2. Of fanciful or arbitrary principles. The following divisions are perhaps true enough on other grounds, but they suffer from the fact that they seem to be based on a mere analogy or fancy: "For civil history, it is of three kinds; not unfitly to be compared with the three kinds of pictures or images. For of pictures or images, we see some are unfinished, some are perfect, and some are defaced. So of histories we may find three kinds, memorials, perfect histories, and antiquities; for memorials are history unfinished, or the first or rough drafts of history; and antiquities are history defaced, or some remnants of history which have casually escaped the shipwreck of time." 1 If, instead of this analogy, he had avowed the principle of state of material, his division would have had the authenticity of logical classification. "The knowledge of man is as the waters, some descending from above, and some springing from beneath; the one informed by the light of nature, the other inspired by divine revelation. The light of nature consisteth in the notions of the mind and the reports of the senses: for as for knowledge which man receiveth by teaching, it is cumulative and not original; as in a water that besides his own springhead is fed with other springs and streams. So then, according to these two differing illuminations or originals, knowledge is first of all divided into divinity and philosophy." 2 In this last sentence the logical principle, the principle of origin, is brought out; but the analogy of waters, while giving imaginative zest to the division, obscures its logical soundness. 2. The MEMBERS of the division. By these are meant the several parts or distinctions which add together to make up the whole. Of these it is requisite: first, that no one member cover the whole field of division, there must be more than one member, otherwise there is no division at all; secondly, that all the members together cover the whole field, no more and no less; thirdly, that each member exclude from its particular field each and every other. NOTE. — If, for example, a classification of geometrical figures should contain plane figures, parallelograms, rectangles, and polygons, the members would not be mutually exclusive, for plane figures would include all the others, and parallelograms would include also rectangles. Nor would 1 BACON, Advancement of Learning, Book ii, p. 90. 2 lb., p. 105. the members taken together equal the whole, because solid figures are not included under the dividing members at all. In fact, the first division of all, which should be into plane and solid, is neglected, and the members given are really subdivisions of plane figures. A sense of the need of exclusion between dividing members is recognized in the commonest thinking. For example, the old colloquial description of something nondescript or anomalous as "neither fish nor flesh nor good red herring" derives its point from the fact that the first member includes also the third. 3. The COMPLETENESS of the division. The requisite that the dividing members taken together shall equal the divided whole gives rise to the chief difficulty in logical division, the difficulty, namely, of making sure that all the coördinate distinctions of the case are mentioned. Any distinction left out might, if supplied, invalidate the whole process; hence the necessity of covering the whole field. The simplest guarantee of completeness in division is what is called bifurcate classification, wherein each superior class is divided into two inferior classes distinguished by the possession or non-possession of the quality taken as basis. While in some cases this manner of division is barren, even absurd, it is especially useful in preparing a question for indirect argument1; useful also in determining the relative rank of a quality, whether immediate or mediate, whether a main division or a subdivision.2 Thus, by this method angles would be classified as 1. Right Angles. 2. (Not right) Oblique Angles { 1 See below, p. 623. Acute (less than right). 2"It would be a great mistake to regard this arrangement as in any way a peculiar or special method; it is not only a natural and important one, but it is the inevitable and only system which is logically perfect, according to the fundamental laws of thought."- JEVONS, Principles of Science, Vol. ii, p. 371. Another name for this manner of division is dichotomy. In ancient Greek logic the illustration of it, as it was carried out to successive subdivisions, was called the Tree of Porphyry. See HYSLOP, Elements of Logic, p. 97. Here evidently the whole field is covered. So also Lord Bacon's classification of natural history, though given by him in three divisions, reduces itself to the bifurcate division with subdivision:: Perverted marvels. 2. Nature not in course {Perverted-mar For literary purposes, however, the taking of a larger number of divisions has the advantage of obviating the necessity of so minute subdivision; while in many cases such a range or circuit of thinking may be devised as to contain a guarantee of completeness. The divisions worked for, in any case, in order to cover the field, must be few and fundamental, not numerous or minute. EXAMPLES. Lord Bacon's triplicate division of philosophy contains by its very expression a sense of completeness: "In philosophy the contemplations of man do either penetrate unto God, or are circumferred to nature, or are reflected or reverted upon himself. Out of which several inquiries there do arise three knowledges: divine philosophy, natural philosophy, and human philosophy or humanity. For all things are marked and stamped with this triple character, of the power of God, the difference of nature, and the use of man.”1 Similarly, the division reduced to bifurcate above, by its simple passing over one stage of subdivision leaves the triple division as complete in sense as the other: "History of nature is of three sorts of nature in course; of nature erring or varying; and of nature altered or wrought; that is, history of creatures, history of marvels, and history of arts.” 2 2. Literary Division, or Partition. The partition of a subject for literary treatment, while the same in essential method as expository division, differs in its object, which is not so much exhaustive classification as convenience and pointedness. It seeks, that is, so to display the articulation of an idea as to help the reader's memory and realizing power in retaining it. On this aspect of division, two remarks are important. 1 BACON, Advancement of Learning, Book ii, p. 105. 2 Ib., p. 86. 1. While the partition may or may not, on its chosen scale, exhaust the aspects of the subject, it is made as an enumeration of topics for present treatment, and lays no claim to completeness. Its divisions, too, do not necessarily relate to the subject as species to genus; they are conceived merely as a way of sweeping broadly over the field of discussion. Fulness of treatment requires that no obvious department of the subject, and especially none whose presence would modify or invalidate the rest, be left out. At the same time, its distinctness from the stricter exposition should be apparent; it should show for what it is, a partition. This fact is generally made clear by an expressed or implied disavowal of complete classification, amounting to a limitation of the writer's claim. 2. The divisions thus made have not the necessity of severity which strict exposition has; they may be expressed in epigram, or figure, or be determined by analogy, as the pointedness of the thought may gain thereby. At the same time, this kind of division will no more bear to be fanciful or arbitrary than will logical division; it still aims to be logically sound, though the severity of the process is covered up; and these literary forms of expression are intended as aids in displaying and enforcing a natural current of thought. EXAMPLES. .—1. Of the subject, the plan of which is given on p. 449, above, Burke thus announces the partition, also justifying the pains he has taken in thus dividing it : "My second condition, necessary to justify me in touching the charter, is, whether the Company's abuse of their trust, with regard to this great object, be an abuse of great atrocity. I shall beg your permission to consider their conduct in two lights: first, the political, and then the commercial. Their political conduct (for distinctness) I divide again into two heads: the external, in which I mean to comprehend their conduct in their federal capacity, as it relates to powers and states independent, or that not long since were such; the other internal, namely, their conduct to the countries either immediately subject to the Company, or to those who, under the apparent government of native sovereigns, are in a state much lower, and much more miserable, than common subjection. "The attention, sir, which I wish to preserve to method will not be considered as unnecessary or affected. Nothing else can help me to selection, out of the infinite mass of materials which have passed under my eye, or can keep my mind steady to the great leading points I have in view."1 2. We can rightly estimate now the divisions from Bacon which are criticised on p. 571, above. As determining a principle of division, the analogies there given are fallacious; we cannot lean weight upon them; but as mere illustration and mnemonic to aid in the literary expression of the division they have their value. II. EXPOSITION OF THE SYMBOLS OF THINGS. Distinction must be made between actual objects on the one side and the terms that name them on the other. These latter are not things, but only the symbols of things, serving as the means of bringing the things themselves into consciousness and comprehension. As such they are subject to the infirmities of every vehicle of expression. Language is a potent working-tool, but not perfect; and its imperfection is most felt, naturally, where it has the finest and exactest work to do. On the expositor's side it may not name all that he has in mind; on the reader's side it may fail to convey a just or full conception. Accordingly, an essential branch of exposition — half of it, we may say has to be taken up with these more or less inadequate symbols of things; their meaning has to be fixed, sources of error have to be eliminated, simplifying and elucidative terms have to be adduced. To some extent this kind of exposition points back over the road that we have come: it takes up again the use of words, syntax, emphasis, connotation, the various ways of conveying and implying thought. But this it does in inverse approach; not now in the attitude of creativeness, but rather of criticism and interpretation. The work that other minds 1 BURKE, Speech on The East India Bill, Select British Eloquence, p. 316. |