Representation of the cardinality principle: early conception of error in a counterfactual test

There is debate over how the integration of non-verbal quantifying and verb al counting relates to the representation of number principles. A stringent representational test would be one in which a child obeyed a number princi ple where it ran counter to a characteristic procedure. We devised a test r elying on the uniqueness principle for using evidence from a miscount in in ferring a counterfactual cardinal number. All the 5-year-olds passed, as di d half the preschoolers. Subtests probed associated number-skills. We sugge st that a crucial preschool step is to start conceptualising error by categ orising relations between counting and miscounting. That step is taken at a similar age to passing a representational theory of mind test but the two were uncorrelated. (C) 2000 Elsevier Science B.V. All rights reserved.