In the same way, we may sidestep the vexata quaestio of the nature of universals, a question that Boethius bequeaths to the Middle Ages, taking the Isagoge itself as his point of departure. Porphyry declares his intention (we do not know how sincere he is) of setting aside the question of whether genera and species exist in and of themselves or if they are concepts of the mind. However that may be, he is the first to translate Aristotle in terms of a tree, and it is certainly difficult to avoid the suspicion that, in so doing, he is indebted to the Neo-Platonic notion of the Great Chain of Being.2 We may safely ignore, however, the metaphysics that underlies the Arbor Porphyriana, given that what interests us is the fact that this tree, whatever its metaphysical roots, is conceived of as a representation of logical relationships.
Porphyry delineates a single tree of substances, whereas Aristotle uses the method of division with a great deal of caution and, we might add, a great deal of skepticism. He seems to give it considerable weight in the Posterior Analytics, but to be more circumspect in On the Parts of Animals (642b et seq.), where he gives the impression of being prepared to construct different trees depending on which problem he is dealing with, even when it comes to defining the same species (see the whole discourse on animals with horns, apropos of which see Eco 1983a).
But Porphyry outlined a single tree of substances, and it is through this model, and not the more problematical discussion in the real Aristotle, that the idea of a dictionary structure of definition is transmitted, via Boethius, down to our own day, even though present-day proponents of a dictionary-based semantics may not know to whom they are indebted.
Porphyry, we were saying, lists five predicables: genus, species, difference, proprium, and accident. The five predicables establish the mode of definition for each of the ten categories. It is possible, then, to imagine ten Porphyrian trees: one for substances, which allows us, for example, to define man as MORTAL RATIONAL ANIMAL, and one for each of the other nine categories—a tree of qualities, for example, in which purple is defined as a species of the genus red.3 Therefore there are ten possible trees, but there is no tree of trees because Being is not a summum genus.
There can be no doubt that the Porphyrian tree of substances aspires to be a hierarchical and finite whole of genera and species. The definition Porphyry gives of “genus” is purely formal: a genus is that to which a species is subordinate. Conversely, a species is what is subordinate to a genus. Genus and species are mutually definable and therefore complementary. Every genus placed on a high node of the tree includes the species that depend upon it; every species subordinate to a genus is a genus for the species subordinate to it, down to the base of the tree, where the specie specialissime, or “second substances,” such as man, for instance, are collocated. At the highest fork is the genus generalissimum (represented by the name of the category), which cannot be a species of anything else. A genus can be a predicate of its own species, whereas the species belong to a genus.
The relationship of species to their superior genera is a relationship of hyponyms to hyperonyms. This phenomenon would guarantee the finite structure of the tree since, granted a given number of specie specialissime, and given that for two (or more) species there is only one genus, then, as we proceed upward, in the end the tree inevitably tapers off till it reaches the root node. In this sense the tree would fulfill all the functions required of a good dictionary.
But a Porphyrian tree cannot be made up only of genera and species. If this were the case, it would take the form illustrated in Figure 1.1.
In a tree of this kind man and horse (or man and cat) could not be distinguished from one another. A man is different from a horse because, though both may be animals, the first is rational and the second isn’t. Rationality is the difference for man. Difference is the crucial element, because accidents are not required to produce a definition.4
Differences may be separable from the subject (such as being hot, being in motion, being sick), in which case they are simply “accidents” (things that may happen—from the Latin accidere [= happen]—to a subject or not happen). But they may also be inseparable: among these some are inseparable but still accidental (like having a snub nose), others belong to the subject in and of itself, or essentially, like being rational or mortal. These are the specific differences and are added to the genus to form the definition of the species.
Figure 1.1
Differences may be divisive or constitutive. For example, the genus LIVING BEING is potentially divisible into the differences sensitive/insensitive, but the sensitive difference may be compounded with the genus LIVING to constitute the species ANIMAL. In its turn ANIMAL becomes a genus divisible into rational/irrational, but the rational difference is constitutive, with the genus that it divides, of the species RATIONAL ANIMAL. Differences, then, divide a genus (and the genus contains them as potential opposites) and they are selected to constitute in practice a subordinate species, destined to become in its turn a genus divisible into new differences.
The Isagoge suggests the idea of the tree only verbally, but medieval tradition visualized the project as seen in Figure 1.2.
In the tree in Figure 1.2 the dotted lines mark the dividing differences, while the solid lines mark the constitutive differences. We remind the reader that the god appears both as an animal and as a body because, in the Platonic theology that constitutes Porphyry’s frame of reference, the gods are intermediary natural forces and not to be identified with the One.5
Figure 1.2
From the contemporary point of view of a distinction between dictionary and encyclopedia, the Porphyrian tree certainly introduces, with its differences, encyclopedic properties into a dictionary structure. In fact, being Sensitive, Animate, Rational, and Mortal are accidents identifiable in terms of knowledge of the world, and it is on the basis of its behavior that we decide whether a being is animate or rational, whether, in other words, it expresses ratiocinative capabilities by means of language. In any case, the end purposes of the tree are those of a dictionary, in which the differences are necessary and sufficient conditions to distinguish one being from another and to make the definiens or definer coextensive with the definiendum or definee, so that, if ANIMAL RATIONAL MORTAL, therefore of necessity human, and vice versa.
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
