Children's reasoning with universal quantifiers like every and all has been an important topic in developmental psychology and psycholinguistics since Piaget's class inclusion studies. One puzzle is why children make two particular kinds of unexpected responses when asked questions like Is every boy riding an elephant?

One type of error occurs when a child is presented with a picture like those shown in figures 12.1a and b and asked to judge whether every boy is riding an elephant in that context. The picture in figure 12.1a depicts an incomplete one-to-one matching context in which each of three boys is riding a different elephant, leaving one elephant unridden. Figure 12.1b depicts a many-toone matching in which three boys are all riding one elephant, leaving two elephants unridden. Adults typically say yes on these tasks, but some children say no.When asked to explain, they point out the unridden elephant or elephants, in a way that suggests that they expected to see each of the elephants matched with a boy. Let us call this the “exhaustive pairing error.”

The other type of error occurs when children are presented with a picture like that in figure 12.2 and asked the same question. Some children answer yes on this task, suggesting that they may fail to search exhaustively through an entire domain of objects, even when that domain is perceptually available. Let us call this the “underexhaustive pairing error.”