Chapter 14: Causes, Contrasts, and the Nontransitivity
of Causation1
Cei Maslen
1. Introduction
Whether one event causes another depends on the
contrast situation with which the alleged cause is
compared. Occasionally this is made explicit. For
example, a toothpaste company claims that regular
brushing with their product will cause teeth to become
up to two shades whiter than with “another leading
brand”. Here, the comparison not only helps to specify
a range of shades of white, but also to specify a
contrast situation. Regular brushing with their product
is not compared to, say, irregular brushing with their
product or not brushing at all, but to regular brushing
with another leading brand.
More often the contrast situation is not made
explicit, but is clear from the context. Hence, in
general, the truth and meaning of causal statements
depend on the context in which they occur. In section
2, I give a more complete formulation of this claim,
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illustrate it with an example and compare it to similar
and superficially similar views. The theory is
incomplete without a description of how contrast events
are fixed by the context, which I supply in section 3.
In section 4, I discuss the context dependence of
counterfactuals. Of course, a major motivation for the
theory is the extent to which it can avoid obstacles
that have defeated other theories of causation,
problems such as the nontransitivity of causation,
preemption, causation by absences, and causation under
indeterminism. In section 5, I explain how a
contrastive counterfactual account solves the first of
these problems: analyzing the nontransitivity of
causation.2
2. A Contrastive Counterfactual Account
Causal statements are systematically dependent on
context.3 The meaning and truth-conditions of causal
statements are dependent on contrast events that are
seldom explicitly stated, but are fixed by
conversational context and charity of interpretation.
Occasionally confusion about contrast events leads to
misunderstandings and indeterminacy of meaning and
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truth-value. This may be expected when causal
statements are taken out of context, for example, in
some philosophical discussions.
This isn’t to make causation a subjective matter.
The causal structure of the world is an objective,
mind-independent three-place relation in the world
between causes, contrasts, and effects. (Compare this
to discovering that motion is relative to frame of
reference. This is not to discover that motion a
subjective matter.)
It would perhaps be ideal to study the properties
of causal statements (e.g. nontransitivity and context
dependence) without appealing to a specific formal
analysis of our concept of causation. All formal
analyses of causation are controversial, and
complicated. The claims that causation is contextdependent, and that causation is non-transitive are
partly independent of any specific analysis. However,
in practice it is impossible to have detailed
discussions of these aspects without settling on one
analysis. The few philosophers who discuss the context
dependence view can be classified into all the major
schools of thought on causation. Hitchcock4
3
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incorporates it into a probability-raising account.
Field5 discusses probabilistic and non-probabilistic
versions of a regularity or law-based view. Holland6
presents a counterfactual account. I support a
counterfactual account also, and concentrate on
singular causal claims.
2.1 Account1
For distinct events c, c* and e, c is a cause of e
relative to contrast event c* iff c and e actually
happened and if c had not happened, but contrast
event c* had happened instead, then e would not
have happened.
This account takes events as the fundamental causal
relata. Either Kim’s or Lewis’s definitions of events
would serve this purpose.7 My hope is that causal
sentences with other kinds of relata (physical objects,
processes, facts, properties, or event aspects) can be
reexpressed in terms of event causation, but I will not
argue for this claim here.8 I discuss counterfactuals
briefly in section 4 below. I think that our intuitive
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understanding of this grammatical form is strong, so I
do not commit myself to an analysis here.9
The only restrictions I place on the contrast
event is that it be compossible with the absence of the
cause and distinct from the absence of the cause.10 I
also require that the cause, effect and contrast event
be distinct events.11 This may seem hopelessly liberal.
What is to stop someone from claiming that brushing my
teeth this morning, in contrast to being hit by a
meteorite, was a cause of my good humor, or that the
price of eggs being low, in contrast to the open fire
having a safety guard, was a cause of the child’s burn?
The inanity of these examples arises from inappropriate
contrast events. Describing appropriateness of contrast
is a difficult task, and I have little more to say
about it at this stage than that events are usually
contrasted with events that occur at a similar time,
and that might have replaced them.12
Let’s assume that any complex of events (the event
which occurs just in case the constituent events occur)
is itself an event. It will be useful to define a
contrast situation as the complex of a contrast event
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and the event in which the absence of the cause
consisted.13 With this terminology, account1 is:
Event c is a cause of event e relative to a
contrast situation iff had the contrast situation
happened, then e would not have happened.
There may also be explicit and implicit
alternatives to the effect. For example, a friend’s
opinions were a cause of my renting the video “Annie
Hall” rather than the video “Mighty Aphrodite”.
Account1 can be generalized in the following way to
allow for contrasts to the effect and for a range of
implicit contrasts. (However, I will mostly continue to
work with the simpler account1).
2.2 Account2
Event c, relative to contrast situations {c*}, is
a cause of event e, relative to contrast
situations {e*}, iff had any events from {c*}
occurred, then an event from {e*} would have
occurred.14
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2.3 Illustrations
Here are two examples to illustrate the context
dependence of causation. First, suppose I have three
cookie recipes: hazelnut cookies, walnut cookies and
pecan cookies. I decide to make hazelnut cookies, then
offer one to Stuart. Unfortunately Stuart has a nut
allergy; he is allergic to all nuts. He eats the cookie
and becomes ill. Was making the hazelnut cookies one of
the causes of his illness?
Well, if I hadn’t made the hazelnut cookies I
would have made the pecan cookies, because I have only
three cookie recipes and I have no walnuts in the
house. So in one sense, making the hazelnut cookies was
not a cause of his illness. Relative to making pecan
cookies, making hazelnut cookies was not a cause of his
illness. However, relative to the alternative of making
no cookies at all, making the hazelnut cookies was a
cause of his illness. Taken out of context, there is no
correct answer to the question whether making hazelnut
cookies was a cause of Stuart’s illness. Out of
context, the only valid claims we can make are relative
claims. However, the conversational context and
unspoken assumptions can make some alternatives more
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salient than others. Our awareness that I only have nut
cookie recipes made the alternatives of baking pecan
cookies and walnut cookies salient alternatives for us,
and in the context of this paper the causal claim
“making hazelnut cookies was a cause of his illness” is
naturally interpreted as meaning “making hazelnut
cookies, relative to making pecan cookies or walnut
cookies, was a cause of his illness.”
The second example, of an electric circuit, comes
from Daniel Hausman, though he uses it for a different
purpose. “The ‘weak circuit’ and the ‘strong circuit’
power a solenoid switch, which closes the ‘bulb
circuit’. If only the weak circuit is closed, the
current through the solenoid is 4 amperes. If only the
strong circuit is closed, the current through the
solenoid is 12 amperes. If both are closed, about 16
amperes flow through the solenoid. It takes 6 amperes
to activate the solenoid switch, close the bulb
circuit, and turn on the light bulb. Whether the weak
circuit is closed or not affects how much current is
flowing through the solenoid, but it has no influence
on whether the light goes on.”15
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[Figure 1]
Suppose that on this occasion, I close both the
strong and the weak circuit, a current of 16 amperes
flows through the coil, the solenoid switch closes, and
the bulb lights. Was the presence of a current of 16
amperes through the coil a cause of the bulb lighting?
The answer to this question is relative to the contrast
event.
16 amperes flowing through the coil, rather than 12
amperes flowing through the coil, was not a cause of
the bulb’s lighting.
16 amperes flowing through the coil, rather than 4
amperes flowing through the coil, was a cause of the
bulb’s lighting.
16 amperes flowing through the coil, rather than 0
amperes flowing through the coil, was a cause of the
bulb’s lighting.
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The fact that there are cases like these where the
context dependence is clear, gives excellent support to
the context dependence view.
2.4 Other views
At this point, it will be helpful to compare account2
to similar and superficially similar views.
I am not proposing a revisionary account of
causation. The realization that causation is contextdependent and that this can lead to misunderstandings
might prompt us to propose a revisionary account of
causation. We could suggest that in the future, in
order to avoid misunderstandings in precise or
important uses of causal claims, we should always state
alternative events together with our causal claims. We
could even follow Bertrand Russell in suggesting that
we abandon the concept of causation altogether.16
Instead we would only use precise counterfactuals with
our assumptions spelt out. But the state of our causal
concept does not warrant such an extreme reaction.
The context dependence that I have described in
the concept of “a cause” is additional to the generally
accepted context dependence of “the cause” or “the
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decisive cause”. I am only concerned here with what it
takes to be “a cause” or “one of the causes” of a given
effect. The context dependence of the concept of “the
cause” is more obvious. It might be suspected that
there is only one source of context dependence here and
that is from the concept of “the cause”. It could be
argued that we confuse “a cause” for “the cause” when
we read the examples, and this is why we find them
convincing. However, this simply isn’t borne out by our
intuitions. We do have an additional contextual element
here.
The context dependence of causation is distinct
from the widely accepted view that explanation is
context-dependent. Van Fraassen is the major defender
of the latter view: “If, as I’m inclined to agree,
counterfactual language is proper to explanation, we
should conclude that explanation harbors a significant
degree of context-dependence.”17 He argues that the
context dependence of explanation takes the form of
determining both the salience of explanatory factors
and also the contrast class. However, those who claim
that explanation is dependent on context assume that
causation is independent of context. For example, it
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seems to be implied by van Fraassen’s claims that the
propositions of the causal net are scientific
propositions, and “scientific propositions are not
context-dependent in any essential way”18 that causal
statements are (essentially) independent of context. I
disagree; both explanation and causation are contextdependent.
Account2 is similar in many ways to Lewis’s recent
“Causation as influence” view and to event-feature
views of causation, for example, Paul’s “Aspect
Causation” view. I do not have space to discuss all the
similarities and differences here. However, note that
all three views imply that causal statements are
strongly context dependent. Lewis talks of “a
substantial range of not-too-distant alterations” of
the cause; what constitutes a substantial range, and
what constitute not-too-distant alterations of the
cause presumably differs with context. Event-feature
views require the context to determine event features
from event nominalizations.
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3. Contrast Events and Context
The context of a statement is the circumstances in
which it occurs. The truth of a statement may depend on
features of the context as well as on matters of fact.
Dependence on matters of fact is contingency;
dependence on features of context is context
dependence. Following the two-stage scheme of
Stalnaker, an interpreted sentence together with a
context determines a proposition, and a proposition
together with a possible world determines a truth
value.19 Hence, which proposition is expressed by an
interpreted sentence may depend on the context in which
it occurs. A classic example of a context-dependent
sentence is “I went to the store”; its interpretation
depends on the identity of the speaker, due to the
indexical “I”.20
In general, a large variety of contextual features
may be required to interpret a sentence on a particular
occasion. For example “the intentions of the speaker,
the knowledge, beliefs, expectations, or interests of
the speaker and his audience, other speech acts that
have been performed in the same context, the time of
utterance, the effects of the utterance, the truth-
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value of the proposition expressed, the semantic
relations between the proposition expressed and some
others involved in some way”.21 Features of context
such as speaker and time of utterance are almost always
obvious and readily observable. The set of contrast
events is a theoretical feature of context; hence, we
owe a description of how contrast events connect with
more obvious features of context. Otherwise, when
disputes arise it might seem as though the
metaphysician is magically summoning the set of
contrast events or choosing the set to fit her case.
Suppose that the contrast event is what the
speaker has in mind for replacing the cause. That is,
it is what the speaker has in mind to be different in
an imagined counterfactual situation where the cause is
removed. Two objections to this immediately arise.
Firstly, unphilosophical speakers may not have anything
of the right sort in mind when uttering causal
statements. When asked what they had in mind, many
speakers may admit that they hadn’t thought about it.
However, usually these speakers then have no problem
responding with a contrast event when prompted. These
responses give the intended interpretation of the
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original causal statement, in some sense of “intended”.
Secondly, as we are not mind readers, if the “have in
mind” picture were the whole story then communication
would be very haphazard.
The rest of the story is that which contrast set
the speaker has in mind, if not communicated directly,
may be clear to the audience by the previous course of
the conversation, acknowledged assumptions,
limitations, plans, and presuppositions. General
pragmatic principles play a large part in this. The set
of contrast events is what Lewis calls a “component of
conversational score”.22 We have a tendency to
interpret utterances generously or charitably, as true
or probable, relevant, useful and informative. The set
of contrast events is fixed and developed through the
course of the conversation. Sometimes the set is left
unsettled or vague until a dispute arises. In a few
cases this vagueness even leads to ambiguity in the
causal statement.
Often there are physical limitations on the ways
in which the cause could have been omitted. This gives
us a “default” set of contrast events. Consider the
following example. My opponent and I are both very
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competitive. We each would have been happy to win, but
we are both unhappy when we reach a draw at chess.
“Reaching a draw at chess was a cause of us both being
unhappy.”
Presuming that we finish the chess game, there are only
two ways in which the event of reaching a draw could
have been omitted: by my winning the game, or by my
opponent winning the game. Hence, there are two natural
interpretations of the causal statement:
“Reaching a draw at chess, in contrast to my winning
the game, was a cause of us both being unhappy”;
“Reaching a draw at chess, in contrast to your winning
the game, was a cause of us both being unhappy.”
Either of these alternative outcomes would have
left one of us happy. Hence reaching a draw can truly
be called a cause of us both being unhappy. The natural
set of contrasts here are the events which the absence
of the cause would have consisted in. Given our
assumption that we did actually finish the chess game,
the absence could only have consisted in my winning the
game, or my opponent winning the game.
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In some cases, there is only one probable way in
which the cause would have been omitted and this is the
natural or default contrast. Suppose that my opponent
is a much better chess player than I. If we hadn’t
reached a draw, he would almost certainly have won.
Given our assumptions, the contrast situation here is
naturally limited to one alternative. The following
causal claim is probably true in that context.
“Reaching a draw on the chess game was a cause of my
opponent being unhappy.”
The default contrast is always overruled by what
the speaker has in mind or intends as the contrast. For
instance, suppose I mistakenly believe that I am the
better player. I could have in mind a contrast with the
case in which I had won the game and deny the above
causal claim. (If my opponent does not realize I have
this mistaken belief, then this will probably lead to
misunderstanding). Even if I recognize that my opponent
would have won the game if we hadn’t drawn, I could
make it clear that I’m contrasting with a wider set,
and then deny the causal statement above. I could
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contrast with the set {playing the chess game and my
winning, playing the chess game and his winning, not
playing the chess game at all}.23
4. The Context Dependence of Counterfactuals
The counterfactual analysis of causation is one of the
most popular approaches to analyzing causation. Hence,
it is strange that counterfactuals are widely
acknowledged to be context-dependent, while causation
is not widely acknowledged to be so.
The context dependence of counterfactuals has been
observed and discussed in most major works on
counterfactuals.24 Here are some classic examples
exhibiting context dependence.
If Caesar had been in command in Korea he would
have used the atom bomb.
If Caesar had been in command in Korea he would
have used catapults. [Example due to Quine]
If this were gold it would be malleable.
If this were gold then some gold things would
not be malleable. [Example due to Chisholm]
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If New York City were in Georgia then New York
City would be in the South.
If New York City were in Georgia then Georgia
would not be entirely in the South. [Example due
to Goodman]
All of these counterfactuals are context-dependent.
Consider just the first pair. Each statement can be
reasonably asserted in the same situation. (We
presuppose that Caesar was ruthless, ambitious and
indifferent to higher authority.) Yet the first
statement implies that the second statement is false.
(We presuppose that it is possible that Caesar was in
command in Korea and it is not possible that he uses
both catapults and atom bombs.) The second statement
cannot be both true and false, so it must express at
least two different propositions depending on factors
other than the background facts. It is contextdependent.
Acknowledging the context dependence of
counterfactuals can help us to understand the context
dependence of causation. I do not wish to commit myself
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to one analysis of counterfactuals here. However, let
me mention how two successful and sophisticated
analyses of counterfactuals account for their context
dependence. One formulation of Lewis’s analysis of
counterfactuals is as follows:
“A counterfactual ‘If it were that A, then it would be
that C’ is (non-vacuously) true if and only if some
(accessible) world where both A and C are true is more
similar to our actual world, overall, than is any world
where A is true but C is false”25
On his account, the context dependence of
counterfactuals arises because our judgments of overall
similarity of possible worlds depend on context. “The
delineating parameter for the vagueness of
counterfactuals is the comparative similarity relation
itself: the system of spheres, comparative similarity
system, selection function, or whatever other entity we
use to carry information about the comparative
similarity of worlds”.26
The tacit premise view of counterfactuals is
presented by Chisholm and by Tichy.27 On this view, a
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counterfactual is true iff its antecedent together with
its tacit premises logically entail its consequent, and
the tacit premises are true. The tacit premises are
simply those assumptions which have been presupposed in
the conversation or which the speaker has in mind on
the occasion of utterance. The context dependence is
obvious on this view.
It is interesting that Lewis observes in his
original paper on causation “The vagueness of
similarity does infect causation, and no correct
analysis can deny it”.28 His original theory already
accounts for some context dependence, admittedly in a
subtle way.
5. The Nontransitivity of Causation
Is causation transitive? That is, is it true for all
events a, b and c that if a is a cause of b and b is a
cause of c then a is a cause of c? Some causal chains
are clearly transitive. Suppose that the lightning is a
cause of the burning of the house, and the burning of
the house is a cause of the roasting of the pig.
(Suppose that the pig was trapped in the house). Then
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surely the lightning is also a cause of the roasting of
the pig. But is this true for all events a, b, and c?
In the past, the transitivity of causation was
commonly assumed in the literature without argument.29
But more recently a host of ingenious examples have
been presented as counterexamples to the transitivity
of causation.30 Before discussing these examples, let’s
briefly consider one argument for the transitivity of
causation.
The only argument that I have found in the
literature for the claim that causation is transitive
comes from Hall. Hall argues “rejecting transitivity
seems intuitively wrong: it certainly goes against one
of the ways in which we commonly justify causal claims.
That is, we often claim that one event is a cause of
another precisely because it causes an intermediate,
which then causes another intermediate, ... which then
causes the effect in question. Are we to believe that
any such justification is fundamentally misguided?”31
This is an important consideration. I agree with
Hall that it is common practice to refer to
intermediates in a causal chain in justifying causal
claims. This seems to apply across many different
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fields of application of the singular causal concept:
history, science, law, and ethics. I don’t think that
this practice is fundamentally misguided, but it may be
a rule of thumb, which should be supplemented with
restrictive guidelines. If we are to reject
transitivity, we have a pressing need for a general
rule for distinguishing the cases in which transitivity
holds from the cases in which it fails, and an
explanation of why transitivity sometimes fails. Hall
agrees with me here. He issues a challenge: “Causation
not transitive? Then explain under what circumstances
we are right to follow our common practice of
justifying the claim that c causes e by pointing to
causal intermediates.”32 I take up this challenge in
the next section after presenting the counterexamples.
The alleged counterexamples to transitivity are
diverse; I will describe three difficult and
representative cases - ‘bomb’, ‘birthday’, and ‘purple
fire’. The first comes from Field.33 Suppose that I
place a bomb outside your door and light the fuse.
Fortunately your friend finds it and defuses it before
it explodes. The following three statements seem to be
true, thus showing that causation is nontransitive.
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(1a) My placing the bomb outside the door is a cause of
your friend’s finding it.
(1b) Your friend’s finding the bomb is a cause of your
survival.
(1c) My placing the bomb outside the door is not a
cause of your survival.
On a more cheerful note, suppose that I intend to
buy you a birthday present, but when the time comes I
forget. Fortunately, you remind me and I buy you a
birthday present after all. The following three
statements seem to be true, thus showing that causation
is nontransitive.
(2a) My forgetting your birthday is a cause of your
reminding me.
(2b) Your reminding me is a cause of my buying you a
birthday present.
(2c) My forgetting your birthday is not a cause of my
buying you a birthday present.
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Finally, consider Ehring’s purple fire example.34
I elaborate. Davidson puts some potassium salts into a
hot fire. The flame changes to a purple color but
otherwise stays the same, because potassium compounds
give a purple flame when heated. Next, the heat of the
fire causes some flammable material to ignite. Very
soon the whole place is ablaze, and Elvis sleeping
upstairs, dies of smoke inhalation. The following three
statements seem to be true and again show that
causation is nontransitive.
(3a) Davidson’s putting potassium salts in the
fireplace is a cause of the purple fire.
(3b) The purple fire is a cause of Elvis’ death.
(3c) Davidson’s putting potassium salts in the
fireplace is not a cause of Elvis’ death.
6. A Contrast Analysis of the Counterexamples
Transitivity is only defined for binary relations, but,
on the context dependence view, causation is not a
binary relation. (It is either a three place relation
between a cause, a context, and an effect, or a fourplace relation between a cause, two sets of contrast
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events, and an effect, depending on how you count it.)
We will discuss a related property, the “variablecontext transitivity” of the three-place causal
relation. The three-place causal relation has
“variable-context transitivity” just in case for all
events e1, e2, e3, and for all contexts c1, c2, c3, if e1
causes e2 in context c1, and e2 causes e3 in context c2,
then e1 causes e3 in context c3. That is, the causal
relation has variable-context transitivity just in case
it appears transitive no matter how you change the
context.
Let’s analyze the bomb example. The example can be
interpreted in many different ways depending on the
contrast events assumed in statements (1a), (1b), and
(1c). Two natural contrasts with the cause in (1a) are
the contrast with my placing nothing outside the door
and the contrast with my carefully concealing the bomb
outside the door. My placing the bomb outside the door,
in contrast to my placing nothing outside the door, is
a cause of your friend’s finding the bomb, because if I
had placed nothing outside the door your friend
wouldn’t have found the bomb. My placing the bomb
outside the door, in contrast to my carefully
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concealing the bomb outside the door, is a cause of
your friend’s finding the bomb, because if I had
carefully concealed the bomb outside the door your
friend would not have found it (let us say).
Some interpretations of the example do not yield
counterexamples to transitivity. Statement (4c) of the
following is false: it seems plausible that my placing
the bomb outside the door, in contrast to my carefully
concealing the bomb outside the door, is a cause of
your survival. So the following causal chain is
transitive.
(4a) My placing the bomb outside the door (vs.
carefully concealing it) is a cause of your friend’s
finding it (vs. overlooking it).
(4b) Your friend’s finding the bomb (vs. overlooking
it) is a cause of your survival (vs. death).
(4c) My placing the bomb outside the door (vs.
carefully concealing it) is not a cause of your
survival (vs. death).
However, with other natural contrasts, we do have
a nontransitive causal chain. For example, all three of
the following statements seem true.
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(5a) My placing the bomb outside the door (vs. placing
nothing outside the door) is a cause of your friend’s
finding the bomb (vs. finding nothing).
(5b) Your friend’s finding the bomb (vs. finding
nothing) is a cause of your survival (vs. death).
(5c) My placing the bomb outside the door (vs. placing
nothing outside the door) is not a cause of your
survival (vs. death).
We can develop a sufficient condition for a causal
chain to be transitive from a special case of inference
by transitivity of counterfactuals:
(T) φ □→ χ , χ□→φ, φ□→ψ χ□→ψ35
Consider a general causal chain:
(6a) a, with contrast situation c1 is a cause of b,
with contrast situation d1.
(6b) b, with contrast situation c2, is a cause of e,
with contrast situation d2.
(6c) a, with contrast situation c3, is a cause of e,
with contrast situation d3.
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Suppose (C1) c1=c3, d1= c2, d2= d3, (in other words,
events a, b, and e have the same contrasts throughout)
and (C2) if c2 had occurred then c1 would have to have
occurred (a backtracking counterfactual).36 From (T),
and account2, these conditions are sufficient for a
causal chain to be transitive.
This can help us to understand what is going on in
example (5) to yield nontransitivity. Example (5)
passes (C1), but fails (C2). It is not true that had
your friend found nothing outside the door then I would
have to have placed nothing outside the door. Had your
friend found nothing outside the door then it might
have been because I carefully concealed the bomb
outside the door and she overlooked it. There is a
sense in which the contrast situations in the example
are incompatible with each other, and this
incompatibility leads to nontransitivity.
Let’s return briefly to the other counterexamples.
Here is one natural interpretation of the birthday
example:
(7a) My forgetting your birthday (vs. my remembering
your birthday) is a cause of your reminding me (vs.
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your forgetting to remind me, or our both forgetting
your birthday).
(7b) Your reminding me (vs. your forgetting to remind
me, or our both forgetting your birthday) is a cause of
my buying you a birthday present (vs. buying you
nothing).
(7c) My forgetting your birthday (vs. my remembering
your birthday) is not a cause of my buying you a
birthday present (vs. buying you nothing).
Notice that condition (C2) fails. It is not true that
if you had forgotten to remind me about your birthday
then I would have to have remembered by myself. If you
had forgotten to remind me about your birthday then I
might have forgotten too. Also, it is not true that if
we had both forgotten your birthday then I would have
to have remembered your birthday. On the contrary, if
we had both forgotten your birthday then I would not
have remembered your birthday.
Here is the example with some other contrast
situations. Statement (8b) is false: if I had
remembered your birthday by myself then I would have
bought you something (let us say!) So the example
exhibits transitivity. Furthermore, conditions (C1) and
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(C2) are satisfied. The same events always have the
same contrasts throughout, and if I had remembered your
birthday by myself then I would have remembered your
birthday.
(8a) My forgetting your birthday (vs. my remembering
your birthday) is a cause of your reminding me (vs. my
remembering your birthday by myself).
(8b) Your reminding me (vs. my remembering your
birthday by myself) is a cause of my buying you a
birthday present (vs. buying nothing).
(8c) My forgetting your birthday (vs. my remembering
your birthday) is not a cause of my buying you a
birthday present (vs. buying nothing).
Finally, here is the purple fire example with some
natural contrasts spelled out:
(9a) Davidson’s putting potassium salts in the
fireplace (vs. Davidson’s putting nothing in the
fireplace) is a cause of the purple fire (vs. a yellow
fire).
(9b) The purple fire (vs. no fire) is a cause of
Elvis’s death (vs. Elvis’s survival).
(9c) Davidson’s putting potassium salts in the
fireplace (vs. Davidson’s putting nothing in the
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fireplace) is not a cause of Elvis’s death (vs. Elvis’s
survival).
This case is nontransitive because it fails both
conditions (C1) and (C2). The event of the purple fire
is contrasted with a yellow fire in (9a) but contrasted
with no fire in (9b). Furthermore, it is not true that
if there had been no fire then Davidson would have to
have put nothing in the fireplace. If there had been no
fire, he might have decided to put potassium salts in
the fireplace anyway.
7. A Fine-grained Event Analysis of the Counterexamples
Hausman describes how allowing for fine-grained events
enables us to explain examples of this sort without
rejecting the transitivity of causation.37 The example
is not of the right form to be a counterexample to
transitivity, because of the equivocation in which
event is being referred to by the phrase “the purple
fire”. In terms of Kimian events, “the purple fire”
could either designate the triple [the fire, being
purple, time] or the triple [the fire, being a fire,
time]. In terms of Lewisian events, the phrase could
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either designate a strong event “the purple fire” which
is essentially purple, or designate a weak event “the
fire” which is only accidentally purple. It is the
strong event of the purple fire (or the triple [the hot
purple fire, being purple, time]) which is caused by
Davidson’s action, and it is the weak event of the fire
(or the triple [the purple fire, being a fire, time])
which is a cause of Elvis’s death.
The fine-grained event analysis of the purple fire
example is similar to the analysis in terms of implicit
contrasts that I gave above. While Hausman locates
context dependence in the reference of the phrase “the
purple fire”, I locate the context dependence in the
interpretation of the whole sentence, “Davidson’s
putting potassium salts in the fireplace is a cause of
the purple fire”. However, if the phrase “the purple
fire vs. a yellow fire” designates a strong event of
the purple fire and the phrase “the purple fire vs. no
fire” designates a weak event of a purple fire, which
they plausibly do, then it can be shown that the two
analyses of this example are equivalent.
However, I do not see how the fine-grained event
analysis can explain the nontransitivity of the bomb
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example in a similar fashion. Perhaps we can locate an
equivocation in the event referred to by the phrase
“your friend’s finding the bomb” by looking at the
contrast analysis of the example. Suppose that there
are two different events referred to by the phrases
“your friend’s finding the bomb, in contrast to your
friend’s overlooking the bomb” and “your friend’s
finding the bomb, in contrast to there being no bomb
and your friend finding nothing”, and that the phrase
“your friend’s finding the bomb could designate either
event. Perhaps we could define event1 as an event that
occurs in worlds in which I place a bomb outside the
door and your friend finds it, and does not occur in
worlds in which I place a bomb outside the door and
your friend overlooks it or in worlds in which I do not
place a bomb outside the door. And we could define
event2 as an event that occurs in worlds in which
either I place a bomb outside your door and your friend
finds it or I place a bomb outside your door and your
friend overlooks it, and does not occur in worlds in
which I do not place a bomb outside the door.
Then,
after some work, we could show that the example
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involves an equivocation rather than a failure of
transitivity.
But how could the phrase “your friend’s finding
the bomb” designate event2? (Surely overlooking the
bomb is not just another way of finding the bomb!) In
order to analyze the example in this way we have built
conditions external to the event into the event
identity conditions for the event. The contrast
analysis of this example is more plausible.