Natural counting and measuring: The role of linguistic and referential cues in determining which quantity is “More”

When we decide “Which is more?” for groups of physical objects or substances, we compare the groups along a quantitative dimension like numerosity or size. The nature of these comparisons is sometimes unclear, however, because the choice of dimension may be uncertain. To clarify this choice, people can rely on linguistic and referential indicators. One type of clue to the right dimension is a classifier or “quantizer” like “ounces” that appears with “more,” as in “Which has more in ounces?” The studies in this paper look at these quantizer-based comparisons, for the first time in an experimental context, and the extent to which they depend on the comparisons’ referents. Participants answered questions like these for pictures of simple objects that differed independently in their size and number. As expected, response times for their answers show robust effects of the quantizers in directing attention to number or measure. However, the quantizers did not always fully dictate this choice. First, some quantizers (e.g., “more in boxfuls/spoonfuls”) are ambiguous between a reading that emphasizes the number of containers (boxes or spoons) and a reading that emphasizes the measure of their contents. Second, the reading of even unambiguous quantifiers (e.g., “more in cubes”) can be swayed by the referents of the comparison (e.g., “more salt in cubes”). These results suggest that people may begin with a generalized sense of “more” that they narrow in response to the quantizer and the referent, considered in tandem. We offer a mathematical model of how this interpretation takes place.