inclusion in its meaning of such and such more general concepts. And furthermore we can see how the explanation can be made, that, properly speaking, this is no relation (between two distinct terms) at all, but simply the identity of the included concept in and out of its particular setting. In like manner, we may add, the only reasonable inference from premises to a conclusion must have the form: A includes B, B includes C, therefore A includes C; the justification of the procedure consisting in the recognition of the identity of C in itself considered, with C as an element in B, whether, again, the latter be considered apart or as an element in A. (So also, if the two premises and the conclusion be regarded as concepts, the fact that the former, taken together, imply the latter, is to be explained by the fact that the meaning of the latter is contained in the joint content of the former.)

But it is obvious that the relation of inclusion cannot obtain between simple concepts; and the question becomes urgent, how the rationalist can save his world from falling apart into a chaos of disconnected elements. For the older rationalists (of whom Descartes is here typical), an answer is to be found in the fact that they really postulate two distinct classes of elements, namely, indefinable concepts and indemonstrable judgments, each of which is simple in its own sense, and each of which serves as a bond of connection for the other. The elementary judgments contain the elementary concepts in (or as) their terms; and the same terms occurring in several judgments unite them into syllogisms.

Now it seems clear that if the judgments are to do their part in the matter they cannot be merely analytical; that is to say, their predicates cannot be contained in the content of their subjects. They must be strictly synthetical. But here, as time went on, scepticism found an entrance. Does intuition ever vouch for the truth of a synthetical judgment? Descartes, indeed, declares so; but others have denied the self-evidence of every one of the examples which he adduces. Is not science thus brought into a perilous condition—to depend for its first principles upon

the mere word of contradicted witnesses?1 Moreover, if we ask why demonstration is ever required for any judgment whatsoever -why a ground must be sought for the predicated connection of its terms-is it not because the judgment as it stands appears to be synthetical and cannot be left so? In a word, is not every synthetical judgment a standing problem? So Leibniz believed; and accordingly he sought to reduce even the axioms of Euclid to analytical form. Thus intuitionalistic rationalism assumes a position substantially identical (despite Leibniz's protest) with that of nominalistic Hobbianism; namely, that all science must be deduced from definitions. But while thus gaining a certain self-consistency, it is lost in that hopeless unproductivity from which Descartes, by means of the assumption of distinct axioms, had sought to save it.

It has been suggested that a final means of synthesis is to be found in the judgment which denies a simple concept of its negative; as, for example, What is unextended is not extended. Here we remark that Descartes is correct in assuming that the negative of a simple concept, if it be itself a concept at all, must also be a simple concept. For since all definition is by means of genus and differentia, the negative is not definable in terms of the positive-as, for example, non-extension is not a species of extension. And if it be suggested that the negative is in every case a species of non-existence, the reply follows, that the positive is then equally a species of existence, and hence equally complex. If, then, unextended is a concept at all, The unextended is not extended is a synthetic judgment; and as such it would appear to be open to much the same criticisms as other supposedly elementary synthetic judgments. Suppose, however, it be said—as Des

1 Cf. Hobbes's criticism of the clare et distincte (quoted by Mr. Mahaffy): “This way of speaking, a great clearness in the understanding (as a test of truth), is metaphorical, and therefore not fitted for an argument; for whenever a man feels no doubt at al! he will pretend to this clearness." Cf. also Kant's explanation of the necessity for a critical deduction of a priori principles,--"without it, our assertion might be suspected of being purely gratuitous." Critique of Pure Reason, Analytic of Principles, Chap II.

cartes does say that while, as ideas, both positive and negative are equally elementary, nevertheless the one denotes a reality of which the other denotes the privation. Then, if this be supposed to be the ground of the negative judgment, we have the paradox of two concepts, in themselves utterly indifferent to each other, held asunder in thought by a characteristic of reality which is known only through the concepts themselves.

From the point of view which these reflections indicate, and which, while it belonged to neither Leibniz nor Spinoza, probably represents the real drift of opinion of both,-leaving aside the question whether any simple negative concepts actually exist,2 it is clear that no simple positive concept can be universally affirmed or denied of any other. On the other hand, there is nothing to prevent any two simple positive concepts, or, indeed, all such concepts, from being predicates of one all-comprehensive concept whose connotation includes them all. This concept, because it can be included in no more intensive one, can never be a predicate. Now this was the ancient meaning of the term substance (that which in judgment must always be subject and never predicate); and it is connected with the modern meaning (the eternally existent) by the simple reflection, that since no simple predicate can be denied of it, it contains all possible reality. As predicates of substance, the simple positive ideas are called attributes. Now because any substance must contain every possible attribute, Spinoza concludes that there can be but one substance ("All determination is negation"); while Leibniz, reflecting that an identical quality can exist in any number of degrees, finds room for an infinite number of substances possessing the same attributes in different degrees, one alone (God) possessing them absolutely, or in an infinite degree.

Thus, as the system works itself out, rationalism conceives the 1Rules for the Direction of the Mind, XII. Torrey, Philosophy of Descartes, p. 99. 2The solution of this question clearly depends upon the further inquiry, whether contradictory concepts imply a genus of which they are alike members. This is, by the way, a formal aspect of Hegel's famous discussion of being and naught; which are conceived, as he says, as simple contradictories, and yet have no higher genus within which they may be distinguished.

real world as expressed in a hierarchy of concepts related only through intensive inclusion, and all converging in one supreme concept whose definition comprehends within itself every necessary truth. Corresponding to this logical hierarchy is the ontological hierarchy of causes and effects. The logical relation and the causal relation are identical. The cause includes the effect in precisely the same way in which the richer concept includes the poorer. The supreme cause is God, in whom, as the sum of all positive predicates, all possible combinations of reality are grounded.

We cannot forbear noting that in Spinoza (and to a lesser degree in other rationalists) this mode of thinking is curiously mixed with another, inherited from neo-Platonism, and commonly called mysticism. According to this theory, the supreme concept in which all others are implicit is so far from being the most intensive of all concepts, that it is the least intensive—the summum genus. To this concept the name of God is ascribed; and he is regarded as the ultimate cause of which all specific realities are but particular effects. The commixture of rationalism with mysticism-whole heavens asunder, as they logically are-is probably due to a very ancient misconception with regard to the processes of definition and demonstration. Definition, it is said, must always be in terms of the higher, that is, the more general and less intensive; and demonstration likewise must be founded upon premises of greater and greater generality. But it is forgotten that though each element of the predicate of the definition is more general than the concept defined, the predicate as a whole is not; and that while one of the premises leading to a conclusion must be more general than the conclusion, the premises together are not. Now it has been customary, on various accounts, to regard the predicate of a definition as falling into two distinct parts, the genus and the specific difference; and it has been found convenient that the difference shall be a simple concept, all the complex remainder of the content of the subject falling within the genus. For the further elucidation of the

subject, the genus must next be resolved into a higher genus and a new difference, and this genus again into a still higher genus and yet another difference; and so on, until a highest genus is reached which is incapable of further analysis and thus marks the limit of the process. But it has frequently been forgotten that in each definition any single element of the subject may be chosen as difference, the whole remainder then standing as genus; or, in other words, that in the process of successive definition by which a complex concept is explained, no one order in which the elements shall be added in is predetermined. Every simple concept is thus a summum genus. But when a certain order of definition has for any reason become regarded as necessary, the successive genera are naturally viewed as presupposing each other in the given order; the equal significance of the differences is forgotten; and the summum genus is regarded as the source and cause of the whole series. To put the matter differently, the summum genus is regarded as being a simple concept in another sense than the various differences. It is capable of being thought by itself, while they are incapable of being thought except as its limitations or determinations. They are aspects of concepts, but not themselves concepts. The summum genus alone expresses the essence of self-subsistent reality; it alone is true Being, the being both of itself and of all things else; and hence all its species must be regarded as particular manifestations to which it determines itself—for there is no other Being to determine it.

Let this brief account of the mystic logic be taken parenthetically. It lies outside the proper field of our inquiry, and is inserted only to prevent misunderstanding. For a clear and striking contrast of the two mental attitudes, compare the following quotations, from Descartes and Spinoza respectively. "We say, in the third place, that these simple elements are all known by themselves." "By substance, I mean that which is in itself, and is conceived through itself: in other words, that of which a conception can be formed independently of any other conception."2 1Rules for the Direction of the Mind, XII; Torrey, op. cit., p. 99.

2 Ethics, Book I, Def. III; Elwes tr.