Four experiments used a preferential looking method to investigate six-month-old infants' capacity to represent numerosity in visual-spatial displays. Building on previous findings that such infants discriminate between arrays of 8 vs. 16 discs, but not 8 vs. 12 discs (Xu & Spelke, 2000), Experiments 1 and 2 investigated whether infants' numerosity discrimination depends on the ratio of the two set sizes with even larger numerosities. Infants successfully discriminated between arrays of 16 vs. 32 discs, but not 16 vs. 24 discs, providing evidence that their discrimination shows the set-size ratio signature of numerosity discrimination in human adults, children, and many non-human animals. Experiments 3 and 4 addressed a controversy concerning infants' ability to discriminate large numerosities (observed under conditions that control for total filled area, array size and density, item size, and correlated properties such as brightness: Brannon, 2002; Xu, 2003; Xu & Spelke, 2000) vs. small numerosities (not observed under conditions that control for total contour length: Clearfield & Mix, 1999). To investigate the sources of these differing findings, Experiment 3 tested infants' large-number discrimination with controls for contour length, and Experiment 4 tested small-number discrimination with controls for total filled area. Infants successfully discriminated the large-number displays but showed no evidence of discriminating the small-number displays. These findings provide evidence that infants have robust abilities to represent large numerosities. In contrast, infants may fail to represent small numerosities in visual-spatial arrays with continuous quantity controls, consistent with the thesis that separate systems serve to represent large vs. small numerosities. A we...

Four experiments investigated whether 12-month-old infants use perceptual property information in a complex object individuation task, using the violation-of-expectancy looking time method (Xu, 2002; Xu & Carey, 1996). Infants were shown two objects with di#erent properties emerge and return behind an occluder, one at a time. The occluder was then removed, revealing either two objects (expected outcome, if property di#erences support individuation) or one object (unexpected outcome). In Experiments 1--3, infants failed to use color, size, or a combination of color, size, and pattern di#erences to establish a representation of two distinct objects behind an occluder. In Experiment 4, infants succeeded in using cross-basic-level-kind shape di#erences to establish a representation of two objects but failed to do so using withinbasic -level-kind shape di#erences. Control conditions found that the methods were sensitive. Infants succeeded when provided unambiguous spatiotemporal information for two objects, and they encoded the property di#erences during these experiments. These findings suggest that by 12 months, di#erent properties play di#erent roles in a complex object individuation task. Certain salient shape di#erences enter into the computation of numerical distinctness of objects before other property di#erences such as color or size. Since shape di#erences are often correlated with object kind di#erences, these results converge with others in the literature that suggest that by the end of the first year of life, infants# representational systems begin to distinguish kinds and properties.

All students of cognitive development agree that the central questions in development are 1) specifying the initial state of a human infant, 2) specifying the final state of development for a human adult, and 3) specifying how to get from the initial state to the final state. Then academic disputes ensue. Cognitive developmental psychologists are roughly divided into two camps: those who are more or less nativists and those who are more or less empiricists. Some psychologists do not like these terms, and some alternatives are “those who believe in innate knowledge ” and “those who believe in learning, ” or “those who believed in initial conceptual knowledge ” and “those who believe in initial perceptual capabilities. ” This division is also correlated with whether a researcher believes in domain specificity or not: nativists tend to argue for domain-specific knowledge (even at the beginning of development) and domain-specific learning mechanisms; empiricists tend to argue for domain-general learning mechanisms that may result in domain-specific knowledge some years into development (for some representative explications of these views, see Carey &

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