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certain points-P1, P2, P3, P4. The objects are then said to be classed, and the class-name defined, by these common marksP1, P2, P3, P. Anything that possesses these common marks is then designated by the class-name, also called the general name. Further, the class-name, as such, cannot possibly specify distinctions between the included sub-classes. The name 'horse' cannot inform me whether a cart-horse or a race-horse is in question. If I wish, therefore, to specify a particular section of a class, or, in other words, to differentiate a species from the genus, I must add a qualifying mark, or differentia. Thus, if I wish to define the kind or species of vehicle known as 'omnibus,' I ask myself : What is the genus or class under which this species falls, and what is the differentia, or specific mark, whereby it is distinguishable from whatever other species fall under the same genus ? Now, practically, as we have seen, we answer this question by bringing together as many words with closely related meanings as possible, and comparing them. Let us compare 'omnibus,' for example, with 'tram.' The terms agree in designating four-wheeled public vehicles; they differ essentially in this: that, whereas the one designates such vehicles of this kind as are confined to rails, the other designates such as are not confined to rails.

Genus: Four-wheeled public vehicle.

Species: Omnibus.

Tram.

Differentia: Not confined to rails.

Confined to rails.

If we had compared the two terms 'omnibus' and 'cab,' we should

have had some such result as this :

Genus: Four-wheeled public vehicle, not confined to rails.

Species: Omnibus.

Differentia: Keeping to well

defined routes.

Cab.

Not keeping to well

defined routes.

If we had compared 'omnibus,' 'cab,' 'tram' together, we should

have had some such result as this :

Genus: Four-wheeled public vehicle.

Species: Omnibus. Differentia: Keeping to well-defined routes, and not confined to rails.

Tram.

Keeping to well-defined
routes, and confined
to rails.

Cab.

Not keeping to welldefined routes, and not confined to rails.

This defining by direct comparison, and by assigning genus and differentia, is by far the most convenient for practical purposes; for it is of the essence of practical requirement that it should adapt itself to the exigencies of the specific occasion. The definition found by consulting a dictionary is likely to have this defect: that it will not precisely suit the occasion. The only way in which to make defirition relevant is to select for ourselves the kindred terms with which the term in question is in risk of being confused, and then to note, from the point of view that happens to be interesting us, the differentia which distinguishes its use from that of all these kindred terms.

The Relation of Genus to Differentia.

Taken together, Genus and Differentia state the marks essential to the definition. They include just those features which are logically indispensable for the unambiguous statement of our meaning.

The relation, however, between the two types of definition-mark -the generic and the specific cannot be adequately represented by placing them side by side as though they were of co-ordinate significance. The differentia, as the specific mark, specifies, and therefore logically presupposes, the generic mark or genus : it is a specification of the genus. And, though the process of comparison through which our occasional definitions are framed does not explicitly bring out this connexion, the connexion is none the less definitely implied. It is concealed only by the logical incompleteness of the comparison process as we conduct it. Were this process thorough-going, the marks of agreement between two terms would include not only determinate, but also indeterminate marks, so far as these latter were relevant to our purpose in defining; and the differentia would then reveal itself quite naturally as a specification of one or other of these indeterminate marks of agreement. To define 'tram,' we compare it with 'omnibus,' from the point of view, say, of public transit. The two terms agree determinately in signifying four-wheeled public vehicles, but they also agree indeterminately in requiring some distinctive method of proceeding from starting-point to destination. The differentia 'confined to rails' just specifies what this distinctive method must be in the case of a tram. It is thus only in relation to the indeterminate elements of the genus that we could endorse Mr. Joseph's contention that 'the genus is the general type or plan, the differentia the "specific " mode in which that is realized or developed.'*

Let us take an illustration suggested by Mr. Joseph himself. The genus of A and N might be taken as 'plane rectilinear three-sided construction, possessing some specifiable arrangement of the three sides.' The differentia of the term 'triangle '-namely, 'enclosing a space '-would then be a specification of the above indeterminate mark; in the case of a triangular construction, the sides are so arranged as to enclose a space.†

* Joseph, 'An Introduction to Logic, p. 68. Cf. p. 70.

† Mr. Joseph points out that the conception of 'species' as the specification of the 'genus' forbids our describing a genus as a larger class including the smaller If further justification be required for the admission of the indeterminate mark into the structure of a definition, we may find it in the fact that it is necessitated by the very nature of the generalization process through which our definition is reached. The process of Generalization-or of its main feature, Abstraction-may be so understood as to stultify the attempt to connect genus and species vitally together. We may understand by it a process whereby differences are ruthlessly eliminated, and points of agreement reduced to mere identities-identities disengaged from all relation to difference. But if the abstraction of genus from species implies this logical isolation of the marks of agreement from the marks of difference, it is manifestly impossible to consider the species as specifications of the genus. If in mounting, through generalization, from species to genus, we sever the vital bond between the lower and the higher class, we cannot, when descending, through differentiation, from genus to species, behave as though this bond were still unsevered.

But it is surely gratuitous to suppose that generalization (or abstraction) is a devitalizing process of this kind. It is, of course, possible to conceive it after this fashion, and the Formal Logician has almost invariably done so. But just in so far as we embrace a true conception of identity, and abandon the old static view of it as typified in the formula 'A is A,' we are compelled to entertain new ideas about Abstraction. To abstract agreement from difference, we find, is not to isolate them one from another, but to connect them in a new way. It is through the Abstraction process itself that the difference becomes a specification of the agreement-the agreement a generalization of the difference. Abstraction does not take us from differences that have no identical element to identities that are out of all relation to differences: it takes us from the determinate to the relatively indeterminate. But the indeterminate so reached still points back to the specifications from which it has been abstracted. ‘Colour' does not mean that which is neither violet, nor red, nor blue, nor any other colour; it means 'colour of some kind,' and, when its meaning is pressed a little further, it is seen to signify 'violet, or red, or blue, or some other colour.' As abstracted from these differences, it still stands to them in what

classes or species within it, and consequently renders the attempt to represent the relation by means of two circles, one within the other, entirely misleading. The word "class," he says (ibid., p. 69), 'suggests a collection, whereas the genus of anything is not a collection to which it belongs, but a scheme which it realizes.' Now, in so far as we are reading the class in intension or conno-denotation (vide p. 72), it is undoubtedly necessary, in the sense above described, to consider it 'as something realized in its various members in a particular way' (ibid., p. 71); but from the point of view of extension (vide p. 158) it is at least reasonable, and may be purposive, to depict the objects indicated by the class-term as included within the larger number of objects indicated by second class-term. But to admit this is to admit that the one class (extensively defined) can be included within the other class (also extensively defined).

a

is at least a pre-disjunctive relation. The genus, as abstracted from the species, still points back to the species from which it has been abstracted. A man is a rational (animal of some kind); an animal is a sentient (organism of some kind). We conclude, then, that Generalization (or Abstraction), when properly interpreted, works in the service of the logical evolution of meaning. The genus. qua abstract vestige, is potentially the rudiment or germ of which the species are the specifications. It requires but the interest in the logical development of meaning to transform it actually from the one to the other.*

The Predicables.

The theory of practical definition, as outlined in the foregoing discussion, is closely connected with the Aristotelian doctrine of the Predicables. The Predicables, for Aristotle, were the various kinds of attribute which might be predicated of a subject. If I make the statement 'S is P' (where S is a class-concept), P may stand to S in any one of five possible relations. It may be its definition-i.e., it may give the genus and differentia of S. Or it may be the genus alone or the differentia alone. Finally, it may give a property or proprium of S, or else an accident. These 'heads of predicables,' as they are sometimes called, 'have passed,' to quote Mr. Joseph again, into the language of science and of ordinary conversation. We ask how to define virtue, momentum, air, or a triangle; we say that the pansy is a species of Viola, limited monarchy a species of constitution; that one genus contains more species than another; that the crab and the lobster are generically different; that man is differentiated from the lower animals by the possession of reason; that quinine is a medicine with many valuable properties; that the jury brought in a verdict of accidental death; and so forth' (ibid., p. 54).

There is a later scheme of Predicables connected with the name of Porphyry, a logician who wrote some six hundred years after Aristotle. Superficially, the sole difference between Porphyry's scheme of Predicables, as given in his Εἰσαγωγή, and the older scheme of Aristotle himself, appears to be the substitution of the predicable of 'species' for the predicable of 'definition.' The predicables, for Porphyry, are genus, species, differentia, proprium, and accidens. But the substitution in question conceals a more fundamental disagreement between the two schemes. In the case of Aristotle the subject-term meant a common nature, a kind, species. or universal, and not the individual object as such. The predicables were, therefore, one and all, predicated about a species, and

* Cf. with the above the discussion in Chapter VIII., p. 88. The distinction between the abstraction implied in generalization and the abstraction which results in 'abstract terms' should be noted.

it would have been obviously tautological to predicate the species of itself, and therefore illogical to include the 'species' among the predicables. With Porphyry the subject about which the predicable was predicated might not only be a species, but an individual object. In this latter case it was reasonable to predicate the species under which it stood, and so 'species' found its place among the predicables.

In adopting the Aristotelian scheme of predicables, we at the same time reinterpret it; for the point of view from which we regard the whole problem of the predicables is essentially different from Aristotle's. Aristotle's outlook was objective. He considered the content of the object as such, and not in its relation to the intenti.e., the intention of the subject. To define a thing was to state that which made it what it was, and was therefore essential to its existence. But if we admit that 'essential' necessarily means 'essential from a certain point of view,' and thus admit the principle that definition is strictly relative to purpose, we have qualified the Aristotelian standpoint in a way so vital as to preclude any appeal to the authority of Aristotle.

With a view to bringing out the positive significance of the position which we have adopted in regard to the problem of definition, we turn now to the vexed question of the OBJECT of Definition. Meaning, we would say, is the direct object of definition. What, then, do we understand by Meaning ?

Meaning, as we conceive it, is, in the first place, a product of thought in its relation to reality, or of reality in relation to thought. Meaning, in other words, is the meaning of an object for a subject; or, more specifically, it tells us what an object is in relation to a specified interest or purpose.

Meaning is thus a product of objective Nature and subjective interest, or, if we prefer it, of objective content and subjective intent. It must not only be the meaning of what is, and so objective in regard to content; it must be our meaning, and so subjective in regard to the definer's intention or intent.

Again, in defining meaning we may have in view either some restricted practical purpose or the broader interests of Science. This distinction we may appropriately equate to the familiar distinction between formal and real definition. The formal definition is a conventional definition framed to fit a specific interest that involves no more than a merely fragmentary hold on objective reality. The framing of real definitions, on the other hand, is ultimately controlled by one and the same unvarying idealnamely, that of bringing the greatest possible simplicity and order into our grasp of Nature.

Meanings, again, are fixed and made definite through the use of words. Hence, to define the meaning of an object is at the same time to define the meaning of the word which symbolizes it. We

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