In this sense semiotic dictionaries and encyclopedias are not directly comparable to dictionaries and encyclopedias “in the flesh,” so to speak, to the published products, in other words, that go by the same name. In fact, dictionaries “in the flesh” are not usually composed according to the dictionary modeclass="underline" a normal dictionary, for instance, may define “cat” as a feline mammal, but usually adds details of an encyclopedic nature that concern the cat’s fur, the shape of its eyes, its behavioral habits, and so on and so forth.
If we wish to identify a dictionary in its pure form—to which various contemporary theoreticians in the field of artificial intelligence still refer when they speak (see section 1.7 below) of “ontologies”—we must return to the model of the Arbor Porphyriana or Porphyrian tree, in other words to the commentary on Aristotle’s Categories written in the third century A.D. by the Neo-Platonist Porphyry in his Isagoge, a text that throughout the Middle Ages (and beyond) will be a constant point of reference for any theory of definition.
1.2. The Dictionary
1.2.1. The First Idea of the Dictionary: The
Arbor Porphyriana
Aristotle (Posterior Analytics, II, iii, 90b 30) says that what is defined is the essence or essential nature. Defining a substance means deciding, among its attributes, which of them appear to be essential, and in particular those that are the cause of the fact that the substance is what it is, in other words, its substantial form.
The problem is coming up with the right attributes that can be predicated as elements of the definition (Posterior Analytics, II, xiii, 96a–b). Aristotle gives the example of the number 3: an attribute such as being certainly applies to the number 3, but also to anything else that is not a number. On the other hand, the fact of being odd applies to the number 3 in such a way that, even if it has a wider application (it also applies, for instance, to the number 5), it nonetheless does not extend beyond the class of numbers. These are the attributes we must look for “up to the point where, although singly they have a wider extension of meaning than the subject, collectively they have not; for this must be the essence of the thing” (II, xiii, 96a 35). What Aristotle means is that, if we define man as MORTAL, ANIMAL and RATIONAL, each of these attributes, taken on its own, can also be applied to other beings (horses, for example, are animal and mortal, and the gods, in the Neo-Platonic sense of the word, are animal and rational), but, taken altogether, as a defining “group,” MORTAL RATIONAL ANIMAL applies only to man, and in a way that is absolutely reciprocal.
A definition is not a demonstration: to reveal the essence of a thing is not the same as to prove a proposition about that thing; a definition says what something is, whereas a demonstration proves that something is (II, iii, 91a 1), and, consequently, in a definition we assume what a demonstration must on the contrary prove (II, 3, 91a 35). Those who define do not prove that something exists (II, iii, 92a 20). This means that for Aristotle a definition is concerned with meaning and has nothing to do with processes of reference to a state of the world (II, iii, 93b 30).
To find the right way to construct good definitions, Aristotle develops the theory of predicables, that is, of the ways in which categories can be predicated of a subject. In his Topics (I, iv, 101b 17–25) he identifies only four predicables (genus, proprium or unique property, definition, and accident), while Porphyry—as we shall see—will speak of five predicables (genus, species, difference, proprium, and accident).1
In a lengthy discussion in the Posterior Analytics (II, xiii), Aristotle outlines a series of rules to develop a proper division, proceeding from the most universal genera to the infimae species, identifying at each stage of the division the proper difference.
This is the method followed by Porphyry in the Isagoge. The fact that Porphyry develops a theory of division in a commentary on the Categories (where the problem of difference is hardly mentioned) is a serious matter for debate (see, for instance, Moody 1935), but it is not particularly relevant to our analysis.
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 formaclass="underline" 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.