Improbable or Impossible? How Children Reason About the Possibility of Extraordinary Events

Abstract

The present study investigated the development of possibility-judgment strategies between the ages of 4 and 8. In Experiment 1, 48 children and 16 adults were asked whether a variety of extraordinary events could or could not occur in real life. Although children of all ages denied the possibility of events that adults also judged impossible, children frequently denied the possibility of events that adults judged improbable but not impossible. Three additional experiments varied the manner in which possibility judgments were elicited and confirmed the robustness of preschoolers' tendency to judge improbable events impossible. Overall, it is argued that children initially mistake their inability to imagine circumstances that would allow an event to occur for evidence that no such circumstances exist.

Full text

Improbable or Impossible? How Children Reason About the Possibility of
Extraordinary Events
Andrew Shtulman and Susan Carey
Harvard University
The present study investigated the development of possibility-judgment strategies between the ages of 4 and 8.
In Experiment 1, 48 children and 16 adults were asked whether a variety of extraordinary events could or could
not occur in real life. Although children of all ages denied the possibility of events that adults also judged
impossible, children frequently denied the possibility of events that adults judged improbable but not impos-
sible. Three additional experiments varied the manner in which possibility judgments were elicited and con-
firmed the robustness of preschoolers’ tendency to judge improbable events impossible. Overall, it is argued that
children initially mistake their inability to imagine circumstances that would allow an event to occur for evi-
dence that no such circumstances exist.
One of the traits that differentiates human beings
from other animals is our ability to learn about
entities and events that we have not personally ob-
served. From the testimony of other individuals, we
regularly learn about people we have never met (e.g.,
Beethoven, Rembrandt, Einstein), places we have
never been (e.g., Pompeii, Antarctica, Mars), and
objects we have never seen (e.g., genes, electrons,
radio waves). We can even conceive of entities and
events that no one has ever observed (e.g., antigravity
machines, time travel, human cloning). Of course,
not everything that is conceivable is possible. The
ability to differentiate possible things from impossi-
ble things is therefore an invaluable skill when rea-
soning about the unobserved and the unobservable.
The development of such an ability is of interest to
cognitive psychologists for at least two reasons. First,
much of the knowledge we acquire in childhood is
learned from the testimony of other individuals, and
the extent to which children are able to differentiate
possible events from impossible events may deter-
mine the extent to which they are able to differentiate
fact from fiction, truth from falsehood. Second, many
researchers have likened conceptual development
to the construction and revision of domain-specific
theories, or conceptual structures that embody one’s
ontological commitments and causal-explanatory
knowledge (Carey, 1985; Gopnik & Meltzoff, 1997;
Keil, 1989; Wellman & Gelman, 1992), and yet it is
unclear when the causal constraints represented by
the child become causal constraints for the child. In
other words, when are children able to reflect upon
the causal constraints implicit in their theories to
make explicit judgments of what is possible and
what is not?
Previous research on children’s understanding of
magic (Chandler & Lalonde, 1994; Johnson & Harris,
1994; Phelps & Woolley, 1994; Rosengren & Hickling,
1994; Rosengren, Kalish, Hickling, & Gelman, 1994;
Subbotsky, 1994, 2004) suggests that the ability to
differentiate possible events from impossible events
develops early in life. For instance, Johnson and
Harris (1994) presented 3- and 4-year-olds with pairs
of events in which one event violated a physical
principle (e.g., moving a marble with one’s mind)
and one event did not (e.g., moving a marble with
one’s hand) and asked the children to decide which
event had been performed by an ordinary person
and which event had been performed by a magic
fairy. Children of all ages tended to claim that the
possible event in each pair was performed by an
ordinary person and the impossible event was per-
formed by a magic fairy, and they did so for events
that violated four different physical principles (i.e.,
inertia, object permanence, object continuity, and the
conservation of matter). Likewise, Rosengren et al.
(1994) found that 4- and 5-year-olds consistently
denied the possibility of events that violated com-
mon biological principles, like growing younger or
growing smaller, but did not deny the possibility of
events that conformed to those principles.
r2007 by the Society for Research in Child Development, Inc.
All rights reserved. 0009-3920/2007/7803-0023
This work was supported by a National Science Foundation
Graduate Research Fellowship to the first author and by the help
of three outstanding research assistants: Jessica Gale, Heidi Reiner,
and Ilana Glosser.
Correspondence concerning this article should be addressed to
Andrew Shtulman, 33 Kirkland Street, Cambridge, MA 02138.
Electronic mail may be sent to aes@wjh.harvard.edu.
Child Development, May/June 2007, Volume 78, Number 3, Pages 1015 – 1032

In reviewing these studies, Rosengren and Hick-
ling (1994) drew the conclusion that ‘‘young children
make a sharp distinction between possible and im-
possible events’’ (p. 1606), and Sharon and Woolley
(2004) drew the conclusion that ‘‘young children
have clear ideas about the kinds of things real enti-
ties can and cannot do’’ (p. 294). However, several
other findings call these strong conclusions into
question. First, children believe in the existence of
fantasy characters whose magical properties (e.g.,
the ability to fly, the ability to visit millions of homes
in a single night) are inconsistent with the causal
principles thought to underlie children’s differenti-
ation of magical events from ordinary events in the
aforementioned experiments. For instance, Prentice,
Manosevitz, and Hubbs (1978) found that most
children under the age of 6 believe in the existence of
Santa Claus, the Tooth Fairy, and the Easter Bunny.
Likewise, Woolley, Boerger, and Markman (2004)
found that most preschoolers were willing to believe
in the existence of a novel fantasy characterFthe
‘‘Candy Witch,’’ or a flying witch that visits children
on Halloween and gives them a toy in exchange for
their unwanted candyFafter only one or two ex-
posures to this counterintuitive concept.
Second, preschoolers will accept the possibility of
impossible transformations, like making an object
shrink or making an object disappear, if they witness
visual illusions in which such transformations ap-
pear to have occurred before their very eyes (Chan-
dler & Lalonde, 1994; Rosengren & Hickling, 1994;
Subbotsky, 2004). For instance, Chandler and La-
londe (1994) asked children between the ages of
3 and 4 whether one object (a screen) could pass
through another object (a box). Although children of
all ages denied the possibility of this event when it
was described to them verbally, 67% changed their
mind after ‘‘witnessing’’ the event first hand. That is,
they insisted that the event they had witnessed was
not a trick but was actually ‘‘real magic.’’
Third, research on children’s understanding of
environmental regularities (Komatsu & Galotti, 1986;
Lockhart, Abrahams, & Osherson, 1977; Miller, Cus-
ter, & Nassau, 2000; Nicholls & Thorkildsen, 1988) has
shown that children not only deny the possibility of
events that violate physical laws but also deny the
possibility of events that violate social laws. For ex-
ample, Komatsu and Galotti (1986) asked children
between the ages of 6 and 10 whether dogs could be
called ‘‘wugs’’ and red traffic lights could be switched
with purple traffic lights if everyone agreed to the
change and found that most 6-year-olds, many 8-
year-olds, and even a few 10-year-olds denied the
possibility of altering these conventions. Likewise,
Miller et al. (2000) found that many 7-year-olds be-
lieve that social laws, like physical laws, are univer-
sally true and impervious to change. Although young
children explain why people conform to social laws
differently than they explain why people conform to
physical lawsFappealing to mental states in the first
case and physical forces in the second (Kalish, 1998;
Schult & Wellman, 1997; Sobel, 2004)Fthe fact that
they deny the possibility of both types of events calls
into question children’s possibility judgments for
physically impossible events.
Despite these inconsistencies in how children
reason about physical possibility, children appear to
understand the concepts possible and impossible in
general. For instance, research on modal language
acquisition (Byrnes & Duff, 1989; Hirst & Weil, 1982;
Noveck, Ho, & Sera, 1996) has found that children
master linguistic distinctions corresponding to the
conceptual distinction between possibility and im-
possibility by the age of 3 (although this may not
indicate a full understanding of modal logic; see
Coates, 1988). Furthermore, research on children’s
inferential search behavior (Fabricius, Sophian, &
Wellman, 1987; Gonsalves, 1999; Sommerville &
Capuani-Shumaker, 1984; Sophian & Somerville,
1988) has found that most 3-year-olds make a clear
distinction between possible object locations and
impossible object locations, searching for hidden
objects in all possible hiding locations but not in any
impossible hiding locations.
Perhaps children understand the concepts of
possibility and impossibility but have difficulty ap-
plying these concepts to a domain as large and as ill-
defined as the ‘‘real world.’’ After all, the evidence
that children understand modal concepts, in general,
has come from studies involving small, well-defined
domains in which all possibilities can be individua-
ted and enumerated. Obviously, one cannot enu-
merate all events possible within the real world to
determine whether a particular event (e.g., calling
dogs ‘‘wugs’’) is among them. Instead, one must
draw upon one’s knowledge of causal processes and
causal constraints to accomplish this task. Accord-
ingly, children who deny the possibility of events
that are actually possible (e.g., altering a social con-
vention) may be unaware of what counts as evidence
of possibility and what counts as evidence of im-
possibility.
As an illustration, consider one of the many
events that children reliably judge impossible:
floating in the air (Browne & Woolley, 2004; Kalish,
1998; Schult & Wellman, 1997; Sobel, 2004). On the
one hand, children may deny the possibility of this
event because they recognize that the event violates
1016 Shtulman and Carey

an explicitly known causal principleFfor example,
‘‘unsupported objects fall,’’ ‘‘gravity pulls us down-
ward,’’ ‘‘people are denser than air,’’ ‘‘everything
that goes up must come down.’’ On the other hand,
children may deny the possibility of this event sim-
ply because they are ignorant of how the event could
occur. In other words, children may attempt to
imagine circumstances that would allow a person to
float in the air, fail to identify these circumstances,
and conclude that the event is impossible without
ever entertaining a causal principle like ‘‘unsup-
ported objects fall.’’ On this view, children who deny
the possibility of calling dogs ‘‘wugs’’ or switching
red traffic lights with purple traffic lights do so not
because they believe that social conventions are
unalterable but because they are unable to think of
any circumstances that would allow those particular
conventions to be altered.
Put differently, children may initially mistake
their inability to imagine circumstances that would
allow an event to occur for evidence that no such
circumstances exist. This claim is reminiscent of
Piaget’s (1987) claim that children initially confuse
necessity with actuality and must learn to differen-
tiate true necessity from ‘‘pseudo-necessity,’’ or the
impression of necessity based on a superficial anal-
ysis of the relevant domain. Piaget supported this
claim with the finding that children under the age of
10, when presented a finite set of objects and asked to
order the objects in as many ways as possible, often
fail to discover the full range of permutations.
In the present study, we explored the applicability
of Piaget’s ideas about logical possibility to chil-
dren’s reasoning about physical possibility. In par-
ticular, we explored the hypothesis that children
initially fail to differentiate physical impossibilities,
like walking through a wall or walking on water,
from ‘‘pseudo-impossibilities,’’ like finding an alli-
gator under the bed or growing a beard to one’s toes.
Although both types of events violate known causal
principles, only the former violates physical laws
and are therefore impossible. By measuring the ex-
tent to which children differentiate these two types
of eventsFthat is, ‘‘improbable events’’ and ‘‘im-
possible events’’Fwe hoped to shed light both on
what children mean when they say that something is
impossible and on how they arrive at this conclusion.
Experiment 1
One of the most frequent ways children learn about
the occurrence of unobserved events is in the context
of stories. We therefore chose a storybook task as an
ecologically valid means of probing children’s intu-
itions about physical possibility. A 1,500-word story
containing a variety of extraordinary eventsFboth
improbable and impossibleFwas written and illus-
trated specifically for this purpose.
Method
Participants. Sixteen 4-year-olds (M54 years 6
months, range 54 years 0 month to 5 years 0 month),
sixteen 6-year-olds (M56 years 4 months, range 55
years 11 months to 6 years 10 months), sixteen
8-year-olds (n517, M58 years 6 months, range 58
years 2 months to 9 years 0 month), and 16 adults
participated in Experiment 1. The adult participants,
mostly Harvard undergraduates, were recruited
from the lobby of the psychology department and
received monetary compensation for their partici-
pation. The 6- and 8-year-olds were recruited from a
suburban elementary school and tested at the school
itself. The 4-year-olds were recruited from the
greater Boston area and tested at the Harvard Lab-
oratory for Developmental Studies, as were those in
the other three experiments. Participants in all four
experiments were predominantly White and from
middle-class families, although a range of ethnic and
socioeconomic backgrounds were represented. Ap-
proximately equal numbers of boys and girls were
included in each experiment.
Materials. The story contained eight ordinary
events, eight improbable events, and eight impossi-
ble events in a random order. The eight ordinary
events (in order of presentation) were wearing a
baseball cap, eating an apple, washing a car, losing
money, meeting a clown, building a house out of
bricks, cleaning a closet, and winning a game. The
eight improbable events were finding an alligator
under the bed, drinking onion juice, growing a beard
to one’s toes, owning a lion for a pet, eating pickle-
flavored ice cream, getting struck by lightning,
making a mug-shaped building, and painting polka
dots on an airplane. And the eight impossible events
were turning applesauce back into an apple, growing
money on a tree, walking through a brick wall,
traveling back in time, making a car vanish into thin
air, walking on water, opening a window with one’s
mind, and eating lightning for dinner.
The eight impossible events were designed to vi-
olate physical laws known at least implicitly by most
children (see Spelke, 1990), and the eight improbable
events were designed to violate empirical regulari-
ties not typically thought of as ‘‘laws,’’ either social
or physical. Note that the improbable events were
intended to be improbable from a conceptual point
of view rather than merely a statistical point of view.
Possibility-Judgment Strategies 1017

Our objective, after all, was to investigate how chil-
dren reason about the possibility of events that vio-
late their causal expectations rather than low-
frequency events that conform to such expectations
(see Hoemann & Ross, 1971, for an example of the
latter). Consequently, our selection criterion for the
improbable events was that they violate ‘‘contingent
truths’’ (e.g., that alligators are found in swamps,
that buildings are rectangular, that people dislike the
taste of onion juice), and our selection criterion for
the impossible events was that they violate ‘‘neces-
sary truths’’ (e.g., that objects are solid, that objects
are permanent, that objects require support). Our
intuition that the improbable events violated con-
tingent truths and the impossible events violated
necessary truths was validated by the adult partici-
pants in Experiment 1, who claimed that the im-
probable events could occur in real life but that the
impossible events could not.
The storybook itself contained twenty 8.500 1100
double-sided pages. Accompanying each page of
text was a photograph illustrating the events de-
scribed on that page. Although the ordinary events
were easily illustrated with a single, unaltered pho-
tograph, the improbable events and the impossible
events were illustrated with ‘‘before’’ and ‘‘after’’
photographs or with a single photograph doctored in
Adobe Photoshop. To ensure that the inclusion of
illustrations did not sway participants’ possibility
judgments, all 16 extraordinary events were illus-
trated in some fashion. Figure 1 depicts two sample
illustrations: one of an improbable event (finding an
alligator under the bed) and one of an impossible
event (eating lightning for dinner).
Procedure. Children were read the entire story at
the beginning of each interview. Children were then
asked whether or not they had experienced each of
the events listed above in the order they appeared in
the story (e.g., ‘‘Have you ever seen a person walk
through a wall?’’). Whenever children denied having
experienced an event, they were asked whether or
not the event could occur in real life (e.g., ‘‘Could a
person walk through a wall in real life?’’). Whenever
participants denied that an event could occur in real
life, they were asked to provide a justification for
their judgment (e.g., ‘‘Why couldn’t a person walk
through a wall in real life?’’). Note that participants
were asked whether the event could be performed
by ‘‘a person,’’ rather than by the participants
themselves, as many of the improbable events could
be performed only by individuals with specialized
training (e.g., owning a lion for a pet, making a mug-
shaped building). Also note that we accepted chil-
dren’s first justification without furthering probing,
both to reduce the length of the task and to maintain
a standard protocol across children of different ages
and different verbal abilities. Adults were asked the
same questions as children but in the form of a
questionnaire rather than an interview.
Coding justifications. Participants provided a total
of 671 justifications for why certain events are im-
possible. These justifications were sorted into two
categories: informative justifications and redundant
justifications. Informative justifications provided in-
formation about the target event that was not already
mentioned in the story. Redundant justifications, on
the other hand, provided no information beyond what
was already mentioned in the story or what was al-
ready discernable from a participant’s initial judgment
(e.g., ‘‘that’s not possible,’’ ‘‘that’s not real,’’ ‘‘no one
can do it,’’ ‘‘it can only happen in stories,’’ ‘‘I don’t
know’’). Justifications that referenced magic (e.g.,
Figure 1. Illustrations of an improbable event (finding an alligator under the bed) and an impossible event (eating lightning for dinner).
1018 Shtulman and Carey

‘‘you would need magic to do that’’) were also in-
cluded in this category, as these justifications com-
prised o6% of all justifications and o7% of the
justifications provided by any particular age group.
Informative justifications were sorted into two sub-
categories: factual justifications and hypothetical justi-
fications. Factual justifications referenced facts about
the world that would preclude an event’s occurrence
(e.g., walking through a wall is impossible because
‘‘walls are solid’’). Hypothetical justifications, on the
other hand, referenced hypothetical events that could
occur, or would occur, in place of the actual event
under consideration (e.g., walking through a wall is
impossible because ‘‘you could walk through a door’’
or because ‘‘you would hit your head’’). Examples of
both types of justifications are displayed in Table 1.
As can be seen from this table, hypothetical justifi-
cations were linguistically distinct from factual justifi-
cations in that only hypothetical justifications included
conditional verbs like ‘‘would,’’ ‘‘could,’’ or ‘‘should.’’
Moreover, hypothetical justifications were conceptually
distinct from factual justifications in that hypothetical
justifications did not actually answer the question at
handFthat is, the question of why an event is im-
possible. Rather, they answered the question of how
the same outcome could be achieved by different
means (e.g., how a person could get to the other side of
a wall without attempting to walk through it) or how a
different outcome could be achieved by the same
means (e.g., how a person could attempt to walk
through a wall without getting to the other side). For
this reason, hypothetical justifications could be con-
sidered evidence of a failed attempt to identify cir-
cumstances that would allow an extraordinary event to
occur. In other words, individuals may have provided
hypothetical justifications whenever they attempted to
think of way the target event could be actualized but
fell short of achieving this goal.
The reliability of our coding scheme was assessed by
comparing the exhaustive classifications of two inde-
pendent coders, each blind to the age of the partici-
pants providing the justifications. Overall agreement
between the two coders was 95%, and all disagree-
ments were resolved through discussion.
Results
Experience judgments. As expected, participants of
all ages claimed to have experienced the ordinary
events far more often than they claimed to have ex-
perienced either the improbable events or the im-
possible events. On average, children claimed to
have experienced 7.0 of the eight ordinary events, 0.1
of the eight improbable events, and 0.1 of the eight
impossible events. Likewise, adults claimed to have
experienced 7.9 of the eight ordinary events, 0.3 of
the eight improbable events, and none of the eight
impossible events. One-way analyses of variance
(ANOVAs) were used to test the effect of age on
participants’ experience with each type of event.
These analyses revealed a significant effect of age for
the ordinary events, F(3, 63) 58.03, po.001, but not
the improbable events, F(3, 63) 51.30, ns, or the
impossible events, F(3, 63) 51.40, ns.
Table1
Sample Factual and Hypothetical Justifications Given in Response to Each Impossible Event
Event Justification type Example
Turning applesauce into an apple Factual ‘‘Applesauce is all mushed’’
Hypothetical ‘‘You could get a new apple’’
Growing money on a tree Factual ‘‘Money is man-made’’
Hypothetical ‘‘It should have leaves on it’’
Walking through a brick wall Factual ‘‘Walls are solid’’
Hypothetical ‘‘You would bonk your head’’
Traveling back in time Factual ‘‘Times goes forward’’
Hypothetical ‘‘A dinosaur would eat you’’
Making a car vanish into thin air Factual ‘‘Nothing just disappears’’
Hypothetical ‘‘You could drive it away’’
Walking on water Factual ‘‘Water is a liquid’’
Hypothetical ‘‘Your feet would sink’’
Opening a window with one’s mind Factual ‘‘Minds do not have that power’’
Hypothetical ‘‘You could pretend to open it’’
Eating lightning for dinner Factual ‘‘You can’t catch lighting’’
Hypothetical ‘‘It would strike your tummy’’
Possibility-Judgment Strategies 1019

On average, 4-year-olds claimed to have experi-
enced 6.6 ordinary events, 6-year-olds claimed to
have experienced 6.9 ordinary events, 8-year-olds
claimed to have experienced 7.6 ordinary events, and
adults claimed to have experienced 7.9 ordinary
events. A contrast analysis confirmed that partici-
pants’ experience with the ordinary events increased
linearly with age, F(1, 63) 516.27, po.001. The three
ordinary events that children claimed to have expe-
rienced least often were wearing a baseball cap
(which 25% of children claimed not to have experi-
enced), cleaning a closet (which 21% claimed not to
have experienced), and winning a game (which 19%
claimed not to have experienced).
Possibility judgments. The average number of or-
dinary, improbable, and impossible events judged
possible by each age group is displayed in Figure 2.
As can be seen from this figure, participants of all
ages reliably affirmed the possibility of ordinary
events, like washing a car or eating an apple, and
reliably denied the possibility of impossible events,
like turning applesauce into an apple or growing
money on a tree. These results confirm those of
Johnson and Harris (1994), Rosengren et al. (1994),
and Subbotsky (2004) in that even the 4-year-olds
distinguished ordinary events from impossible
events. However, the meaning of this discrimination
was clearly different for children and adults, as only
adults reliably affirmed the possibility of improbable
events, like owning a lion for a pet or eating pickle-
flavored ice cream. Whereas adults judged 99% of
the improbable events possible, 4-year-olds judged
22% of the improbable events possible, 6-year-olds
judged 50% of the improbable events possible, and
8-year-olds judged 65% of the improbable events
possible. The three improbable events that children
judged possible least often were finding an alligator
under the bed (judged possible by 6% of children),
owning a lion for a pet (judged possible by 38%
of children), and making a mug-shaped building
(judged possible by 42% of children).
A repeated measures ANOVA was used to test the
effect of age group (4-, 6-, 8-year-olds, adults) and
event type (ordinary, improbable, impossible) on
participants’ possibility judgments. Age was ana-
lyzed between participants and event type was an-
alyzed within participants. As expected, this analysis
revealed a significant main effect of age,
F(3, 63) 532.02, po.001; a significant main effect of
event type, F(3, 63) 5775.23, po.001; and a signifi-
cant interaction between the two factors,
F(3, 63) 531.82, po.001. This interaction was ex-
plored with contrast analyses of the number of or-
dinary events, improbable events, and impossible
events judged possible at each age. These analyses
confirmed that participants’ possibility judgments
increased linearly with age for only one type of
event: the improbable events, F(1, 63) 5120.29,
po.001.
To determine the extent to which participants in
each age group differentiated the three types of
events, we performed separate repeated measures
ANOVAs for each age group. These analyses re-
vealed a significant effect of event type for all four
age groups: 4-year-olds, F(2, 32) 5323.05, po.001;
6-year-olds, F(2, 28) 599.78, po.001, 8-year-olds,
F(2, 32) 5241.40, po.001; and adults, F(2, 34) 5
497.45, po.001. Bonferroni comparisons of the three
event types revealed that all four age groups judged
improbable events possible significantly more often
than they judged impossible events possible. Only
adults, however, judged improbable events possible
as often as they judged ordinary events possible. In
other words, children of all ages judged improbable
events possible significantly less often than they
judged ordinary events possible.
Four-year-olds, as a group, judged improbable
events possible significantly more often than they
judged impossible events possible, but half of the
individuals within this group judged fewer than two
improbable events possible, as shown in Table 2. This
table, which displays the number of participants in
each age group who judged few (0 – 1), some (2 – 3),
many (4 – 6), or most (7 – 8) improbable events pos-
sible, highlights two aspects of the data not obvious
from group means. First, 50% of the 4-year-olds and
25% of the 6-year-olds judged improbable events
possible significantly less often than predicted by
Improbable
Ordinary
Impossible
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
Average Number of Events Judged Possible
4-yr-olds Adults
Age Group
6-yr-olds 8-yr-olds
Figure 2. Average number of ordinary, improbable, and impossible
events judged possible by each age group (out of eight).
1020 Shtulman and Carey

chance (binomial probability, po.05). Second, only
31% of the 8-year-olds judged improbable events
possible significantly more often than predicted by
chance (in contrast to 100% of the adults). Thus, most
4-year-olds effectively denied the possibility of all
improbable events, and only a few of the 8-year-olds
effectively affirmed the possibility of all improbable
events.
Justifications. Participants were asked to provide a
justification for every event they judged impossible,
thereby providing anywhere from 4 justifications to
16 justifications. Justifications for ordinary events
were excluded from further analysis due to their
infrequency. On average, 4-year-olds provided 13.9
justifications, 6-year-olds provided 11.0 justifica-
tions, 8-year-olds provided 10.3 justifications, and
adults provided 6.8 justifications. Justifications were
coded as factual, hypothetical, or redundant in ac-
cordance with the criteria discussed above. Because
participants provided different numbers of justifi-
cations, absolute frequencies were converted to rel-
ative frequencies (by dividing the number of times a
participant provided a particular type of justification
by the total number of justifications he or she pro-
vided) in order to compare justifications across in-
dividuals. These data were normally distributed and
did not require a logarithmic transformation. The
average proportion of factual, hypothetical, and re-
dundant justifications provided by each age group is
displayed in Figure 3. As can be seen from this fig-
ure, the tendency to provide hypothetical justifica-
tions and redundant justifications decreased with
age, but the tendency to provide factual justifications
increased with age.
One-way ANOVAs were used to test the effect of
age on participants’ tendency to provide each type of
justification. As expected, the effect of age was sig-
nificant for all three types: redundant justifications,
F(3, 63) 56.43, po.01; hypothetical justifications,
F(3, 63) 512.63, po.001; and factual justifications,
F(3, 63) 527.94, po.001. Moreover, contrast analyses
confirmed that the tendency to provide factual jus-
tifications increased linearly with age, F(1, 63) 5
70.68, po.001, but the tendency to provide hypo-
thetical justifications decreased linearly with age,
F(1, 63) 511.54, po.01, and the tendency to provide
redundant justifications decreased linearly with age,
F(1, 63) 536.96, po.001. Bonferroni comparisons of
the four age groups revealed that children of all ages
provided significantly more hypothetical justifica-
tions than adults but that 4-year-olds did not provide
significantly more hypothetical justifications than
either 6- or 8-year-olds. Apparently, children of all
ages thought that hypothetical justifications were
pragmatically acceptable.
Pearsons correlations were used to determine
whether children’s tendency to provide a particular
type of justification was related to their tendency
to judge improbable events possible. Whereas chil-
dren’s tendency to provide factual justifications was
positively correlated with their tendency to judge
improbable events possible, r(48) 5.35, po.001, their
tendency to provide redundant justifications was
negatively correlated with this same tendency,
r(48) 5.31, po.001. Neither correlation, however,
remained significant after controlling for the chil-
dren’s age (in months), possibly because age was not
a continuous variable.
To determine whether children provided different
types of justifications for the different types of
events, we divided children’s justifications into two
groupsFthose provided for improbable events and
those provided for impossible eventsFand calcu-
lated the proportion of factual, hypothetical, and
redundant justifications within each group. These
proportions were highly similar for all justification
types and for all age groups. In fact, none of the nine
comparisons were statistically significant, indicating
Table2
Number of Participants in Each Age Group Who Judged Few (0 – 1),
Some (2 – 4), Many (5 – 6), or Most (7 – 8) Improbable Events Possible
Age group
No. of improbable events judged possible
1–2 3–4 5–6 7–8
Four-year-olds 8 8 0 0
Six-year-olds 4 4 5 3
Eight-year-olds 0 7 4 5
Adults 0 0 0 16
Note. The first and last columns represent frequencies with a bi-
nomial probability o.05.
0.0
0.2
0.4
0.6
0.8
1.0
Average Proportion of Justifications
Hypothetical
Redundant
Factual
4-yr-olds Adults
Age Group
6-yr-olds 8-yr-olds
Figure 3. Average proportion of redundant, hypothetical, and
factual justifications provided by each age group.
Possibility-Judgment Strategies 1021

that children justified their judgments of impossi-
bility for the improbable events no differently than
they justified their judgments of impossibility for the
impossible events. Even factual justifications were
provided equally often for both types of events, as
some children claimed that drinking onion juice is
impossible because ‘‘onions don’t have juice’’ or that
getting struck by lightning is impossible because
‘‘lightning is too short.’’ From an adult’s perspective,
these ‘‘facts’’ are either untrue (as in the case of on-
ions) or only occasionally true (as in the case of
lightning). From a child’s perspective, on the other
hand, these facts may be as universally true as the
kinds of facts they provided in response to the im-
possible events.
In sum, not only were children markedly more
likely than adults to judge improbable events im-
possible, they also failed to differentiate improbable
events from impossible events in how they justified
those judgments.
Discussion
When judging the possibility of events in a do-
main as large and as ill-defined as the ‘‘real world,’’
individuals must draw upon their prior knowledge
of causal processes and causal constraints to make
such judgments. Experiment 1 investigated the de-
velopment of this ability by asking children between
the ages of 4 and 8 to decide whether a variety of
extraordinary events could or could not occur in the
real world. Like adults, children of all ages denied
the possibility of events that violated physical laws.
However, unlike adults, they also denied the possi-
bility of events that did not violate any kind of law,
like finding an alligator under the bed or making a
mug-shaped building, and they rarely justified their
judgments of impossibility with facts about the
world that would preclude an event’s occurrence.
One interpretation of these results is that children
and adults rely on different standards of evidence for
deciding that an event is impossible. Whereas adults
rely on identifying facts about the world that would
preclude an event’s occurrence, children rely on their
ability to identify circumstances that would allow an
event to occur. Failing to identify such circumstanc-
es, they deny the possibility of many events that
adults judge to be possible. Granted, even adults
may base their initial impressions of an event’s
possibility on their ability to imagine circumstances
that would allow the event to occur, but the adult
participants in Experiment 1 rarely based their final
judgments on such considerations. Rather, they
sought out principled reasons (i.e., factual justifica-
tions) for why an event that seemed impossible was
impossible.
Of course, part of the reason why children showed
little evidence of using explicit causal principles to
guide their possibility judgments may be that chil-
dren are less capable than adults at articulating the
reasoning behind such judgments. Indeed, children
of all ages might have provided more factual justi-
fications for their judgments of impossibility if we
had probed their reasoning further. They might even
have changed their minds about the possibility of
improbable events initially judged impossible. Chil-
dren’s justifications should not therefore be taken as
evidence that children cannot differentiate improb-
able events from impossible events in principle. Still,
the fact that 4-year-olds rarely appealed to causal
principles in their spontaneous justifications sug-
gests that these principles did not play a large role
For at least not an explicit roleFin their initial
judgments.
In truth, there are at least two ways children could
have arrived at the conclusion that an event is im-
possible without ever having referenced an explicit
causal principle. First, they may have attempted to
identify circumstances that would allow the event to
occur, failed in their attempt to do so, and concluded
that the event must be impossible. Second, they may
not have attempted to ‘‘model’’ the event per se but
simply based their judgment on the phenomeno-
logical experience of having an expectation violat-
edFthat is, feelings of surprise, confusion, or
disbelief. Evidence of both processing accounts can
be found in the way in which children most typically
justified their judgments of impossibility. Whereas
children’s hypothetical justifications (e.g., ‘‘he
couldn’t find a real alligator under the bed but he
could find a toy alligator’’) are consistent with the
first account, children’s redundant justifications
(e.g., ‘‘it can’t happen’’) are consistent with the sec-
ond. Note that this explanation, if correct, implies
that children who provided mainly redundant jus-
tifications (i.e., 4- and 6-year-olds) based most of
their judgments on pure phenomenological experi-
ence.
Two relatively trivial explanations for children’s
tendency to deny the possibility of improbable
events can be ruled out immediately. First, it was not
the case that children denied the possibility of any
event they had not personally experienced. Children
denied the possibility of 55% of the improbable
events they had not personally experienced, but only
15% of the ordinary events they had not personally
experienced. Moreover, 3 of the 5 children who oc-
casionally denied the possibility of ordinary events
1022 Shtulman and Carey

affirmed the possibility of other ordinary events that
they had not personally experienced.
Second, it was not the case that children denied
the possibility of any event with a negative emo-
tional valence. Although half of the improbable
events had a negative emotional valence (i.e., finding
an alligator under the bed, drinking onion juice,
eating pickle-flavored ice cream, and getting struck
by lightning), the other half did not (i.e., growing a
beard to one’s toes, owning a lion for a pet, making a
mug-shaped building, and painting polka dots on an
airplane), and children denied the possibility of both
types of events equally often (i.e., 57% of the time vs.
54% of the time). Furthermore, children consistently
denied the possibility of impossible events with
positive emotional valences, like growing money on a
tree or walking on water, even though many partic-
ipants may have wished that these events were, in
fact, possible. Clearly, the events’ emotional valence
cannot explain children’s overall patterns of judg-
ments.
Two other explanations for children’s failure to
judge improbable events possible are not as easily
dismissed. First, children may have interpreted the
task as a test of their factual knowledge rather than a
test of their modal intuitions. In other words, chil-
dren may have interpreted the question ‘‘Could [the
event] happen in real life?’’ as ‘‘Does [the event]
happen in real life?’’ This explanation is unlikely to
be true given that children as young as 3 differentiate
factual verbs from modal verbs (as noted previous-
ly). Nevertheless, we tested this possibility directly
in Experiment 2 by assessing children’s under-
standing of the modal verb ‘‘could’’ before admin-
istering the storybook task. Second, children may
have denied the possibility of improbable events
because they systematically underestimated the
scope of the possibility judgment they were being
asked to make. In other words, children may have
interpreted the question ‘‘Could [the event] happen
in real life?’’ as ‘‘Could [the event] happen under
normal circumstances?’’ Experiment 3 tests this pos-
sibility by asking children to make magic judgments
rather than possibility judgments.
Experiment 2
In English, one can express the likelihood that a
statement is true using modal verbs (e.g., must,
might, may, can, could, should), modal adjectives
(e.g., possible, probable, likely, certain), modal ad-
verbs (e.g., definitely, maybe, perhaps), and modal
inflections (e.g., imperative tense, subjunctive tense,
conditional tense; See Perkins, 1983). From the per-
spective of a mature modal language user, the lin-
guistic distinction between ‘‘could’’ and ‘‘could not’’
maps onto the conceptual distinction between pos-
sible and impossible states of affairs, not the dis-
tinction between actual and hypothetical states of
affairs. Might deficits in modal language (or modal
logic) have led the youngest participants in Experi-
ment 1 to interpret modal questions like ‘‘Could a
person find an alligator under the bed in real life?’’
as factual questions like ‘‘Do people find alligators
under the bed in real life?’’
This explanation would be consistent with the
claim made by Pieraut-LeBonniec (1980) that young
children systematically misunderstand modal lan-
guage. In one of several studies, Pieraut-LeBonniec
showed children a stick, a marble, and a box with
two holes cut into its top. Although the stick fit
through both holes, the marble fit through only the
larger of the two holes. After children were famil-
iarized with these materials, the experimenter put
one of the objects into the large hole and asked the
child ‘‘Can you tell without opening the [box’s] door
what it is?’’ None of the 4-year-olds, 25% of the
6-year-olds, 40% of the 8-year-olds, and 85% of the
10-year-olds in her study were able to answer the
question correctly (i.e., ‘‘no’’). The remaining chil-
dren claimed that they knew for sure which object
had been put into the box: the marble.
Pieraut-LeBonniec interpreted her findings as
evidence that children under the age of 12 use a
modal logic that is qualitatively different from that
used by adults, which, if true, might explain the
developmental change documented in Experiment 1.
There are, however, at least two reasons to doubt
Pieraut-LeBonniec’s general claim in favor of a more
specific claimFnamely, that many children under
the age of 12 fail to understand the distinction be-
tween guessing and knowing (see Fay & Klahr, 1996;
Klahr & Chen, 2003).
First, even though none of the 4-year-olds in
Pieraut-LeBonniec’s original experiments could an-
swer questions about epistemic certainty, virtually
all of them could answer questions about physical
possibility, like ‘‘Can the marble fit through the small
hole?’’ or ‘‘Can the stick fit through the large hole?’’
In other words, children who failed to acknowledge
the uncertainty of which possibility was an actuality
still acknowledged the existence of multiple possi-
bilities (see also Horobin & Acredolo, 1989). Second,
multiple researchers (e.g., Byrnes & Duff, 1989; Hirst
& Weil, 1982; Noveck et al., 1996) have found that
children as young as 3 understand that statements
expressed with a factive verb (e.g., ‘‘the peanut is
under the box’’) are more likely to be true than
Possibility-Judgment Strategies 1023

statements expressed with certain modal verbs (e.g.,
‘‘the peanut may be under the box’’), further
strengthening the claim that young children under-
stand modal language as applied to the world even if
they fail to understand modal language as applied to
states of knowledge.
Given that the participants in Experiment 1 were
asked modal questions about the world, it is unlikely
that their failure to judge improbable events possible
was due to deficits in modal language or modal
logic. In Experiment 2, we attempted to confirm this
assumption by asking 4-year-olds (the youngest
participants in Experiment 1) to judge the possibility
of probable, improbable, and impossible events in
two well-defined domains before asking them to
judge the possibility of ordinary, improbable, and
impossible events with respect to the world at
large. If preschoolers’ failure to judge improbable
events possible is due to general deficits in modal
language or modal logic, then they should deny the
possibility of improbable events in both tasks. If, on
the other hand, preschoolers’ failure to judge im-
probable events possible is specific to reasoning
about physical possibility, then they should affirm
the possibility of improbable events in the first task
but continue to deny the possibility of improbable
events in the second. Furthermore, if young
children’s performance in Experiment 1 reflects a
shaky command of modal language, then practice
answering modal questions may improve their
performance.
Method
Participants. Twelve 4-year-olds (M54 years 3
months, range 54 years 0 month to 4 years 9
months) similar to those in Experiment 1 partici-
pated in Experiment 2. One additional participant
was replaced after his mother intervened during the
storybook task.
Marbles task. The purpose of this task was to as-
sess the children’s ability to make a frequency-based
modal inference. Each child was shown a container
containing 10 blue marbles and one red marble. Af-
ter the child had counted both kinds of marbles, the
experimenter poured the marbles from the container
into an empty bag. The experimenter then retrieved
one marble from inside the bag and, without re-
vealing the color of the marble in his hand, asked the
child three questions: (1) ‘‘Could the marble in my
hand be blue?’’ (a probable event), (2) ‘‘Could the
marble in my hand be red?’’ (an improbable event),
and (3) ‘‘Could the marble in my hand be yellow?’’
(an impossible event). If 4-year-olds correctly inter-
pret ‘‘could’’ as a modal verb, then they should re-
spond affirmatively to the first two questions and
negatively to the last. If, on the other hand, 4-year-
olds incorrectly interpret ‘‘could’’ as a factive verb,
then they should respond affirmatively to one, and
only one, of the first two questions (as the marble in
the experimenter’s hand could not be both blue and
red).
Mouse task. This task, which was modeled after a
task used by Gonsalves (1999), was used to assess
children’s ability to make a rule-based modal infer-
ence. Each child was shown an array of six cupsF
four red cups and two blue cupsFand told that two
toy miceF‘‘Mickey’’ and ‘‘Minnie’’Fwere hiding
under separate cups of the same color. Once the child
could successfully repeat this rule, the experimenter
asked the child two questions: (1) ‘‘Could Mickey
and Minnie be hiding under the red cups?’’ (a
probable event), and (2) ‘‘Could Mickey and Minnie
be hiding under the blue cups?’’ (an improbable
event). The experimenter then lifted one of the blue
cups, revealing Mickey, and asked one final question:
‘‘Could Minnie be hiding under a red cup?’’ (an
impossible event, at least within the context of the
task). Again, if 4-year-olds correctly interpret
‘‘could’’ as a modal verb, then they should respond
affirmatively to the first two questions and nega-
tively to the last. If, on the other hand, 4-year-olds
incorrectly interpret ‘‘could’’ as a factive verb, then
they should respond affirmatively to one, and only
one, of the first two questions about Mickey’s loca-
tion.
Storybook task. Following the modal language
tasks, the experimenter administered the storybook
task as described in the methods section of Experi-
ment 1.
Results and Discussion
As expected, children performed quite accurately
in both the marble task and the mouse task. Ten of
the 12 children affirmed the possibility of both
probable events, 10 affirmed the possibility of both
improbable events, and 9 denied the possibility of
both impossible events. Thus, as a group, children
affirmed the possibility of 92% of the probable
events, 92% of the improbable events, and 21% of the
impossible events. Moreover, only 1 child failed in
both tasks to affirm the possibility of both the prob-
able event and the improbable event, which is what
all children should have done if they interpreted
‘‘could’’ as a factive verb.
Although children rarely denied the possibility
of improbable events in the objects tasks, they
1024 Shtulman and Carey

frequently denied the possibility of improbable
events in the storybook task. A comparison of the
percentage of children who judged each improbable
event possible in the objects tasks and the percentage
of children who judged each improbable event pos-
sible in the storybook task is displayed in Table 3. As
can be seen from this table, children denied the pos-
sibility of each improbable event in the storybook task
at least twice as often as they denied the possibility of
each improbable event in the objects tasks. Paired t
tests were used to test the effect of task type (objects
tasks, storybook task) on the proportion of ordinary/
probable, improbable, and impossible events judged
possible by each participant. These analyses revealed
a significant effect of task for the improbable events,
t(1, 11) 510.31, po.001, but not the ordinary/proba-
ble events, t(1, 11) 50, ns, or the impossible events,
t(1, 11) 51.15, ns. Apparently, children’s tendency to
deny the possibility of improbable events in the sto-
rybook task is not due to deficits in modal language
or modal logic. Rather, this tendency appears to be
specific to reasoning about possibility within a do-
main as large and as ill-defined as the ‘‘real world.’’
Answering modal questions in the objects tasks
did not appear to improve 4-year-olds’ performance
in the storybook task relative to the performance of
the 4-year-olds in Experiment 1. On average, the 4-
year-olds in Experiment 2 judged 7.3 of the eight
ordinary events possible, 2.1 of the eight improbable
events possible, and 0.7 of the eight impossible
events possible. The comparable numbers in Exper-
iment 1 were 7.4, 1.6, and 0.6. A repeated measures
ANOVA confirmed that children’s possibility judg-
ments in Experiment 2 varied significantly by event
type, F(2, 22) 5143.68, po.001. Bonferroni compari-
sons of the different types of events revealed that
children judged improbable events possible signifi-
cantly less often than they judged ordinary events
possible but significantly more often than they
judged impossible events possible. That said, 5
children judged improbable events possible signifi-
cantly less often than would be predicted by chance
(binomial probability, po.05). In short, the 4-year-
olds in Experiment 2 denied the possibility of im-
probable storybook events as often as the 4-year-olds
in Experiment 1FM52.1 versus M51.6,
t(26) 50.98, nsFdespite having just succeeded on
tasks that required (and potentially primed) accurate
comprehension of the modal verb ‘‘could.’’
As in Experiment 1, children were asked to justify
their judgments of impossibility. The number of jus-
tifications provided by individual children ranged
from 9 to 16. The average proportion of children’s
justifications that were factual, hypothetical, and re-
dundant were .33, .21, and .46. These proportions
were statistically similar to the proportions of factual,
hypothetical, and redundant justifications provided
by the 4-year-olds in Experiment 1, and children
provided approximately the same proportion of fac-
tual, hypothetical, and redundant justifications for the
improbable events as they provided for the impossi-
ble events. Thus, once again, 4-year-olds failed to
differentiate improbable events from impossible
events both in their judgments of impossibility and in
their justifications for those judgments.
In summary, these data corroborate the claims
made by other authors (e.g., Hirst & Weil, 1982) that
young children distinguish between possibility and
actuality and have learned various linguistic mark-
ers for this distinction. Why then did children per-
form comparably to adults in the objects tasks but
not comparably to adults in the storybook task? Both
the objects tasks and the storybook task required
children to answer modal questions about the world.
However, only the storybook task required children
to draw upon their prior knowledge of causal pro-
cesses and causal constraints to generate their own
evidence of possibility or impossibility. In contrast,
the space of possible events in the both objects tasks
was finite and well specified, allowing the child to
discern that the improbable events (i.e., pulling a red
marble from the bag, finding both mice under the
blue cups) were among those events but the impos-
sible events (i.e., pulling a yellow marble from the
bag, finding one mouse under a red cup and one
mouse under a blue cup) were not. In other words,
when children discovered a contradiction between
the target event and the set of events deducible from
the information they had been given, that con-
tradiction normatively specified an impossibility.
This was not true for the storybook task, as con-
Table3
Percentage of 4-Year-Olds in Experiment 2 Who Affirmed the Possibility
of Each Improbable Event in the Objects Task and the Storybook Task
Task Event
Judged
possible
Object Pulling a red marble from the bag 100
Finding both mice under the blue cups 83
Storybook Eating pickle-flavored ice cream 42
Getting struck by lightning 42
Painting polka dots on an airplane 33
Drinking onion juice 33
Growing a beard to one’s toes 17
Making a mug-shaped building 8
Owning a lion for a pet 0
Finding an alligator under the bed 0
Possibility-Judgment Strategies 1025

tradictions between the target event and all ‘‘imag-
inable’’ events may or may not have specified an
impossibility.
Having established that the failure to judge improb-
able events possible documented in Experiment 1 and
replicated in Experiment 2 cannot be attributed to lan-
guage deficits, we now turn to the question of whether
children systematically underestimated the scope of the
possibility judgment they were asked to make.
Experiment 3
Philosophers interested in modal logic have often
pointed out that modal language is context-depen-
dent (see Johnson-Laird, 1978). The sentence ‘‘John
may leave,’’ for example, can be interpreted meta-
physically, as in ‘‘it is logically/physically possible
for John to leave’’; epistemically, as in ‘‘I am uncer-
tain whether John will leave’’; deontically, as in
‘‘John is allowed to leave’’; or dynamically, as in
‘‘John has the ability to leave.’’ Because of this
ambiguity, we specified the scope of the possibility
judgments that participants were asked to make
(possible in real life) with every question. Still, chil-
dren may have interpreted questions like ‘‘Could a
person drink onion juice in real life?’’ as ‘‘Could a
person drink onion juice under normal circumstances?’’
Onewaytoaddressthisconcernwouldbeto
‘‘contextualize’’ the improbable eventsFthat is, to
provide a context in which the events might actually
occurFand compare children’s judgments for the
contextualized events with their judgments for the
‘‘decontextualized’’ events in the original story. If this
manipulation improved children’s performance, one
could conclude that children do, in fact, understand
themodalquestionposedtothembutareimpairedat
identifying circumstances that might allow an im-
probable event to occur. If, on the other hand, this
manipulation did not improve children’s performance,
one would be unable to determine whether children
failed to understand the modal question posed to them
or failed to find the contextualized events more plau-
sible than the decontextualized events.
Another way of addressing this same concern
would be to circumvent the ambiguities inherent in
modal language altogether and ask children to make
‘‘magic’’ judgments rather than possibility judg-
ments. We decided to adopt this approach, rather
than the previous approach, for two reasons. First,
many authors (e.g., Johnson & Harris, 1994; Phelps &
Woolley, 1994; Rosengren & Hickling, 1994) have
shown that children appeal to magic when asked to
explain the occurrence of physically impossible
events, implying that children interpret the word
‘‘magic’’ as synonymous with ‘‘impossible.’’ Second,
Browne and Woolley (2004) have shown that chil-
dren as young as 3 are better able to differentiate
events that violate social laws from events that
violate physical laws when asked to make magic
judgments than when asked to make possibility
judgments, although the magnitude of this differ-
entiation was small (i.e., a 31% difference). Posing
modal questions in terms of magic may therefore
make the scope of such questions clearer, thereby
allowing children as young as 4 to treat improbable
events like ordinary events if their failure to do so in
Experiments 1 and 2 was due mainly to a misinter-
pretation of the question.
Method
Participants. Twelve 4-year-olds (M54 years 5
months, range 54 years 1 month to 4 years 10
months) similar to those in previous experiments
participated in Experiment 3. Two children objected
to the premises of the task, insisting that magic is not
real, and had to be replaced.
Procedure. The storybook task was administered
in the same manner as it was administered in Ex-
periments 1 and 2 with the exception that whenever
children denied having experienced an event, they
were asked whether or not the event required magic
to occur in real life (e.g., ‘‘Would it take magic to
walk through a wall in real life?’’) as opposed to
whether or not the event was possible. Thus, the
measure of interest is the number of improbable
events that children claimed could occur in real life
without magic.
Results and Discussion
Overall, the magic judgments of the 4-year-olds in
Experiment 3 were quite similar to the possibility
judgments of the 4-year-olds in Experiments 1 and 2.
On average, children claimed that 7.7 of the eight or-
dinary events could occur without magic, 2.6 of the
eight improbable events could occur without magic,
and 0.5 of the eight impossible events could occur
without magic. In comparison, the 4-year-olds in Ex-
periment 1 claimed that 7.4 of the eight ordinary events
could occur in real life, 1.6 of the eight improbable
events could occur in real life, and 0.6 of the eight
impossible events could occur in real life (on average).
A repeated measures ANOVA confirmed that
children’s magic judgments varied significantly by
event type, F(2, 22) 5180.90, po.001. Bonferroni
comparisons of the different events revealed that
children associated improbable events with magic
significantly more often than they associated ordi-
1026 Shtulman and Carey

nary events with magic but significantly less often
than they associated impossible events with magic.
Still, 3 of the 12 children claimed that fewer than two
improbable events could occur without magic and
only 1 child claimed that more than half of the im-
probable events could occur without magic.
Overall, the number of improbable events that the
4-year-olds in Experiment 3 claimed could occur
without magic was greater than the number of im-
probable events that the 4-year-olds in Experiment 1
claimed could occur in real life, t(27) 52.19, po.05.
However, the magnitude of this difference was 1.0
out of eight events (or 12.5%), a very modest differ-
ence. Indeed, similar to 4-year-olds in Experiment 1,
92% of the 4-year-olds in Experiment 2 claimed that
it would take magic to make a mug-shaped building,
83% claimed it would take magic to find an alligator
under the bed, and 75% claimed it would take magic
to grow a beard to one’s toes.
In short, children’s ability to differentiate im-
probable events from impossible events was not
substantially improved when children were asked to
make magic judgments rather than possibility judg-
ments. Children claimed that it would take magic
not only to turn applesauce into an apple or to make
a car vanish into thin air but also to paint polka dots
on an airplane or to own a lion for a pet. Although
different children may have interpreted the word
‘‘magic’’ in different ways, children’s overall usage
was consistent with Phelps and Woolley’s (1994)
claim that children initially appeal to magic to ex-
plain events that ‘‘both violate their expectations and
elude adequate physical explanation’’ (p. 385). In
support of this claim, they show that children be-
tween the ages of 4 and 8 use the word ‘‘magic’’ to
describe extraordinary physical transformations that
they are unable to explain in terms of known causal
processes (e.g., thermodynamically induced color
changes, magnetically induced motion changes) but
refrain from using the word ‘‘magic’’ to describe
extraordinary transformations that they are able to
explain. Presumably, the act of making a mug-
shaped building is as unexplainable to most 4-year-
olds as the act of changing an object’s color with
heat, but is the act of making a mug-shaped building
no less mysterious than the act of walking through a
wall? This question is addressed in Experiment 4
with the use of a forced-choice paradigm.
Experiment 4
Some of the aforementioned studies that purported to
reveal an early-developing understanding of physical
impossibility used a forced-choice paradigm in which
children were asked to identify which of two events
was possible and which was impossible (e.g., Browne
& Woolley, 2004; Johnson & Harris, 1994). Under these
conditions, even 3-year-olds are able to differentiate
impossible events from possible events (albeit, ordi-
nary events). Would 4-year-olds, who fail to judge
improbable events possible when presented in isola-
tion, be able to distinguish improbable events from
impossible events when these two types of events are
presented in a pair?
One reason to believe they could is that the
impossible events in the story violate expectations
present in infancyFfor example, expectations re-
garding object permanence (Wynn, 1992), object so-
lidity (Baillargeon, Spelke, & Wasserman, 1985),
object continuity (Spelke, Kestenbaum, Simons, &
Wein, 1995), object support (Needham & Baillargeon,
1993), and contact causality (Leslie & Keeble,
1987)Fbut the improbable events in the story violate
expectations acquired later in life. Even though such
differences in knowledge entrenchment do not ap-
pear to affect children’s possibility judgments, they
may affect the certainty with which those judgments
are held. Accordingly, we should expect at least
some improvement in 4-year-olds’ ability to judge
improbable events possible if children are forced to
choose between an improbable event and an im-
possible event. At issue, however, is whether this
improvement is categoricalFthat is, whether giving
children some training on the contrast of interest and
highlighting this contrast in a forced-choice para-
digm induces adult-like performance.
To investigate this issue, we paired each improb-
able event with an impossible event and asked 4-
year-olds to decide which event could occur in real
life and which event could not. If 4-year-olds are
equally confident that both types of events cannot
occur in real life, then they should claim that the
improbable event is possible on half the trials and
that the impossible event is possible on the other
half. If, on the other hand, 4-year-olds are more
confident that the impossible events cannot occur in
real life than they are that the improbable events
cannot occur in real life, then they should claim that
the improbable event is possible on significantly
more trials than they claim that the impossible event
is possible.
Method
Participants. Twelve 4-year-olds (M54 years 7
months, range 54 years 0 month to 4 years 11
months) similar to those in previous experiments
Possibility-Judgment Strategies 1027

participated in Experiment 4. One child refused to
complete the task and was replaced.
Materials. The story used in Experiments 1 – 3 was
used in Experiment 4 as well. Each improbable event
in the story was paired with each impossible event in
the story to create 64 unique pairs of events. These
pairs were divided into eight groups of eight such
that each group contained one instance of every
event. The order of the events within each pair was
counterbalanced such that the improbable event
preceded the impossible event in half of the pairs
and the impossible event preceded the improbable
event in the other half. Illustrations from the story
were then reproduced on 300 300 cards. Each card
corresponded to a unique event. Six additional cards
were created for the purpose of training children on
how to complete the task. These cards depicted three
ordinary events (a chicken laying eggs, two children
talking, and a flying bird) and three impossible
events (a chicken laying tennis balls, two dogs talk-
ing, and a flying pig).
Procedure. Children were shown two contain-
ersFone labeled with a ‘‘thumbs-up’’ sticker and
one labeled with a ‘‘thumbs-down’’ stickerFand
told that the thumbs-up container was for pictures of
things that can happen in real life and that the
thumbs-down container was for pictures of things
that cannot happen in real life. The experimenter
demonstrated the function of each container by
sorting one pair of training cards (the chickens) into
the appropriate containers. Each child was then en-
couraged to sort the remaining pairs of training
cards on their own. All 12 children sorted the cards
correctly on their first attempt. Of course, these
training trials contrasted impossible events with or-
dinary events, a differentiation that 4-year-olds eas-
ily made in Experiments 1 – 3. Following the training
procedure, the experimenter read the story in its
entirety. The children were then asked to sort the
eight pairs of pictures taken from the story itself.
Because we tested 12 children but constructed only
eight groups of event pairings, half of the event
pairings were used twice.
Results and Discussion
Overall, the forced-choice paradigm improved
children’s ability to differentiate improbable events
from impossible events, relative to that of Experi-
ments 1 – 3, but did not induce adult-like perfor-
mance. On average, each child placed 6.0
improbable-event cards in the thumbs-up container
and 2.0 improbable-event cards in the thumbs-down
container. The frequency of placing improbable-
event cards in the correct container (i.e., the thumbs-
up container) was significantly 44.0, the frequency
predicted by chance, t(11) 55.75, po.001. In addi-
tion, all improbable-event cards were placed in the
thumbs-up container more often than they were
placed in the thumbs-down container, and all im-
possible-event cards were placed in the thumbs-
down container more often than they were placed in
the thumbs-up container, as shown in Table 4. In
other words, children judged each improbable event
possible more often than they judged each impossi-
ble event possible (as a group).
Despite the 4-year-olds’ successful performance
as a group, only 4 children placed more improbable-
event cards in the thumbs-up container than the
number predicted by chance (i.e., 7 or 8). Indeed, a
quarter of the children placed fewer than six im-
probable-event cards in the thumbs-up container,
and half of the children tried to place both cards in
the thumbs-down container at some point in the
experimentFa situation in which the experimenter
intervened and asked the child to place one, and
only one, card in each container.
A comparison of the performance of the 4-year-
olds in Experiment 4 and the performance of the 4-
year-olds in Experiments 1 – 3 is displayed in Figure
4. Because the 4-year-olds in Experiment 4 could be
expected to judge four improbable events possible
by chance alone, we could not use the number of
improbable events judged possible as a metric of
Table4
Percentage of 4-Year-Olds in Experiment 4 Who Placed Each Extraor-
dinary Event in the Thumbs-Up Container, Thereby Judging the Event
Possible
Event type Event description
Judged
possible
Improbable Drinking onion juice 100
Eating pickle-flavored ice cream 92
Owning a lion for a pet 83
Growing a beard to one’s toes 67
Painting polka dots on an airplane 67
Finding an alligator under the bed 58
Getting struck by lightning 58
Making a mug-shaped building 58
Impossible Opening a window with one’s mind 42
Eating lightning for dinner 42
Traveling back in time 33
Walking on water 33
Walking through a brick wall 17
Making a car vanish into thin air 17
Turning applesauce back into an apple 8
Growing money on a tree 8
1028 Shtulman and Carey

comparison. Instead, we used the difference between
the number of improbable events judged possible (or
nonmagical, in the case of Experiment 3) and the
number of impossible events judged possible (or
nonmagical) as a metric of comparison.
As can be seen from this figure, the 4-year-olds in
Experiment 4 differentiated improbable events from
impossible events to a much greater extent than the
4-years-olds in Experiments 1 – 3 did. Indeed, a one-
way ANOVA confirmed that participants’ difference
scores varied significantly by experiment,
F(3, 51) 58.80, po.001. Moreover, Bonferroni com-
parisons of the four experiments revealed that the
average difference scores in Experiments 1 – 3 were
significantly smaller than the average difference
score in Experiment 4 but did not differ from one
another. Thus, even though 4-year-olds deny the
possibility of improbable events when evaluating
these events in isolation, they recognize that im-
probable events are more likely to occur in the real
world than impossible events when evaluating these
two types of events in conjunction.
That said, 4-year-olds’ success in the forced-choice
paradigm was still quite moderate. Rather than
judging all eight improbable events possible under
these constraints, most children judged only six im-
probable events possible under these constraints.
Furthermore, the paradigm used in Experiment 4
was highly artificial, for the kinds of possibility
judgments that individuals need to make outside the
psychology laboratory are almost always single-
event judgments. Although Experiment 4 confirms
the fact that the causal constraints violated by the
impossible events (i.e., physical laws) are more
deeply entrenched than those violated by the im-
probable events (i.e., empirical regularities), it does
not elucidate how children would treat these events
in any real-world situation. Thus, it may be inap-
propriate to attribute to children an understanding
of the distinction between possible events and im-
possible events on the basis of such evidence, as
others (e.g., Browne & Woolley, 2004; Johnson &
Harris, 1994) have done.
General Discussion
Previous research has shown that, from a very early
age, children deny the possibility of many impossi-
ble events, like floating in the air, walking through a
wall, moving a marble with one’s mind, or hanging
on a tree branch forever. The present study sheds
new light on how children make these judgments.
When adults reason about the possibility of expec-
tation-defying events, they consistently differentiate
events that violate physical laws (impossible events)
from those that do not (improbable events), and they
tend to justify their judgments of impossibility by
appealing to those laws. Children, on the other hand,
deny the possibility of both impossible events and
improbable events, and they typically justify their
judgments in redundant or pragmatically inappro-
priate ways. Moreover, children’s justifications for
why impossible events could not occur in real life do
not differ from their justifications for why improba-
ble events could not occur in real life.
This pattern of results, which was replicated in
three experiments, cannot be due to general deficits
in modal language or modal logic given that the
children in Experiment 2 drew accurate modal in-
ferences when operating within small, well-defined
domains. Why, then, might children differ from
adults in how they reason about physical possibility?
Clearly, part of the answer is that children possess
less domain-specific knowledge than adults do. One
cannot reflect upon the laws of nature to decide
whether an event is possible or impossible unless
one knows those laws. Likewise, one cannot identify
the circumstances under which an improbable event
could occur if those circumstances involve unfamil-
iar causal mechanisms. Still, there are at least three
reasons to doubt that differences in domain-specific
knowledge are the only relevant differences between
children and adults.
First, it is difficult to specify exactly what knowl-
edge is needed to affirm the possibility of improba-
ble events like growing a beard to one’s toes or
painting polka dots on an airplane that 4-year-olds
do not already possess. Second, children frequently
justified their judgments of impossibility in a way
that adults almost never didFthat is, by referencing
hypothetical events that could occur, or would occur,
Exp. 1 Exp. 2 Exp. 3 Exp. 4
0.0
1.0
2.0
3.0
4.0
5.0
Average Difference Score
Figure 4. Average difference between the number of improbable
events judged possible (or nonmagical) and the number of im-
possible events judged possible (or nonmagical) by each 4-year-
old in Experiments 1 – 4.
Possibility-Judgment Strategies 1029

in place of the actual event under consider-
ationFwhich suggests that children may often rely
on a different form of reasoning than adults do.
Third, it is unclear why lacking domain-specific
knowledge would lead children to judge possible
events impossible but would not also lead them to
judge impossible events possible, and yet children
systematically exhibited one bias but not the other.
How, then, might children have approached the
task differently than adults? As mentioned previ-
ously, there are at least two possibilities: (1) children
denied the possibility of any event they found bi-
zarre or surprising and (2) children denied the pos-
sibility of any event for which they were unable to
identify circumstances that would allow the event to
occur. Note that these accounts are not mutually
exclusive. Rather, both accounts assume that chil-
dren’s judgments of impossibility are based on ig-
norance of how an event could occur rather than
knowledge of why the event could not occur. If either
account is accurate, then young children’s possibility
judgments cannot be taken as evidence of an explicit
appreciation of the causal principles that constrain
real-world events, as many authors have done in the
past (e.g., Johnson & Harris, 1994; Rosengren &
Hickling, 1994).
Admittedly, the above hypotheses are supported
only indirectly by the findings of Experiments 1 – 3.
Direct support for these hypotheses would entail
prior measurement of children’s causal expectations
or the intentional manipulation of children’s imagi-
native activities. For instance, one could vary the
context in which an improbable event is presented
and compare children’s willingness to affirm the
possibility of this event in different contexts (e.g.,
drinking onion juice at home vs. drinking onion juice
at an onion-themed festival). Alternatively, one
could vary the content of an improbable event and
compare children’s willingness to affirm the possi-
bility of different versions of the same event (e.g.,
finding an alligator under the bed vs. finding a rabbit
under the bed).
On the whole, the present study helps to resolve
several inconsistencies highlighted in the introduc-
tion regarding children’s understanding of magic,
fantasy, and physical necessity. First, our findings
help to explain why young children not only deny
the possibility of events that violate physical laws
but also deny the possibility of events that violate
social laws, like going barefoot at school or calling
dogs ‘‘wugs’’ (Kalish, 1998; Komatsu & Galotti, 1986;
Miller et al., 2000; Nicholls & Thorkildsen, 1988).
Although these findings have typically been inter-
preted as evidence that children initially conflate
different types of necessitiesFthat is, physical ne-
cessity and social necessityFour findings suggest
that children may initially base their possibility
judgments on information that does not allow them
to distinguish between these two types of necessity.
For instance, children may deny the possibility of
calling dogs ‘‘wugs’’ not because they believe that
social laws are unalterable but because they are un-
able to think of any circumstances under which all
English speakers would change their lexicons ac-
cordingly. We believe that a process-based interpre-
tation of children’s failure to differentiate social laws
from physical laws is more parsimonious than a
knowledge-based interpretation of this failure in
light of our finding that children deny the possibility
of events that do not embody any type of necessity,
physical or social.
Second, our findings help to explain why most
4-year-olds endorse the existence of ‘‘real magic’’
and will accept the possibility of impossible physical
transformations if those transformations are ‘‘per-
formed’’ before their very eyes (Chandler & Lalonde,
1994; Rosengren & Hickling, 1994; Subbotsky, 2004).
These findings, although seemingly inconsistent with
children’s early-developing ability to differentiate
impossible events from ordinary events, are consistent
with our finding that children rarely identify princi-
pled reasons for why impossible events are, in fact,
impossible. Thus, children’s judgments of impossi-
bility may be easily overturned in the face of con-
flicting evidence, particularly perceptual evidence.
After all, what is actual must be possible. Interest-
ingly, children begin to doubt the existence of real
magic around the same time they begin to differenti-
ate improbable events from impossible events (i.e.,
age 6), which suggests that both behaviors may be
due to an initial absence of principle-based reasoning.
Third, our findings help to explain why children
believe in the existence of fantasy characters, like
Santa Claus, the Tooth Fairy, and the Easter Bunny
(Prentice et al., 1978; Sharon & Woolley, 2004; Woolley
et al., 2004). On its surface, children’s skepticism
toward the possibility of expectation-defying events,
appears to be inconsistent with their belief in
the existence of fantasy characters who possess
numerous expectation-defying properties. Never-
theless, the fact that children rarely identify reasons
as to why impossible events are impossible might
leave them vulnerable to suggestion in the same way
that it might leave them vulnerable to magic tricks
and visual illusions. That is, serious testimony from a
credible adult (e.g., ‘‘yes, Virginia, there is a Santa
Claus’’) may be sufficient to convince children of the
actuality of these fantasy characters if children have
1030 Shtulman and Carey

not identified a reason as to why such characters
could not exist in the real world.
To conclude, we would like to raise two questions
in need of further research. First, what kind of
knowledge is needed to judge improbable events
possible? On the one hand, children may need to
know more about the specific circumstances that
would allow an improbable event to occur. For in-
stances, children may need to know something about
construction practices and construction materials in
order to affirm the possibility of making a mug-
shaped building. On the other hand, children may
simply need additional experience reasoning about a
particular type of causality (e.g., intentional causali-
ty) or a particular type of causal violation (e.g., the
creation of unconventional artifacts, buildings or
otherwise). Future research could address this
question by systematically varying the type of cau-
sality violated by the improbable events (e.g., in-
tentional causality, physical causality, biological
causality) and comparing children’s willingness to
affirm the possibility of each class of events.
Second, how consistent are adults’ possibility
judgments across different individuals and different
events? Little is known about how adults judge the
possibility of events in domains other than those in
which all possibilities can be defined and enumerated
(see Bell & Johnson-Laird, 1998; Goldvarg & Johnson-
Laird, 2000). Although the adults in Experiment 1
were quite consistent in their judgment of improbable
events, they were somewhat inconsistent in their
ability to provide factual justifications for their judg-
ments of impossibility. Indeed, two adults provided
redundant justifications as often as they provided
factual ones. One explanation for this variation is that
some adults were more engaged in the task than
others. Another explanation is that some adults, like
children, continue to mistake their inability to imag-
ine circumstances that would allow an event to occur
for evidence that no such circumstances exist. Dis-
tinguishing between these two possibilities would not
only clarify the endpoint of the developmental tra-
jectory outlined in this article but would also shed
light on the question of why adults often disagree
about what is possible and what is not.
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