From the Tree to the Labyrinth Page 2
Once more, however, in its canonical version, this tree reveals its inadequacy, because it distinguishes, in a logically satisfactory fashion, God from man, but not, let’s say, a man from a horse. If we had to define the horse, the tree would have to be enriched with further disjunctions: we would need, for example, to divide ANIMALS into mortal and immortal, and the next species down—that of MORTAL ANIMALS—into rational (men) and irrational (horses, for instance), even though, unfortunately, this subdivision, as is apparent in Figure 1.3, would not allow us to distinguish horses from donkeys, cats, or dogs.
Figure 1.3
Even if we were willing to pay this price, however, we still could not reintroduce God into the tree. The only solution would be to insert the same difference twice (at least) under two different genera (Figure 1.4).
Figure 1.4
Porphyry would not have discouraged this decision, given that he himself says (18.20) that the same difference “can often be observed in different species, such as having four legs in many animals that belong to different species.”6
Aristotle too said that when two or more genera are subordinate to a superior genus (as occurs in the case of the man and the horse, insofar as they are both animals), there is nothing to prevent them having the same differences (Categories 1b 15 et seq.; Topics VI, 164b 10). In the Posterior Analytics (II, 90b et seq.), Aristotle demonstrates how one can arrive at an unambiguous definition of the number 3. Given that the number 1 was not a number for the Greeks (but the source and measure of all the other numbers), 3 could be defined as that odd number that is prime in both senses (that is, neither the sum nor the product of other numbers). This definition is fully reciprocable with the expression three. But it is interesting to reconstruct in Figure 1.5 the process of division by which Aristotle arrives at this definition.
Figure 1.5
This type of division shows how properties like not the sum and not the product (which are differences) are not exclusive to any one disjuncture but can occur under several nodes. The same pair of dividing differences, then, can occur under several genera. Not only that, but the moment a certain difference has proved useful in defining a certain species unambiguously, it is no longer important to consider all the other subjects of which it is equally predicable (which amounts to saying that, once one or more differences have served to define the number 3, it is irrelevant that it may occur in the definition of other numbers).7 Once we have said, then, that, given several subordinate genera, nothing prevents them having the same differences, it is difficult to say how many times the same pair of differences can occur.
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 g
enus 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 facto (in word and deed), through exterior actions, psychological and physical behaviors (and those actions are accidents, not substances!). We say humans are rational because they demonstrate their rational powers by means of acts of cognition, or by an internal discourse (the activity of thought) or an external discourse, that is, by means of language (Summa Theologiae I, 78, 8 co.). In a decisive text in the Contra Gentiles (3, 46, n. 11), Thomas says that human beings do not know what they are (quid est), but they know what they are like (quod est) insofar as they perceive themselves as actors in rational thought. We know what are our spiritual powers only “ex ipsorum actuum qualitate” (“from the nature of these same acts”). Thus rational is an accident, and so are all the differences into which the Porphyrian tree can be dissolved.
From this discovery, Thomas does not draw all the conclusions he should have regarding the possible nature of the tree of substances: he cannot bring himself (psychologically perhaps) to call the tree into question as a logical tool for obtaining definitions (something he could have done without going out on a limb), because the entire Middle Ages is dominated by the conviction (however unconscious) that the tree mimics the structure of reality, and this Neo-Platonic conviction also affects the most rigorous of Aristotelians.
It is clear, however, if we follow its inner logic, that the tree of genera and species, however constructed, explodes into a swirl of accidents, into a nonhierarchizable network of qualia. The dictionary dissolves of necessity, as a result of internal tensions, into a potentially orderless and limitless galaxy of elements of knowledge of the world. It becomes, in other words, an encyclopedia, and it does so because it was already in fact an encyclopedia without knowing it, an artifice invented to camouflage the inevitability of the encyclopedia.
1.2.2. The Utopia of the Dictionary in Modern Semantics
We see a return to the dictionary model in the linguistics of the second half of twentieth century, when the first attempts appear to postulate or recognize—in order to define the contents expressed by the terms of a natural language—a finite system of figures possessing the same characteristics as a phonological system (based on a limited number of phonemes and their systematic oppositions). Thus, a feature semantics (features being primitive semantic atoms) was postulated, designed to establish the conditions necessary and sufficient for a definition of meaning, excluding knowledge of the world. In this way, in order to be recognized as a cat, something must have an ANIMAL feature, but it is not requested that it meows. These necessary and sufficient features are dictionary markers. Something along these lines was anticipated by Hjelmslev (1943[1961]) when he proposed to analyze the concepts corresponding to the twelve terms ram, ewe, boy, girl, stallion, mare through a combination of the male/female opposition and the assumed primitives SHEEP, HUMAN BEING, CHILD, HORSE.
Hjelmslev’s was not the only modern proposal for a dictionary representation, though the many others proposed in the area of linguistics or of analytic philosophy, almost always in ignorance of Hjelmslev’s proposal, did no more than repropose his model.12
Reconsidering Hjelmslev’s model, we see that a dictionary representation would allow us to solve the following problems (as Katz 1972 will suggest later): synonymy and paraphrase (a ewe is a female ovine); similarity and difference (the pairs ewe and mare and mare and stallion have some features in common, while we can establish on the basis of what other features they can be distinguished); antonymy, complementarity, and contrariety (stallion is the antonym of mare); hyponymia and hyperonymia (equine is the hyperonym of which stallion is the hyponym); sensibleness and semantic anomaly (stallions are male makes sense while a female stallion is semantically anomalous; redundancy (male stallion); ambiguity (the terms bear and bull, for example, have more than one meaning); analytical truth (stallions are male is analytically true, because the definition of the subject contains the predicate); contradictoriness (there are no male mares); syntheticity (that ewes produce wool does not depend on the dictionary but on our knowledge of the world); inconsistency (this is a ewe and this is a ram cannot be equally true if referred to the same individual); semantic entailment (if ram, then ovine).
Unfortunately this model does not permit us to represent what we must know about sheep and horses if we are to understa
nd many discourses about them. It does not allow us, for instance, to reject expressions like the stallion was bleating desperately like a ram (justifiable only in a metaphorical context, and a very daring one at that), given that the mechanism of definition does not explain what sound horses naturally emit.
And this is not all. Even if a system of this kind could be implemented based on assumed primitives, and if SHEEP and HORSE were primitives, they would serve to define only a very limited share of the terms concerning part of the animal kingdom. How many primitive features would be needed to define all the terms in any given lexicon? And how do we define a “primitive” feature?
It has been said that primitives are innate ideas of a Platonic nature, but not even Plato succeeded in satisfactorily deciding how many or of what kind were the universally innate ideas (either there is an idea for every natural genus, like equinity, in which case the list is an open one, or there are a few far more abstract ideas, like the One, the Many, the Good, or mathematical concepts, which are insufficient to distinguish the meaning of lexical terms).