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)

Perception provides us with access to the external world, but that access is shaped by our own experiential histories. Through perceptual learning, we can enhance our capacities for perceptual discrimination, categorization, and attention to salient properties. We can also encode harmful biases and stereotypes. This article reviews interdisciplinary research on perceptual learning, with an emphasis on the implications for our rational and normative theorizing. Perceptual learning raises the possibility that our inquiries into topics such as epistemic justification, aesthetic criticism, and (...) moral knowledge should include not only an examination of cognition but also of perception. (shrink)