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. 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(s) of number being represented. In response, we propose that the ANS represents not only natural numbers (e.g., 7), but also non-natural rational numbers (e.g., 3.5). It does not represent irrational numbers (e.g., √2), 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.

Investigating the Effect of Perioperative Chlorzoxazone on Acute Postoperative Pain After Total Hip and Knee Replacement Surgery.

BACKGROUND AND AIMS: Severe preoperative and acute postoperative pain have been associated with the development of chronic postoperative pain. Chlorzoxazone (a muscle relaxant) has been suggested to enhance acute postoperative pain recovery, but the lack of larger randomized controlled trials has, however, questioned the continued use. Despite this, chlorzoxazone is still used for acute postoperative pain management following total knee replacement (TKR) or total hip replacement (THR). The current randomized, double-blinded, placebo-controlled, parallel-group, clinical trial aimed to assess the effect of chlorzoxazone for postoperative pain management following TKR or THR. METHODS: A total of 393 patients scheduled for TKR or THR were included in the trial. Patients were assigned to 250 mg chlorzoxazone 3 times daily for the first 7 days postoperatively or to placebo. The primary outcome was pain after 5 m walk assessed 24 hours postoperatively. Secondary outcomes included changes in preoperative pain at rest, worst pain in the last 24 hours, and Oxford Knee or Hip Score compared with 12 months' follow-up. In addition, adverse events were assessed in the perioperative period. RESULTS: No significant differences were found for any of the outcome parameters after TKR or THR. As regards TKR or THR, no effects were demonstrated for pain after 5 m walk 24 hours after surgery (P>0.313), or for any of the secondary outcomes (P>0.288) or adverse events (P>0.112) in the group receiving chlorzoxazone compared with placebo. CONCLUSION: The current study demonstrated no analgesic effects of postoperative chlorzoxazone administration compared with placebo on acute or chronic postoperative pain 12 months following TKR and THR.

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. This article is categorized under: Philosophy > Foundations of Cognitive Science Philosophy > Representation Philosophy > Psychological Capacities.

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. Drawing on discussions of concept learning from the philosophical literature, this article develops a detailed interpretation of bootstrapping that can answer the circularity challenge. The key to this interpretation is the recognition of computational constraints, both internal and external to the mind, which can endow empty symbols with new conceptual roles and thus new contents.

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. A rating scale and small probe points indicating image locations were used to investigate the differential perception of gloss within a single object. Gloss ratings given by observers were not uniform across a surface, but decreased as a function of distance from a highlight. When, by design, the distance from a highlight was uncoupled from the luminance value at corresponding probe points, the decrease in rated gloss correlated more with distance than with luminance change. Experiments also indicated that gloss ratings may change as a function of estimated surface distance, rather than as a function of image distance. Surface continuity affected gloss ratings, suggesting that surface and gloss processing are closely related.

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. However, departures from the onset-onset rule were also present. While the two conditions yielded virtually identical identification accuracy with an SOA of 80 ms, small but significant differences were found for shorter and longer intervals. Possible theoretical explanations of the results are presented.