Numbers, numerosities, and new directions.

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 (ANS) represents numbers or numerosities, and why the ANS represents rational (but not irrational) numbers.

The number sense represents (rational) numbers.

On a now orthodox view, humans and many other animals possess a "number sense," or approximate number system (ANS), 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.

Analog mental representation.

Over the past 50 years, philosophers and psychologists have perennially argued for the existence of analog mental representations of one type or another. This study critically reviews a number of these arguments as they pertain to three different types of mental representation: perceptual representations, imagery representations, and numerosity representations. Along the way, careful consideration is given to the meaning of "analog" presupposed by these arguments for analog mental representation, and to open avenues for future research.

Can bootstrapping explain concept learning?

Susan Carey's account of Quinean bootstrapping has been heavily criticized. While it purports to explain how important new concepts are learned, many commentators complain that it is unclear just what bootstrapping is supposed to be or how it is supposed to work. Others allege that bootstrapping falls prey to the circularity challenge: it cannot explain how new concepts are learned without presupposing that learners already have those very concepts.

Remote effects of highlights on gloss perception.

The perception of a glossy surface in a static monochromatic image can occur when a bright highlight is embedded in a compatible context of shading and a bounding contour. Some images naturally give rise to the impression that a surface has a uniform reflectance, characteristic of a shiny object, even though the highlight may only cover a small portion of the surface. Nonetheless, an observer's impression of gloss may be partial and nonuniform at image regions outside of a highlight.

Effects of ISI and flash duration on the identification of briefly flashed stimuli.

The identification accuracy of briefly flashed stimuli followed by an interstimulus interval (ISI) of variable length was compared to that obtained with longer flashes that prolonged the exposure of the stimulus throughout the ISI. The interval between the onset of the stimulus and the onset of the mask (stimulus onset asynchrony (SOA)) was the same in the two conditions. Consistent with a dependence of visual identification on SOA, the percentages of correct identification in the two conditions were approximately similar at all SOAs irrespective of the level of noise, stimulus familiarity, and stimulus complexity.