do not, of course, define words apart from their meaning. What is defined by the term 'rational animal' is not the mere sound-sign 'man,' but its meaning. If by words we mean the mere soundsigns in themselves, we cannot be said to define words, nor even to describe' them, but only to utilize them as sensory supports for meanings which can be defined.

4

The

The question 'What is it that we define, things, meanings, or words?' has been the theme of immemorial controversy. There have been three rival parties. The realists have maintained that it is things that we define; the conceptualists, that we define meanings; the nominalists, that we define words and names. controversy hinged on the meaning of the 'universal.' The realists held that things had, in all those relations in which they resembled each other, a common or universal nature, and that, in defining this common nature, we were defining what was at least as genuine and indispensable a constituent of reality as was the individual nature of objects. The conceptualists held that the universal element existed, not in the objects themselves, but only in the thought which conceived them; the true universal was the concept. Finally, the nominalists held that things called by the same name had nothing in common but the name. The universal was thus a mere convenience of language. The only true existent, whether in reality or in thought, was the individual, and the individual was conceived by the nominalist in a sense which excluded the presence within it of any universal nature.

The conflict between these rival views was a conflict between abstractions which, far from being intrinsically hostile to each other, were, in reality, mutually complementary and indispensable.

We have already suggested that the definition of meaning is always at the same time the definition of an object, and to this extent the definition is realistic: definition is always definition of objective content. On the other hand, such objective content, we hold, is definable only in relation to subjective intent, so that, in defining the object, we are defining it as conceived in the light of this or that specific interest. To this extent our point of view might be characterized as conceptualistic. Still, it is not abstract, but, shall we say, concrete conceptualism. The conceptualism we have adopted is simply realism tempered by the requisite of reference to purpose.

According to the interest or purpose engaged, this plastic conceptualism may bear any shade of meaning, from the limiting case of a mere conceptualism to an idealism in which the realistic element is completely transfigured. If what is essential to me in defining a term is primarily and predominantly this, that my meaning shall be clearly and unambiguously understood, the nature of the object counts for little in the definition, and my meaning has but a vanishing reference to objective reality. This is logical conceptualism in a strict but still intelligible sense. It is governed by an interest in the logical purity of meanings as such. If, on the other hand, my interest in the meaning of an object-the interest that it has for me, the subject-lies primarily in discovering what that object means, or tends to mean, within the spiritual unity of the universe, the conceptualism is transformed into idealism, and my definition will answer to the logical requirements of idealistic conviction.

We have finally to add that the true logical nominalism, in its relation to the problem of definition, is indistinguishable from conceptualism. To define a word is to define its meaning: we do not define as a mere sound-complex the aggregate of vowels and consonants which make up a word. When we say 'Man is a rational animal,' we are not defining the mere verbal label or sign represented by the three letters m, a, n, arranged in a certain order. All definition of meaning is at the same time verbal definition, and vice versa. The distinction between nominalism and conceptualism, in definition, is a distinction without a difference.

The statement that we do not define mere sound-complexes as such may easily be misunderstood. It may be taken to mean that we do not even define the meanings of symbols qua symbols. But this is by no means implied in the statement. Any and every meaning, as we hope eventually to show, is definable in some true sense of the word. The meanings of symbols as such are indeed definable. I define the conventional symbol 'man' when I say:

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Man" is a conventional verbal symbol representing the concept "rational animal."' Every symbol has, in fact, a twofold meaning: the meaning of the symbol qua symbol, and the meaning of the idea which is symbolized by the symbol. The meaning, in a word, may be the meaning either of the sign or of the signification. When I say 'man' means a rational animal, I am defining the meaning of the sign; when I say 'man' is a rational animal, I am defining the meaning of the significate.*

We now proceed to apply the logical doctrine of meaning and of definition, as we have just been formulating it, to the non-defining predicables, property and accident.

A property or proprium is an attribute which, though not necessary to the definition itself, is still relevant to the defining interest. It is thus already present by implication in the meaning which an object has for us in the light of a specified interest.

Thus, in the geometrical proposition 'The equilateral triangle is equiangular, the predicate states a proprium of the subject. 'Triangle' is the genus, 'equal-sided 'the differentia, 'equiangular' the proprium. The equiangularity of an equilateral triangle is implied in the system of spatial relations, apart from which an equilateral triangle has no geometrical meaning, and our geometrical interest no real object. The geometrical interest in an equilateral

* For a further development of this point, of. pp. 115, 121.

triangle presupposes this reference to the nature of Space, and the equilateral triangle is conceived as constructed in Space as Geometry treats of it. The very construction furnishes the definition. We trace out a plane rectilinear figure with three equal sides, enclosing a space-i.e., a triangle with three equal sides. But when we come to examine the 'properties' of the triangle as thus constructed, we discover that one of these is 'equiangularity.' As a further property of an equilateral triangle, qua triangle, we have the fact that the three internal angles are collectively equal to two right angles.

Let us look a little more closely at the relation between proprium and definition. A definition, as we have seen, is the definition of an objective nature qua related to some definite interest or point of view. It would, however, be irrelevant to include within the definition whatever was relevant to the interest; for the function of Definition does not extend beyond the removal of ambiguity, and there may be much that is perfectly relevant to the interest, but which, so far as mere non-ambiguity is concerned, need not be explicitly stated. The propria, therefore, develop, from the point at which Definition stops, the meaning of the objective nature that is being defined. What the definition states is only that fraction of the essence which its own logical principle-the principle of nonambiguity-requires it to state. The residue is developed in the form of propria.

We must distinguish between two types of propria-two at least, for we may eventually find it convenient to add a third. Properties may be either implied' or 'characteristic.' They are 'implied' when they are deducible with logical necessity from the nature we are interpreting, as fixed by the definition in strict relevance to the defining interest. Thus 'equiangular' is an 'implied' property of 'equilateral triangle,' for it can be deduced with logical necessity from the geometrical space-construction defined by 'three-sided plane rectilinear figure enclosing a space' and by the differentia of 'equal-sidedness.'

A property is 'characteristic' when it predicates of the nature we are interpreting an attribute which, without being 'implied,' can be shown by observation or experience to be both typical of that nature and relevant to our interpreting interest. Thus, from the point of view of biological science, such attributes as 'contractile,' 'irritable,' 'assimilating food,' 'reproducing itself after its kind,' would be characteristic properties of an 'organism.'

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The Meaning of 'Essence.'

By 'essence or 'essential meaning' we aim at expressing the contact between an objective nature and a subjective interest. What is indispensable to the conception of 'essence' is this interplay between content and intent. It will thus be seen that, from the logical point of view, the point of view of right-thinking, 'essence' and 'meaning' are synonymous terms. All meaning is essential meaning, though some types of meaning are more intimately essential than others. From the point of view we have adopted, the non-essential or accidental that which implies no interplay between content and intent is logically meaningless. It is meaningless for the interest in question, and therefore meaningless for rightthinking, which is so constructed as to be unable to assimilate the irrelevant as such.

Some types of meaning, we have just said, are more intimately essential than others. In so far as the intent is an interest in defining the content up to the point required for satisfying the principle of non-ambiguity, the essence of our meaning is given by genus and differentia. In so far as the intent takes us beyond genus and differentia to other marks which are still relevant to it and characteristic of the content, the essence of our meaning is given more inclusively by propria as well, by 'implied' or 'characteristic properties. But there is yet a third form of interplay between content and intent. The essence of our meaning becomes still more inclusive if we reckon among the marks which are relevant to our intent, and in this sense essential to it, features which, though relevant, are problematic. Thus a building may be a palace, a palace may be the palace of a king. From the point of view of a general interest in buildings as edifices for social uses, the possibility of being a palace is a perfectly relevant mark of a building, and the possibility of a palace being a royal palace a perfectly relevant mark of a palace. Such 'problematic' properties, as we may call them, need not be actually realized in any concrete instances of the meaning or nature in question. Any type of building which the architect could imagine, plan, and realize if need be, would be a problematic property of 'building.' It might be convenient to give a special name to such problematic properties as were not only capable of realization, but actually realized in at least one concrete instance or occasion. We might refer to these as 'occasional' properties. Thus, from the architect's point of view, it would be an occasional property of a building to be a palace or a country-house. Problematic properties which were not occasional in this sense might be referred to as 'purely problematic.' It might be possible to build a house which should have the precise shape of an elephant or of an icosahedron; but, until such houses are actually built, the device in question remains a purely problematic property.

Problematic properties should not be identified with accidents or accidental marks, as we have defined them above. The genuine accidents, from the general point of view we have adopted, must be marks which are irrelevant to our intent, and so entirely outside the interplay of intent and content. Thus, in a flower, the colour, which to the artist is essential, is to the botanist relatively accidental, whilst the microscopic characters so important to the botanist are, from the artist's point of view, entirely negligible. Again, if my interest lies in the assuaging of my thirst, tumbler, mug, and other appropriate vessels are all alike to me: the handle of the mug and its absence in the tumbler are mere accidents, for they do not in any way affect the fulfilling of my interest. So. again, despite the fact that the burning of wood and the rusting of iron are both processes of oxidation, and so chemically akin, they are still essentially different for the person who is seeking warmth. To such an one the resemblances which interest the chemist are purely irrelevant, and in this sense accidental.

It may be objected that accidents as pure 'irrelevants' are not predicables at all, for no one can logically predicate of a subject what is irrelevant to it. Subject and predicate are united in the interest which prompts the making of the statement, and, as so united, are relevant to each other. This may very well be granted, in which case the 'accidents' of Aristotle's scheme become identical with the 'problematic properties' of the scheme that we have adopted, and the accident, in the guise of a realizable possibility, enters, in an intelligible way, into the essence of our meaning. The predicables are then reducible to four-definition, genus, differentia, and property; a property being either 'implied,' 'characteristic,' or 'problematic,' and a problematic property being either 'pure' or 'occasional.'

One word more on the problem of Essence. Once the intent or defining purpose is determined, and the content limited to what is strictly relevant to the intent, the meaning of Essence is logically clear. But in ordinary irreflective thought we are, as a rule, neither self-conscious of our defining purpose, nor do we consistently apply it to the deciphering of a given content. We are largely the slaves of suggestion and habit. When we habitually experience certain things together, we come, in accordance with well-known laws of mental association, to conceive them as inherently belonging to each other. Indeed, we show independence of mind just in proportion as we cease to be the slaves of such association. I quote the following from Dr. Watts's 'Logic':

'A court lady, born and bred amongst pomp and equipage and the vain notions of birth and quality, constantly joins and mixes all these with the idea of herself, and she imagines these to be essential to her nature, and, as it were, necessary to her being. Thence she is tempted to look upon menial servants and the lowest rank of mankind as another species of beings, quite distinct from herself. A ploughboy that has never travelled beyond his own village, and has seen nothing but thatched houses and his parish church, is naturally led to imagine that thatch belongs to the very nature of a house, and that that must be a church which is built of stone, and es