Wednesday, June 07, 2006

Typology and Natural Classification

One of the more interesting aspects of Whewell's theory of natural classification is his argument that natural classes are to be fixed not by definition by by type. The general line of thought is very nicely summarized in Whewell's aphorisms (vol. 2, p. 460-461):

XCII. Natural Groups are best described, not by any definition which marks their boundaries, but by a Type which marks their center. The Type of any natural group is an example which possesses in a marked degree all the leading characters of the class. (VIII. 2.)

XCIII. A Natural Group is steadily fixed, though not precisely limited; it is given in position, though not circumscribed; it is determined, not by a boundary without, but by a central point within;--not by what it strictly excludes, but by what it eminently includes;--by a Type, not by a Definition. (VIII. 2.)

XCIV. The prevalence of Mathematics as an element of education has made us think Definition the philosophical mode of fixing the meaning of a word: if (Scientific) Natural History were introduced into education, men might become familiar with the fixation of the signification of words by Types; and this process agrees more nearly with the common processes by which words acquire their significations. (VIII. 2.)

It might be helpful to look at the argument behind aphorism XCII in a bit more detail. Whewell argues that definitions in natural history will tend to become indefinite and inconsistent; definitions are quite OK for abstract sciences, but natural history is concerned with classifying actual, concrete things, which admit of considerable variation. We might think that this means that the classes established by natural history are "quite loose, without any certain standard or guide," but it is not actuall so (vol. 1, p. 494). As Whewell puts it (vol. 1, p. 494):

The class is steadily fixed, though not precisely limited; it is given, though not circumscribed; it is determined, not by a boundary line without, but by a central point within; not by what it strictly excludes, but by what it eminently includes; by an example, not by a precept; in short, instead of a Definition we have a Type for our director.

A type is an idealized example of a class: one that eminently possesses all the characters of the class. Other types are ranged around it, deviating from it in various degrees and in various ways. This forms our classification. And, as Whewell notes, the fact that there might be some species whose relations to a type are hard to determine doesn't change the general effectivenessness of the classification as a whole, any more than scattered trees between two hills makes it impossible to talk rationally about two different forests on two different hills.

An example of type-based classificationThe type of the rose family has alternate stipulate leaves, no albumen, non-erect ovules, simple stigmata, and so forth. It is entirely possible for individual roses to break this pattern without ceasing to be roses. But while individual roses vary around it, the type forms a center for all the variation. It's as if you shot a paintball at a target: the type is the point in the center, and the variants are the splatter around it.

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