Children's understanding of the abstract logic of counting

When children learn to count, do they understand its logic independent of the number list that they learned to count with? Here we tested CP-knowers' (ages three to five) understanding of how counting reveals a set's cardinality, even when non-numerical lists are used to count. Participants watched an agent count unobservable objects in two boxes and were asked to identify the larger set. Participants successfully identified the box with more objects when the agent counted using their familiar number list (Experiment 1) and when the agent counted using a non-numeric ordered list, as long as the items in the list were not linguistically used as number words (Experiments 2-3). Additionally, children's performance was strongly influenced by visual cues that helped them link the list's order to representations of magnitude (Experiment 4). Our findings suggest that three- to six-year-olds who can count also understand how counting reveals a set's cardinality, but they require additional time to understand how symbols on any arbitrary ordered list can be used as numerals.