Cognitive Processes 407both C and D. Thus, if some novel cue were to signal D
exclusively, it would be more valid than B, and it (rather
than B) would become the better signal for D. This would
result in the formation of the series A-B-C-B-D-E into two
chunks, A-B-C-B and D-E.
Numerical Abilities
In recent years, much experimental effort has been invested
in detecting numerical abilities in animals, most notably
birds, rats, monkeys, and chimpanzees (see, e.g., Boysen &
Capaldi, 1993). At a relatively simple level, animals may be
asked to discriminate between two quantities, more versus
less—a relative numerousness discrimination. At a more
complicated level, animals may be asked to perform some
operation on numbers, such as addition or subtraction. In be-
tween these extremes animals may be asked to count—that
is, to enumerate items explicitly. The accumulating evidence
reveals that animals may be able to do each of these things,
although operating on numbers has as yet been demonstrated
only in the chimpanzee (Boysen & Berntson, 1989). In that
study a chimpanzee that visited a number of food sites, each
containing a different number of food items, was able at the
end of the circuit to select an Arabic numeral corresponding
to the total number of items seen. The animal had not been
explicitly trained to add items, only to enumerate them.
Inexplicit countingstudies, items have been presented
either simultaneously or successively. In such investigations
a variety of stimuli are confounded with number of items, and
these confounds must be removed. For example, all else
being equal, it takes longer to present three items than two
items. Contemporary counting studies (e.g., Capaldi, 1998)
have gone to great lengths to eliminate these confounds suc-
cessively. Those studies and others have found that animals
such as birds, rats, and monkeys can make discriminations
based upon the number of items. One of the major issues in
counting studies is whether animals count reluctantly and
only when the number of items is the only discriminative cue
available (Davis & Pérusse, 1988). Furthermore, do animals
count routinely and rather easily, employing the number of
items as a discriminative cue even when number is con-
founded with other variables (e.g., Capaldi & Miller, 1988b)?
An animal may be said to be counting if its behavior sug-
gests conformance with three principles. The items to be
counted or enumerated should be arrayed in one-to-one cor-
respondence to internal number tags, which in the case of
people are conventional symbols such as one, two, three, and
so on. The tags should be applied to events in a stable order.
Thus we may not enumerate items one, two, three in one
occasion and one, three, two on another occasion. The order
irrelevance principle suggests that items may be enumer-
ated in any order. For example, in enumerating three different
items X, Y, and Z we may do so in any order: X first and Z
last, or Z first and X last, and so on. In experiments reported
by Capaldi and collaborators (see, e.g., Capaldi, 1993;
Capaldi & Miller, 1988b), rats were shown to be able to enu-
merate successively presented food items according to the
three principles just outlined. In those experiments, control
was exercised over variables confounded with number of
successively presented food items, such as amount eaten,
time spent eating, response effort expended in obtaining food
items, and so on (see Capaldi, 1993, 1998).
Gelman and Gallistel (1978) suggested that children count
effortlessly and as a matter of course. One might say that
counting is an instinct in humans (see, e.g., Spelke, 2001).
Capaldi and Miller (1988b; see also Capaldi, 1993) suggested
that rats also enumerate items as a matter of course and will
do so even when number of items is confounded with other
variables. In one experiment, Capaldi and Miller (1988b)
trained rats such that number of food items was confounded
with a number of other variables, among them, time and
effort. When the confounds were removed and only number
of food items was a valid cue, the rats continued to behave
appropriately, indicating that counting occurred even when
other valid cues were simultaneously available.
Highly interesting data relevant to this important issue
were recently reported by Brannon and Terrace (2000). In
that investigation, rhesus monkeys were trained to enumerate
items (such as geometrical forms) that were presented visu-
ally. In initial training sessions the animals enumerated 1 to 4
items. Having mastered 1 to 4 items, the monkeys were now
asked to enumerate 5 to 9 items without explicit training. The
monkeys quickly did so. Brannon and Terrace suggested that
these findings indicated that monkeys count even when not
forced to do so.
The interests of investigators concerned with counting in
animals vary. Some seem interested in animal counting for its
own sake. Some seem interested in similarities and dif-
ferences between human and animal cognition (see, e.g.,
Brannon & Terrace, 2000). Still others have suggested that
counting is of interest because it is routinely involved in
many learning situations ranging from irregular reward
schedule to serial learning (e.g., Capaldi, 1994; Capaldi &
Miller, 1988b).Theory of MindAs applied to humans, having a theory of mind means that we
attribute behavior—our own as well as that of others—to
beliefs and desires. Baron-Cohen (1995) has suggested that