In his attempt to find out a right method for inferring satisfactory definitions, Aristotle develops the theory of predicables, that is, the modes in which the categories can be applied to a subject. In Topics (1.101bl7— 24) Aristotle lists only four predicables, namely, genus, property (proprium), definition, and accident. Since Porphyry will defi-nitely list five predicables (genus, species, differentia, property, and ac-cident), this discrepancy has aroused many discussions. There was a serious reason why Aristotle did not insert the differentia among predic-ables: the differentia «being generic in character, it should be ranged with the genus» (Topics 1.10lb20), and to define consists in putting the subject into its genus and then adding the differentiae (Topics 6.139а30). Thus one can say that, in a way, the differentia is automatically (via genus and definition) inserted into the list. As far as the species is con-cerned, Aristotle does not mention it because the species cannot be predicated of anything, being the ultimate subject of any predication. Since, however, the species is expressed by the definition, this probably explains why Porphyry in his lists replaces species with definition.
2.2.2. The Porphyrian tree
In a long discussion in Posterior Analytics (2. I2.96b25— 97bi5), Aristotle outlines a series of rules for developing a right division from the most universal genera to the infimae species, by isolating at every step the right differentiae.
This is the method carried out by Porphyry in his Isagoge. The fact that Porphyry develops a theory of division in commenting upon Aristo-tle’s Categories (where the problem of differentia and genus is just men-tioned) is a matter that requires serious discussion (see Moody 1935) but is not relevant for the purposes of the present analysis. We can also disregard the discussion on the nature of universals, opened by the Isagoge though the commentary of Boethius. Porphyry says that he in-tends to «put aside the investigation of certain profound questions,» namely, whether genera or species exist in themselves or reside in mere concepts alone. As a matter of fact, he is the first to translate Aristotle s suggestion on definition under the form of a tree, and it is difficult to avoid the suspicion that he is portraying (rather iconically) a Neoplatonic chain of beings.
But we can disregard the metaphysics underlying the Porphyrian tree, since we are interested in the fact that this tree, independent of its alleged metaphysical grounds and conceived as a repre-sentation of mere logical relationships, has influenced all subsequent dis-cussions on the method of definition. We are not interested in the metaphysical perspective according to which Porphyry outlines a unique tree of substances, and it is doubtful whether Aristotle thought in this way or was more flexibly eager to imagine different and differently struc-tured trees according to the definitory problem he had to solve. Aristotle deals cautiously with this method of division and, if he seems to ap-preciate it in the Posterior Analytics, he seems to be more skeptical in Parts of Animals (6426bff). Nevertheless, Porphyry designed a unique tree for substances, and it is from this model that every subsequent idea of a dictionary-like representation stems.
Porphyry lists five predicables: genus, species, differentia, property, and accident. The five predicables establish the modes of definition for all the ten categories (substance plus nine accidents). It is therefore pos-sible to think of ten Porphyrian trees: one for substances, which allows, for instance, the definition of man as a rational mortal animal, and one for each of the other nine categories; for instance, a tree of qualities will allow the definition of purple as a species of the genus ‘red’. Aristotle said that even accidents are susceptible to definition, even though an accident can be said to have an essence only in reference to substances (Metaphysics 8.1028a10-1031a10). There are, thus, ten possible trees, but there is not a tree of the ten trees, because the Being is not a summumgenus.
Undoubtedly, the substance-tree proposed by Porphyry aims at being considered a finite set of genera and species (we will see in which sense this assumption is untenable); it is not said whether the other nine pos-sible trees are to be finite or not, and Porphyry is rather elusive on this subject.
The definition Porphyry gives of genus is a purely formal one: a genus is that to which the species is subordinate. Likewise the species is what is subordinate to a genus. Thus genus and species are relative to each other, that is, mutually definable. Any genus posited on a given node of the tree encompasses its dependent species, but each species becomes at its turn the genus of another underlying species, and so on, until the last row of the tree, where the species specialissimae or second substances are located. At the upper node of the tree there is the genus generalissimus (represented by the name of the category), and this genus cannot be the species of something else.
Thus every species postulates its upper genus, while the opposite does not hold. A genus can be ‘predicated of its species, while species ‘belong to’ their genus. However, a Porphyrian tree cannot be composed only of genera and species; otherwise, it would assume the format repre-sented in Figure 2.4. (Incidentally, in the Neoplatonic tradition, gods are listed among bodies and animals because they are intermediate natu ral forces, not to be identified with the inaccessible and immaterial One. The Christian medieval tradition adopts this example as a conventional assumption, more or less as modern logicians assume that the Morning Star is identical with the Evening Star).
substancesbody nonbody (incorporeal substances)
living being nonliving being
animal vegetal
rational animal
man god
irrational animal
horse cat
et ceteraFIGURE2.4
In a tree of this sort, man and god, as well as horse and cat, could not be distinguished from each other. Man is different from god because the former is mortal and the latter is not. The mortality of man represents his differentia. Now, the tree of Figure 2.4 does not account for differentiae.
In order to understand better the nature of differentia, one must care-fully distinguish between accident, differentia, and proprium. This is a crucial point, since accidents are not required to produce a definition, and the ‘property’ {proprium) has a curious status: it belongs to the spe-cies, but it is not required to build up the definition. There are different types of propria: (a) occurring in one species, although not in every member of it (as the capability of healing in men); (b) occurring in the whole species, but not in a single species only (as being two-footed); (c) occurring in the whole species, and only in a single one, but only at some time (as being grey in old age); (d) occurring in a whole species, only in a single one, and at every time (as the capacity of laughing in man). This last case is the one most frequently quoted in classical litera-ture and has an interesting feature: it is biconditionally equivalent with its subject (only men are laughing beings, and vice versa). The nature of proprium remains mysterious, both in Aristotle and in Porphyry, since it looks like something midway between an essential and analytic property and an encyclopedic and synthetic one.
Let us come back to the differentia. Differentiae can be separable from the subject (as to be hot, moving, ill), and in this sense they are mere accidents. But they can also be inseparable: some of them are inseparable but still accidental, as to be hook-nosed, but there are differentiae that belong to the subject per se, or essentially, as being rational, mortal, and capable of knowledge. These are the specific differentiae which are added to the genus in order to form the definition of the species.
Differentiae can be both divisive and constitutive. For instance, the genus ‘Living Beings’ is potentially divisible into the differentiae ‘sensi-tive/insensitive’ (endowed or not with sensitivity), but the differentia ‘sensitive’ can be composed with the genus ‘living being’ to constitute the genus ‘animal’. The genus ‘animal’ is divisible into ‘rational/ irra-tional’, but the difference ‘rational’ is constitutive (along with the genus it divides) of the species ‘animal rational animal’. Thus the differentiae divide a genus (the genus potentially contains these opposites) and are selected to constitute in fact a lower genus.
The Isagoge only suggests verbally the idea of the tree, but the medieval tradition has definitely built it up, as in Figure 2.5. In the tree of Figure 2.5, the dotted lines marks the divisive differentiae, while the continuous lines mark the same differentiae insofar as they are consid-ered constitutive.
2.2.3. A tree which is not a tree
It seems that the tree of Figure 2.5 does show the difference between man and God, but not the one between man and horse. As a matter of fact, all the instances of a Porphyrian tree, following a common standard, aim at showing how man can be defined and are therefore incomplete. In order to isolate the essence of horses, the diagram should display a different series of disjunctions on its right side so as to isolate (along with a rational animal) an irrational (and mortal) one. Even in this case, how-ever, a horse could not be
