A Critique of Numerical Taxonomy

There is a little-known branch of logic known as critique, which examines the statements of science. An idea cannot be examined by minds other than the one in which it occurs, but when statements are made about the idea, the statements can be examined, and verified or criticized. This is possible because the statement arouses a fresh idea in the second mind, one which can then be examined there. Science is not made up of ideas but of statements about the things and processes of the material world. The critique seeks to find the significance and limitations of the statements of science. Without this critique, science would soon become filled with inaccurate statements, faulty conclusions, and illogical ideas, because it is not only human to err but to use other ideas out of context and to support a preconceived notion in a variety of questionable ways. Although critique is a word seldom used, the process is universal, as in the judgment of scientists on all published statements. Numerical taxonomy purports to be a new field of systematics, employing statistical and computer techniques to overcome faults of conventional taxonomy. It would be difficult to criticize the field as a whole if only scattered publications by several authors were available. The general aims and philosophy would be difficult to extract from the diverse views. It is therefore necessary to find a set of general statements that summarizes the field and sets forth its goals, its advantages, and its weaknesses. The publication of "Principles of Numerical Taxonomy" by R. R. Sokal and P. H. A. Sneath fills this need, and the following critique is addressed to the field but largely refers to the statements of this book. Although this book is not the most recent publication on numerical methods, it is the most recent summary. It appears to be a satisfactory exposition of the present state of statistical analysis of taxonomic data. One of the first things noted about numerical taxonomy is that it is not only described as a new method in taxonomy but as one of several new methods. These are: numerical methods, comparative serology, chromatography, electrophoresis, infrared spectroscopy, cytotaxonomy, and a miscellaneous group including chemistry, electron microscope cytology, behavior, ecology, histology, and parasitology. Leaving aside for the moment the first of these, all the rest produce data about the organisms, data which are at least potentially comparative. As such, these data are automatically taxonomic and can be recorded in the taxonomic system, and can be directly employed in that system if there is need to do so. There are four words basic to this discussion: comparison, resemblance, difference, and correspondence. Classification implies that there are "classes" of things. If a taxonomist starts with individual things and compares one with another, he can unite similar ones in classes based at first thought on similarities. If he starts with many things at once and divides them into classes and subclasses, he will have used differences as his first criterion. These two approaches are the two basic methods of classifying. Both of them are based on comparison of the objects or their attributes. In the first, the comparison is to find what there is that is similar; in the second, to find what there is that is different. The key word and concept is comparison. Two things can be compared even if they have nothing in common, but there may seem to be no purpose to the comparison. To group, or classify, things there must also be some similarities among them. This is resemblance. Resemblance may be pro-