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 CANINES, of the suborder of FISSIPEDS, of the order of CARNIVORES, of the subclass of PLACENTALS, of the class of MAMMALS. This classification, however, does not tell us (and is not meant to tell us) either what the properties of a dog are or how to recognize a dog or refer to a dog. Every node of the classification is in fact a pointer that refers to another chapter of zoology in which the properties of Mammals, Placentalia, Carnivores, Fissipeds, and so on are specified.
A dictionary classification, then, does not serve to define a term but merely to allow us to use it in a logically correct fashion. Given, let’s say, that the imaginary order of the Prixides is classified as belonging to the genus Prosides and the Prosides are a species of the genus Proceides, we do not need to know what the properties of a proceid or a prosid are to draw (true) inferences along the lines of: if this is a prixid then it has to be a prosid, and it is impossible that something that is a prixid should not be a proceid.
But these are not the bases which allow us to understand expressions in which terms like prixid and proceid appear: it is one thing to know that it is logically incorrect to say that a prixid is not a proceid; it is quite another to say what a proceid is, and, if it means anything to say that terms have a meaning, the classification does not supply that meaning.
Gil (1981: 1027) suggests that genera and species may be used as extensional parameters (classes), whereas only the differences decide the intensional regime. This is tantamount to saying that the meaning of a term depends on the differences and not on the genera or the species. Now, what makes it difficult to regiment the differences under a Porphyrian tree is that the differences are accidents, and accidents are infinite or at least indefinite in number.
The differences are qualities (and it is no accident that, while genera and species, which represent substances, are expressed by common nouns, the differences are expressed by adjectives). The differences come from a tree that is not the same as the substances, and their number is not known a priori (Metaphysics VIII, 1042a–1042b). Granted, Aristotle makes these remarks about nonessential differences, but at this point who can say which differences are essential and which not? Aristotle plays on a few examples (like rational and mortal), but when he speaks about species other than human, such as animals or artificial objects, he becomes much more vague and the differences multiply.
In theory we are entitled to put forward the hypothesis that Aristotle would not have been capable of constructing a finite Porphyrian tree, but in practice as well (on the basis, that is, of the philological evidence), when we read On the Parts of Animals, we see that he gives up in practice on constructing a single tree and readjusts complementary trees according to the properties whose cause and essential nature he wishes to explain (cf. Balme 1961 and Eco 1983a).