The Role of Counterfactual
Reasoning in Causal
Judgements
peter.menzies@mq.edu.au
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1. Introduction
What is the connexion between counterfactuals and
actual/token causation?
One idea that has been much explored in
philosophy and psychology is that the causal
judgement “c caused e” is analytically tied to the
counterfactual “If c hadn’t occurred, e wouldn’t
have occurred”.
The consensus among philosophers is that the
concept of actual causation can’t be reduced to
counterfactuals. Pre-emption examples pose an
insuperable obstacle to such a reduction.
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1. Introduction
The consensus view among psychologists seems to
be that counterfactual reasoning and causal
reasoning are distinct forms of reasoning.
Mandel and Lehman (1996), Mandel (2003), and
Byrne (2005) cite experimental data that show that
people’s causal judgements of the form “c caused
e” are dissociated from counterfactual judgements
of the form “If c hadn’t occurred, e wouldn’t have
occurred”.
The former seem to go with judgements about
sufficient conditions and productive mechanisms,
whereas the latter seem to go with judgements
about enabling conditions and preventative
mechanisms.
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1. Introduction
My aim is to argue that philosophers and
psychologists have been premature in
dismissing the possibility that our causal
judgements are analytically connected to
counterfactual concepts.
But we have to adopt a more subtle view of
the connexion in order to able to
accommodate the many examples cited as
problematic for counterfactual theories.
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1. Introduction
My plan of action:
• Outline David Lewis’s counterfactual theory. Explain some
problems facing this theory, concentrating on the distinction
between enabling conditions and causes, and the
distinction between positive and negative causes.
• Examine two attempts to rescue the counterfactual theory
from these problems
– a theory of Chris Hitchcock and Joshua Knobe
– a theory of James Woodward
• Outline a new theory I think is superior to both these
theories.
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2. Lewis’s Counterfactual Theory
Lewis claims that causation can be analyzed in terms
of counterfactual dependence defined as:
e counterfactually depends on c iff (i) if c were to occur,
e would occur; and (ii) if c weren’t to occur, e wouldn’t
occur.
Counterfactuals are understood in terms of similarity
relations between possible worlds.
He imposes a constraint on the similarity relation
which ensures that a counterfactual with a true
antecedent and consquent is itself automatically
true.
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2. Lewis’s Counterfactual Theory
This constraint means that his counterfactual dependence
can be simplifed to:
An occurrent event e counterfactually depends on occurrent
event c iff if c weren’t to occur, e wouldn’t occur.
Lewis’s definitions of causal concepts:
c is a cause of e iff (i) c and e are wholly distinct events; and (ii)
there is a chain of counterfactual dependences from c to e.
It follows that from this definition that:
If e counterfactually depends on a distinct event c, then c
causes e.
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3. Problems for Lewis’s Theory
The theory glosses over the distinction between causes and enabling
conditions.
Example 1: Birth and Death.
A man is born and much later dies in a car accident. If he hadn’t been
involved in the car accident, he wouldn’t have died. So the car accident
counts as a cause of his death. But if he hadn’t been born, he wouldn’t
have died. So his birth counts as a cause too.
The problem is exacerbated by the fact that the theory is supposed to
cover omission and absences.
Example 2: The Absence of Meteor Strike.
I’m writing this paper at my computer. If I had been struck by a meteor
shower, I would not be writing this essay. So the failure of a meteor
strike counts as a cause of my writing this essay.
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3. Problems for Lewis’s Theory
The theory has trouble distinguishing between
genuine and spurious causes among omissions.
Example 3: The Gardener and the Plant
A gardener whose job it is to water a plant during
hot weather fails to do so and the plant dies. If the
gardener had watered the plant, it would have
survived. So his failure counts as a cause of the
plant’s death. But if the Queen had watered the
plant, it would have survived as well. So the
Queen’s failure counts as a cause too.
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3. Problems for Lewis’s Theory
Carolina Sartorio (2009) has noted the theory faces
the Prince of Wales problem: the problem of
unwanted positive causes.
Example 4: The Prince and the Plant’s Death
The Queen has asked the Prince to water her pot
plant in the afternoon. But his priorities are to eat
oaten biscuits instead of watering the plant and so
the plant dies. The Prince’s failure to water the
plants caused the plant’s death.
If we add the assumption that if the Prince had not
eaten the oaten biscuits, he would have watered the
plant, it turns out his eating oaten biscuits counts as
a cause of the plant’s death.
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3. Problems for Lewis’s Theory
The problem of unwanted negative causes.
Example 5: The Prince and the Stomach Ache
The Prince eats oaten biscuits instead of
watering the plant. He eats so many biscuits he
gets a stomach ache. The Prince’s eating too
many oaten biscuits was a cause of his stomach
ache. But so too is his failure to water the plant: if
he had watered the plant instead of eating the
biscuits, he would not have had the stomach
ache.
Indeed, any action precluded by the Prince’s eating
the oaten biscuits (ie talking to the Duke, walking
in the garden) will have a corresponding omission
that counts as a cause.
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4. Hitchcock and Knobe’s Theory
These problems indicate that a counterfactual of the form “If
c weren’t to occur, e wouldn’t occur” is not a sufficient
condition for “c is a cause of e”.
Lewis defended his theory against such counterexamples
by appealing to Grice’s pragmatic theory of conversational
implicature.
It is literally true that any event or absence on which an
effect causally depends is a cause of the effect. “There
are ever so many reasons why it might be inappropriate to
say something true. It might be irrelevant to the
conversation, it might convey a false hint, it might be
known to all concerned…”
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4. Hitchcock and Knobe’s Theory
Grice’s maxims are general principles of rationality
applied to information exchange. Yet the principles
that lie behind our judgements about the examples
above seem to be particular to causal judgements.
Is it possible to formulate a theory that captures the
causation-specific principles that lie behind our
judgements?
Hitchcock and Knobe (2009) have formulated one
such pragmatic theory that preserves the centrality
of counterfactual dependence to the causal concept
while explaining the selectivity of the causal
concept.
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4. Hitchcock and Knobe’s Theory
Their theory appeals to findings in the literature on psychological
availability of counterfactual suppositions.
One of the most robust findings in this literature is that people
are disposed to entertain counterfactual hypotheses that undo
the past by changing abnormal occurrences into normal ones,
but seldom, if ever, do they mentally undo the past by
changing normal occurrences into abnormal ones.
Kahneman and Tversky (1982) gave subjects a story describing
a fatal road accident in which a truck ran a red light and
crashed into a passing car, killing its occupant, Mr Jones.
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4. Hitchcock and Knobe’s Theory
Two versions of the story were constructed: one in which Mr
Jones left his home at the regular time but took an unusual
route home, and the other in which he took the usual route
home but left early to do some chores. In 80% of the
responses, subjects indicated they mentally undid the
accident by mutating the abnormal event and restoring it
back to normality.
In the first version of the story, subjects were inclined to
entertain counterfactuals about what would have happened
if Mr Jones had taken his usual route home. In the second
version they were more inclined to entertain counterfactuals
about what would have happened if Mr Jones had left work
at his usual time.
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4. Hitchcock and Knobe’s Theory
Hitchcock and Knobe use this finding to explain
the selectivity of the causal concept.
We readily accept a causal judgement “c caused e”
when the counterfactual “If c hadn’t occurred, e
would have occurred” involves changing an abnormal
occurrence into a normal one; we rarely accept such
a causal judgement when the counterfactual involves
changing a normal occurrence into an abnormal one.
They claim that we classify events in terms of
single scale of normality that takes into account
both statistical and prescriptive considerations.
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4. Hitchcock and Knobe’s Theory
They presented subjects with a vignette in which a receptionist in the
philosophy department keeps her desk stocked with pens. In contrast to
administrative assistants who are permitted to take pens, faculty
members are supposed to buy their own. One day an administrative
assistant and Professor Smith walk past the receptionist’s desk and both
take pens. Later that day, the receptionist needs to take a message but
can’t do so because there are no pens on her desk. When subjects are
asked whether the administrative assistant or Professor Smith caused the
problem, most subjects say that Professor Smith was the cause.
Hitchcock and Knobe’s explanation:
“If Professor Smith had not taken a pen, there would have been no problem”
involves a norm-restoring antecedent and so the corresponding causal
judgement is acceptable.
“If the administrative assistant had not taken a pen, there would have been
no problem” involves replacing a normal occurrence with an abnormal or
neutral occurrence and so the corresponding causal judgement is not
acceptable.
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4. Hitchcock and Knobe’s Theory
How does their theory fare in dealing with Problems 1 to 5?
Problem 2: The Absence of Meteor
“The absence of the meteor strike caused me to write this paper” is not
acceptable because the corresponding counterfactual involves
changing a normal event into an abnormal event.
Problem 3: The Gardener and the Plant
“The gardener’s failure to water the plants caused the pant to die” is
acceptable because the corresponding counterfactual involves a
norm-restoring change.
“The Queen’s failure to water the plants caused the plant to die” is
not acceptable because the corresponding counterfactual doesn’t
involve a norm-restoring change.
Problem 4: Prince of Wales: Unwanted Positive Causes
“The Prince’s failure to water the plant caused its death” is
acceptable for the same reasons as above.
“The Prince’s eating oaten biscuits caused the plant’s death” is
unacceptable for the same reasons as above.
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4. Hitchcock and Knobe’s Theory
Note that in all the examples, the counterfactuals
corresponding to both causes and non-causes are true. In
the Problem 3 The Gardener and the Plant, it is true both:
If the gardener had watered the plant, it would not have died.
If the Queen had watered the plant, it would not have died.
Hitchcock and Knobe say that the first counterfactual is more
“relevant” than the second. But what is relevance?
Relevant = spring to mind readily. We need an account of the
difference in causal status that’s independent of whether something
springs to mind readily.
Relevant = acceptable when explicitly entertained. Both
counterfactuals seem to be acceptable.
Relevant = worth entertaining for practical purposes. From our
perspective, neither counterfactual is practically significant.
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4. Hitchcock and Knobe’s Theory
Another problem concerns the psychological findings that
demonstrate a dissociation between causal judgements
and reasoning about counterfactuals.
Mandel (2003) made a study using the example of Mr Jones
and the drunk driver.
When asked for their counterfactual judgements, many
subjects responded with judgements “If Mr Jones hadn’t
taken the unusual route (or left at the unusual time), he
would not have died”.
When asked for their causal judgements, most respond
with the judgement “The drunk driver caused Mr Jones’s
death”.
Such studies cast doubt on the claim that the acceptability of
the causal judgement “c caused e” goes hand-in-hand
with the acceptability of “If c hadn’t occurred,e wouldn’t
have occurred.”
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5. Woodward’s Theory
Like Hitchcock and Knobe’s theory, Woodward’s theory
attempts to explain the selectivity of causal judgements by
augmenting Lewis’s counterfactual theory with additional
constraints.
Like Lewis, he defines counterfactual dependence between
states (including events, absences and omissions) in terms
of these counterfactuals:
(i) If c were to occur, e would occur [occurrence
counterfactual]
(ii) If c weren’t to occur, e wouldn’t occur [non-occurrence
counterfactual]
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5. Woodward’s Theory
Woodward says that for the causal judgement “c caused e” to
be acceptable, the occurrence-counterfactual (i) must be
insensitive: ie. there is a broad range of background
conditions Bi that are not “too improbable or far-fetched”
such that the following counterfactual is true:
If c were to occur in circumstances Bi different from
the actual circumstances, then e would occur.
Example of insensitive causation:
Shooting a person at close range with a large calibre
bullet caused his death.
Example of sensitive causation:
Lewis’s writing a letter of recommendation for jobseeker
X caused the death of a descendant of another
jobseeker Y who was displaced by X.
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5. Woodward’s Theory
Woodward’s theory links our readiness to accept a causal
judgement to the degree of insensitivity of the occurrencecounterfactual (i).
It explains some of our causal judgements about the earlier
examples.
Problem 2: The Absence of the Meteor Strike
“The absence of the meteor strike caused me to write this
paper” is not acceptable because the corresponding
occurrence-counterfactual “If there were no meteor, I
would write this paper” is not insensitive.
Note that if I had been struck by a meteor, then the
occurrence-counterfactual would be “If there were a
meteor strike, I would not write this paper”, which is
insensitive.
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5. Woodward’s Theory
However, Woodward’s theory doesn’t deal satisfactorily with
example of Mr Jones and the Drunk Driver:
“Mr Jones’ taking an unusual route home caused his death”
has a sensitive occurrence-counterfactual: an admissible
variation is one in which drunk driver doesn’t run the red
light.
“The drunk driver’s running the red light caused Mr Jones’s
death” also has a sensitive occurrence-counterfactual: an
admissible variation is one in which Mr Jones doesn’t take
the unusual route home.
Accordingly, we should say that neither Mr Jones’s taking the
unusual route home nor the drunk driver’s running the red
light caused Mr Jones’ death.
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5. Woodward’s Theory
Woodward’s theory doesn’t handle one half of the Prince of
Wales problem: problem of unwanted positive causes.
“The Prince’s failure to water the plant caused its death” has an
insensitive occurrence-counterfactual. So the Prince’s failure
to water the plant counts as a cause of the plant’s death.
But “Prince’s eating oaten biscuits caused plant’s death” also
has an insensitive occurrence-counterfactual: any variation
on the actual circumstances which respects the stipulation
that the Prince’s eating oaten biscuits precludes him from
watering the plant will make the occurrence-counterfactual
true.
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5. Woodward’s Theory
It’s not clear that the theory has a satisfactory
explanation of the problem of the professor and
the administrative assistant.
Is the occurrence-counterfactual “If the professor
were to take a pen, there would be a problem”
insensitive?
There seem to be admissible variations in which
the professor takes a pen but the administrative
assistant does not, in which case there would be
no problem.
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6. A New Theory
Hitchcock and Knobe’s theory seems to be closer to the truth
than Woodward’s. I offer a theory that builds on and
improves on the Hitchcock and Knobe theory.
(a) Semantic rather than pragmatic theory.
Hitchcock and Knobe’s theory is a pragmatic theory of
relevance added onto a standard semantics of
counterfactuals.
I believe it is more fruitful to see our causal judgements about
the various examples as reflecting their actual meaning.
The theory I’m presenting states that the meaning of a causal
judgement involves a contrast between the actual course of
events and a counterfactual course of events.
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6. A New Theory
In this pair of contrasting situations, the actual situation
contains an abnormal sequence of events which invites
explanation or the ascription of responsibility.
Counterfactual situation=
default course of events
Actual situation=
deviant course of events
The actual situation deviates from the default situation by
virtue of containing abnormal sequence of events. The
paradigm case is a sequence of events initiated by an
intentional action that is an exogenous interference in
the normal course of events.
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6. A New Theory
(b) Salience of counterfactual possibilities rather
relevance of counterfactuals
The theory says that in considering a causal judgement we tacitly treat
certain counterfactual possibilities as salient.
We select a counterfactual possibility as a default to the actual situation
in which a state c obtains in such a manner that it meets the
following condition: the counterfactual possibility must be a
norm-conforming situation in which c does not obtain.
As in Hitchcock and Knobe’s theory, the norms include statistical norms,
social and ethical norms, and norms of proper functioning. I also
assume that in a given context we judge situations to be more or less
normal in terms of single scale.
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6. A New Theory
While this theory appeals to counterfactual possibilities, it
avoids the use of counterfactuals.
As we saw earlier, in most of the examples, both the causes
and non-causes have true non-occurrence counterfactuals.
Eg
If the gardener had watered the plant, it would not have died.
If the Queen had watered the plant, it would not have died.
Hitchcock and Knobe’s theory then has to invoke the notion of
“relevance” to sort out the causes from the non-causes.
It is best simply to miss out the distracting detour through
counterfactuals.
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6. A New Theory
(c) Causation as difference-making without
counterfactuals.
Hitchcock and Knobe’s theory appeals to nonoccurrence counterfactuals to spell out the idea
that causation is linked to difference-making. The
present theory spells out this idea out more
directly:
“c is a (difference-making) cause e” is true iff there is a
contrast pair <A,C>, where A is the actual situation
and C is an appropriate default counterfactual
situation such that c and e are present in A but absent
in C.
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6. A New Theory
(d) Better explanation of causal judgements.
The theory explains our causal judgements about the examples roughly in the
same way as Hitchcock and Knobe’s theory.
The Absence of the Meteor Strike:
“The absence of a meteor strike was a cause of my writing this paper” is false
because there is no contrast pair with an appropriate default counterfactual
situation (any situation in which I am struck by a meteor is abnormal)
Prince of Wales: Unwanted Positive Causes
“The Prince’s failure to water the plant was a cause of its death” is true
because there is contrast pair with a default counterfactual situation (where
the Prince meets his obligation) which meets the difference-making condition.
“The Prince’s eating oaten biscuits was a cause of the plant’s death” is false
because there is a contrast pair with a salient default counterfactual situation
(where he meets his obligation) but it doesn’t meet the difference-making
condition.
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6. A New Theory
The present theory is consistent with the psychological
studies showing that causal judgements are dissociated
from judgements about counterfactuals. The present
theory employs counterfactual possibilities but not
counterfactuals.
Nonetheless, it strikes me that Mandel’s use of the example
about Mr Jones and drunk driver doesn’t bear out this
dissociation very well.
In this example, Mr Jones’s taking an unusual route and
the drunk driver’s running the red light were causes of his
death. In each case there is an appropriate contrast pair
meeting the difference-making condition.
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6. A New Theory
(e) Better Rationale for Causal Concept
Why do we have the concept of actual causation (in addition to the
concept of objective causal structure)?
Hitchcock and Knobe claim that its purpose lies in its connexion with
norms: through its connexion with non-occurrence counterfactuals, the
concept enables us to focus on what must be done to bring events into
conformity with certain norms. “In short, the concept of actual causation
enables us to pick out appropriate targets for intervention.”
In contrast, the concept of actual causation has a very easy-to-understand
rationale according to the present theory. The concept has its home in
our practices of explanation and the attribution of responsibility. When
an occurrence violates a statistical norm, we want to have an
explanation of it. When it violates a prescription norm, we want to
attribute responsibility for it to someone. A cause that makes a
difference is perfectly suited to meet these functions.
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