In his Topics too (VI, 6, 144b), Aristotle admitted that the same difference may occur twice under two different genera (as long as they are not subordinate): “the earthbound animal and the flying animal are in fact genera not contained the one within the other, even though the notion of two-leggedness is the difference of both.”8
If the same difference can recur a number of times, the finiteness and logical purity of the tree—which runs the risk of exploding into a dust cloud of differences, reproduced identically under different genera—are compromised. Indeed, if we reflect that species are a combination of genus and difference, and the genus higher up is in its turn a combination of another genus plus a difference (and therefore genera and species are abstractions, intellectual figments which serve to sum up various organizations of differences or accidents), the most logical solution would be for the tree to be made up solely of differences, properties that can 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 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).
The notion of specific difference is, rhetorically speaking, an oxymoron. Saying specific difference is tantamount to saying essential accident. But this oxymoron conceals (or reveals) a far more serious ontological contradiction.
The thinker who understood the problem without prevarication (though he pointed it out with his customary prudence) was Thomas Aquinas. In his De ente et essentia he says that specific difference corresponds to substantial form (another ontological oxymoron, if we may put it that way, since the most substantial thing we can think of is identified with an accident). But Thomas’s thought does not leave room for misunderstanding: what defines substantial form is difference as an accident.
In order to justify such a scandalous conclusion, Thomas excogitates—with one of his habitual strokes of genius—an extremely brilliant solution. There exist essential differences; but which and what they are we do not know; what we know as specific differences are not the essential differences themselves, but are, so to speak, signs of them, symptoms, clues, superficial manifestations of the being of something else that we cannot know. We infer the presence of essential differences through a semiotic process, with knowable accidents as our point of departure.11
That the effect is a sign of the cause is Thomas’s customary idea (much of his theory of analogy depends on this assumption, which is, if we were to trace it back, Stoic in origin: effects are indicative signs). The idea reappears, for instance, in Summa Theologiae I, 29, 2 ad 3 and I, 77, 1 ad 7: a difference such as rational is not the real specific difference that constitutes the substantial form. Ratio (reason) as potentia animae (a power of the soul) appears outwardly verbo et
