Can an ape
reason analogically?
Comprehension
and production of analogical problems by Sarah, a chimpanzee
(Pan troglodytes).
David L.
Oden
La Salle
University
Roger K.
R. Thompson
Franklin
& Marshall College
David
Premack
Somis CA
Running
Head: Analogical Reasoning by a Chimpanzee
Classical analogy problems involve perceptions and judgments about relations
between relations For example, the
simple verbal analogy, "Dog / Cat // Puppy / Kitten" reflects the
same relation, "Canine / Feline", within each side of the expression,
and the same relation, "Adult / Juvenile", across corresponding
elements of the two sides. This
fundamental pattern of relations between relations is also present or implicit
in the powerful literary devices of metaphor and simile, and is a key element
in the development of scientific models (e.g., Gentner, 1998; Thagard, 1992;
Holyoak & Thagard, 1997). Analogical reasoning is typically regarded as
computationally complex and developmentally sophisticated (see, e.g., Goswami,
1991; Holyoak & Thagard, 1997; Piaget, 1977; Sternberg, 1977, 1982;
Sternberg & Nigro, 1980; Vosniadou & Ortony, 1989).
The question of whether such
sophisticated reasoning is unique to humans has been a perennial topic for
debate (cf., Darwin, 1871; Griffin, 1992; James, 1981/1890; Vauclair, 1996;
Weiskrantz, 1985). Recently, techniques
have been developed which allow a systematic examination of analogical
reasoning and its component processes in species other than humans. For
example, Premack and his colleagues (e.g., Premack, 1978; Oden, Thompson &
Premack, 1990) used a matching-to-sample (MTS) procedure with chimpanzees (Pan
troglodytes) in which the sample and the choice alternatives consisted
of pairs of objects or pictures of items.
The stimulus pairs were composed of either two identical items -
instantiating the relation of "Identity" (I) - or two non-identical items - instantiating
the relation of "Non-Identity" (NI).
On a particular trial, either an I pair or an NI pair served as sample
and the choice alternatives consisted of one I pair and one NI pair. Since none
of the items comprising the choice pairs were used in sample pairs, Premack
labeled this task "conceptual matching-to-sample".
Although the format of this task
might not be immediately recognized as requiring analogical reasoning, it is in
essence an analogy problem in which all the arguments are provided for the
subject, along with irrelevant items. Successful performance on the CMTS task
involves assessments of relations between relations. That is, the relations
reflected in the choice pairs (i.e., Identity and Nonidentity) must be
comprehended and compared to the relation ( Identity or Nonidentity) reflected
in the sample pair.
Returning to our earlier example of
a verbal analogy, we could adopt the matching procedure to explore a verbal
human's reasoning by first presenting our subject with the initial argument
(i.e., sample) -- "Dog / Cat"
-- and then asking her or him to complete the expression by choosing between
the two arguments "Puppy / Kitten" vs. "Horse / Rider".
Obviously, as noted above, words are replaced with more concrete arguments
consisting of objects or pictures when exploring the reasoning of a nonverbal
species. Nevertheless, the cognitive demands of the CMTS task remain the same.
It follows, then, that any chimpanzee capable of performing the conceptual
matching task possesses the computational cognitive foundations upon which
formal analogical reasoning rests. Gillan,
Premack and Woodruff (1981) reported that Sarah, a chimpanzee (Pan troglodytes)
with a history of conceptual matching, succeeded also in completing partially
constructed analogies involving either complex geometric forms or functional
relationships between common objects. The elements of these analogies were presented to Sarah in a 2 X 2
matrix format where, as shown here, the stimuli A and A' exemplified a certain
relation, the stimuli B and B' exemplified the same relation but with different
items, and "same" was the plastic token or word for this concept from
the chimpanzee's artificial language (Premack, 1976, Premack & Premack,
1972).
A B
"Same"
A' B'
As noted above, the elements (A, A', B & B') in some of these
experiments were geometric forms and the relations on the vertical and
horizontal dimensions involved transformations of physical properties, e.g.:
Large Blue Triangle Large Yellow
Crescent
"Same"
Small Blue Triangle Small Yellow
Crescent
In other
experiments the elements were familiar objects and the relations were
functional ones, e.g.:
Padlock Tin Can
"same"
Key Can
Opener
In one set of experiments, Sarah was
presented with just three terms of an analogy (A, A', and B) positioned
according to the format described above and was required to select the
appropriate fourth term (B') when presented with two alternatives. In another set of experiments, four items
were arranged in the 2 X 2 analogy format.
Sarah was required to choose between her word for "same" and
her word for "different" depending on whether the arrangement did or
did not constitute a true analogy.
Sarah succeeded in solving both types of problems.
Gillan, et al. (1981) interpreted
Sarah's successful performance on both geometric and functional analogy
problems as reflecting her ability to reason analogically about
relations-between-relations. That is, she presumably established the higher
order analogical relationship "same" (or "different") between
the two sides of the analogy by first assessing the lower order relationships within
each side and then comparing them.
However, a close examination of the data reported by Gillan, et al.
(1981) suggests that at least some of her apparently analogical based
performances could have reflected far less sophisticated strategies.
This possibility was first brought
to our attention by Sue Savage-Rumbaugh (personal communication, 1989) who
provided a detailed analysis of Sarah’s performance on those problems which
required her to select a fourth item to complete a partially-constructed
geometric analogy. This analysis indicated that Sarah's performance could have
been the same even if she had not attended to the relationship instantiated by
the A and A' elements on the left-hand side of the matrix. Rather,
Savage-Rumbaugh argued, Sarah's choices could have been determined solely by a
hierarchical set of featural matching rules by which she identified the
choice item most similar, if not identical, to the single item (i.e., B) on the
right-hand side of the matrix. Savage-Rumbaugh's analysis was compelling
because it not only predicted the chimpanzee's correct choices, but also her
errors. Furthermore, independent studies of analogical reasoning in 4- and
5-year old children (Alexander et al., 1989; Goswami, 1989) revealed that the less-proficient
of these young human reasoners frequently resorted to such strategies.
Although Savage-Rumbaugh's featural
similarity matching analysis cannot account for Sarah's performance in other
experiments in the Gillan et al. (1981) study (e.g., functional analogy
problems) it is nevertheless important for two reasons. First, it alerts us to
a variant of the Psychologist's Fallacy (James, 1890/1950) wherein the
experimenter confusing his or her perspective or understanding of a phenomenon
with that of the subject confuses product with process. An
experimental animal's, or for that matter child's, production of analogical
relationships at a frequency greater than chance does not necessarily mean that
either species necessarily uses analogical reasoning processes to complete the
task. The cognitive revolution
notwithstanding, Lloyd Morgan's Canon (1906) has served psychology well during
the past century and should not be eschewed in the new. Morgan stated that, "in no case may we interpret an action
as the outcome of the exercise of a higher psychical faculty, if it can be
interpreted as the outcome of the exercise of one which stands lower in the
psychological scale." (Morgan, 1906, p. 53). Around the latter quarter
of the 20th century more recent practitioners of animal behavior (e.g.,
Griffin, 1976) suggested it was time to take a more cognitively oriented
perspective. But, if one is to empirically rule out the use of simpler (i.e.,
associative) strategies in putatively cognitive tasks then finer-grained
analyses of performance than is typically the case are warranted
Savage-Rumbaugh's
analysis also raises a second fundamental question regarding the conditions
necessary for the expression of analogical reasoning abilities (cf., Oden,
Thompson & Premack, 1990). For
example, Sarah's analogical reasoning ability may only have been expressed in
situations where it was mandated by the structure of the task. Consider, for
example, the case of functional analogies.
Faced with the question, "Padlock is to key as tin can is
to...?" Sarah could not have chosen a can-opener instead of a paint-brush
other than by comparing functional relationships. The utility of associative
strategies in this task was precluded by the experimental design.
Recent
advances in the study of analogies by a chimpanzee.
We present here a preliminary
summary of ongoing extensive re-analyses of data from more recent research
conducted with Sarah on analogical problem solving tasks (Oden, Thompson &
Premack, in preparation a; Oden, Thompson & Premack, in preparation b).
These experiments were conducted in part to determine the boundary conditions
for Sarah's analogical reasoning. For
example, would Sarah use analogical reasoning spontaneously in situations where
a simpler associative strategy would suffice? If so, then one could
argue that she is predisposed, as are we humans, to reason about relations
between relations; seeking out metaphor even when it is not explicitly
required.
Another goal of this research then
was to determine whether Sarah could also construct, rather than merely complete,
analogies. This task is substantially
more demanding than those she faced in her earlier work. On the one hand,
completing or evaluating analogies requires one to compare relations which have
been previously established. On the other hand, constructing analogies,
additionally requires one to seek out relations which reside among stimuli, but
which have not been explicitly specified in advance.
The materials used in this series of
analogy tasks were similar to those used in the Gillan, et al (1981) geometric
analogy problems. Sarah worked with an
analogy board; a blue cardboard rectangle with an attached white cardboard
cross, the arms of which extended across the length and width of the rectangle. This provided, at each corner of the
rectangle, a recess into which stimuli could be placed to construct an
analogy. Sarah's plastic token for the
concept "same." was placed at the intersection of the display board's
arms (see figure 1).
Insert
Figure 1 About Here
The experimental stimuli were
squares of white cardboard, each with a geometric form stenciled on it. The forms varied in color (4), shape (3),
size (2), and whether they were filled in with color or simply a colored
outline. All possible combinations of these properties were used to create a
pool of 48 different items which were used in the experiments reported here.
The following rules were used to
select items for the analogies. A and A' differed with respect to a single
dimension (size, color, shape or fill).
B and B’ also differed in this single dimension. A differed from B (and thus A' differed from
B') on two dimensions, each different from the property distinguishing A and
A'. Hence, for example, if A'
represented a size transformation of A, then B might differ from A with respect
to color and shape or shape and fill.
These were defined as 1 x 2 analogies (e.g., size x shape+fill). Following these rules, a total of 612 unique
combinations of 4 stimuli could be selected which, when appropriately placed on
the board, would create an analogy.
When experimental conditions required presentation of an additional
(error) alternative choice item, this item (C) differed from B' along the
dimension which was not used in constructing the analogy. For example, if the analogy was a "size
x shape+fill", then C differed from B' in color.
Sarah worked with these materials
under four conditions. In two
conditions, she was required to complete partially-constructed analogies which
were presented on the analogy board. In
two other conditions, she was presented with an empty analogy board along with
the appropriate stimulus items and had to construct an analogy from scratch. Throughout the study, a unique set of 4
analogy items was used on each trial.
General test procedures. A standard test procedure was used in all
conditions. On each trial of a test
session, the trainer placed the analogy board just inside the wire mesh of
Sarah's home cage enclosure. The board
contained either a partially-constructed analogy (Completion Conditions 1 &
2) or no stimuli at all (Construction Conditions 3 & 4). The stimuli which served as 'answer'
alternatives were contained in a covered cardboard box which the trainer placed
in front of the analogy board. After
presenting the materials, the trainer left the room and recorded Sarah's
behavior via a one-way mirror. Sarah's
task was to open the alternatives box, make her selections and place the items
in the empty recesses of the analogy board.
Any unused items were either left in the box or, at Sarah's discretion,
placed in a pie tin adjacent to the testing area. She then rang a small bell inside her enclosure, summoning the
trainer back into the room.
In those sessions where the design
called for differential feedback (Completion Condition 1), Sarah was praised
and given a piece of fruit after each trial when she had completed an
analogy. When she erred, Sarah was
mildly admonished and the trainer demonstrated the proper arrangement of
stimuli but gave no food reward. In
those sessions which called for non-differential feedback (Completion Condition
2; Construction Conditions 3 & 4), Sarah was praised and given a food
reward for every trial regardless of her accuracy, unless she had left an
unfilled space on her analogy board. In
that case, the trainer pointed to the empty recess and instructed Sarah to
"Do better next time." No other feedback was given on such
trials. Under non-differential
feedback, no particular problem-solving strategy is explicitly required,
allowing the chimpanzee, if she is so inclined, to demonstrate spontaneous
analogical reasoning (cf., Oden, Thompson & Premack, 1988).
Condition 1: Completion with two
alternatives. This condition was a
replication of the forced-choice task used by Gillan, et al. (1981), in which
Sarah was required to select a single item (B') to complete a
partially-constructed analogy. This
condition was intended to familiarize Sarah with the new analogy board and
stimulus items, and to provide a performance baseline - regardless of the
strategy or process used to generate it. The analogy elements A, A' and B were
placed in their appropriate positions on the board by the trainer. Two items, B' and an error alternative (C),
were placed in the alternatives box. One session of twelve trials was run using differential feedback.
Condition 2: Completion with
three alternatives. This condition
was run to determine whether Sarah could not only select items necessary to
complete an analogy, but also position them on the board so that the final
product reflected an analogical arrangement.
In this condition, the trainer placed only A and A' on the board. B, B' and C were placed in the alternatives
box. Sarah's task was to select and
properly arrange B and B' on the board.
The arrangement of the items in the alternatives box was random. Four sessions of twelve trials each were
run, using non-differential feedback.
Condition 3: Construction with
four alternatives. In this
condition, Sarah was presented with her analogy board with only the
"same" symbol on it. All four
items necessary to construct an analogy were placed in her alternatives
box. For two sessions of 12 trials each,
the items were selected according to the construction rules followed in
Conditions 1 and 2. We wondered also whether increased similarity among items
would help or hinder Sarah's performance. And so, in two other sessions of 12
trials each, A differed from B (and A' from B') in only one dimension instead
of two ("1 x 1 analogies").
The two types of sessions (1 x 1 - and 1 x 2 - analogies) were run in an
ABBA sequence, using non-differential feedback.
Condition 4: Construction with
five alternatives. This condition
was used to explore the effect of requiring an additional selection process as
part of analogy construction. We were
curious whether Sarah, faced with this additional complexity, would resort to a
simpler associative strategy or perhaps abandon all strategies in favor of
random selection and placement. In this
condition, Sarah was presented with an empty analogy board and her box of
alternatives which contained four elements that could be used to construct an
analogy, and a fifth, unusable item (C, the error alternative). As in Condition 3, Sarah’s task was simply
to fill the four empty spaces on the board.
Six sessions of 12 trials each were run, using non-differential
feedback.
Results
and discussion.
The results from all conditions are
summarized in Table 1. For each
condition, the percentage of trials on which Sarah constructed an analogy are
presented, along with the percentage expected on the basis of chance. Although Sarah's scores in all but Condition
1 were somewhat lower than those reported by Gillan, et al. (1981) her performance
was nevertheless significantly greater than chance in all conditions.
Insert
Table 1 about here
This overall pattern of significant
results strongly suggested that Sarah could indeed reason analogically both in
completing partially-constructed analogies and in creating her own analogies from
scratch. Indeed, we drew this conclusion in an early report of these results
(Oden & Thompson, 1991). Our more recent concern, however, about the
possibility of committing the previously noted fallacies has led us to
reconsider that conclusion. First, as noted above, one commits the
"psychologist's fallacy," when one assumes that if we adult humans
would produce a particular result by reasoning analogically, then Sarah must do
likewise. The second fallacy is to assume that because Sarah convincingly demonstrated
analogical reasoning in the Gillan, et al. (1981) functional analogy
problems, she must also have used that ability to solve the geometric
analogy problems in the present study. Heedful of these possibly fallacious
assumptions, we have re-examined the details of Sarah's performance for
evidence which would either confirm our early conclusion or alternatively
provide clues of simpler, non-analogical processes which may have produced the
same results.
Condition 1: Completion with two
alternatives. Three of the 12
trials in this condition could not be scored because one or more of the
recesses on the analogy board were empty when the trainer was summoned by
Sarah's bell. In two of these cases, this was the result of Sarah having
dismantled the partially-constructed analogy to closely inspect the new
stimulus materials. In the third case, both alternatives were laid on the floor
beside the intact analogy board. Sarah succeeded in completing the analogy on 8
of the 9 trials which could be scored.
This level of performance (89%) compares favorably with the 75% overall
accuracy reported in the original analogy studies (Gillan, et al., 1981) and
provides a current behavioral baseline for performance using the new analogy
materials. However, since this condition
was intentionally similar to those of the Gillan, et al. study, our results are
also subject to a similarity-matching interpretation. That is, the B' alternative was more similar to B (already on the
right side of the analogy board) than was the C (error) alternative. Thus, a similarity-matching strategy using B
as a sample would lead to an analogical product without the use of an
analogical process.
Condition 2: Completion with
three alternatives. Sarah completed
an analogy on 22 of 48 trials (46%) , significantly more often than the 17%
expected by chance. She selected the analogy pair (B, B') on 27 of 48 trials
(56%; chance = 33%). On 22 of these 27 trials (81%; chance = 50 %) the selected
items were placed on the board in the B/B' arrangement which completed the
analogy begun with A/A'.
Sarah's overall success at
completing analogies under this second condition, while statistically
significant, was substantially lower than in Condition 1. An examination of her relative success on
the two components of this task (item selection and analogical placement)
indicates that, for Sarah, the first component was the more difficult of the
two. That is, she selected the potential analogy choice pair on only 56% of the
trials, but once this pair was selected, Sarah arranged them analogically 81%
of the time. Although it might be
possible to interpret these data as reflecting some elaborate series of
similarity-matching processes (Oden, Thompson & Premack, in preparation,
a), we believe, given these data, that a more parsimonious interpretation is
that Sarah's performance was guided by her comprehending the relations
between features in the A/A' arrangement presented on her analogy board.
If our interpretation is correct,
then Sarah's attention to relations is particularly striking given that
non-differential reinforcement was used in Condition 2. This meant that she
could have used any strategy whatsoever (including random selection and
placement) to fill the analogy board.
Nevertheless, she appears to have spontaneously adopted the strategy of
mapping relations between relations. The next two conditions were intended to
determine whether Sarah could detect and use relations to construct an
analogy when presented with the necessary elements and an empty analogy board.
Condition 3: Construction with
four alternatives. In this
condition, and in Condition 4 with five alternatives, the criteria used for
scoring Sarah's constructions were as follows.
Sarah did not have to place the stimulus items originally designated by
the investigators as A, A', B, B' in any particular recess. Any arrangement using these four elements
was accepted as an analogy if A and B appeared together on one axis (row or
column) of the board, and where A and A' appeared together on the alternative
axis (column or row). This scoring rule
was based on the property of an analogy that its elements and arguments may be
interchanged in certain ways and still maintain analogical relations. For example, the construction, "Dog /
Cat // Puppy / Kitten" is as valid as, "Cat / Kitten // Dog /
Puppy" even though the relations expressed are rearranged. However, "Cat / Puppy // Kitten /
Dog" would not be accepted as a valid analogy.
There were 24 possible arrangements
of the items for a given trial, 8 of which (33%) would qualify as analogies
according to the above scoring rule.
Sarah constructed valid analogies on 14/24 trials with 1 x 1 analogies
and on 12/21 trials with 1 x 2 analogies (overall performance = 58%),
significantly more often than expected by chance. On three of the trials with 1 x 2 analogies she left one or more
recesses empty and thus her construction was not scored.
Insight into the processes involved
in these constructions comes from an examination of Sarah's selection and
placement of her first two choices. We
were able to score Sarah's sequence of choices and placements on 45 of the 48
trials. On all but three of the trials,
Sarah placed her first two choices in the same row or column of the analogy
board, thereby determining whether an analogy could be completed.
With 4 alternatives, there were 12
possible ways that the first 2 items could be chosen. Eight of these combinations, when placed in the same row or
column of the analogy board, constituted a "potential analogy" (i.e.,
they could become part of a valid analogy if the remaining items were arranged
properly). Thus, Sarah could create,
randomly, a potential analogy 67% of the time. But, in fact, her first two choices and placements produced
potential analogies 82% (37/45 trials) of the time. With 1 x 2 analogies, Sarah showed no preference for a pair with
one featural difference between its elements compared to a pair involving two
featural differences. This is difficult
to reconcile with a similarity-matching hypothesis, but perfectly consistent
with the analogical reasoning perspective.
We have here evidence that the
relational properties of the final analogical product (rather than mere item
similarity) engaged the corresponding analogical processes when Sarah began
work on each trial. This exercise of
apparent "foresight" enabled Sarah to create for herself the initial
conditions that had been previously provided by the experimenters in Condition
2 of the completion task.
In the present construction condition,
Sarah completed the construction of a valid analogy on 76% (28/37) of those
trials in which her first choices had created potential analogies. This level of success is comparable to her
prior performances on the completion tasks reported here and by Gillan et al.
(1981). Overall, the results from this
condition suggest that Sarah not only reasoned analogically, but also, through
her exercise of foresight, understood the nature of the task before her.
Condition 4: Construction with
five alternatives. Recall that in
Condition 2, where Sarah was required to select and arrange two items from a
group of three alternatives, the selection process proved to be more fragile
than the arrangement process. As
preliminary results discussed below demonstrate, This differential difficulty with selection as opposed to arrangement
did not prove to be the case in the present condition, where the addition of a
fifth, "error" alternative required Sarah to select, as well as
arrange, four items in her constructions.
In this condition, Sarah constructed
analogies on 15/72 (21%) of the trials.
This level of performance was substantially lower than performance in
the three preceding conditions, but
it was nevertheless still significant (p < .001, binomial test). As before,
we examined the sequence of Sarah’s selections and placements to
determine whether her performance truly reflected analogical reasoning or if it
was the accidental byproduct of some simpler strategy. Two such strategies are considered below.
Strategy 1: Minimizing Featural
differences. Perhaps Sarah was
guided by an appreciation of the global pattern of similarities among items in
an analogy, rather than the relations between particular pairs of items. If so,
she may have adopted the strategy, "minimize featural differences on the
board." Tables 2 and 3 help
clarify this possibility.
Insert
Tables 2 and 3 about here
In Table 2 we have
tabulated the number of featural differences between each of the five items which we used to construct a 1 x 2
analogy with a single error alternative. For example, consider the top row of
Table 2. Item A, might differ from A’ in size (one featural difference) and A
might differ from B in shape and fill (two featural differences). B’ would thus
necessarily differ from A in size, shape, and fill (three featural differences)
and C would differ from A in size, shape, fill and color (four featural
differences). From Table 2, one can compute the total number of featural
differences among members of 4-item sets drawn from the five alternatives
presented. These totals are shown in Table 3, along with the frequency of
Sarah's selections of each set indicated in the last column. Note that
Set 1, which could be used to construct an analogy (A, A', B, B') involved a
minimum number of featural differences.
However, Set 5 (C, A', B, B') also minimized the number of featural
differences between its members.
A strategy of minimizing featural
differences on the board would have led to completion of analogies in Condition
1 which entailed Sarah's completing an analogy with two alternatives. In Condition 2, this strategy would have led
to the appropriate selection, but not necessarily to the appropriate
arrangement, of items needed to construct an analogy. In the present condition, this strategy would have led to the
selection of Set 1, the potential analogy set.
However, it should also have led equally often to the selection of Set
5, containing item C, the error alternative.
In fact, Sarah selected the potential analogy set 33 times in 72 trials
and chose Set 5, with an equal number of featural differences, only 9
times. Thus, Sarah was clearly not
trying to simply maximize overall similarity among the four items placed on the
board. It would be tempting, therefore,
to conclude that the relationship between particular items (a prerequisite of
analogical reasoning) was of significance to Sarah. However, an alternative strategy must be considered before
accepting this conclusion.
Strategy 2: Exclusion of C, “the
Odd man Out”. It could be that
Sarah indirectly maximized similarity among the items in her constructions by excluding
alternative C that possessed a single property (size, shape, color or fill)
which was not shared with any other of the five items. This particular strategy would have
predisposed Sarah to select those four items which, if arranged appropriately
on the board, would produce an analogy. As noted above, Sarah in fact selected
such a 'potential analogy' set 33 times
over 72 trials. The statistical question then becomes: Did the actual analogies constructed by
Sarah on 15 of these 33 trials result simply from chance arrangements of these
four 'potential analogy' elements?
Given a selection of the appropriate
items, one-third of their possible arrangements would meet our criteria,
described previously, for an analogy. If one uses this proportion as an
estimate of chance success, then Sarah's construction of 15 analogies on 33
trials was not statistically significant.
This finding suggests, therefore, that Sarah had not attended to
relations between relations in this condition.
However, as described below, a more detailed analysis of the temporal
sequence in which Sarah placed the four items on the board has led us to reject
this pessimistic conclusion.
Sarah's
analogical strategy: Equating
within-pair differences. As Sarah
selected items and placed them on the board, she seems to have followed a
strategy of equating the number of within-pair featural differences,
independently of the physical nature of those differences. This strategy
is illustrated in Figures 2a - 2d.
Sarah consistently placed her first two choices on the same horizontal
or vertical axis of the analogy board, as illustrated in Figure 2a. Here, B' (choice 2) and A (choice 1) have
been placed respectively in the upper and lower recesses (i.e., a vertical
axis) on the left hand side of the board.
We can now describe Sarah's third and fourth choices as being placed
adjacent to either her first or her second choices. In this example Sarah placed item C (choice 3) in the upper
right-hand recess adjacent to her second choice (see Figure 2b). Sarah's fourth choice (A’) was then placed in the lower right-hand
recess adjacent to her first choice (see Figure 2c). Thus, Sarah's last two
placements of her third and fourth choices could be described as creating two
pairs as shown in Figure 2d. The number of featural differences within
each pair is the same. That is, there is one featural difference in the B’
& C pair created by Sarah's placements of her second and third choices. The
A & A’ pair created by her placements of her first and fourth choices
similarly contains a single featural difference.
Insert
Figure 2a-df about here
Each trial from Condition 4 of the
analogy construction was analyzed in the manner described above (Oden et al.,
in preparation b). The expected frequencies of each combination of featural
differences were obtained by determining the six possible outcomes given her
two initial choices. The observed frequencies of pairings which equated
within-pair differences significantly exceeded their expected frequencies.
Sarah apparently followed a strategy
of numerically equating within-pair featural differences as she made her last
two selections and placed them on the board.
When Sarah placed her third choice next to one of the items already on
the board the resulting number of within-pair featural differences tended to be
subsequently matched within the pair created by her placing her fourth choice
next to the remaining item.
We argue that this pattern of
results reveals analogical reasoning; it involves reasoning about relations
between relations. There is a
difference, of course, between the strategy employed by Sarah and the a priori
rules we used to construct analogies.
Whereas we had attended to the nature of specific features, as
well as their number, Sarah attended only to the number of featural
differences. For example, we regarded a
(color+shape) transformation as differing from a (size+fill) transformation. In Sarah's eyes these transformations were
equivalent because they both entailed two featural differences. Thus, compared to our reasoning, Sarah’s may
lack rigor, but fundamentally, she still reasoned about relations between relations. We do not believe that Sarah’s failure to
attend to featural details beyond number reflects a fundamental constraint on
her reasoning abilities. Recall that
the results from Condition 2 of the completion task indicated that selection of
items was a more difficult task than their arrangement. We believe that the decline in Sarah's
performance in the present condition of the construction task resulted from the
inherent complexity of the 5-item stimulus array with which she was presented.
Summary.
Collectively, the results from the
four conditions reported here not only confirm that an adult chimpanzee can
solve analogies (Gillan et al., 1981), but also demonstrate that she does so
spontaneously, even in situations where a simpler associative strategy would
suffice.
In condition one we replicated
Gillan et al. (1981) earlier findings which demonstrated that when faced with a
partially constructed analogy problem Sarah, the same adult chimpanzee subject,
successfully selected from two available choices that item which would complete
the analogy. In condition 2 of the
completion task, Sarah demonstrated conclusively that her performances was
mediated by analogical relationships and not a simple associative similarity
matching strategy. When presented with
only the two base elements of a classical analogy problem she successfully
chose from 3 alternatives the two elements necessary to complete the target
pair of the problem. More importantly
however, was the finding that Sarah's spatial arrangement of these choices was
guided by the relation initially established by the experimenters and not on
the basis of mere similarity along any single physical dimension.
In conditions 3 and 4 we further
demonstrated that the same chimpanzee, Sarah, could not only complete, but also
could construct analogies. When
presented with a randomized grouping of elements from which an analogy could be
constructed she proceeded to do spontaneously.
When presented with the minimum of 4 elements she proceeded to arrange
all of them in analogical fashion. When
presented with 5 elements of which 4 could be used to construct an analogy she
ignored the inappropriate item and successfully arranged the remaining items
analogically. However, she did so in a
manner analogous to, but not identical with that of her human experimenters. On the one hand, we had attended to both
specific physical factors and their number in each within pair
transformation. Sarah, on the other
hand, attended to only the latter numerical dimension.
Precursors
for analogical reasoning.
Some investigators have argued that
analogical reasoning is the common foundation (denominator) of much of human
reasoning including logical inference (e.g., Halford, 1992). Our results confirm earlier reports (Gillan
et al., 1981) that it is well within the capabilities of at least one adult
chimpanzee. Might this capacity be
expected in chimpanzees other than Sarah? And if so, what about other nonhuman
primates?
Our answer to the first question is
a qualified yes. As previously noted,
prior to her experience with formal analogical problem solving Sarah had
mastered a conceptual matching task which, at the age of 39 years, she still
successfully performed under conditions of nondifferential reinforcement
(Thompson, Oden & Boysen, 1997). Recall that in the conceptual matching
task a subject is required to match a pair of physically identical sample items
(e.g., a pair of locks) with another pair of identical items (e.g., a pair of
cups) as opposed to a pair on physically nonidentical items like, for example,
a pencil and an eraser. Conversely,
this latter nonidentical pair would be the correct match given another
nonidentical sample pair such as a shoe and ball.
Successful performance of the
conceptual matching task as described above involves the matching of relations
between relations and hence, as noted above in our introduction, it is itself,
therefore, an analogy problem in which all the arguments are provided for the
subject. It follows then that any
chimpanzee or nonhuman subject capable of performing the conceptual matching
task possesses the computational cognitive foundations upon which formal
analogical reasoning rests.
There is good evidence, however,
that not all chimpanzees, let alone any other nonhuman primate species, can
match relations between relations despite their success on physical matching
tasks (Thompson & Oden, in press). Prior experience with tokens, analogous
to words, that symbolize abstract same/different relations is a powerful
facilitator enabling a chimpanzee or child to explicitly express in judgment
tasks, like conceptual matching, their otherwise implicit perceptual knowledge
about relations between relations. (Premack, 1983; Rattermann & Gentner,
1998, submitted; Thompson & Oden. 1993; Tyrrell, Stauffer and Snowman,
1991).
Interestingly, these analogical
perceptual and conceptual capacities have been documented only in chimpanzees
and humans. As yet, there is no compelling evidence that old-world monkeys
spontaneously perceive, let alone judge, analogical relations (Thompson &
Oden, in press, Thompson & Oden, 1996; Thompson & Oden, 1998). Old-world macaque monkeys (Macaca mulatta),
for example, trained with symbols for same and different with procedures
comparable to those experienced by chimpanzees, subsequently failed to judge
the analogical equivalence of stimulus pairs in a conceptual-matching task
(Washburn, Thompson & Oden, 1997; in preparation).
Experience with an external symbolic
relational labeling system in some way provides child and chimpanzee, if not
monkey, with the requisite representational scaffolding for the complex
computational operations necessary to solve problems involving conceptually
abstract similarity judgments as in analogies (Clark & Thornton, 1997;
Gentner & Markman, 1997; Gentner, Rattermann, Markman, & Kotovsky,
1995; Sternberg & Nigro, 1980).
Conclusion.
Analogical reasoning may be indeed a
hallmark of human reasoning. Nevertheless, the results summarized above on
completion and construction of analogical problems solving by Sarah, a representative
of the common chimpanzee species Pan troglodytes, demonstrate
that this uncommon individual is predisposed, as are adult humans, to reason
about relations between relations. The data presented here provide a cautionary
tale for psychologists as to the potential traps and snares of the
psychologists fallacy discussed above. When constructing both the base and
target relations of an analogy from 4 of 5 elements Sarah did so in a manner
analogous to, but not identical with that of her human experimenters.
Furthermore, the analyses of Sarah's
selection and arrangement of items on her analogy board in both types of
analogy task provide no evidence that she attempted to use a less efficient
associative strategy, as can occur with young children (Alexander et al,
1989). We can only be confident in this
conclusion because of our exhaustive re-analyses of Sarah' response patterns.
We concur with the recent recognition by some developmental psychologists of
the theoretical and empirical utility of such detailed "microgenetic"
analysis (Siegler, & Crowley, 1991).
References
Alexander, P. A., Willson, V. L.,
White, C. S., Fuqua, J. D., Clark, G. D., Wilson, A. F., & Kulikowich, J.
M. (1989). Development of analogical reasoning in 4- and 5-year-old children. Cognitive Development, 4, 65-88.
Clark, A., Thornton, C. (1997). Trading
Spaces: Computation, representation, and the limits of uniformed learning. Behavioral and Brain Sciences, 20, 57-90.
Darwin, C. (1871). The descent of man
and selection in relation to sex. London, U.K.: Murray.
Gentner, D. (1998). Analogy. In W.
Bechtel, & G. Graham (Eds.), A companion to cognitive science (Blackwell
companions to philosophy; 13). (pp. 107-113). Malden, MA.: Blackwell
Publishers.
Gentner, D. & Markman, A. B. (1997).
Structural mapping in analogy and similarity. American Psychologist, 52, 45-56.
Gentner, D., Rattermann, M.J., Markman,
A., & Kotovsky, L. (1995). Two
forces in the development of relational similarity. In T. Simon & G.
Halford (Eds.), Developing cognitive competence: New approaches to process
modeling. Hillsdale, N.J.: Erlbaum.
Gillan, D. D., Premack, D., &
Woodruff, G. (1981). Reasoning in the chimpanzee: I. Analogical reasoning. Journal of Experimental Psychology: Animal
Behavior Processes, 7, 1-17.
Goswami, U. (1989). Relational
complexity and the development of analogical reasoning. Cognitive Development, 4, 251-268.
Goswami, U. (1991). Analogical
reasoning: What develops? A review of research and theory. Child Development, 62, 1-22.
Griffin, D. R. (1976). The question of animal awareness. New
York, N.Y.: Rockefeller University Press.
Griffin, D. R. (1992). Animal thinking. Chicago, IL.: Chicago
University Press.
Halford, G. S. (1992). Analogical
reasoning and conceptual complexity in cognitive development. Human Development, 35, 193-217.
Holyoak, K. J. & Thagard, P.
(1997). The analogical mind. American
Psychologist, 52 (1), 35-44.
James W. (1981/1890) The principles of psychology, vol. I.
Cambridge, MA: Harvard University Press. (Original work published 1890).
Morgan, C. L. (1906). An introduction to comparative psychology.
(Rev. Ed.). New York, N.Y.: Scribner's.
Oden, D. L., & Thompson, R. K. R.
(November, 1991). The construction of
analogies by a chimpanzee. Paper presented at the meeting of the
Psychonomic Society, San Francisco, CA.
Oden, D. L., Thompson, R. K. R., &
Premack, D. (1988). Spontaneous transfer of matching by infant chimpanzees (Pan troglodytes). Journal of
Experimental Psychology: Animal Behavior Processes.
Oden, D. L., Thompson, R. K. R., &
Premack, D. (1990). Infant chimpanzees (Pan
troglodytes) spontaneously perceive
both concrete and abstract same/different relations. Child Development, 61, 621-631.
Oden, D. L., Thompson, R. K. R., &
Premack, D. (In preparation a). A chimpanzee completes analogy problems
analogically.
Oden, D. L., Thompson, R. K. R., &
Premack, D. (In preparation b). Construction of analogies by a chimpanzee.
Piaget, J. (1977). L'Abstraction reflechissante. Paris, FR.: Presses Universitaires de
France.
Premack, D. (1976). Intelligence in ape
and man. Hillsdale, N. J.: Erlbaum Associates.
Premack, D. (1978). On the abstractness
of human concepts: Why it would be difficult to talk to a pigeon. In S. Hulse,
H. Fowler, & W. K. Honig (Eds.), Cognitive
processes in animal behavior (pp. 423-451). Hillsdale, NJ: Erlbaum
Associates.
Premack,
D. (1983). The codes of man and beast. The
Behavioral and Brain Sciences, 6, 125-137.
Premack, A. J., & Premack, D.
(1972). Teaching language to an ape. Scientific American, 227, 92-99.
Rattermann, M.J., & Gentner, D. (submitted). The effect of language on similarity: The use of relational labels improves young
children's performance in a mapping task.
Cognitive Psychology.
Rattermann, M.J., & Gentner, D.
(1998). The Effect of relational language on children's performance in an
analogical mapping task. In K. Holyoak,
D. Gentner and B. Kokinov (Eds.) Advances in Analogy Research: Integration of
theory and data from the cognitive, computational, and neural sciences.
Siegler, R. S. & Crowley, K.
(1991). The microgenetic method: A direct means for studying cognitive
development. American Psychologist, 46,
606-620.
Sternberg, R. J. (1977). Intelligence, information processing, and
analogical reasoning. Hillsdale, NJ: Erlbaum.
Sternberg, R. J. (1982). Reasoning,
problem solving, and intelligence. In R. J. Sternberg, (ed.), Handbook of human intelligence (pp.
225-307). New York, N. Y.: Cambridge University Press.
Sternberg, R. J. & Nigro, G. (1980).
Developmental patterns in the solution of verbal analogies, Child Development, 51, 27-38.
Thagard, P. (1992). Conceptual revolutions. Princeton, N.J.:
Princeton University Press.
Thompson, R. K. R., & Oden, D. L.
(1993). "Language training" and its role in the expression of tacit
propositional knowledge in chimpanzees (Pan
troglodytes). In H. L. Roitblat, L.
M. Herman, & P. E. Nachtigall (Eds.), Language
and communication: Comparative perspectives., pp. 365-384. Hillsdale, N. J.: Erlbaum Associates.
Thompson, R. K. R., & Oden, D. L.
(1996). A profound disparity revisited: Perception and judgment of abstract
identity relations by chimpanzees, human infants, and monkeys. Behavioral Processes, 35, 149-161.
Thompson & Oden, (1998). Why
monkeys and pigeons, unlike certain apes, cannot reason analogically. Proceedings of the Analogy '98 workshop on
advances in analogy research: Integration of theory and data from the
cognitive, computational, and neural Sciences.
Thompson R. K. R. & Oden, D. L. (In
press). Categorical perception & conceptual judgments by nonhuman primates:
The paleological monkey and the analogical ape. Cognitive Science,
(special
issue on primate cognition; Guest editor, M. Tomasello).
Thompson, R. K. R., Oden, D. L. &
Boysen, S. T. (1997). Language-naive chimpanzees (Pan troglodytes) judge relations between relations in a conceptual
matching-to-sample task. Journal of
Experimental Psychology: Animal behavior processes, 23, 31-43.
Tyrrell, D. J., Stauffer, L. B., &
Snowman, L. G. (1991). Perception of abstract identity/ difference
relationships by infants. Infant behavior
and Development, 14, 125-129.
Vosniadou S. & Ortony, A. (Eds.).
(1989). Similarity and analogical
reasoning, Cambridge, England: Cambridge University Press.
Vauclair, J. (1996). Animal cognition: An introduction to modern
comparative psychology. Cambridge, MA.: Harvard University Press.
Washburn, D. A., Thompson, R. K. R.
& Oden D. L. (1997). Monkeys trained
with same/different symbols do not match relations. Paper presented at the
38th Annual Meeting of the Psychonomic Society. Philadelphia, PA.
Weiskrantz, L. (Ed.). (1985). Animal intelligence. (Oxford Psychology
Series No. 7). Oxford, U. K.: Clarendon Press.
Acknowledgments: We thank Bonnie Dennis and Teresa Anderson their
assistance in data collection. We also thank M. J. Rattermann for her helpful
comments. The research reported here and preparation of this paper were
supported by funds from the National Science Foundation (NSF-BNS 8418942 and
NSF-IBN 9420756).
Table 1
Percent
valid analogies constructed (Performance) and percent of random arrangements of
items which would result in valid analogies (Chance) under each experimental
condition.
* = p < .05, ** = p < .01, *** = p < .001, Binomial tests.
-------------------------------------------------------------------------------------------
Condition Performance Chance
(% Correct) (% Predicted)
-------------------------------------------------------------------------------------------
1 Completion (B') 89* 50
2 Completion (B & B') 46*** 17
3 Construction (4 item)
1 x 1 analogies 58** 33
1 x 2 analogies 57* 33
4 Construction (5 item) 21*** 7
-------------------------------------------------------------------------------------------
Table 2.
Number of Featural Differences
Between Individual Items Used to
Construct a 1 x 2 Analogy With One Error Alternative in Condition 4.
A A' B B' C
A 1 2 3 4
A' 1 3 2 3
B 2 3 1 2
B' 3 2 1 1
C 4 3 2 1
Table 3.
Total Featural Differences
Within Groups of Four Items in Condition 4.
Sets Items Total Featural Number of Times
Differences Selected in 72 Trials
1 A A' B B' 12 33
2 A A' B C 15 10
3 A A' C B' 14 10
4 A C B B' 13 10
5 C A' B B' 12 9
Figure
Captions
Figure
1. The 2 x 2 matrix format used by
Gillan et al., 1981.
Figure
2. An illustrative sequence of Sarah's
choices and placements in condition 4: Analogy construction with five
alternatives.
