When and why parts count: linking categorization and counting of partial objects

When asked to count using basic-level noun descriptions (e.g. fork), children often count both whole objects and “partial objects” (e.g. a broken fork-piece) as one unit, diverging systematically from adults. We test one class of explanations for this “over-counting” behavior: that children apply nouns to objects more permissively than adults, and then count those objects they have labeled with the noun. In a two-task study, we examined how categorization of a partial object under a count noun related to numerical evaluations of sets that included that object, including cases where the numerical expressions involved fractions. Adults categorized and counted partial objects conservatively, often excluding them from the category and counting them, at most, for a fractional share (1/2). Children were more permissive in both tasks: they frequently accepted partial objects as noun category members and counted them on par with wholes (as |1|). Strikingly, children’s numerical judgments were often incongruous with their categorization: They sometimes rejected a partial object as a category member, but still counted it as |1|. We argue that while children are indeed more flexible in their noun application, their counting behavior calls for a different account. We propose that children lack the numerical capacities to represent and reason over fractional amounts, and default to a natural number scale even when adults use a finer-grained measurement scale. Children may recognize that the partial fork contributes some non-zero amount to a sum, but the only way they can add it to that sum is as |1|.