In any case, the whole system of Figure 2.3 is г finite one, which accounts also for synonymy, paraphrase,and semantic difference and which permits the production of definitions. Only a cat is a «felis cams, felis, felid, fissiped, carnivorous placental animal», and, if something does not have all these properties in conjunction, then it cannot be a cat.
This tree accounts for all the phenomena that a good dictionary is supposed to explain. It is a very flexible tool. Suppose one has to explain also the meaning of /halibut/; it will be sufficient to insert the disjunc-tion ‘fish/mammal’ under the node ‘animal’, and the tree would equally taper toward an ultimate node. With further complications one could also distinguish /bachelor/ as a seal from /bachelor/ as a human being. The tree would always result in being finite.
The tree does not offer the possibility of distinguishing between male and female, adult and young. It is a pity; we shall see apropos of the Porphyrian Tree (in 2.1.3) how embarrassing these kinds of ‘accidents’ are. But before coming to grips with these formidable questions, we have to raise a more urgent criticism.
2.1.3. The interpretation of the markers
The tree explains without ambiguity that a cat is nothing else but a ‘felis catus’. But in Latin (even though at two different historical stages of this language) both /felis/ and /catus/ (or cattus) are synonymous with the English word /cat/. Thus the definiens and the definiendum are certainly interchangeable, but only because they are absolutely and redundantly synonymous: a cat is a cat is a cat is a cat. If one asks what a felis catus is, one knows that it is a felis, which is not enough to distinguish a cat from a tiger.
However, when a zoologist says that what we call cat is a ‘Felis catus’ he is not merely playing on words. He uses Felis as the name of a genus and catus as the name of a differentia, but by these short-hand ex-pressions he intends to signify other biological properties. To be a catus
means to have the properties p1, p2 . . . pn> and to be a Felis means to have the properties p1, p2, . . . pn (and so on for the upper nodes).
The taxonomy of the zoologist does not intend to be a way to analyze the meaning of the word /cat/; it represents a mere classification of natu-ral kinds, accidentally labeled with certain names (changing from natural language to natural language). The zoologist as such is strongly inter-ested in defining the actual properties of the species he classifies, yet these properties are simply contained or meant by the terms he uses as taxonomic labels.
If a zoologist is told that gorillas grow in Ireland, he can react in two ways. Either he understands the sentence in the sense that some gorillas are born in Ireland, and in this case he is eager to concede that similar events happen in zoological gardens, or he takes the sentence as convey-ing an ‘eternal’ proposition (all the animals belonging to this species grow in Ireland), and then he would say that the proposition is analytically false because it challenges some information that belongs to his definition of gorillas. Likewise he would not discuss the statement this sheep has three feet, since he knows that there can be handicapped sheep, but he would challenge the statement sheep are not four-footed be-cause in his definition of a sheep there is a marker (probably ‘ungulata’) that must be interpreted in terms of four-footedness. Perhaps the zoologist would not say that sheep are four-footed necessarily or analytically, but he would say that the property of being four-footed belongs to sheep in some strong sense of /belonging/.
Zoologists know that their classificatory markers are interpretable and that they are not metalinguistic constructs but words of their specific object-language. Zoologically speaking, ‘mammal’ is not only a metalin-guistic construct that guarantees the semantic anomaly of such assertions as a stone is a mammal: /mammal/ means more or less «an animal which nourishes its young with milk secreted by mammary glands». Speakers of natural language do the same, obviously: when they say that a land is rich in minerals, they do not intend only that that land is rich in nonliv-ing natural objects, but intend many other interesting properties as well.
In natural language we frequently use expressions as animal, object, and vegetal as many times as we speak of cats and wolves, and maybe more often. This means either that we are using many terms of a metalan-guage as items of a natural language or that there is a difference between ‘animal’ as a semantic marker and /animal/ as a linguistic expression. But this is indeed a mere wordplay; in fact, when lexicographers or phi-losophers of language use the semantic marker ‘animal’ they are using a word of their natural language to build up a metalanguage. One can say that, as soon as a natural expression has become a metalinguistic term, it should not be further interpreted; such a rigorous decision is indeed possible and the tree of Figure 2.1 proves it, but, once this decision has been made, it is difficult to know not only what a sheep and a mouflon are but also what /sheep/ and /mouflon/ mean.
It would be sufficient to say that a dictionary has the sole function of providing a computer with the capability of parsing sentences in order to test whether they are semantically consistent, redundant, or analytically true, without explaining the meaning of their component words to someone who is not acquainted with any corresponding state of the world. Yet even the most rigorous theories of a dictionary competence try to escape this fate, and in two ways: from a practical point of view, by matching a representation of meaning with some instructions for the in-dividuation of the referents (see Katz 1979 for the «neoclassical» theory of meaning), and from a theoretical point of view, by defining even the analytic markers. Katz analyzes the lexeme /chair/ as (Object) (Physical) (Non living) (Artifact) (Furniture) (Portable) (Some-thing with legs) (Something with a back) (Something with a seat) (Seat for one)
so mixing up analytical properties and pieces of world knowledge; but at the same time he says that each of the concepts represented by the semantic markers «can itself be broken into components. For example the concept of an object represented by ‘(object)’ might be analyzed as an organization of parts that are spatio-temporally contiguous which form a
stable whole having an orientation in space» (1972:40).
If so, the tree of Figure 2.3 should host other markers such as ‘organization’, ‘part’, ‘orientation’, ‘space’, ‘contiguous’, and so on. Even ad-mitting that all these markers can be inserted into a bidimensional tree (and without asking what will happen when one decides to analyze, along with ‘object’, also ‘living’ or ‘furniture’, not to mention all the rest), we are not sure that markers such as ‘contiguous’ are of the same nature as ‘space’ or ‘animal’.
Moreover, to make the markers interpretable, usually a theory has to give up on their hierarchy and consider them as an unordered set, that is, it has to adopt a cross-classificatory criterion (cf. the remarks of Dean Fodor 1977:153). We have demonstrated that, if the tree is not hierarchi-cally organized, one has no more guarantees of dealing with a finite number of markers.
Thus either the primitives cannot be interpreted, and one cannot ex-plain the meaning of a term, or they can and must be interpreted, and one cannot limit their number. The latter is the case of the Porphyrian tree, in which the notion of differentia specified is posited exactly in order to provide a minimal, but sufficient, interpretation for every marker. Un-fortunately, as we shall see, as soon as the differentiae are introduced, a Porphyrian tree loses the properties of a dictionary and becomes an en-cyclopedia.
2.2· Critique of the Porphyrian tree
2.2.1. Aristotle on definition
Aristotle says that «definition is of the essence or essential nature» (Post, An. 2.90b30). To define a substance means to establish, among various accidental attributes, the essential ones, particularly that one which causes the substance to be as it is —its substantial form. The problem is then to «hunt» for the right attributes that must be predicated as ele-ments in the definition (96a15). Aristotle gives the example of the attri-butes that can apply to the number 3: an attribute such as ‘being’ un-doubtedly applies to 3, but also to other things that are not numbers. On the contrary, ‘oddness’ applies to every 3 and, even though it has a wider application (it also applies to 5), it nevertheless does not extend beyond the genus ‘number’. «We must select attributes of this kind, up to the point where, although each of them has a wider extension that the sub-ject, all together they have not; this will be the essence of the thing» (96a35). Aristotle means that, if one defines man as a rational, mortal animal, each of these attributes, singly, also applies to other entities (for instance, also horses are animals, dogs are mortals, angels are rational), but, taken as a whole, as a definitional cluster, these attributes apply only to man (thus definiens and definiendum are convertible or biconditionally linked: p = q).
However, a definition is not a demonstration: to show the essence
