Interactions between normative
(philosophical/ computational) theories
of causation and empirical research on
causal cognition
Jim Woodward
HPS, Pittsburgh
Causality: Perspectives from Different
Two Sets of Distinctions:
1) (a) Normative versus descriptive projects
(b) Distinguishing causal from non-causal
claims versus making further distinctions
within the general category of causal claims.
My focus in this talk will be on (1b). I will use
work on stability and double prevention and
on “proportionality” and the choice of “level”
of explanation to illustrate interactions between
normative and descriptive theorizing.
Two different projects regarding
1) Normative projects. Purport to tell us how
we ought to learn about, reason about causal
relationships and make causal judgments.
2) Descriptive/empirical projects: how do
people (and other subjects) learn about, reason
about, judge wrt causal relationships.
What is relation between these?
I see them as closely related and think that each can
be fruitfully influenced by the other.
In other words, Interactions can flow in both
First, theories of causation can suggest psychological
hypotheses and possible experiments.
Second, psychological results can also be suggestive
for normative/ philosophical theories
One key to appreciating this is thinking of
normative theories as providing benchmarks or
ideals with which actual performance can be
Explaining Success
This in turn connected to two other ideas.
1) The importance of explaining success.
Part of task of descriptive theories is to explain
why causal learning and causal judgment of
various subjects is successful to the extent that
it is.
Analogy with visual system.
Similarly descriptively adequate theory of causal learning, judgment
etc. should explain success, just as in the analogous case involving
the visual system.
For example, if our normative theories suggest that learning about
the causal structure of the world will be successful if our learning
strategies possesses feature F, we should check whether human or
other subject causal cognition has feature F this might help to
explain success. Conversely, if we see that as a matter of empirical
fact people’s causal cognition and learning exhibits certain features
F, we might want to at least consider the possibility that some of
these features F contribute to such success and thus are candidates
for incorporation into normative theory.
Thinking About Causation Functionally
2) The importance of trying to understand
causal learning, reasoning and judgment in
functional terms. This means thinking about
causal cognition in terms of goals or aims it
attempts to serve and evaluating proposals
about causal learning, judgment etc in terms of
how well they achieve those goals. Causal
reasoning is for various goals, not just an end in
General point is that in the human sciences,
normative theories of reasoning and decisionmaking can often play an important role in
guiding descriptive investigations.
Normative theories of decision-making, reward
learning as another illustration. Understanding
behavior of dopamine neurons in terms of
temporal difference learning, reward prediction
What are the goals or functions of
causal cognition?
Interventionists think of these goals as having
to do with manipulation and control, but
there are other possibilities as well– e.g.
perhaps the compressed, simplified, unified
representation of correlational information.
Or finding representations in which some
structures are independent of others.
A Second Distinction
Also distinction between two other projects:
1) On the one hand, providing a basis for the
distinction between causal relationship and
non-causal (e.g. merely correlational)
2) On the other hand, drawing distinctions
among causal relationships.
First project has received much more
philosophical attention than the second.
Interventionist framework for thinking about
causation is directed toward the first
question (distinguishing causation from
something else and provides one answer to
this question) :
(M) C causes E if and only if there is some
intervention that changes the value of C, such
that if that intervention were to occur, the
value of E or the probability distribution of E
would change.
Second project asks the following question:
suppose we have various causal relationships
that are minimally causal in the sense of
satisfying (M). Are there further distinctions to
be made among these relationships?
Examples of distinctions among causal
relationships (not remotely
• Causal relationships (that is, relationships that
satisfy M) can more or less stable or invariant
• A cause can satisfy (M) and be proportional or
at the right level for its effect or not.
• Causes satisfying (M) can be more or less
This project of making distinctions among causal
relationships above also has a normative and
empirical component. On the normative side, we
can ask we can ask whether it makes normative
sense for people to make these distinctions, given
the goals they have? How if at all do these
distinctions connect to functions or aims of causal
thinking. On the empirical/descriptive side, we can
ask whether people in fact make these distinctions
in their causal judgments.
My view : these are all features such we have a
normative rationale for caring about whether they
are present or not in causal relationships, given an
interventionist framework: that is, their presence
or absence is connected to possibilities for
manipulation and control, as I hope to illustrate.
Understanding this normative rationale can help us
to understand why causal judgments possess these
features (or at least that is the project I want to
Stability and Double Prevention
Results supporting the claim that subjects
seem to care about stability in the form of
Lombrozo’s experiments on double prevention
Double Prevention
Cases in which if d were to occur, it would
prevent the occurrence of e (which would
otherwise occur in the absence of d) and in
which the occurrence of c prevents the
occurrence of d, with the upshot that e
Suzy’s plane will bomb a target (e) if not
prevented from doing so. An enemy pilot p
will shoot down Suzy’s plane (d) unless
prevented from doing so. Billy, piloting
another plane, shoots down p (c), and Suzy
bombs the target
Overall counterfactual dependence of e on c
(with the dependence in question being the
sort of non-backtracking dependence
associated with causal relatedness on
counterfactual theories of causation)
Many counterfactual theories , including
Lewis’, as well as my M judge this relation to
be causal
But common reaction is that double
prevention cases are either not cases of
causation at all, or at least lack some feature
which is central to many other cases of
causation– absence of biff, umph, physical
Ned Hall: We operate with two distinct
notions of causation: dependence and
production. Double prevention exemplifies
dependence but not production.
Several questions:
As a matter of descriptive psychology, how widely shared are these intuitive
judgments reported by Hall and others about the causal status of double prevention?
Are some cases of double prevention are regarded as more causal or more
paradigmatically causal than others?
Second, to the extent this is the case, what is going on when people make
judgments about double prevention and production? Can we say anything further
about why people bother to distinguish between production and “mere”
counterfactual dependence or why they might make distinctions among different
cases of double production? These are questions naturally suggested by the
functional conception of causal thinking advocated earlier.
Explore these questions by making use of some recent
psychological experiments concerning causal judgment by Steve
Sloman and Clare Walsh and by Tania Lombrozo.
Walsh, C. and Sloman, S. (2011). “The Meaning of Cause and
Prevent: The Role of Causal Mechanism.” Mind and Language, 26:
Lombrozo, T. 2010. “Causal-explanatory Pluralism: How Intentions,
Functions, and Mechanisms Influence Causal Ascriptions”. Cognitive
Psychology 61: 303-332.
Lombrozo and Carey, “Functional explanation and the function of
explanation” Cognition 99 (2006) 167–204
Walsh and Sloman, (2011) presented subjects
with a series of scenarios, two of special
interest. In first, coin is standing unstably
on its edge and about to fall tails. Billy and
Suzy roll marbles in such a way that each will
strike the coin and in each case after impact
the coin will land heads but Billy’s marble
strikes first. In this scenario, 74% of subjects
judged that Billy’s marble caused the coin to
land heads.
Results seem to support the conclusion that
at least as far as folk thinking about causation
goes, cases in which something like
“production” or a “generating mechanism” or
a “physical connection” or “transference” is
present are more likely to be judged as causal
than cases of double prevention.
Some additional experiments, due to Tania Lombrozo
complicate this picture :
Lombrozo’s experiments explore people’s causal
judgments about double prevention scenarios in
contexts involving intentional action, artifacts with
designed functions, and biological adaptations.
Example of the pairs of scenarios that Lombrozo
employs—the first item in the pair is the description
with the material in bracket removed and the second
item includes the material in brackets
The diet of a certain kind of Australian shrimp consists of three kinds
of foods: alphaplankton, bacterioplankton, and cromplankton.
Alphaplankton contain chemical A, which triggers a reaction that
changes the shrimp’s skin to make it reflect high frequencies of
ultraviolet light. Bacterioplankton contain chemical B, which
neutralizes chemical A and thereby prevents the shrimp from
reflecting high frequencies of ultraviolet light. However,
cromplankton contain chemical C, which binds to chemical B and
thereby prevents chemical B from preventing chemical A from
making the shrimp reflect high frequencies of ultraviolet light.
Because of these interactions, a shrimp that has eaten
alphaplankton, bacterioplankton, and cromplankton will reflect high
frequencies of UV light.
• [Reflecting high frequencies of UV light is
biologically important, as it aids the shrimp in
regulating its temperature by reflecting the
frequencies of light with the most energy. In
fact, while eating bacterioplankton is
important for nutritional reasons, Australian
shrimp have evolved to eat alphaplankton and
cromplankton because these foods result in
the reflection of high frequencies of UV light
and thereby improve temperature regulation.]
Subjects asked whether alphaplankton,
bacterioplankton, and/or cromplankton caused
specimen S to reflect high frequencies of UV light.
Manipulation is whether subjects are told that
the effect of interest is a biological adaptation
(has “functional status”) or not. Lombrozo finds
when effect has functional status, subjects more
willing to say that is appropriate to rate cases of
double prevention as “causal” than when the
same effect occurs “incidentally” and not as a
result of an adaptation.
General pattern: although as in the Sloman and Walsh
experiments, Lombrozo finds (in experiments I have
not described) subjects are more willing to judge that
cases involving “production” than (at least some)
cases involving double prevention are causal, subjects
also distinguish among cases of double prevention,
treating those involving intentional action, designed
function and biological adaptation as more
appropriately described as causal than cases of double
prevention not involving these features.
What then accounts for this differential
response to the different double prevention
scenarios in Walsh’s and Sloman’s
experiments in comparison with Lombrozo’s?
Stability, insensitivity etc. :
Suppose some event e (or type of event E or the values of
a variable E*-- the differences won’t matter much for our
purposes) counterfactually depends on another event c (or
type of event C etc.), where the dependence is of the right
sort to support a causal interpretation—it is nonbacktracking, supports interventions, and so on.
Sensitivity of this relation of counterfactual dependence
has to do with whether it would continue to hold as we
change other background factors.
Woodward, J. (2006) “Sensitive and Insensitive Causation.”
Philosophical Review 115: 1-50.
Writing a letter of recommendation vs
shooting someone at point-blank range.
Differences in sensitivity seem to track to a
considerable extent how “good” or
paradigmatic a dependence relationship is as
an example of a causal relationship. That is,
cases of counterfactual dependence which
are relatively unstable or sensitive tend to be
judged as less paradigmatically causal (as less
“good” causes”) than cases of counterfactual
dependence which are more stable or less
My 2006 paper suggests that cases of double
prevention in which there is an overall
relation of counterfactual dependence
between c and e can similarly vary in the
extent to which this relationship is stable and
conjectured that this is related to the extent
to which the double prevention relation is
regarded as paradigmatically causal.
Billy/ Suzy example illustrates this.
Contrast is with metabolization of lactose by
e. coli.
Similar analysis applies to Lombrozo’s examples —a
claim that she also endorses. That is, double
prevention relations in her examples are judged more
paradigmatically causal depending on how stable they
are, and similarly for examples involving designed
artifacts. In other words, in all of these cases we may
provide a relatively unified explanation of people’s
judgments by appealing to the greater stability of the
double prevention relations when adaptation, design
or intention are present, in comparison with their
….causal ascriptions are valuable insofar as they identify
relationships that are sufficiently stable or invariant across
situations to be useful in prediction and intervention. This
proposal mirrors a hypothesis in Lombrozo and Carey (2006)
about the function of explanation, called ‘‘Explanation for
Export.” According to Explanation for Export, explanations
identify factors that are ‘‘exportable” in the sense that they
are likely to subserve future prediction and intervention. If the
function of isolating parts of causal structure, be it in an
explanation or a causal claim, is to subserve future prediction
and intervention, then ‘‘good” causes should be those that
reflect stable, invariant relationships that are exportable to
relevant situations
Lombrozo, T. 2010. “Causal-explanatory Pluralism: How Intentions,
Functions, and Mechanisms Influence Causal Ascriptions”.
Lombrozo’s treatment illustrates the explanatory
strategy associated with the importance of thinking
of causal reasoning in functional terms discussed
earlier (and the associated idea about the importance
of thinking in terms of normative theory) One reason
why people care about the difference between causal
relationships and relationships of correlation that are
not direct expressions of causal dependence (as when
the correlation between two effects is entirely due to
a common cause) is that the former are exploitable (
at least in principle and often in fact) for purposes of
manipulation/intervention and control in a way that
the latter are not
Once this accepted, also natural to recognize
that different relationships of counterfactual
dependence can serve this function or satisfy
this aim to different degrees. In particular, the
more stable a relationship of counterfactual
dependence is, then (other things being
equal) the more useful or suitable it is likely to
be for purposes of manipulation and control.
Note the overall strategy here:
Instead of asking whether double prevention relations are “really causal” or worse
trying to use our intuitions about cases to determine whether double prevention
relations are really causal— an ill-posed question, in my view, we should ask:
1)Why do people (ordinary people, scientists) bother to distinguish between relations
of counterfactual dependence that involve double prevention and relations of
counterfactual dependence that involve physical transference or production? . Part of
the answer: Other things being equal, Productive relations tend to be more stable.
2) Do people distinguish among double prevention relations and if so, why, and on
what basis? Answer: they distinguish among double prevention relations with respect
to their degree of stability.
Proportionality and finding the right
level of explanation
Switch gears to another set of experiments:
Yunnwen Lien and Patricia Cheng
(“Distinguishing Genuine from Spurious
Causes: A Coherence Hypothesis”). One of
the many issues explored in this paper – this
is my description— is the choice of level of
abstraction at which people characterize
To illustrate with example from philosophical
literature, consider, following Yablo, a pigeon
that has been trained to peck at red and only
red targets—that is, the pigeon pecks at
targets of any shade of red and only these.
Suppose that the pigeon is presented, either
once or (if you like) on a series of occasions,
with a target of particular shade of scarlet and
pigeon pecks.
Now consider the following causal claims:
( 3) The scarlet color of the target (or the fact
that the target was scarlet etc.) caused the
pigeon to peck it
(4) The red color of the target (or the fact
that the target was red etc.) caused the
pigeon to peck it
Yablo thinks that, given the facts specified in the
example, most people will prefer claim (4= pecks
because target red) to (3= pecks because target
scarlet). Yablo links this preference to the idea that
causes should satisfy what he calls a “proportionality”
requirement with respect to their effects; the idea is
that the cause should contain neither too little (being
inappropriately narrow, omitting crucial elements) nor
contain too much ( being overly broad, containing
superfluous elements) for its effect.
Yablo tries to explain this preference in terms of
some complex metaphysical considerations
having to do with “event essences” and the like.
In what follows I will put these aside and focus
instead on the methodological thesis suggested
by (3)- (4) which is that some levels of
description of causes and effects can be “better”
or “more appropriate” than others and in
particular that (4) is at a more suitable level of
description or abstraction than (3), given the
facts that Yablo specifies.
This thesis raises some obvious questions.
First, as a descriptive matter, do subjects
exhibit a preference for or more readily learn
causal claims at certain levels as opposed to
others? Second, again as a descriptive matter,
what principles govern (and what factors
influence) such preferences? Third, is there
some normative rationale or justification for
the preferences that subjects exhibit?
Think of Lien’s and Cheng’s experiments as
directed (in part) at just these questions.
Compressing greatly, their experiments
consisted in presenting subjects with
hypothetical soil ingredients that were
potential causes of plant blooming; the task
was to identify from covariational information
the causes of blooming and to predict on this
basis how plants would respond to various soil
treatments with the ingredients.
Ingredients/potential causes exhibited variation that
fell into hierarchical structures or classes of increasing
abstractness. For example, the ingredients varied as
to color and could be represented at each of three
levels of abstractness – particular shades of color (pinegreen), general type of color (green), and whether the
color was “warm or cool”. Similarly, shapes could be
represented in a highly specific way ( a particular
regular shape of certain dimensions), at an
intermediate level of specificity ( a type of shape) or in
a more abstract way (regular in the sense of
rotationally symmetrical versus irregular).
Data presented to the subjects took the form of
maximally specific descriptions of the soil
ingredients (that is stimuli were specific shapes
and specific colors) and descriptions of how these
covaried with plant blooming. The patterns of
covariation were chosen in such a way that ∆p =
Pr(E/C)- Pr (E/-C) was maximized when C was
taken to be the most abstract category in these
hierarchies—that is, when blooming/nonblooming co-varied maximally with possessing an
irregular versus a regular shape or with
possessing a warm versus a cool color.
Under these conditions, subjects preferred
characterizations of the causes of blooming at
these abstract levels (rather than more
specific levels) in the sense that they learned
the abstract relationships from the
covariational data more readily and used
them, in preference to more specific
relationships, to predict extent of blooming
under new treatments.
These experiments provide an additional
illustration of the interplay between descriptive
and normative considerations that I have been
discussing in this paper. First, in agreement with
Yablo’s claims, the experiments show that
subjects do sometimes prefer (learn and make
use of) causal relationships or descriptions of
causal relationships that are not characterized in
a maximally specific or detailed way. Instead,
they sometimes prefer more abstract
Second, the experiment suggests an obvious and very intuitive
explanation/rationale for when and why subjects do this – thus suggesting
that this preference is not a mistake or merely due to confusion. Other
things being equal, subjects favor characterizations of cause and effect at
the level that maximizes the contrast ∆p between the probability of the
effect in the presence of the cause and the probability of the effect in the
absence of the cause. For example, if the presence of (any) irregular
shapes in the soil always leads to blooming and the presence of regular
shapes never does, and the presence of five-sided shapes increases the
probability of blooming in comparison with the absence of five-sided
shapes, but five-sided shapes do not always lead to blooming (only
irregular five-sided shapes do) and the absence of five sided shapes does
not always lead to non-blooming (only regular non- five-sided shapes have
this effect) then the irregular versus regular level of description of the
cause will be preferred to the more specific description.
Obvious normative rationale for this practice
is that the more abstract level of description in
this case provides more information about the
conditions under which the effect will and will
not occur than the more specific description;
thus it provides information that is more
useful for purposes of prediction and control.
Of course this rationale also fits the judgments
Yablo finds intuitive. Under the conditions
described in the example, regarding redness of
target as cause maximizes ∆p.
So again we have a normative story about why
subjects do what they do, that exhibits and
makes sense of their judgments.
The Role of Information Theoretic
Is there perhaps some more general account in
terms of maximizing information (or information
of certain kinds or that answers certain
questions) that explains the role of both stability
and proportionality (as well as perhaps
specificity) in identifying causal relationships and
in variable choice? Idea would NOT be that more
stable or proportional relationships are more
likely to be true or correct, but rather that
among those candidate relations that are
empirically adequate we favor those that are
more informative.
Thanks for Listening!!!

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