Here we see that wherever A is C is also found, so that C is a generic property; D occurs always with B, so that it constitutes a specific property, while E is indifferently present and absent, so as not to be in any way correlated with any of the other letters; it represents, therefore, an accident. It will now be seen that the Logical Abecedarium really represents an interminable series of subordinate genera and species; it is but a concise symbolic statement of what was involved in the ancient doctrine of the Predicables.

Summum Genus and Infima Species.

As a genus means any class whatever which is regarded as composed of minor classes or species, it follows that the same class will be a genus in one point of view and a species in another. Metal is a genus as regards alkaline metal, a species as regards element, and any extensive system of classes consists of a series of subordinate, or as they are technically called, subaltern genera and species. The question, however, arises, whether any such chain of classes has a definite termination at either end. The doctrine of the old logicians was to the effect that it terminated upwards in a genus generalissimum or summum genus, which was not a species of any wider class. Some very general notion, such as substance, object or thing, was supposed to be so comprehensive as to include all thinkable objects, and for all practical purposes this might be so. But as I have already explained (vol. i. p. 88), we cannot really think of any object or class without thereby separating it from what is not that object or class. All thinking is relative, and implies discrimination, so that every class and every logical notion must have its negative. If so, there is no such thing as a summum

genus, for we cannot frame the requisite notion of a class forming it without implying the existence of another class discriminated from it, but which with the supposed summum genus will form the species of a still higher genus, which is absurd.

Although there is no absolute summum genus, nevertheless relatively to any branch of knowledge or any special argument, there is always some class or notion which bounds our horizon as it were. The chemist restricts his view to material substances and the forces manifested in them; the mathematician extends his view so as to comprehend all notions capable of numerical discrimination. The biologist, on the other hand, has a narrower sphere containing only organized bodies, and of these the botanist and the zoologist take parts. In other subjects there may be a still narrower summum genus, as when the lawyer regards only living and reasoning beings of his own country.

In the description of the Logical Abecedarium, it was pointed out (vol. i. p. 108) that every series of combinations was really the development of some one single class, denoted by X, which letter indeed was accordingly placed in the first column of the table on p. 109. This is the formal acknowledgment of the principle clearly stated by De Morgan, that all reasoning proceeds within some assumed summum genus. But at the same time the fact that X as a logical term must have its negative x, shows that it cannot be an absolute summum genus.

There arises, again, the question whether there be any such thing as an infima species, which cannot be divided into any smaller species. The ancient logicians were of opinion that there always was some assignable class which could only be divided into individuals, but this doctrine appears to me theoretically incorrect, as Mr. George

Bentham indeed long ago stated P. We may always put an arbitrary limit to the subdivisions of our classification at any point convenient to our purpose. The crystallographer would not generally consider as different species of crystalline form those which differ only in the degree of development of the faces. The naturalist overlooks innumerable slight differences between plants or animals which he refers to the same species. But in a strictly logical point of view classification might be carried on so long as there is a single point of difference, however minute, between two objects, and we might thus go on until we arrived at individual objects which are numerically distinct in the logical sense attributed to that expression in the chapter upon Number. We must either, then, call the individual the infima species or allow that there is no such species at all.

The Tree of Porphyry.

The bifurcate method of classification, arising as it does from the primary laws of thought, is the very foundation of all strict scientific method, and its application in formal logic constitutes the method of Indirect Inference, of which the nature and importance were shown in Chapter VI. So slight, however, has been the attention paid to this all important subject, that I shall in this case break the rule which I have laid down for myself, not to mingle the subject of logic as a science with the history of logic.

Both Plato and Aristotle were fully acquainted with the value of bifurcate division which they occasionally employed in an explicit manner. It is impossible, too,

Outline of a New System of Logic,' 1827, p. 117.

6

that Aristotle should state the laws of thought, and
employ the predicables without implicitly recognising the
logical necessity of that method. It is, however, in Por-
phyry's remarkable and in many respects excellent Intro-
duction to the Categories of Aristotle' that we find the
most distinct account of it. Porphyry not only fully and
accurately describes the Predicables, but incidently intro-
duces an example for illustrating those predicables, which
constitutes a good specimen of bifurcate classification.
Translating his words freely we may say that he takes
Substance as the genus to be divided, under which are
successively placed as Species-Body, Animated Body,
Animal, Rational Animal, and Man. Under Man, again,
come Socrates, Plato, and other particular men. Now of
these notions Substance is the genus generalissimum, and
is a genus only, not a species. Man, on the other hand,
is the species specialissima (infima species), and is a species
only, not a genus. Body is a species of substance, but a
genus of animated body, which, again, is a species of body
but a genus of animal. Animal is a species of animated
body, but a genus of rational animal, which, again, is
a species of animal, but a genus of man. Finally, man
is a species of rational animal, but is a species merely
and not a genus, being divisible only into particular

men.

Porphyry proceeds at some length to employ his example in further illustration of the predicables. We do not find in Porphyry's own work any scheme or diagram exhibiting this curious specimen of classification, but some of the earlier commentators and epitome writers drew what has long been called the Tree of Porphyry.

Thus in the 'Epitome Logica' of Nicephorus Blemmidas,

a 'Porphyrii Isagoge,' Caput ii. 24.

r

we find a diagram of which the following is nearly

facsimile:

ἡ ουσία

διαιρῆται

εἰς

σῶμα ἀσώματον

ἔμψυχον ἄψυχον

αἰσθητικὸν ἀναίσθητον

μεταβατικὸν ἀμετάβατον

λογικὸν ἄλογον τὸν ἄνθρωπον.

In the above scheme we find the bifurcate principle accurately but not completely applied. Each genus is subdivided into two species, described by a pair of positive and negative terms, so that the species are together equal in extent to the genus. But it will of course be observed that each negative branch is left without further subdivision, so that there is only a single infima species, namely man, instead of thirty-two final branches, as there would be in a theoretically complete system.

This tree was subsequently reproduced in the works of a multitude of logicians in a form which is more complicated and not so good as that of Nicephorus. Thus Epitome Logica, Augustæ Vindel.' 1605, p. 118.

r