Inspired by Barsalou's (Journal of Experimental Psychology: Learning, Memory, and Cognition, 11, 629-654, 1985) proposal that categories can be represented by ideals, we develop and test a computational model, the ideal dimension model (IDM). The IDM is tested in its account of the typicality gradient for 11 superordinate natural language concepts and, using Bayesian model evaluation, contrasted with a standard exemplar model and a central prototype model. The IDM is found to capture typicality better than do the exemplar model and the central tendency prototype model, in terms of both goodness of fit and generalizability. The present findings challenge the dominant view that exemplar representations are most successful and present compelling evidence that superordinate natural language categories can be represented using an abstract summary, in the form of ideal representations. Supplemental appendices for this article can be downloaded from http://mc. psychonomic-journals.org/content/supplemental.