The species problem is one of the oldest controversies in natural history. Its persistence suggests that it is something more than a problem of fact or definition. Considerable light is shed on the species problem when it is viewed as a problem in the representation of the natural system (sensu Griffiths, 1974, Acta Biotheor. 23:85–131; de Queiroz, 1988, Philos. Sci. 55:238–259). Just as maps are representations of the earth and are subject to what is called cartographic generalization, so diagrams of the natural system (evolutionary trees) are representations of the evolutionary chronicle and are subject to a temporal version of cartographic generalization, which may be termed systematic generalization. Cartographic generalization is based on judgements of geographical importance, and systematic generalization is based on judgements of historical importance, judgements expressed in narrative sentences (sensu Danto, 1985, Narration and knowledge, Columbia Univ. Press, New York). At higher systematic levels, these narrative sentences are conventional and retrospective, but near the species level they become prospective, that is, dependent upon expectations of the future. The truth of prospective narrative sentences is logically indeterminable in the present, and since all the common species concepts depend upon prospective narration, it is impossible for any of them to be applied with precision.