Dividing Plato's kinds

A dilemma has stymied interpretations of the Stranger's method of dividing kinds into subkinds in Plato's Sophist and Statesman. The dilemma assumes that the kinds are either extensions (like sets) or intensions (like Platonic Forms). Now kinds divide like extensions, not intensions. But extensions cannot explain the distinct identities of kinds that possess the very same members. We propose understanding a kind as like an animal body - the Stranger's simile for division - possessing both an extension (in its members) and an intension (in its form). We find textual support in the Stranger's paradigmatic four steps for collecting a subkind.