Monday, June 05, 2006

Whewell on Constructing Classificatory Sciences

From the Apohorisms Concerning Ideas (The Philosophy of the Inductive Sciences, volume 2, second edition [1847], p. 460):

LXXXVII. The construction of a Classificatory Science includes Terminology, the formation of a descriptive language;--Diataxis, the Plan of the System of Classification, called also the Systematick;--Diagnosis, the Scheme of the Characters by which the different Classes are known, called also the Characteristick. Physiography is the knowledge which the system is employed to convey. Diataxis includes Nomenclature. (VIII.2)

Or, as he says in VIII.2, which this aphorism summarizes (volume 1, pp. 480-481):

We may begin by remarking that the Idea of Likeness, in its systematic employment, is governed by the same principle which we have already spoken of as regulating the distribution of things into kinds, and the assignment of names in unsystematic thought and speech; namely, the condition that general propositions shall be possible. But as in this case the propositions are to be of a scientific form and exactness, the likeness must be treated with a corresponding precision; and its consequences traced by steady and distinct processes. Naturalists must, for their purposes, employ the resemblances of objects in a technical manner. This technical process may be considered as consisting of three steps;--The fixation of the resemblances; The use of them in making a classification; The means of applying the classification. These three steps may be spoken of as the Terminology, the Plan of the System, and the Scheme of the Characters.

As Whewell notes, classification is an example of the importance of words, because a great deal of the knowledge acquired by sciences like botany and mineralogy is built up by honing the descriptive language available for talking about things in a systematic way; the lack of such a terminology makes it very difficult to classify anything with precision or accuracy. With this in hand, however, it is possible to have a healthy taxonomy or diataxis, which, however, requires more than mere fixation of resemblances, because it is an attempt to find a natural classification, one that involves no arbitrary classification. The end result of this is a nomenclature, which is the system of labels by which different classes are named. To use this classification, we must have a diagnosis, a means of placing things in their proper classes according to identifying characteristics (which are not necessarily those that distinguish the classes in the classification itself). As Whewell calls it, the diagnosis for a natural classification is "an Artificial Key to a Natural System": as natural it is based on as few characteristics as possible; as natural, the characteristics chosen are not selected by any arbitrary rule but follow from the natural affinities we learn about in the natural classification.

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