were in any respect meaningless we could never know it, being unable to think what is meaningless; we may go further, and say that if there were any such unknowable, we should not be suspecting the possibility of its existence. To be conscious of a limit is to have already transcended it; the barrier that closes upon our knowledge closes also upon our ignorance.

(ii.) Is the Infima Species Divisible ?

The reference to logical interest which has determined the nature of our answer to the question, 'Is the summum genus definable ?' suffices to give a definite answer to the further question, 'Is the infima species divisible?' For, if a given species is 'lowest' relatively to a stated interest, any further division of the species would be necessarily irrelevant, and would involve that overdistinction and false subtlety which is the inevitable penalty of irrelevance. If we know our purpose and point of view, it must always be possible to fix the critical point beyond which refinement and the differentiation of meaning degenerates into irrelevant subtlety. Where a classification is dominated by a scientific interest, the extent to which a division is carried will depend not only on the degree of accuracy required, but on the progress of scientific knowledge. Thus 'giraffe' (Camelopardis giraffa), which used formerly to stand as an infima species, is now known to include eight or ten distinct varieties. We conclude, then, that while the infima species, as such, should be regarded as logically indivisible, yet fresh advances in scientific knowledge are always promoting infimæ species to a higher grade, and thus making them divisible. Division, like Definition, is essentially progressive.

(iii.) Can Proper Names be Defined?

Let us once more consider the celebrated conceptual Tree of Porphyry, the tree that grows downwards through a series of successive divisions from the heights of independent Being, through the distinctions between Animate and Inanimate, Sensible and Insensible, Rational and Irrational, to Socrates, Plato, Aristotle, etc. at the terminus (vide p. 47). This tree of concepts is made to include individual elements, and the point which here concerns us is the question whether this inclusion can be logically justified. Can the infima species of a conceptual tree be a proper name?

It seems reasonable, and perhaps necessary, to suppose that it can. A division of the term 'Man' might conceivably be so carried out as to pass from Man to Statesman, thence to Prime Minister, then to the Prime Minister of England in May, 1907. This last concept would necessarily be singular in its reference, and would be represented by the proper name, 'Henry CampbellBannerman.' Similarly we might pass by successive subdivisions through the subaltern genera Greek, Athenian, Philosopher, etc. to the Socrates and Plato of Porphyry's tree. So long as the single individual represented by the proper name is not considered as he is for himself, but in the same external way as are the many individuals indicated by any ordinary class-name such as 'Man' or 'Athenian,' there seems to be no ground for differentiating between the status of the general name and that of the proper name in regard to the problem of the development of meaning. The latter becomes simply a limiting case of the former.

With the above-mentioned proviso, we seem to be justified in including individual elements in a conceptual tree and in regarding them as intrinsically general or conceptual in character, though sharpened-intensively to such a point of conceptual fineness and determinacy as to have extensively a unique reference. They are then singular names, the function of a singular name, from the point of view of Extension, being to refer us unambiguously to some single individual object or person.

Regarded in this light, the singular name or meaning belongs, by natural birthright, to the organized system of logical concepts. There is no opposition between the class-concept and the singular or individual concept, nor is the phrase 'singular concept' a contradiction in terms. The individual meaning is simply the concept in its limiting form. Where the only relevant element in this meaning is the individuality of its reference, the name which represents it is known as a proper name.

The singular concept is that limiting form which the infima species of a division tends in last resort to take, though whether this terminus is actually reached or not depends entirely on the answer to the question whether it is logically relevant or advantageous to reach it. The singular concept, or the proper name which represents it, we hold to be definable by means of a significant singular name-a name which, by virtue of its very significance, is singular. This appears to be the natural connexion between the proper name and the significant singular term. 'Rational animal,' which defines the general concept 'Man,' is a significant general expression ; 'The mother of the two Gracchi,' which defines the singular concept 'Cornelia,' is a significant singular expression.* Significant singular expressions, precisely alike in this to significant general expressions, are self-defining. Thus, 'The highest mountain on the Earth at this present stage of our planet's geological history' defines itself.

* Significant singular expressions are sometimes more briefly called 'designations.' Thus Mr. Joseph ('An Introduction to Logic,' p. 21) defines a designation as 'a phrase which by a pronoun or what not serves to indicate an individual otherwise than by a name of its own.' This briefer title, however, does not render the longer one superfluous. A singular symbol may either designate or signify. It may designate an individual (Extension), or it may signify a meaning (Intersion).

Its significance consists in the meaning of the marks that make up the term. The very expression tells us that the single object referred to is a mountain in our planet, and the highest of all at the present time. As other instances of the significant singular term we may mention 'The centre of the Earth,' 'The first Emperor of Rome,' 'The town at present situated at the mouth of the Dart.' Our attempt to maintain the definability of the individual may be met by certain objections :

1. It may be urged that proper names do indeed suggest, but do not imply, attributes. The distinction between suggestion, according to psychological laws of association, and logical implication is, indeed, fundamental, and there is a great difference between unregulated 'subjective' meaning and logical connotation. But once we recognize that such 'implication' is relative to purposethat it is only through knowing what our defining purpose is that the implication can be relevantly fixed-the objection loses its point. 'Common' natures, no less than individual natures, suggest a great deal more than is relevant to the purpose for which their definition may chance to be required. But the defining interest once clearly stated, those attributes or marks can be selected which, in the most direct and economical way, suffice to render our meaning and reference unambiguous. The unselected marks that are not required for the fixation of our meaning will then assume the status of propria, and will remain propria so long as our defining interest remains the same. It may be sufficient, from a given point of view, to identify Mr. Balfour with 'the British Prime Minister in the year 1900,' or with 'the philosopher who wrote "The Foundations of Belief." These identifications will give just such meaning as the name relevantly, and therefore logically, implies in respect to the interest which dominates the definition. They will be definitions of a proper name. Proper names, like general names, require as many definitions as there are points of view from which they can serviceably be used.

2. An objection of quite another kind may be raised against the definition of the proper name. It may be contended that it is just a meaningless mark. 'The only names of objects which connote nothing,' writes Mill, 'are proper names; and these have, strictly speaking, no signification.... A proper name is but an unmeaning mark which we connect in our minds with the idea of the object, in order that whenever the mark meets our eyes or occurs to our thoughts, we may think of that individual object.'*

In the use of the phrase 'unmeaning mark' it is evident that Mill does not intend us to understand that the name is bereft of all meaning whatsoever. It must at least retain a meaning as a complex of sounds or letters, for if the proper name were bereft of this meaning it could not function as a mark at all. By the phrase * J. S. Mill, 'A System of Logic, Book I, ch. ii., § 5.

'unmeaning mark' he seems to mean a sign which stands for the 'that' and not for the 'what' of the object which it indicates. But is this possible? Is the 'that' intelligible apart from its development into a 'what'? A case might conceivably be made out for the pure thatness of a summum genus, but not of a proper name. Mill compares the imposition of a proper name to the marking of Ali Baba's house by the robber in the 'Arabian Nights.'* But the chalk-mark affixed to the house in order to distinguish it from the other houses in the row did not represent a mere 'that.' It was a sign which meant 'The house of Ali Baba,' and to this extent it stood for and signified what was the object to which it was attached. It therefore cannot be regarded as an unmeaning mark.'

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3. The best (though, in our opinion, still unconvincing) defence for the indefinability of the proper name is based upon the conviction that an individual's principium individuationis is not what the individual is for an outside spectator-or logician-but what it is for itself, the contention being that the individual, qua inwardly individual-qua experient-is strictly indefinable. But is this so? If we cannot here have Definition per genus et differentiam, may we not have Experience-definition reflecting the point of view of the experient himself? Such definitions would present in systematic form the meaning of our own immediate experiences stamped with the impress of our own relevant reflection upon them. Concepts like 'Thou' and 'I,' concepts which mark immediate experiences of feeling or sensation, such as 'blue,' 'hot,' ' angry,' 'tired' (considered not as concepts of Physics or Physiology, but as genuine psychological meanings grounded in immediate experience)-may not all these gain a definite meaning through a reflective reconstruction of what is primarily self-evident? As experience-concepts they could not belong to any conceptual tree which, in its arrangement, failed to recognize either that meaning is 'for a subject' or that the subject is also an experient. 'Now' ' here,' ' ultramarine,' 'I,' and all proper names, qua personal, belong neither to Porphyry's tree nor to any branch of strictly scientific Classification. They belong, as perhaps all concepts ultimately do, whether directly or indirectly, to the tree of self-knowledge which is rooted in immediate experience.

The difficulties which beset the attempt to define experienceconcepts apart from their relation to the experience which they signify are excellently illustrated by the following passage from an article by Professor Stout.†

'When I refer to the present Lord Chancellor, I determine him as the particular Lord Chancellor existing at the time at which I am speaking; when I refer to this table, I determine the table as that

* J. S. Mill, 'A System of Logic,' Book I., ch. ii., § 5.

† Proceedings of the Aristotelian Society, N.S., vol. vi., pp. 360-362.

which is near me or at which I am pointing, or as that of which I have just been talking. The application of proper names is determined by the particular occasions on which they have been utterede.g., in the baptismal service. And so, quite generally, we can never mark off in language the particular existence we mean except by its relation to some other particular existence presupposed as already known. But this process obviously involves a vicious circle unless there is ultimately some direct apprehension of particular existence which supplies a point of departure for thought. If we attempt to reach this ultimate basis by a regressive process, we find ourselves approaching nearer and nearer to our own psychical life as the final centre of reference through which all other particular existence is determined. The limit of this regress is marked by such words as "now" and "I." In such words we indicate a particular existence which is not determined by the thought of relation to some other particular existence, but by the direct apprehension of particular existence just as it is actually existing. For this reason it is impossible without a logical circle to define adequately in language what it is we refer to when we say "now or "I." This is impossible because we can only express in language the relatively complex cognition of which immediate apprehension is an element. What is immediately apprehended cannot be so detached as to become by itself a distinct object of knowledge. It is not nameable except as being an element of a relatively complex object. Thus, if I am right, when the application of words to particular existents is directly determined by immediate experience, it ought to be impossible to explain what is meant without a vicious circle. And, as a matter of fact, this is so. Let anyone try to explain what time it is which he refers to when he says "now." It is not enough to say that " now means the time at which a person is speaking, for persons speak at different times, constituting a great many nows; but in saying "now," the reference is to only one particular time. How is this particular time distinguished from the others? It is circular to say that by now" I mean the "time at which I am now speaking." Yet anything short of this is inadequate. Again, we cannot define the time meant by assigning its relation to past or future time. For the " now "forms the ultimate starting-point from which we determine temporal position in the past or future. The future is what follows the "now," and the past is what precedes it. Thus, any attempt to determine the meaning of the now merely by its relation to the past or the future involves a vicious circle. The "now" must be stamped by a peculiar signature of its own-a peculiar character intrinsic to it. What is this peculiar character? We may attempt to express it by saying that the "now" is the moment of actual experience. We may say that it is the moment in which sensations, pleasures, pains, etc. are not merely being thought but actually existing. But, again,

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