CHAPTER XII.

DIVISION.

IN the old treatment of Logic the subject of Division is generally found to follow closely upon that of Definition. Widely as the conception of these two operations, as required for Inductive purposes, has departed from that which tradition has handed down, and the departure in the case of Division is far wider than in that of Definition,-it will be advisable still to keep to the usual order of discussion. We will begin with a few introductory remarks of comparison between these operations as regarded from the narrow and formal point of view.

Reverting then to the familiar fact that terms have, as a general rule, both Connotation and Denotation, we see that we may propose to analyse them under either aspect; but when we proceed to do this we see that these processes of analysis stand on a very different footing.

Definition, for instance, is from the nature of the case (1) a direct and (2) a formal process. (1) It is direct, because the Connotation consists of, i.e. actually is, the attributes which we are therein proposing to enumerate, and which we must therefore presume to be actually present to the mind of every one who is fully informed of the meaning of the word in question. Definition, on the other hand, as we saw, is open to the superficial objection that it tells us nothing, in telling us only what we are already supposed to know. (2) It is, for the same sort of reasons, formal. That is, a true Definition should not step outside the known connotation, nor therefore stand in need of any appeal to fresh experience; for such exceptional kinds of definition as those of a genetic character, and those which are

commonly called Descriptions, involve a departure from strict propriety of treatment.

That this purity of formal treatment could not quite be attained was true. For instance, we noticed that one practical way of abbreviating the process of simply enumerating all the items of the connotation, consisted in selecting some higher class or genus which included all but one of the constituent attributes, and then adding on this final one separately. This was the time-honoured method of assigning a Definition 'by genus and differentia'. Now it is clear that, if we attended to formal considerations only, there would be a complete ambiguity or indeterminateness in this process; for why should we select any one attribute rather than another to act as 'difference'? We should of course have as many such varieties of definition before us as there were attributes in the Connotation. This, however, was never allowed in the old treatment. Practical considerations, partly arising from conventions of language, partly suggested by convenience and common sense, hindered such excess of formality. It was always understood that there was a genus, to which each species naturally belonged, instead of a plurality to any of which it might equally be referred. Thus 'man' would never be referred to any other genus than 'animal', from which it was differenced by 'rationality'.

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Division, on the other hand, is indirect and material. It is indirect, because in strict formal logic it is the connotation. which is regarded as primary, the denotation being dependent upon this and therefore secondary. And this could hardly have been otherwise. In a mental stage which might be characterized as one of great clearness and consistency of thinking, but at the same time as one which was much lacking in material information, it was only natural that peculiar stress should be laid upon that element which could best be dealt with by mere introspection. The connotation demanded no knowledge over what range the things which possessed it might be spread, nor even whether there were any such things. Thus the mere meaning of Dragon and Ghost might admit of decision without much trouble; the real task was only commenced when we undertook to say when and where they were to be found. Hence in great part, as I

cannot but think, the preponderating importance attached to the subjective side of the term, viz. the connotation, which is so distinctive of the old logic.

We have greatly altered our comparative estimate in this respect, and must regard the two aspects of the term, the denotative and the connotative,-as being of equal importance, and as being both capable, according to the circumstances of the case, of taking the lead. If however we are asked which of the two must in general be regarded as the prior one, there can be no doubt that we must decide, with the old logicians, in favour of the connotation. We could not rationally start with a denotation pure and simple, and then try to fit on a connotation to it. To do this would involve taking a perfectly chance lot of things and ascertaining what set of attributes they happened to possess in common. What we always really do, of course, even in our nearest approaches to a random choice, is to start with some principle of selection and to choose under certain guiding restrictions, and this clearly implies a certain priority of the connotation over the denotation. This holds true of every class which we compose or select, and therefore the process of Division is generally an indirect one as compared with Definition; it presupposes, if not a complete definition, at any rate some knowledge of the attributes possessed by the things which, through our process of selection, are to constitute a division of the assigned class.

Division, again, is material rather than formal; that is, it demands a fresh appeal to the subject-matter. It cannot be carried on, at least not to any rational purpose, by a mere consideration of the materials in hand. Of course we might take a random lot of things, as above indicated, and break this up again at random, and call this process one of Division; but if the division is to be of any value we must appeal to accidental attributes, viz. to such as are not supposed to be given in or with the notion itself. This is obvious, for every attribute which is included in the connotation must be present in every member without exception of the individuals denoted, so that we cannot introduce any ground of separation amongst these individuals by the retention or omission of any one of these attributes. If we are to distinguish amongst them it

must be by appeal to attributes which are accidental, i.e. which are discovered by a fresh appeal to experience. It is this circumstance which has induced some purists in Formal Logic,-e.g. Mansel,-to object altogether to the introduction of the process of Division.

For such reasons as these it is obvious that very little can be made of this subject in its ungeneralized or non-inductive treatment, and that what little has been said about it has always involved some transgression of strict formal considerations. Some notice however must here be taken of the old method of treatment, if only for the purpose of showing how and where enlargement is called for when we turn to a broader view of the subject.

The Porphyrian Tree. The process of division found its main expression in what is commonly called the Porphyrian Tree. To understand the nature of this we must step back a moment to the doctrine of the Categories or Predicaments. It is often supposed,—as indeed is expressly stated by Mill,—that what was aimed at in these was the same sort of thing as is aimed at by the modern logician when he attempts a summary classification of all the objects with which his science proposes to deal. This however was by no means the case. The famous ten categories, whatever may have been the intention of their propounder, were by the later Aristotelians expressly denied to be all-embracive. They only professed to be general heads of predication, that is, to be a classification of all possible predicates. Now, from the nature of the case, there may be things fitted to be the subjects of propositions which could not well be predicates, and these were omitted from the Categories:'God', for instance, was excluded from the list. What was aimed at in fact was something very practical, the want of which must often have been felt in the disputations of the schools. When a given thesis was proposed for attack and defence the disputant was constantly in want of middle terms whereby to connect his conclusion with some admitted premise. The Categories were his hunting ground for this purpose; and rules were given for guiding his search, directing him to which class to appeal and how to limit his enquiries within its field. But it was never contemplated that every logical entity was to find a place there.

Another practical departure from the modern conception, as expressed by Mill, is to be found in the fact that no attempt was made to embrace the ten categories under one general head, that of being'. Each of the highest divisions was considered as truly 'sui generis', that is, as belonging to the highest class of which account need be taken in Logic, which was reasonable enough from the practical point of view. But, starting with any one of these upper classes, the division downwards was carried on with some care. As several of the technical terms still in use in Logic, and even in common life, are not easily intelligible without reference to the processes adopted by the older logicians we shall find it convenient to take a simple example. Start, for instance, with the first of the categoric classes, viz. that of substance. It is thus divided by Seton'.

Such an arrangement as this is called the Porphyrian Tree; a few remarks may be offered in explanation of some of its characteristics.

(1) For one thing, it may be remarked in passing, the whole of this arrangement was collectively called the Category. In the modern usage this name is confined to the uppermost class, i.e. substantia'.

1 Dialectica: a small volume much used at Cambridge in the seventeenth century. In the Aristippus (about 1630) of Thomas Randolf, fellow of Trinity, a sort of students' chorus occurs in which are the words

"I'll be no more beaten for greasy Jack Seaton

Or conning of Sandersonus."