From the Tree to the Labyrinth Read Free Page A

be arranged into different trees according to the things to be defined, jettisoning the distinction between substances and accidents.
    Many medieval commentators of the Isagoge appear to endorse this conclusion. Boethius in his De divisione (VI, 7) suggests that substances like pearl, ebony, milk, and some accidents like white or liquid may give rise to alternative trees. In one, for example, given a genus Liquids, with the differences White/Black, we would have the two species Milk and Ink; in the other, the genus White Things, with the differences Liquid/Solid, would generate the two species of Milk and Pearl ( Figure 1.6 ).
    True, in this passage Boethius is speaking only of accidents, but, in De divisione XII, 37, he applies the same principle to all divisions of genus (“generis unius fit multiplex divisio” [“a single genus is divisible in more than one way”]). 9

    Figure 1.6

    Abelard says the same thing in his Editio super Porphyrium (150, 12), where he reminds us that “Pluraliter ideo dicit genera, quia animal dividitur per rationale animal et irrationale; et rationale per mortale et immortale dividitur; et mortale per rationale et irrationale dividitur” (“He [Porphyry] refers then to genera in more than one way, for animal is divisible into rational animal and irrational animal; and rational is divisible into mortal and immortal; and mortal is divisible into rational and irrational”) ( Figure 1.7 ). 10

    Figure 1.7

    In a tree composed solely of differences, these can be continually reorganized following the description under which a given subject is considered, and the tree thus becomes a structure sensitive to contexts, not an absolute dictionary.
    On the other hand, when Aristotle (who is interested in defining accidents as well as substances) asserts ( Posterior Analytics I, 3, 83a, 15) that definitions must stick to a finite number of determinations, in either an ascending or a descending series, he does not in the least seem to be suggesting that their number and function are already established by a previous categorical structure. In fact in his various researches into natural phenomena, from the eclipse to the definition of ruminants, he shows a great deal of flexibility in setting up subdivisions and suggesting trees in which genera, species, and differences exchange roles according to the problem one intends to resolve.
    In Posterior Analytics II, 3, 90a, 15, he says that the eclipse is a deprivation of the sun’s light by the earth’s interposition. In order to define it this way we must suppose a division into genus and species like the one in Figure 1.8 .

    Figure 1.8

    But what is the deprivation of the sun’s light a species of? Are we talking about a tree that takes cognizance of the various kinds of deprivation (among which, let’s say, are the deprivation of food and of life) or a tree that takes cognizance of various astronomical phenomena and opposes the radiation of the sun’s light to its deprivation?
    In II, 3, 93b, 5, the example of thunder is discussed. It is defined as extinction of fire in the clouds. Hence a tree as in Figure 1.9 :

    Figure 1.9

    But what if the definition had been “noise produced by the extinction of fire in the clouds”? In that case, the tree would have to look like Figure 1.10 .
    As can be seen, in the first case thunder is a species of the genus extinction, in the second case of the genus noises.

    Figure 1.10

    This flexibility is due to the fact that, when he is dealing with concrete phenomena, it is the philosopher’s intention to define them, while a tree with a fixed hierarchy and a finite number of determinations serves only to classify. Merely classificatory, for example, is a device that embeds genera, species, and differences without explaining the nature of the definiendum. This model is that of the taxonomy of today’s natural sciences, in which it is established, for instance, that a dog belongs to the genus CANIS, of the family of