Leibovich et al. offered the provocative thesis that the idea of an innate “number sense” in humans and other animals may be misleading given the empirical tests that are used to assess such a sense. They proposed that most research in this area confounds numerical properties of stimuli with continuous properties such as area and density, and it is these continuous features that control responding more than true numerosity. We agree, in principle, with this position regarding typically used methods in comparative research, having also argued that tasks given to nonhuman animals may not be directly related to number, concepts but instead rely on non-numerical cues to guide responding (Beran et al. Reference Beran, Parrish, Evans, Geary, Berch and Koepke2015a; Reference Beran, Perdue, Evans, Kadosh and Dowker2015b). We also agree that comparative contributions to the broadly defined area of “numerical cognition” research need to carefully assess the competencies that are reported in adult humans, human children, and nonhuman animals by paying close attention to non-numerical confounds that may contribute to performance on these tasks (Beran & Parrish Reference Beran, Parrish and Henik2016).
However, we also believe that there are instances in which judgments by some animals are made on the basis of numerosity, where careful controls have eliminated the possibility they are using non-numerical, continuous quantitative information. For example, Beran (Reference Beran2012) showed that chimpanzees listened to food items being dropped into an opaque container and then compared that number of items with a visible, static set and chose the larger amount even though there were no continuous properties that would account for such performances (also see Beran et al. Reference Beran, Evans, Leighty, Harris and Rice2008). Animals also were trained with number symbols representing specific cardinal values, rather than specific magnitudes of stimuli. These include Arabic numeral-based studies with chimpanzees in which they labeled arrays of items with numerals (e.g., Matsuzawa Reference Matsuzawa1985) and even combined multiple sets of items before labeling them (e.g., Boysen & Berntson Reference Boysen and Berntson1989). A parrot also learned to vocally label arrays, even when queries about the number of items involved subsets of a specific class of items within a larger array (e.g., reporting the number of blue keys in a mixed array of blue and red keys and trucks [Pepperberg Reference Pepperberg1994]). In addition, chimpanzees learned to collect sets of items to match a presented Arabic numeral using a computerized enumeration task (e.g., Beran & Rumbaugh Reference Beran and Rumbaugh2001). In these cases, we argue that numerosity is the dimension to which animals are responding, even though their performances typically showed the same “fuzziness” in representational acuity that is seen in magnitude judgment tasks (see Cantlon et al. Reference Cantlon, Platt and Brannon2009b), and training often took months or years to establish. These studies suggest that number concepts can emerge in a variety of nonhuman species, but may not do so as easily as representations of non-numerical magnitudes.
When numerical and non-numerical properties co-vary in tasks, this does not mean that non-numerical properties must be controlling responding. Brannon and Terrace (Reference Brannon and Terrace2000) showed that across combinations of stimulus presentation formats where density, area, size, and contour length each co-varied to different degrees with number in a relative discrimination task, rhesus monkeys still used number in some cases. Beran (Reference Beran2007) showed that after training monkeys to discriminate which of two sequentially presented arrays of items on a computer screen was greater, the monkeys' performance withstood the introduction of trials where item size and rate of presentation offered potential distractions if monkeys were using those properties. This does not mean that monkeys or other animals do not use non-numerical properties when they can. And they may even preferentially use them, a point that is also true for human performance in many tasks. But when such performance can survive the control of such confounds, it suggests that a number sense is at work, even if it is not the dominant sensory signal to which a nonhuman animal may be attuned. The question then is whether an innate sense of number requires that numerosity operates as a dominant stimulus property in the face of other properties that compete to control responding. We do not see why this must be true.
Hence, we do not advocate abandoning the idea of an innate number sense in some nonhuman species or in humans. Rather, we acknowledge that this number sense likely emerged through evolution from a more generalized analog magnitude system for perceiving and representing quantitative information, and that the “number sense” and “magnitude sense” of nonhuman animals both suffer from the same processing and representational constraints (Cantlon et al. Reference Cantlon, Platt and Brannon2009b). In this perspective, an innate number sense can exist, and can be activated and used by many species, even if it is not a dominant conceptual system within a cognitive architecture. At the same time, this does not mean it is a “last resort” (Davis & Memmott Reference Davis and Memmott1982), but rather that it is an available system that can be accessed when other more generalized perceptual-discriminative processes for magnitude-based stimuli are insufficient to generate adaptive responses. For example, Cantlon and Brannon (Reference Cantlon and Brannon2007) presented rhesus monkeys with a number matching-to-sample task in which monkeys could match on one of two dimensions, including number and some non-numerical cue such as color, surface area, or shape. Although monkeys preferred color and shape cues to number cues, they responded on the basis of number when the numerical difference between the sets was high (and therefore easier to discriminate).
The alternate view offered in the target article (and see Leibovich & Henik Reference Leibovich and Henik2013) that a sense of number is not present in nonhuman animals (or perhaps even humans) at birth, but emerges through experiencing the correlation between numerosity and continuous magnitudes is an interesting proposal. If true, developmental research with pre-counting age children and a longitudinal comparison of true numerical processes for individuals with and without a history of experiences with continuous quantities would be particularly valuable. The latter approach would be a test that could only be conducted with nonhuman species, for obvious reasons, and would offer another chance for comparative research to make an important contribution.
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Leibovich et al. offered the provocative thesis that the idea of an innate “number sense” in humans and other animals may be misleading given the empirical tests that are used to assess such a sense. They proposed that most research in this area confounds numerical properties of stimuli with continuous properties such as area and density, and it is these continuous features that control responding more than true numerosity. We agree, in principle, with this position regarding typically used methods in comparative research, having also argued that tasks given to nonhuman animals may not be directly related to number, concepts but instead rely on non-numerical cues to guide responding (Beran et al. Reference Beran, Parrish, Evans, Geary, Berch and Koepke2015a; Reference Beran, Perdue, Evans, Kadosh and Dowker2015b). We also agree that comparative contributions to the broadly defined area of “numerical cognition” research need to carefully assess the competencies that are reported in adult humans, human children, and nonhuman animals by paying close attention to non-numerical confounds that may contribute to performance on these tasks (Beran & Parrish Reference Beran, Parrish and Henik2016).
However, we also believe that there are instances in which judgments by some animals are made on the basis of numerosity, where careful controls have eliminated the possibility they are using non-numerical, continuous quantitative information. For example, Beran (Reference Beran2012) showed that chimpanzees listened to food items being dropped into an opaque container and then compared that number of items with a visible, static set and chose the larger amount even though there were no continuous properties that would account for such performances (also see Beran et al. Reference Beran, Evans, Leighty, Harris and Rice2008). Animals also were trained with number symbols representing specific cardinal values, rather than specific magnitudes of stimuli. These include Arabic numeral-based studies with chimpanzees in which they labeled arrays of items with numerals (e.g., Matsuzawa Reference Matsuzawa1985) and even combined multiple sets of items before labeling them (e.g., Boysen & Berntson Reference Boysen and Berntson1989). A parrot also learned to vocally label arrays, even when queries about the number of items involved subsets of a specific class of items within a larger array (e.g., reporting the number of blue keys in a mixed array of blue and red keys and trucks [Pepperberg Reference Pepperberg1994]). In addition, chimpanzees learned to collect sets of items to match a presented Arabic numeral using a computerized enumeration task (e.g., Beran & Rumbaugh Reference Beran and Rumbaugh2001). In these cases, we argue that numerosity is the dimension to which animals are responding, even though their performances typically showed the same “fuzziness” in representational acuity that is seen in magnitude judgment tasks (see Cantlon et al. Reference Cantlon, Platt and Brannon2009b), and training often took months or years to establish. These studies suggest that number concepts can emerge in a variety of nonhuman species, but may not do so as easily as representations of non-numerical magnitudes.
When numerical and non-numerical properties co-vary in tasks, this does not mean that non-numerical properties must be controlling responding. Brannon and Terrace (Reference Brannon and Terrace2000) showed that across combinations of stimulus presentation formats where density, area, size, and contour length each co-varied to different degrees with number in a relative discrimination task, rhesus monkeys still used number in some cases. Beran (Reference Beran2007) showed that after training monkeys to discriminate which of two sequentially presented arrays of items on a computer screen was greater, the monkeys' performance withstood the introduction of trials where item size and rate of presentation offered potential distractions if monkeys were using those properties. This does not mean that monkeys or other animals do not use non-numerical properties when they can. And they may even preferentially use them, a point that is also true for human performance in many tasks. But when such performance can survive the control of such confounds, it suggests that a number sense is at work, even if it is not the dominant sensory signal to which a nonhuman animal may be attuned. The question then is whether an innate sense of number requires that numerosity operates as a dominant stimulus property in the face of other properties that compete to control responding. We do not see why this must be true.
Hence, we do not advocate abandoning the idea of an innate number sense in some nonhuman species or in humans. Rather, we acknowledge that this number sense likely emerged through evolution from a more generalized analog magnitude system for perceiving and representing quantitative information, and that the “number sense” and “magnitude sense” of nonhuman animals both suffer from the same processing and representational constraints (Cantlon et al. Reference Cantlon, Platt and Brannon2009b). In this perspective, an innate number sense can exist, and can be activated and used by many species, even if it is not a dominant conceptual system within a cognitive architecture. At the same time, this does not mean it is a “last resort” (Davis & Memmott Reference Davis and Memmott1982), but rather that it is an available system that can be accessed when other more generalized perceptual-discriminative processes for magnitude-based stimuli are insufficient to generate adaptive responses. For example, Cantlon and Brannon (Reference Cantlon and Brannon2007) presented rhesus monkeys with a number matching-to-sample task in which monkeys could match on one of two dimensions, including number and some non-numerical cue such as color, surface area, or shape. Although monkeys preferred color and shape cues to number cues, they responded on the basis of number when the numerical difference between the sets was high (and therefore easier to discriminate).
The alternate view offered in the target article (and see Leibovich & Henik Reference Leibovich and Henik2013) that a sense of number is not present in nonhuman animals (or perhaps even humans) at birth, but emerges through experiencing the correlation between numerosity and continuous magnitudes is an interesting proposal. If true, developmental research with pre-counting age children and a longitudinal comparison of true numerical processes for individuals with and without a history of experiences with continuous quantities would be particularly valuable. The latter approach would be a test that could only be conducted with nonhuman species, for obvious reasons, and would offer another chance for comparative research to make an important contribution.