The Language of Taxonomy

T HE encouragement of scholarship and the conditions conducive to the birth of new truth were the theme of Columbia University's bicentennial celebration last year. Among the samples of the University's scholarship that are being published to signalize this event, there is one of great potential interest to systematists. The Language of Taxonomy by John R. Gregg, Associate Professor of Zoology at Columbia, is a very small book. It is not one, however, which will be read and understood in a short time by anyone except a logician. It solves none of the problems of taxonomy; it will not answer the questions currently arising between systematists. Nevertheless, this book may well prove -to be the clue to the solution of some of these important problems. Taxonomy is the study of kinds of organisms. This book is an attempt to develop a language for use in taxonomy. It is therefore not a book on taxonomy but on metataxonomy-the study of taxonomic statements. Taxonomy and metataxonomy differ in having different subject matters, in having different vocabularies, and in being unequally developed. This book is an attempt to develop one aspect of metataxonomy by illustrating the utility of set-theory concepts in the study of taxonomic classification. In order to present examples of the application of the theory of sets, Gregg finds it necessary to outline the principles of this subject, which is one of the symbolic methods of formal logic. The resulting semimathematical expressions can be made explicit and definable, thus circumventing the unsuitable prescientific idioms borrowed from everyday language which have heretofore led taxonomists into endless semantic difficulties. Set-theory is one of the methods of logic which can emphasize for the taxonomist the distinctions between kinds, classes of kinds, and categories of classes. Confusion between the latter two, or failure to distinguish them clearly, seems to be at the root of much of taxonomy's difficulties over the reality of species and the philosophic nature of the higher categories. Dr. Gregg has not set out to solve these difficulties in this book, but rather to present the basis for a language which will be suitable for conveying such a solution. Dr. Gregg has pointed out to the reviewer an error that might not be obvious even upon close study. In the footnote on page 47 a definition of "taxonomic classificatory system" is proposed that is intended as an improvement upon the definition given in the main body of the text. Owing to printer's omissions, the new definition is not adequate as it stands, but matters will be set right by replacing each of the two occurrences of "z" in the fourth line from the bottom of the page with "*Z." (The sign "*z," designating the ancestral of the relation z, is defined on page 24.) Thus restored, the new definition states in effect that any relation ordering a set of taxonomic groups may be regarded as a taxonomic system provided that the following conditions are satisfied: (1) there is one all-inclusive group in the set; (2) any two groups in the set stand in the relation only if one immediately includes the other; and (3) given any two groups in the set, either they have no members in common or else one bears the ancestral of the relation to the other. The reviewer believes that the diffi-