Numerical competence is one of the many aspects of animal cognition that have enjoyed a resurgence of interest during the past decade. Evidence for numerical abilities in animals has followed a tortuous path to respectability, however, from Clever Hans, the counting horse, to modern experimental studies. Recent surveys of the literaturereveal theoretical as well as definitional confusion arising from inconsistent terminology for numerical processes and procedures. The term “counting” has been applied to situations having little to do with its meaning in the human literature. We propose a consistent vocabulary and theoretical framework for evaluating numerical competence. Relative numerousness judgments, subitizing, counting, and estimation may be the essential processes by which animals perform numerical discriminations. Ordinality, cardinality, and transitivity also play an important role in these processes. Our schema is applied to a variety of recent experimental situations. Some evidence of transfer is essential in demonstrating higher-order ability such as counting or “sense of number.” Those instances of numerical competence in which all viable alternatives to counting (e.g., subitizing) have been precluded, but no evidence of transfer has been demonstrated might be described as “protocounting.” To show that animals are capable of “true” counting future research will have to demonstrate generality across situations.
In this article we present a critical evaluation of evidence bearing on the question of whether animals can count. A definition of counting is adopted from Gelman and Gallistel (1978) and Piaget (1952) that allows us to compare the form of counting behavior observed in animals with its counterpart in humans. The evidence, which ranges from early anecdotal reports to modern experimental analyses, suggests that a variety of infrahumans ranging from birds to primates can learn to count, although successful demonstrations are most likely to occur under relatively extreme experimental conditions when alternative predictors of food or safety are unavailable. Counting behavior appears to be a relatively unnatural response in infrahumans, and its acquisition may reflect the boundaries of the animal's associative abilities. This paper will present a critical evaluation of some of the evidence that has been brought to bear on the question of whether animals can count. Perhaps a better title would have been "Counting Behavior in Animals: When Does It Occur?" for we intend to argue that counting behavior, as we will define it, can and does occur in infrahuman animals. In taking this position, we will avoid the euphemism countinglikebehavior, which has been used to describe much of the experimental work of the past 20 years.Counting Behavior Denned Some definitions of counting behavior preclude the possibility that animals can count. In contrast, it is possible to define counting in a way that is not only consistent with its occurrence in humans but also allows for its demonstration in other species. We will attempt to evolve such a definition.
Although Piagetian theory proposes that the ability to make transitive inferences is confined to humans above age 7, recent evidence has suggested that this logical ability may be more broad based. In nonverbal tests, transitive inference has been demonstrated in preschool children and 2 species of nonhuman primates. In these experiments, I demonstrate evidence of transitive inference in rats (Rattus norvegicus). I used an ordered series of 5 olfactory stimuli (A < B < C < D < E) from which correct inferences were made about the novel B versus D pair. Control procedures indicated that performance did not depend on the recency with which the correct answer was rewarded during training and may be disrupted by the addition of logically inconsistent premises (F > E and A > F). The possibility that logical transitivity may reflect a form of spatial paralogic rather than formal deductions from a syllogistic-verbal system is discussed.
In this article we are concerned with the often surprising degree of behavioral control exerted by what are, in many cases, unscheduled and unintended relationships between important experimental events. A distinction is proposed between traditional contingencies (i.e., if event X-then event Y) and a second class of relationships which are termed autocontingencies. The logical relationships which generate autocontingencies are derived from systematic constraints in the distribution of event Y itself, which allow prediction of the subsequent occurrence or absence of event Y.Supportive evidence for behavioral control by autocontingencies is presented from a survey of operant and Pavlovian conditioning procedures which involve both appetitive and aversive stimuli. Autocontingency effects are examined within a variety of situations which include such well-established phenomena as "scalloping" under fixed-interval food schedules, as well as the "reverse scalloping" or negatively accelerated responding which occurs when food-reinforced responding is punished under a fixed-interval schedule. An analysis of several recently published experiments suggests the possibility that subjects may occasionally have become "aware" of an autocpntingency before the experimenter who programmed it did. These experiments, which typically yield puzzling behavioral effects, have often forced the underlying autocontingency into the investigator's attention. Such instances support the notion that autocontingencies involve subtle relationships, despite the fact that their effects are often far from subtle.An additional source of support for and elaboration of the concept of autocontingencies comes from our own conditioned suppression data. We exposed rats to different experimental arrangements of signal and shock. Subjects for whom no signal preceded each shock delivery learned to find "safety" in more subtle features of the experimental situation. For example, these subjects showed reliably increased responding in the brief periods following each shock delivery once they learned that shocks were separated by a minimum 3-min interval. Similarly, a constraint of three shock deliveries per session yielded a "subtle safety signal" and resulted in enhanced responding following offset of the third shock. These data also suggest the function of "need" (i.e., the simultaneous presence of other predictors) in determining the degree of control exerted by autocontingencies. Subjects in our experiment for whom a traditional tone-shock contingency reliably produced warning did not show behavioral control by autocontingencies which were simultaneously available.The use of the term subtle to describe the relationships underlying autocontingencies suggests that a certain degree of neurological sophistication may be necessary to integrate or process the information provided by autocontingencies. Pre-169
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