genus higher than itself. It might seem, then, that summa genera were indefinable. So, again, it would seem that the infimæ species, being 'lowest' in the ranks of a division, were not relevantly subdivisible.

There are, moreover, other difficulties-those, namely, which are associated with the ambiguity of the term 'infima species.' If the infima species is a class-concept, it should be definable in a sense precisely similar to that in which a subaltern genus is definable. If, on the other hand, the proper name, or the singular meaning, is to be identified with the infima species as its limiting form, we are confronted by a new set of difficulties which centre round the question: 'Can a proper name be defined ?'

Having thus briefly stated the difficulties, we pass on to consider how they can best be met.

(i.) Is the Summum Genus Definable ?

It is manifestly true that in the case of the summum genus 'Animal' there is, within the classification, no higher genus by the help of which it could be defined. But this simply points the moral that the zoölogist cannot develop the full meaning of his leading concept, 'Animal,' without connecting it with the leading concepts of other sciences-e.g., the botanical concept 'Plant' - and recognizing a superordinate genus, 'Organism,' which dominates both interests alike. At the same time, even within the limits of the specific classification which it represents, a summum genus must admit of a partial definition through an indeterminate attribute, the primary F.D., of which all subsequent fundamenta divisionis are the specifications. Thus, taking as our summum genus one of the two primary groups into which the Animal Kingdom is divided, the Sub-Kingdom 'Metazoön,'* this summum genus is definable as 'an animal organism possessing an anatomical structure of some kind.' This last-named characteristic, though indeterminate or indefinite, supplies, none the less, a perfectly unambiguous mark, and, as we have seen, an indefiniteness which does not amount to ambiguity is no disqualification for the purposes of Definition.

* Protozoa cannot unambiguously be said to possess anatomical structure. If we have shirked the definition of 'Animal,' it is because scientists do not yet seem to have discovered a satisfactory differentia between 'animal' and 'plant.' But if this should not be obtainable, the logical course would be to absorb the so-called 'Animal' and 'Plant' Classifications within the single Classification of Organic species. The Summum Genus 'Organism' might thus be defined as 'a cellular structure of some kind,' or, better still, 'a protoplasmic structure of some kind.' The essential point is that no classificatory system can be developed without a primary F.D., and this primary F.D. supplies an adequate differentia of the Summum Genus, distinguishing it unambiguously from all other Summa Genera. The reader who is interested in the attempt to fix the distinction between 'plant' and 'animal' will find an excellent treatment of the problem in Prof. Bergson's 'L'Evolution Créatrice' (deuxième édition, pp. 115-130).

The disjunctive specification of this dominating fundamentum gives the division of 'Vertebrate or Invertebrate'; and all the subsequent fundamenta-e.g., 'Dentition '-are so many modifications of this original attribute of the summum genus-the possession of some kind of anatomical structure.

But a fresh difficulty arises when we conceive the process of abstraction, whereby summa genera are reached, carried to its limit, and culminating in a concept like 'Being' or 'Existence.' Such a concept or meaning can have no more general concept beyond it, since it is posited as ultimate for our thinking. We cannot, therefore, bring it under any superordinate genus, nor can we connect it with any co-ordinate species fulfilling a function logically similar to its own, as we can connect 'Animal' with 'Plant.' The ultimate summum genus cannot be defined per genus et differentiam. We cannot compare this unique definiendum with any co-species; we therefore cannot sift agreement from difference, and so distinguish a genus from a differentia. We must look elsewhere for a solution of the problem.

It might be urged that this arch-concept is self-defining. But if so, in what sense? It cannot be self-defining in the sense in which connotations are self-defining. The ultimate concept does not tell us its own meaning as do the expressions 'rational animal' and 'the mother of the two Gracchi' (vide p. 80). But if not selfdefining in this determinate form of self-definition, may it not still be self-evident, and therefore in last resort self-definable ?

There is no logical justification for supposing this. The ultimate abstraction can make no appeal to immediate experience; it therefore does not proclaim its own meaning, in however vague and undeveloped a form, by the easy way of unreasoned intuition.

But it might conceivably be self-evident in another sense. It might proclaim its meaning indisputably to the trained insight of the logical reason, though it failed to impress the exoteric consciousCan it be self-evident in this esoteric sense? In order to test this point we apply the well-known logical criterion of intuitive certainty; we ask whether it is impossible to deny the self-evidence of Pure Being without falling into self-contradiction.*

ness.

Let us first consider the argument in favour of the logical selfevidence of the statement that 'Something, qua pure being, is.' We take as our model Dr. McTaggart's defence of the indubitable certainty of Hegel's dialectical starting-point, the Category of Pure Being stated in the form 'Something is.' Hegel's Pure Being differs in some respects from the summum genus we are here considering, but the differences do not affect the present argument, and our proof of the non-self-evidence of the 'Being' which gives the summum genus tells equally well, in our opinion, against Dr. McTaggart's

* The 'self-affirmation' of Being-namely, the affirmation that it exists-is. in a sense, a statement of what it is, and to this extent implies its definability.

defence of the self-evident character of the 'Something is,' which gives the leading category of the Dialectic.

To deny the self-evidence of 'Being 'so runs the argument-is to deny the self-evidence of the assertion that 'Something is.'* But this assertion cannot be denied without being at the same time reaffirmed. For the denial at least 'is.' And to doubt the assertion is as conclusive in its favour as to deny it. For our doubt must be either genuine or not. If it is genuine, then we do not doubt that we doubt; we hold that something is namely, our doubt : and if it is not genuine, then we are all the while admitting the truth that 'Something is,' while we pretend to doubt it.

Now if this argument were sound we should have to admit the self-evidence of Pure Being. But the argument is surely fallacious. Suppose I deny the self-evident character of Pure Being. I assert my denial, certainly, but not in the sense of 'pure being.' I assert it in a much less abstract sense. I may, therefore, without any logical inconsistency, deny that 'Something qua pure being is,' for the assertion of my denial is the assertion not that 'Something is ' qua pure being, but that 'Something is' for me as an immediate experience. In the two propositions' Pure Being is ' and 'My denial of the existence of Pure Being is' the word 'is' has two quite different meanings.

We therefore cannot admit that the ultimate summum genus is either self-defining or self-evident; nor, as we have seen, can it be defined per genus et differentiam.

It would, no doubt, be convenient if at this point we could cut the knot with the short sharp word ' indefinable.' The stroke would, however, be suicidal, for it would cut at the root of the whole logical theory of Definition. If a term is 'indefinable' in the strict sense of the word, it must remain permanently infected with ambiguity, should ambiguity ever come to cleave to it; for, the remedy of Definition being unavailable, the ambiguity must remain to tease logicians to the end of time. But no one will pretend that the term 'Pure Being,' that 'x' which is the ultimate summum genus, is free from ambiguity. Moreover, if an incurable ambiguity attaches to the summum genus, there is no root of soundness in any classificatory system developed on the genus et differentia principle. For in such a system there is no class-term of which the meaning does not rest ultimately upon the summum genus. 'Man,' we say, 'is a rational animal'; but both rationality and animality are in last resort specifications of the wholly indeterminate concept from which the development of all meaning initially flows. If the summum genus is indefinable, our definitions are, one and all, illusory, and we can never ultimately know what we really do mean. Our definitions will all be more or less remote specifications of 'that we know not what.' If xm be the ultimate concept, and xn-1 a penulti

* Vide McTaggart, 'Studies in the Hegelian Dialectic,' § 18, p. 21.

mate concept-a species of x with differentia d-we say that xn-1 is x qualified by dr. But what is xm? Similarly xn_2 is 2n-1 qualified by 8-1. Thus, xn-2 inherits the vice of 2n-1 which originated in ; and so we might go on to the limit of the infima species.

At this point we may be met with the impatient reply that the whole difficulty is surely gratuitous, and that the ultimate concept is not only definable, but definable in many ways. When we call Being' the 'summum genus,' are we not defining it? Or we may define 'Being' as the ultimate category or concept, the wholly indeterminate meaning. And are not these meanings, it will be added, unidetermining? Can 'the wholly indeterminate' be confused with any other meaning ?

To these plausibilities the sufficient response is that, from the point of view of Definition per genus et differentiam, they all involve a circulus in definiendo. 'Wholly' and 'indeterminate' must themselves be specifications of the wholly indeterminate concept they profess to define, for the ultimate concept is, by hypothesis, ultimate, the ultimate generality whence proceed all the determinate forms of conceptual being. Every term of every definition presupposes this ultimate summum genus.

We have, then, still before us the task of showing in what sense, if any, the summum genus is definable.

Our first step must be to name the summum genus more precisely. From the standpoint of a merely objective view of the nature of 'meaning' there might be good reason for retaining 'Being' or 'Pure Being' as the ultimate concept. But we have already repudiated this abstractly realistic conception of 'meaning,' and have adopted an inclusively idealistic conception, which claims that meaning, whatever else it is, must always be the meaning of an object for a subject. This fundamental conviction, which has been stated rather than defended, or defended only through its power to reconcile conflicting views, calls for a correspondingly idealistic framing of the ultimate concept. Shall we, then, call it 'Knowable Being'? If it were urged that this concept suggests a further-lying concept, 'Being as such, which may be specified as either knowable or unknowable, we should reply that 'unknowable being' is, from our point of view, meaningless. We might, indeed, content ourselves here with Professor Ferrier's simple argument that ignorance is relative to knowledge, and that where no knowledge is possible there can be no possible ignorance. If there be an unknowable, it is out of all relation to Consciousness, and we cannot logically refer to it as 'it.' We cannot say that we are ignorant of it, or that we don't know what it is. It must be nothing for our ignorance as well as for our knowledge.

Adopting 'Knowable Being' as our ultimate concept, we abandon, as intrinsically unreasonable, the attempt to define the ultimate concept except in relation to the logical interest through which we know it, and we begin to realize that the search for the hidden sources of meaning must take us beyond the limits of any conceptual tree which does not, throughout its ramifications, involve this reference to interest and to knowledge. Nor is the appeal from 'object' to 'object of interest' an appeal to the deus ex machina. For the reference to logical interest is involved in the very notion of a concept. A concept is a concept-in-relation-to-logical-interest. If the addendum be torn away, the concept itself vanishes. Hence the appeal from the concept per se to the concept as known is simply the demand to have made explicit what is already implied. But to bring out implications is precisely to do that which renders superfluous all unintelligible assistance from a deus ex machina.

The problem now presents a somewhat different aspect. The ultimate genus, the genus that has no superordinate, * is seen to have as its correlative a thorough-going logical interest. It therefore cannot get its whole meaning from itself. If it is definable at all, it must be definable through the relation in which it stands to such an interest.

This relation is, in brief, the subject-object relation. Though bereft of all determinate content, the summum genus is still an object, the object of a logical interest. Hence the problem of its definition becomes the problem of deciding what we mean in general by an object of logical inquiry. The attempt to cope with this problem would bring us to the fundamental question of Kant's whole critical inquiry: 'What are the conditions of a possible object of experience?' It is not necessary for us to reconsider this problem, or to gauge the value of Kant's solution of it. It is not necessary because our aim is not to give the definition of 'Object,' but to consider, and in some sense to answer, the question as to its definability. We, therefore, content ourselves with noting the following points: (1) That there is no meaning more ambiguous or more in need of careful definition than the term 'object of experience'; (2) that the problem of its definition-i.e., the question of its function and significance within the unity of experience is a fundamental problem of the Theory of Knowledge; (3) that the ultimate logical postulate which this defining-process presupposes is the postulate of the radical intelligibility of experience. We have only to add that this postulate is not optional. We cannot think at all without making it. For to think is the same thing as to think what is not self-contradictory (vide Chapter X. c); the self-contradictory cannot be thought. But there is nothing ultimately meaningless save the self-contradictory (vide pp. 103, 104). Hence, to think at all is to think what has meaning and is pro tanto radically intelligible. This ultimate postulate, then, may be accepted as a ποῦ στῶ. Not only is it true to say that if the universe

* It makes no difference to the general argument if, with Porphyry and Aristotle. we hold that there are as many ultimate genera as there are categories.