The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck, 2021a). Prior work demonstrates that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here, we use a well-known “connectedness illusion” to provide evidence that these (...) ratio-dependent ratio discriminations are (a) based on the perceived number of items in seen displays (and not just non-numerical confounds), (b) are not dependent on verbal working memory, or explicit counting routines, and (c) involve representations with a part-whole (or subset-superset) format, like a fraction, rather than a part-part format, like a ratio. These results vindicate key predictions of the hypothesis that the ANS represents rational numbers. (shrink)

In 1939, the influential psychophysicist S. S. Stevens proposed definitional distinctions between the terms ‘number,’ ‘numerosity,’ and ‘numerousness.’ Although the definitions he proposed were adopted by syeveral psychophysicists and experimental psychologists in the 1940s and 1950s, they were almost forgotten in the subsequent decades, making room for what has been described as a “terminological chaos” in the field of numerical cognition. In this paper, I review Stevens’s distinctions to help bring order to this alleged chaos and to shed light on (...) two closely related questions: whether it is adequate to speak of a number sense and how philosophers can make sense of the claim by cognitive scientists that numbers are perceptual entities. Moreover, I offer further support to Stevens’s distinction between numerosity and numerousness by showing that they are relational properties that emerge through different relationships between agents and their environments. The final conclusion is that, by adopting Stevens’s distinctions, numbers do not need to be seen as perceptual entities, since the so-called number sense is better described as a sense of numerousness. (shrink)

In our target article, we argued that the number sense represents natural and rational numbers. Here, we respond to the 26 commentaries we received, highlighting new directions for empirical and theoretical research. We discuss two background assumptions, arguments against the number sense, whether the approximate number system represents numbers or numerosities, and why the ANS represents rational numbers.

On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system, that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for (...) number, such as “numerosities” or “quanticals,” as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind of number being represented. In response, we propose that the ANS represents not only natural numbers, but also non-natural rational numbers. It does not represent irrational numbers, however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research. (shrink)

We can perceive not only low-level features of events such as color and motion, but also seemingly higher-level properties such as causality. A prototypical example of causal perception is the ”launching effect’: one object moves toward a stationary second object until they are adjacent, at which point A stops and B starts moving in the same direction. Beyond these motions themselves --- and regardless of any higher-level beliefs --- this display induces a vivid visual impression of causality, wherein A is (...) seen to cause B’s motion. Do such percepts reflect a unitary category of visual processing, or might there be multiple distinct forms of causal perception? While launching is often simply equated with causal perception, researchers have sometimes described other phenomena such as ”triggering’ and ”entraining’. We used psychophysical methods to determine whether these labels really carve visual processing at its joints, and how putatively different forms of causal perception relate to each other. Previous research demonstrated retinotopically specific adaptation to causality: exposure to causal launching makes subsequent ambiguous events in that same location more likely to be seen as non-causal ”passing’. Here, after replicating this effect, we show that exposure to triggering also yields retinotopically specific adaptation for subsequent ambiguous launching displays, but that exposure to entraining does not. Collectively, these results reveal that visual processing distinguishes some types of causal interactions. (shrink)

The adaptation aftereffect plays a critical role in human development and survival. Existing studies have found that, compared with general individuals, individuals with learning disability, autism and dyslexia show a smaller amount of non-affective-based cognitive adaptation aftereffect. Nevertheless, it is unclear whether individuals with depression or depression tendency show similar phenomenon in the adaptation aftereffect, and whether such depression tendency occurs in the non-affective-based cognitive or emotional adaptation aftereffect. To address this question, the present study conducted two experiments. Experiments 1A (...) and 1B used the emotional facial expression adaptation paradigm to examine whether Chinese participants showed the emotional adaptation aftereffect and whether the emotional adaptation aftereffect was influenced by physical features of faces, respectively. Experiment 2 recruited two groups of participants, with high and low depression, respectively, to examine whether they showed differences in the emotional or cognitive adaptation aftereffect. Results showed that Chinese participants showed the typical emotional adaptation aftereffect, which was not influenced by physical features of faces. More importantly, compared to the low-depression group, the high-depression group showed a smaller emotional adaptation aftereffect, but the two groups showed a similar cognitive adaptation aftereffect. These results suggest that level of depressive symptoms is associated with the emotional adaptation aftereffect. (shrink)

Numerosity perception is a key ability for human and non-human species, probably mediated by dedicated brain mechanisms. Electrophysiological studies revealed the existence of both early and mid-latency components of the Electrophysiological (EEG) signal sensitive to numerosity changes. However, it is still unknown whether these components respond to physical or perceived variation in numerical attributes. We here tackled this point by recording electrophysiological signal while participants performed a numerosity adaptation task, a robust psychophysical method yielding changes in perceived numerosity judgments despite (...) physical numerosity invariance. Behavioral measures confirmed that the test stimulus was consistently underestimated when presented after a high numerous adaptor while perceived as veridical when presented after a neutral adaptor. Congruently, EEG results revealed a potential at around 200 ms (P2p) which was reduced when the test stimulus was presented after the high numerous adaptor. This result was much prominent over the left posterior cluster of electrodes and correlated significantly with the amount of adaptation. No earlier modulations were retrievable when changes in numerosity were illusory while both early and mid-latency modulations occurred for physical changes. Taken together, our results reveal that mid-latency P2p mainly reflects perceived changes in numerical attributes, while earlier components are likely to be bounded to the physical characteristics of the stimuli. These results suggest that short-term plastic mechanisms induced by numerosity adaptation may involve a relatively late processing stage of the visual hierarchy likely engaging cortical areas beyond the primary visual cortex. Furthermore, these results also indicate mid-latency electrophysiological correlates as a signature of the internal representation of numerical information. (shrink)