retreat to a position in which the possibility that
things could have been different would be either purely logical, metaphysical or epistemic. It
could no longer count as a natural possibility. Yet there would also be enough of our core
argument that remained. Any individual causal process could still have been prevented had
things been different and by our lights is thus not necessary. In that sense, causation is not
necessary. What brings the necessity is the fixity of everything else: all the background
conditions and processes are set so that it is determined what causes what. With Anscombe, it
cannot be derived simply from the concept of causation that the world is like that.
9 Thanks to Stephen Barker for raising this point.
If A comes from B, this does not imply that every A-like thing comes from some B-
like thing or set-up or that every B-like thing or set-up has an A-like thing coming
from it; or that given B, A had to come from it, or that given A, there had to be B for it
to come from. Any of these may be true, but if any is, that will be an additional fact,
not comprised in A‟s coming from B. (Anscombe 1971: 136)
The deterministic assumption has to be added and cannot be derived merely from the notion
of causal production alone. The notion of causal production developed in section 2 is
consistent both with determinism and indeterminism and it seems quite correct that any theory
of causation should be likewise open to both possibilities.
5. Probabilistic causation
The thesis that causes do not necessitate their effects has thus far been independent of an
assumption of indeterminism and also of probabilistic causation. The thesis does not rest on
such things. Nevertheless, probabilistic causation has to be acknowledged as a possible kind
of causation that may indeed occur and even be widespread according to some theories. It is
relatively easy to understand probabilistic cases once one accepts the essentially dispositional
nature of causation.
By probabilistic causation we do not mean completely random chance events, which may best
be described as uncaused. Rather, we mean causation that is chancy yet probabilistically
constrained. Let us assume, as a model of such causation, a coin that when tossed has a 50:50
chance of landing heads or tails. Not all probabilistic causes of course have only two
outcomes: a dice roll has six. And not all probabilities are equal: a loaded coin may have a
disposition to land heads more frequently than tails. The simplest case, however two
outcomes with equal probability contains all the features we need.
Our preference would be a propensity interpretation of this kind of probabilistic chance (see
Mellor 1971). The propensity interpretation makes it sensible to ascribe a chance to an
individual coin toss instead of talking about frequencies but also, according to the
dispositional ontology, any truths about what is most likely for a whole group of coin tosses
would ultimately rest on the dispositions of the individual coins. A probabilistic disposition
could be plotted as a single double-headed vector, disposing partly towards F and partly
towards G (see figure 5). A 50:50 propensity will point to both in equal measure but other
propensities could point more towards one outcome than another.
Figure 5: A probabilistic case with two possible, equally likely, outcomes.
It is important that this be a single, probabilistic disposition rather than two distinct
dispositions. This would explain, for instance, why the combined probabilities must always
add up to one. It would be a disposition for a certain distribution between possible outcomes,
where all such outcomes comprise a single whole. The single, double-headed vector also
distinguishes this kind of power from a regular, non-probabilistic one. Once a probabilistic
power is involved, the rules of the game for vector addition are changed. A resultant can still
be calculated, but now more than ever it needs to be understood that the resultant only
disposes towards that outcome. If at least one probabilistic power is involved, then there
remains a chance of other possible outcomes.
Understanding irreducibly probabilistically constrained causation is not easy unless one
accepts that it involves a dispositional connection that is neither entirely necessary nor
entirely contingent. Our coin tends towards a 50:50 distribution, but in a sequence of trials
there could be any distribution of heads and tails. We know that an actual 50:50 distribution is
unlikely, especially when the number of trails is low. But we also know that if the number of
trials is high then a distribution wildly at odds with an equal distribution is highly unlikely.
There is a principle of probabilistic distribution that, applied to this case, says that the
proportion of heads and tails will tend to 50:50 as the number of tosses tends to infinity; or,
the higher the number of tosses then the closer to 50:50 the distribution is likely to be. This
principle is appealing and yet we might wonder why it is true. Is it just some brute fact about
the world or does it have a truthmaker? The powers theory offers a truthmaker for the
principle. The coin has a tendency to land heads and tails with equal chance, a tendency
which manifests itself over a sequence of trails. But this is „only‟ a disposition towards such a
distribution. It does not necessitate it, as we know when we acknowledge that any actual
distribution is possible for any sequence of tosses. Yet the distribution is not entirely
contingent either, as we know when we acknowledge that distributions at variance widely
from 50:50 are unlikely, proportionate to the number of trails.
The case of probabilistically constrained causation thus corroborates our account. It is
noteworthy in so far as the account seems to accord entirely with what we already accept pre-
theoretically to be the data of chancy causes.
6. Causation by absence?
A theory in which causation is essentially dispositional suggests the ontological reality of
powers and that causation occurs when powers manifest themselves. In that case, causation
could look like the passing around of powers (see Mumford 2009). There is an objection to
this, and to many similar theories of causation, that sometimes causes are absences, such as
when lack of water causes a plant to die or the lack of a nail causes a horseshoe to come loose
(see Schaffer 2004). Were there to be causation by genuine absences, that is, by nothing at all,
then it would indeed seem to create a problem for the present account. Absences are nothing
and how can nothing have causal powers?10 Powers, like properties, must be instantiated by
It is not, however, necessary to invoke absences as real causes. Why they are sometimes
invoked as such can be explained and justified by the powers theory. The solution we offer to
this difficulty resembles that of Dowe (2001) though with powers at its centre. The claim
would be that all cases of genuine causation involve the manifestations of dispositions. Where
an absence is invoked, what we have in mind is a counterfactual that the effect would not
have occurred had the removed or absent power been present. In figure 6, for instance, power
b is removed, such as when I stop watering my plant. When b was present, the plant was in
balance, disposing overall neither to death by drowning (F) nor death by dehydration (G).
Once we remove the water, it now disposes towards death by dehydration, but note that what
kills the plant is the remaining powers, c and d. The surrounding atmosphere had the power,
for instance, to suck moisture out of the roots, soil and leaves. This power is operative on the
plant and leads to its death. The absent water does nothing. The thesis that all causation
involves the exercise of powers could therefore still remain. Considering the vector model,
however, we can see that had the water been present, the plant would not have dehydrated,
which is why its absence is explanatorily useful.
Figure 6: Causation ‘by absence’
10 One might of course try to defend the line that an absence can have causal powers. David Lewis‟s (2004)
deadly void, for instance, might have a causal power to kill, but we do not think it is necessary to make this
move to account for such cases.
7. Where Hume really went wrong
Hume‟s account of causation has proved immensely seductive to such an extent that even
those who would refute him have nevertheless accepted many of his starting assumptions.
Hume produced an objection for his opponents, to those who believed that there were real
causal powers and that causation was something more than constant conjunction. They, Hume
insisted, were people who believed in a „necessary connexion‟ (1739: 77). This move was
made with little ceremony as follows:
… we must be able to place this power in some particular being, and conceive that
being as endow‟d with a real force or energy, by which such a particular effect
necessarily results from its operation. We must distinctly and particularly conceive the
connexion betwixt the cause and effect, and be able to pronounce, from a simple view
of the one, that it must be follow‟d or preceded by the other. (1739: 161)
But he was then able to argue that „Such a connexion wou‟d amount to a demonstration, and
wou‟d imply the absolute impossibility for the one object not to follow, or to be conceiv‟d not
to follow upon the other‟ (1739: 161-2). There was no such thing, he concluded.
We have used the same argument as Hume but against the claim that causal production entails
causal necessitarianism. However, it would be a mistake to acquiesce in Hume‟s
characterisation of powers. Those who believe in real causal powers should not at all accept
that they involve necessary connections between events. Hume has effectively wrong-footed
his opponents, saddling them with a position they should never and need never adopt. Realists
about dispositions have long rejected the so-called conditional analysis of dispositions (see
especially Martin 1994). But they have not yet been as ready to reject a necessitarian version
of the same view: that a disposition ascription means that if a certain stimulus occurs then a
certain effect will be necessitated. Just as much, this is an attempt to reduce the dispositional
to something else, supposedly more familiar. Anti-Humeans should instead believe in causal
connections that are short of necessity, yet more than contingent. This connection is anti-
Humean enough, but we should not be misled by his talk of necessity to go further than we
ought. The main point is that dispositionality has an important, real and irreducible modal
force of its own. Any attempt to replace it with something non-dispositional will miss the
most important thing about dispositionality and, as we argue here, causation.
Indeed, we think that Hume was also incorrect to think that constant conjunction was a part of
the notion of causation.11 That we experience the kind of constant conjunction that Hume had
in mind is a dubious claim. Even in his perfect instance of causation, the billiard table (1740:
11 We believe that Hume‟s condition of temporal priority was also a mistake. We do not think that causes
precede their effects but that they are simultaneous with them. We have not the space to discuss this claim in
detail here, however.
137), it is implausible that an absolute constant conjunction is really to be found. The object
ball that is struck, he claims, always moves away across the table towards the pocket. It never
flies into the air, he protests. But we know that there are cases where it does precisely that:
where there is an unexpected kick of the kind feared by professional snooker players.
The possibility of exceptions is something that Hume admits when he considers cases where
there are only „inferior degrees of evidence‟ (1739: 403) of causation. But of cases where
there is a less than constant conjunction he surmises that
supposing that the usual contrariety proceeds from the operation of contrary and
conceal‟d causes, we conclude, that the chance or indifference lies only in our
judgement on account of our imperfect knowledge, not in the things themselves,
which are in every case equally necessary, tho‟ to appearance not equally constant or
certain. (1739: 403-4)
Such cases, we argue, are the norm, not the exception. What they show is that constant
conjunction, contrary to what Hume elsewhere routinely claims, is not a part of our immediate
experience. Instead, constant conjunction is something that is inferred from our experience of
less than constant conjunction. And as the passage above quoted reveals, that inference is of a
highly theoretical nature. It would seem that it is motivated by nothing more than an
assumption that wherever there is an exception to a constant conjunction it is because there is
some other constant conjunction at work, of which we are ignorant. Having made that
assumption, Hume then immediately goes back to his usual claim that the idea of cause and
effect arise from „the experience and the observation or their constant union‟ (1739: 405). We
urge that a true consideration of the situation shows that constant union is not something that
confronts our experience of causation. The union, we argue, is always less than constant and
is instead of what Hume calls inferior degrees. Where it is not inferior, we argue the union is
most likely not causal but rather something else such as classification, essence or identity. The
assumption that there is always a concealed constant union at work in causation therefore
looks under-motivated.
8. Conclusion
We hope to have shown in this paper that causal production is not the same as causal
necessitation. This claim should be no threat to our pre-existing causal thinking. All that has
been advanced should be consistent with common sense. The idea that causes dispose towards
their effects is natural and makes sense of certain phenomena that by other theories will be
philosophically problematic. The dispositional theory of causation shows that the possibility
of preventions and exceptions is not something that has to be explained away but something
that should be accepted as central to the nature of causation, showing its essentially
dispositional character.
A cause can then be understood as a disposition towards an effect, where causal powers are
doing their work and manifesting themselves. This is what we think should be basic to a
dispositional theory of causation and we take to be a promising this-worldly alternative to
Lewis counterfactual dependence account of causation. Assessing whether this or the
counterfactual dependence account is the best theory of causation could be done only after
careful consideration of the relative merits of each and while we are optimistic about how the
dispositional theory would come out of such a consideration, we will leave that work for
elsewhere. 12
12 Earlier versions of this paper were presented at the Metaphysics of Science workshop in Münster, Germany,
the Powers, Causation & Laws conference at Durham University, the Nottingham dispositions group, the
University of Köln, the University of Athens, Bogazici University, the Powers, Dispositions and Singular
Causation conference in Buffalo and the University of Warsaw. We thank all who gave comments. This research
was conducted with the financial support of the AHRC-funded Metaphysics of Science project and the
Norwegian Research Council (NFR). We also thank Manuel de Pineda and Markus Schrenk, Matthew Tugby
and Charlotte Matheson for helpful support and criticism.
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