pecially if it has a spire upon it. A child, again, whose uncle has been excessively fond, and his schoolmaster very severe, easily believes that fondness always belongs to uncles, and that severity is essential to masters or instructors. He has seen also soldiers with red coats, or ministers with long black gowns, and therefore he persuades himself that these garbs are essential to the character, and that he is not a minister who has not a long black gown, nor can he be a soldier who is not dressed in red. It would be well if all such mistakes ended in childhood.' I can add an instance from my own experience. I was taken as a child to see the Crystal Palace. From that day onwards right on to advanced boyhood I firmly believed that a palace was not a palace unless it was made of crystal. Palace and stone were two ideas that would not blend in my mind until my further reading gave the necessary shocks to this old superstition, and the power of reflective thought at length slowly dissolved it. Real or Scientific Definition. Of all the special purposes we have in view in framing definitions, one stands out pre-eminently above all others that of meeting the requirements of Science. The logical function of Definition is here adjusted to the ideal of a systematized knowledge of Nature, and consists in the removal of all ambiguities which arise in the pursuit of this ideal. It will be readily understood that the definitions which are required for ordering our meanings within the vastly complex network of relations which subserve the organization of Science cannot be reached in quite so simple a manner as can the occasional definitions which subserve our varied practical interests. Thus, the mere process of comparing one concept with another will not in any way suffice to define a fundamental physical concept such as that of inertia, weight, mass, or gravitation. In each of these concepts we have the condensed expression of great scientific discoveries, the embodiment of highly elaborated theory; hence the path to definition here lies not in a process of simple comparison, but in a searching analysis of the interactions and interrelations of the facts of Nature. In Geometry such analysis proceeds by the help of construction, and it is by ideally constructing its concepts-e.g., those of straight line and circle-that the definitions of Geometry are reached. Here the specifying mark is genetic, a mark embodying a rule of construction. Thus, 'The circumference of a circle is a line traced by a point which moves in one plane at a constant distance from a fixed point in that plane.' Cf. also the definition of a circle as a section of a cone drawn square to its axis. Outside Geometry the genetic definition is not usual, though it is common in Chemistry, when we wish to define compounds as made up of their elements. The main interest which Science has in defining the terms it uses is in connexion with the problem of Classification. Order is here the dominating need, and the work of definition is therefore dominated by this general requirement of order. Thus the relatively simple and schematic requirements of formal definition are quite inadequate for the purposes of Science: the distinction between formal and scientific definition is inevitable; but the main value of a distinction of this kind would be lost if, by insisting on it, we were in any way to obscure the essential unity of the defining process at whatever stage of thought we choose to consider it. In formal and in scientific definition alike we have necessarily to define by relations, and in reference to a purpose stated or implied. In formal definition the subjective reference to purpose is more conspicuous than the objective relatedness to a system of kindred meanings. But the connexion of the defined meaning, through its very definition, with a system of interrelated meanings is none the less present for not being so obvious. If, in the interest of some restricted purpose, we find it sufficient to define 'Man' as 'rational animal,' we have still three closely related meanings-those of humanity, rationality, and animality-systematically involved in the definition. Thus formal definition is essentially relational in character, though in some cases the relational reference is more apparent than in others. 'King' can hardly be defined without explicit reference to the relations in which Kingship stands to the government of the country ruled ; and in a whole class of cases-the so-called class of correlatives (e.g., 'Whole and part,' 'Genus and species ')-the definition of either term involves the statement of its relation to the other. In scientific definition, where meanings are so much more systematically interconnected, the relatedness of the defined meaning, as defined, to a system of kindred meanings is a much more patent characteristic of the definition than is the reference to purpose, which here comes more definitely under objective control. It is true that different sciences have different points of view, but the reference to purpose which this distinction in view-point involves is implied rather than expressed, whereas the relatedness of the meaning to be defined to a whole system of other meanings tends to enter more and more explicitly into the very structure of the definition itself. The essential unity of the defining process, whether formal or real, practical or scientific, is perhaps brought out most clearly by the consideration that the process of 'comparison' through which our practical or occasional definitions are obtained is only a special, simple case of the more general procedure of analysis and synthesis, which we utilize in all definition processes of a scientific character. To have defined a term or concept scientifically is to have analyzed its relations to other concepts characteristic of the same scientific system, and to have then synthesized these relations in the simplest and most relevant way possible. But this involves just those very processes of criticism and reconstruction which we shall find indispensable in formal definition when we endeavour to remodel certain given definitions in a methodical manner (vide Chapter III.). Note on the Categories. It has for long been customary to preface a doctrine of Terms with a statement about 'Categories.' There are forms of thinking about reality which are, in a certain important sense, irreducible. Activity is not passivity, time is not place, nor quantity quality, nor substance relation. If we add to these eight varieties the concepts of state' and 'situation,' we have before us Aristotle's complete list of Categories-that is, of 'predicates one or other of which must in the last resort be affirmed of any subject, if we ask what in itself it is' (Joseph, ibid., p. 38). In his excellent chapter on the Categories (ibid., ch.iii.), Mr. Joseph insists on the importance of this ancient enumeration of the ultimate forms of being. Of the importance of a theory of Categories from the point of view of an analysis of knowledge there can be no possible doubt. The subject is, indeed, so important that, were the discussion once broached, a thorough-going treatment would be indispensable. Mr. Joseph has done invaluable service in so lucidly connecting the Aristotelian and Kantian doctrines of the Categories; but, by the very necessities of an 'introductory' discussion, the story of the Categories is made to end with this reconcilement of Aristotle and Kant, and the great attempt of Hegel to systematize the Categories afresh from the point of view of Thought's own logical development is completely ignored. But even Hegel has not said the last word. There are Neo-Hegelian improvements, post-Hegelian developments, and antiHegelian reactions; there are even some who choose to ignore Hegel altogether. The Categories are, in fact, 'living options,' and cannot be adequately discussed as monuments, however imperishable, of a past that has no longer any relation to the present. It seemed better, therefore, not to enter upon any systematic discussion of the Categories. At this initial stage, at any rate, logical propriety required that the Categories should yield precedence to the Predicables, and that the discussion of terms 'according to the nature of their meaning' should make way for that more relevant discussion of them which is 'based upon the relation in which a predicate may stand to the subject of which it is predicated' (ibid., p. 53). [On the whole subject of Predicables and of Categories, Mr. Joseph's masterly treatment ('An Introduction to Logic,' ch. iii. and iv.) cannot be too strongly recommended, even by those who venture to differ from the Aristotelian standpoint from which those two chapters are written.] CHAPTER III. II. (iii.) THE TESTING OF DEFINITIONS. Rules towards securing Soundness in Definition. 1. We must distinguish definitions from translations and derivations. E.g., if we have two equivalent symbols for one and the same idea, we do not define the one symbol by substituting the other for it. To say that 'dyspepsia' is indigestion, or that a laundress is a washerwoman, is not to state what dyspepsia or laundress means. Such statements are sometimes called circular definitions; but why call them definitions at all? They have as little title to be called definitions as have the statements, 'Anima is the soul,' 'Mère is mother.' So, again, such statements as 'Sycophant means figshewer' (σῦκον φαίνω) suggest mere derivations. They answer the question, 'What did the word mean once?' not, 'What does it mean now?' They derive but do not define the term. Still a derivation is in a sense a fossil definition, and so has more right to the name than a mere translation. It might be reasonable to refer to it as an etymological definition. The statement 'Assiduity is sitting close to one's work' is an etymological definition, so far as sitting close' is concerned. 2. We must see that the definition fits that it is neither too narrow nor too wide, that it exactly expresses the meaning we wish to convey by the term we use. In other words, definiendum and definition must be commensurate with each other-i.e., whatever can be relevantly predicated of the object defined must be predicable of the definition also, and vice versa. This is, perhaps, the most important rule of all, and can best be observed by always adopting the natural method of defining, which consists in comparing the word or class to be defined with those other words or classes which approach it most closely in sense. This natural method of defining by simple comparison of what is most allied in meaning ensures a proximate genus being reached instead of some remoter genus; and, further, the differentia can be so chosen as to cover just the one species, and exclude all the sister-species, the class-terms most liable to be confused with it. If the genus is not proximate, the definition is likely to be too wide. Suppose I wish to define 'square.' I compare it with 'rhombus,' and find at once, as genus, equilateral quadrilateral, and as differentia, rectangular; or I compare it with 'oblong,' and find at once, as genus, rectangular quadrilateral, and as differentia, equilateral. But if I reach my definition through comparison with terms less closely allied in meaning, the definition is less likely to fit well. Thus if I compare square' with 'circle,' the obvious genus is 'plane figure.' The square is then quite sufficiently distinguished from the circle by means of the differentia 'rectilinear.' But the resulting definition, 'A square is a rectilinear plane figure,' is very much too wide. As an important corollary from this second rule we have the requirement that a definition should contain nothing superfluous. Thus, the following attempt at defining a tip' obviously needs pruning: 'A tip is an extra gratuity paid out of goodwill over and above what can be demanded by contract.' Here 'extra,' gratuity,' 'over and above' all involve the same idea. When reduced to the more economical and 'fitting' form, 'A tip is a gift paid out of goodwill, the definition, though still faulty, is much improved. When practically applying this rule, we may profitably guide ourselves by the following test-questions : (i.) Do all the kinds of objects denoted by the term possess the differentia given? If not, the definition is, to this extent, too narrow. Example: A dog is a domestic animal. Are all kinds of dogs domestic? No; 'dingoes' are wild. Therefore, the definition fails to include all kinds of dogs, and is consequently too narrow. (ii.) Having ascertained that the definition is not too narrow, we ask, 'Is it too wide?' This test-question we may state in two equivalent forms: (a) Are there no other terms that satisfy the same definition? (b) Is the definition simply convertible ?-i.e., given that A is B, is it equally true that Bis A? Example: The house-dog is a domestic animal that barks. Is it equally true to say that a domestic animal that barks is a house-dog? 3. The terms of a definition must be of the same order as the term defined. They must not be figurative or metaphorical. A metaphor is* 'the use of a word in a transferred sense, the transference being from the order to which it properly belongs to some other order.' Thus, if I define 'faith' as 'the eye of the soul,' I am transferring to the spiritual order the word ' eye,' which belongs to the physical order, and primarily means an organ of the body. So in the definition of a camel as 'the ship of the desert,' the term ship' is transferred from the inorganic to the organic order. The definition, in fact, must be homogeneous throughout with the term defined. ! Example. Logic is the medicine of the mind. * Father Clarke, 'Logic,' p. 222. |