Number and Size Matter: Discrete versus continuous entities

Number and Size matter: Discrete versus continuous entities Lisa M. Cantrell (cantrell@indiana.edu) and Linda B. Smith (smith4@indiana.edu) Indiana University, Department of Psychological and Brain Sciences 1101 E Tenth St, Bloomington, IN, 47405 Abstract The distinction between discrete and continuous entities plays an important role in understanding of quantities as well as in categorical knowledge. There is a robust literature both in the domain of quantity perception and in noun learning concerning the factors relevant to this distinction; however, there has been little joint investigation of these issues. Here, we investigated the effects of number and size of named entities on the interpretation of a novel noun as an object or continuous mass. We found that number and size matter and may relate deeply to current distinctions between discrete and continuous estimators of quantity. Keywords: number; size; discrete; continuous; object name learning. Introduction What determines whether some entity is conceptualized as being discrete versus continuous? Discrete entities are conceptualized as bounded, cohesive and countable. Continuous masses are noncohesive and are divisible only into portions of their whole. This distinction is important for issues of word learning as well as understanding of quantity; discovering the factors that influence it may also shed light on other processes related to perception. Noun categories Many languages, such as English, mandatorily mark the distinction between discrete and continuous mass such that count nouns label discrete items and mass nouns label continuous ones. Count nouns use plural marking and numeric quantifiers to indicate quantity (e.g., four cups, three clouds), whereas mass nouns are preceded by continuous quantifiers and no plural marking (e.g., much dough). The distinction is conceptual and is used to mark both concrete and abstract nouns; however, among the common words learned by children prior to 3 years of age, the vast majority of count nouns refer to solid entities (e.g., chair, cup, house) that are in categories well organized by similarities in shape. In contrast, early common mass nouns predominantly refer to nonsolid things (e.g., water, milk) that are in categories well organized by material (see Samuelson & Smith, 1999 for a relevant analysis of early nouns). Conceptually, then, in the early word learning environment discrete countable entities are those with bounded and fixed forms, and for which shape is a defining feature. Continuous masses have variable and nondefining shapes, and material is the defining feature of such entities. There is considerable research indicating that infants, children and adults honor this distinction in nonlinguistic tasks as well as word learning. When shown rigid cohesive objects, eight month olds successfully track their movement behind an occluder; however, they do not track noncohesive or nonrigid entities (Chiang & Wynn, 2000; Huntley- Fenner, Carey, & Solimando, 2002;). When collections of dots move together in a cohesive manner, five month olds track them as if they were a unified whole (Wynn, Bloom, & Chiang, 2002). In word learning, cohesion of entities affects object name generalizations. Studies investigating word object mappings in children and adults frequently test attention to shape versus material using a novel noun generalization task. In this task, a novel entity is shown, it is labeled with a novel name (e.g., Look at the dax), and participants are then asked to judge whether other items are also in the same category. If the named exemplar is a single solid thing, children and adults judge category membership based on shape. If the named exemplar is a nonsolid substance, children and adults extend membership to entities of the same material (Colunga & Smith, 2005; Imai & Gentner, 1997; Landau, Smith, & Jones, 1988; Soja, 1992; Soja, Carey, & Spelke, 1991). Further, embedding the novel name in a count noun frame (e.g., This is a wug) increases generalizations by shape; embedding the novel noun in a mass noun frame (e.g., This is some wug) increases attention to material (Soja, 1992). In sum, count nouns quantify over individuals whereas mass nouns quantify over non individuals, and—importantly— shape matters for categories of discrete countable things, whereas material matters for categories of substances. Estimators and counters A large and robust literature suggests that humans directly apprehend the number of discrete instances in a set when the size is small (less than 4) (Feigenson & Carey, 2003, 2005; Trick & Pylyshyn, 1994; Wynn, 1998; Xu & Spelke, 2000). Recently, there has been a growing consensus that two distinct perceptual systems exist for determining the number of items in a set: a discrete number system that applies to small set sizes and an analogue or estimator system for large set sizes (Carey, 2001, 2004; Feigenson, Dehaene, & Spelke, 2004; Xu, 2003; Xu & Spelke, 2000). By some theoretical analyses, small sets of objects (≤3 or 4) are encoded separately as object files (Scholl, 2001; Simon, 1997; Trick & Pylyshyn, 1994; Uller, Huntley-Fenner, Carey, & Klatt, 1999); larger sets (≥4 or are represented in an analogue magnitude system that