The general structure of taxonomic data sets, the alpha and beta elements of this structure, the departures of this structure from randomness, and the rationale by which departures are viewed as historical evidence have been demonstrated. An operational method for selecting character sets is illustrated, an estimate of the genealogy that produced the species is derived from these sets, and this estimate is presented as a phylogeny. In addition, I have demonstrated a method that discloses a stable structure that is relatively insensitive to distortion through addition of new data. Still further, I have shown a procedure that produced clusters of species having phenetic properties that are at least as good as those of clusters produced by direct phenetic methods. It has been demonstrated that different characters have different predictive properties, that different character states of the same character have different predictive properties, and that, in general, derivative states are the sole bearers of valid historical information. Taxonomists cannot, with propriety, weight either characters or character states. They must select and evaluate sets of character states, and this evaluation should be carried out every time new data, breaking established character sets, are incorporated into data tables.