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John R. Dequindre
Jeremy Kirby
Philosophy 389
April 13, 2012
Causation and Counterfactuals
Causation can be most simply defined as, if A, then C. We are all well familiar with the
concept because of simple intuition. We observe that in the world around us, there is a direct
relationship between an event (which we view as the cause) and a second event (which we see as
the effect). We can also imagine a situation in which the antecedent (cause) is not true and
intuitively conclude what the effect would be. This kind of hypothetical situation is known as a
counterfactual conditional. In philosophy, both ideas are used in conjunction. David Hume
defined causation in terms of counterfactuals as: “We may define a cause to be an object
followed by another, and where all the objects, similar to the first, are followed by objects
similar to the second. Or, in other words, where, if the first object had not been, the second
never had existed” (Hume, Sec. VII). However, perhaps the most interesting analysis of
causation in terms of counterfactuals came with the development of “possible world semantics”
in the early 1970s; particularly by David Lewis. At the time, Lewis’ theory was groundbreaking
and has subsequently been widely discussed. However, such discussions have cast doubt as to
whether Lewis’ analysis causation in terms of counterfactuals is adequate. More recent dialogue
has focused on refining Lewis’ theory in order to connect it with more commonsense opinions
concerning causation. Nevertheless, Lewis’ original theory is unique and certainly worthy of
consideration.
The centerpiece of Lewis’ theory is the idea of possible world semantics, which examine
truth conditions for counterfactuals in terms of their similarity between possible worlds. One
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world is considered “closer” to the actual (counterfactual) world than another possible world if it
resembles the actual world more so than the second. Lewis lays down two limits: First, that we
can order any possible worlds in terms of their “closeness” to the actual world; and second, that
the actual world resembles itself more so than any other possible world. With this in mind,
Lewis defines the counterfactuals he wishes to examine as a situation where C and E are two
distinct events taking place in the actual world, E causally depends on C if and only if C were
not to occur E would not occur. With this simple definition of counterfactuals, however, Lewis
recognizes a problematic interpretation which he calls, “Backtracking” counterfactuals. These
counterfactuals basically assume that if the present effects were different, the past causes must be
different as well. For instance, Jim and Jack quarreled yesterday, and Jack is still hopping mad.
We conclude that if Jim asked Jack for help today, Jack would not help him. But wait: Jim is a
prideful fellow. He never would ask for help after such a quarrel; if Jim were to ask Jack for
help today, there would have to have been no quarrel yesterday. In that case Jack would be his
usual generous self. So if Jim asked Jack for help today, Jack would help him after all (1979, p.
456). The problem results from the fact that if Jim asked Jim for help, there would have been no
quarrel; yet it is useless for Jim to ask for help because if he asks Jack for help, the quarrel
nevertheless took place yesterday. To overcome this problem, Lewis states that counterfactuals
are, by nature, vague. In order to resolve their vagueness, it is necessary to give them a certain
context. He uses the example of Caesar in Korea: had he been in command, would he have used
the atom bomb? Or would he have used catapults (1979, p. 457)? Either answer is right, though
it is not right to say both together. Often because the counterfactual situation is vague, context
becomes necessary in order to determine the actual outcome. In general, however, Lewis claims
that such “Backtracking” counterfactuals need be avoided in order to get at a clear cut sense of
asymmetrical counterfactual dependence.
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The previous example about Jim and Jack suggest that the events of the past cause the
events of the present; just as the events of the present cause those of the future. This seems
logical because we are more familiar with events of the past and much less familiar with those of
the future. However, Lewis argues that the direction of causation is the direction of causal
dependence; meaning that though it is often true that events causally depend on earlier events but
not on later events, he does not rule out the possibility of backwards causation. He claims,
Any particular fact about a deterministic world is predetermined throughout the past and
postdetermined throughout the future. At any time, past or future, it has at least one
determinant: a minimal set of conditions jointly sufficient, given the laws of nature, for
the fact in question. (Members of such a set may be causes of the fact, or traces of it, or
neither) (1979, p. 473-74).
Furthermore, he claims that events frequently have very few earlier determinants but a great deal
of later determinants. Such an event may even have two or more different determinants at the
same time; a phenomenon which Lewis refers to as “overdetermination.” He combines this idea
with his analysis of the comparative similarity relation between possible worlds. When
evaluating non-backtracking counterfactuals, Lewis describes four areas of similarity to be taken
into consideration:
(1) It is of the first importance to avoid big, widespread, diverse violations of the law. (2)
It is of the second importance to maximize the spatio-temporal region throughout which
perfect match of particular fact prevails. (3) It is of the third importance to avoid even
small, localized, simple violations of the law. (4) It is of little or no importance to secure
approximate similarity of particular fact, even in matters that concern us greatly (1979, p.
472).
By themselves, these points do not suggest any sort of time asymmetry; but they do when
combined with overdeterminism. The best example of this is known as the “Nixon and the
Nuclear Holocaust” counterfactual, which follows: “If Nixon had pressed the button, there
would have been a nuclear holocaust.” Kit Fine supposed that a nearby possible world in which
Nixon pushed the button, but for whatever reason, the missiles failed to launch would be closer
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to the actual world than a possible world where Nixon pushed the button and there was a nuclear
holocaust. Lewis responds by setting up four possible worlds: World 0 (W0) is a world with
deterministic laws, in which Nixon does not press the button at time t and no nuclear holocaust
occurs. World 1 (W1) is exactly like W0 until t, at which point the laws of nature are violated in
a small localized way. A tiny miracle takes place, as a result of which, Nixon presses the button.
No other miraculous events take place and there is a nuclear holocaust. World 3 (W3) begins
like W0 until t, when a tiny miracle takes place, permitting divergence and Nixon presses the
button. But there is no holocaust, because a second tiny miracle takes place and the wiring from
the button to the missiles short-circuits. At first it seems that W0 and W3 remain similar in
matters of particular fact, but they are no longer exactly alike. Nixon’s fingerprints are on the
button, he wonders what went wrong, the click of the button is preserved on tape, etc. World 4 is
similar to W3, with everything happening in the same fashion, except moments after t, all traces
of Nixon pushing the button vanish. This constitutes a big miracle, as a large divergence with
the laws of nature takes place (the fingerprint disappears, Nixon’s has no memory of pushing the
button, the tape plays innocent sounds, etc.). Therefore, in contrast to Fine, who said that W3 or
W4 would be more similar to W0 (because the holocaust didn’t occur), Lewis concludes that W4
diverges most (and is therefore farthest) from W0 because of the big miracle, differences in
perfect match and the two small miracles (1979, p. 467-72). Though Lewis admits that
“unresolved vagueness remains,” he succeeds in showing that worlds that oblige counterfactual
change by preserving the actual past and allow for divergence miracles are closer to the actual
world than worlds that facilitate counterfactual change by allowing convergence miracles that
preserve the actual future. Thus, the events of the present depend counterfactually depend upon
those of the past, but not the future.
Though Lewis’ theory is unique, complex and interesting, it is nevertheless a theory and
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is not without faults. One criticism of Lewis’ concept of causation is that it overlooks sensitivity
to contextual factors. It presumes that causation can be looked upon as an absolute relation
which does not need to change from one situation to another. To Lewis, who believes in causalchains of events, any event but for which an effect would not have occurred is one of the effect’s
causes. However, if we consider, for example, a man is working on a scaffold repairing the roof
of a church spire, a gust of wind blows him off the scaffold and he lands on a pedestrian, killing
him. It is true that if the man was not working on the scaffolding, the pedestrian would not have
died. But it is also true that the pedestrian’s death would not have happened if the worker had
never been born or he had been crippled in a car accident years before. Common sense dictates a
clear difference between causes and background conditions, the man working on the scaffold
being a cause, and his birth and failure to be crippled being background conditions. Lewis
overlooks these distinctions (as we see in his earlier arguments about Jim and Jack), focusing on
a much broader notion of causation. His view consists of chains of causation – meaning
essentially that every event has an objective causal history consisting of enormous structures of
events ordered neatly by causal dependence. In terms of Lewis’ causation theory, if we consider
the case of the man on the church steeple, we must surmise what would have happened in those
closest possible worlds in which the cause did not occur. In an evaluation of whether the man
working on the scaffold caused the pedestrian’s death, we must take into account what would
have happened in the close possible worlds in which the worker’s action of working on the spire
did not take place. Are there possible worlds in which the worker is not on the scaffold at all, or
are they worlds where he is wearing a safety harness or working five minutes later? Lewis
would need a quantification in order to answer these questions; whether how much of a change
or a delay long enough for the event to become a completely different event, rather than a
different version of the same one. He would claim that the problem is a linguistic one: that being
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that we possess no unique way of quantifying these situations. He writes:
We have not made up our minds: and if we presuppose sometimes one answer and
sometimes another answer, we are entirely within our linguistic rights. This is itself a big
problem for a counterfactual analysis of causation, quite apart from the problem of
preemption (2000, p. 186).
This statement supports the notion that Lewis’s arguments rely on a degree of haziness to meet
the ends he wishes them to meet. Essentially, this argument against his theory uses the same
ambiguity his theory does.
As mentioned in the previous paragraph, Lewis’s theory of causation through
counterfactuals has also come under scrutiny over the problem of preemption. It is true that by
defining causation in terms of chains of causal dependence he makes causation transitive, but
also to combat preemption. However, the preemption problem has proved the most damaging to
Lewis’s theory. One of the best examples is as follows: At a party rally, two assassins (A and E)
are attempting to kill the Prime Minister. Assassin A throws a knife at the PM’s head at time t.
At exactly the same moment the knife leaves Assassin A’s hand, Assassin E appears behind the
PM with a katana and decapitates him at t (right before the knife would have arrived). Thus,
blood shoots out of the PM’s neck and he subsequently dies. In this case, Assassin E’s act was
the actual cause of the PM’s demise and Assassin A’s act is a preempted potential cause. Lewis
claims that a case such as this is not a suitable test case for his theory of causation because it
does not produce clear judgments. However, the actions of both assassins can certainly be
considered valid from the point of view of causal dependence: if neither A nor E had acted, then
the PM would have lived. If either A or E had acted without the other, the dictator would have
died. Lewis’s idea that causation occurs as the result of causal chains is also problematic in this
situation. There is a chain of events from assassin E’s actions which leads to the PM’s death, but
not so with assassin A. The action of assassin E lopping off the PM’s head with a katana was the
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only cause for his death, whereas assassin A’s knife did not. Therefore, according to Lewis,
there is no connection between A’s actions and the PM’s death; thus, A’s actions do not count as
the actual cause of death. This is certainly problematic for Lewis’s theory because, as stated
previously, had assassin E not acted, the PM would nevertheless have died.
Though Lewis’s theory has proven problematic in some regards, it nevertheless served to
break new ground in the philosophical discussion concerning causation and counterfactuals. At
the time he began advocating his theory, the typical formula for causation read: c is a cause of e
if and only c belongs to a minimal set of conditions that are jointly sufficient for e, given the
laws. This sort of thinking is wrought with many counterexamples, for instance: c might be a
part of a set of conditions for e when c is an indisputable cause of e, or if c is an effect of e – an
effect which is not possible, give the laws and circumstances, except by being caused by e; or if c
and e are combined effects of a common cause. Lewis’s theory does not suffer from these
counterexamples, considering that he does not consider backtracking counterfactuals within his
theory. Using the same counterexamples as before, to Lewis, even if c is part of a set of
conditions for e, e will not causally depend on c when c occurs after e as an effect, since earlier
events usually do not causally depend on later events. Nor will e causally depend on c when c
and e are combined effects of a common cause, since the non-backtracking counterfactual “If c
had not occurred, e would still have occurred” is true. Therefore, at the time it was proposed,
Lewis’s theory did well to better explain causation arguments than the arguments that existed.
Nevertheless, like all philosophical theories, Lewis’s ran into its own problems that he could not
answer. For the most part, it seems that his arguments rely heavily on the circumstances which
he establishes for them to be true, rather than relying on universal truth. Despite this, Lewis’s
efforts cannot be discounted, as they present a wholly new and intriguing method of perceiving
causation in terms of counterfactuals.
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Works Cited
Hume, David. An Enquiry concerning Human Understanding. 1748.
Lewis, David. “Causation as Influence.” Journal of Philosophy. 2000.
Lewis, David. “Counterfactual Dependence and Time’s Arrow.” Noûs: Vol. 13, No. 4. 1979