immediate thus holds such rank (Stellung) that this outer, in so far as it subsists and has actual-being (Daseyn), remains only an incidental world out of which the Absolute takes itself up into the spiritual and inner, and thus for the first time really arrives at the truth. At this stage the outer is looked upon as an indifferent element to which the spirit can no longer give credence, and in which it no longer has an abode. The less worthy the spirit esteems this outer actuality, by so much the less is it possible for the spirit ever to seek its satisfaction therein, or to find itself reconciled through union with the external as with itself.

3. In Romantic Art, therefore, on the side of external manifestation, the mode of actual representation in accordance with this principle does not go essentially beyond specific, ordinary actuality, and in nowise fears to take up into itself this real outer existence (Daseyn) in its finite incompleteness and particularity. Here, again, has vanished that ideal beauty which repudiates the external view of temporality and the traces of transitoriness in order to replace its hitherto imperfect development by the blooming beauty of existence. mantic Art no longer has for its aim this free vitality of actual existence, in its infinite calmness and submergence of the soul in the corporeal, nor even this life, as such, in its most precise significance, but turns its back upon this highest phase of beauty. Indeed, it interweaves its inner being with the accidentality of external organization, and allows unrestricted play room to the marked characteristics of the ugly.

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In the Romantic, therefore, we have two worlds. The one is the spiritual realm, which is complete in itself-the soul, which finds its reconciliation within itself, and which now for the first time bends round the otherwise rectilinear repetition of genesis, destruction and renewal, to the true circle, to return-into-self, to the genuine Phoenix-life of the spirit. The other is the realm of the external, as such, which, shut out from a firmly cohering unity with the spirit, now becomes a wholly empirical actuality, respecting whose form the soul is unconcerned. In Classic Art, spirit controlled empirical manifestation and pervaded it completely, because it was that form

itself in which spirit was to gain its perfect reality. Now, however, the inner or spiritual is indifferent respecting the mode of manifestation of the immediate or sensuous world, because immediacy is unworthy of the happiness of the soul in itself. The external and phenomenal is no longer able to express internality; and since, indeed, it is no longer called upon to do this, it thus retains the task of proving that the external or sensuous is an incomplete existence, and must refer back to the internal or spiritual, to intellect (Gemüth) and sensibility, as to the essential element. But for this very reason Romantic Art allows externality to again appear on its own account, and in this respect permits each and every matter to enter unhindered into the representation. Even flowers, trees, and the most ordinary household furniture are admitted, and this, too, in the natural accidentality of mere present existence. This content, however, bears with it at the same time the characteristic that as mere external matter it is insignificant and low; that it only attains to its true value when it is pervaded by human interest; and that it must express not merely the inner or subjective, but even internality or subjectivity itself, which, instead of blending or fusing itself with the outer or material, appears reconciled only in and with itself. Thus driven to extremity, the inner at this point becomes manifestation destitute of externality. It is, as it were, invisible, and comprehended only by itself; a tone, as such without objectivity or form; a wave upon water; a resounding through a world, which in and upon its heterogeneous phenomena can only take up and send back a reflected this independent-being (Insichseyns) of the soul.

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We may now comprise in a single word this relation between content and form as it appears in the Romantic — for here it is that this relation attains to its complete characterization. It is this just because the ever-increasing universality and restless working depth of the soul constitute the fundamental principle of the Romantic, the key-note thereof is musical, and, in connection with the particularized content of the imagination, lyrical. For Romantic Art the lyrical is, as it were, the elementary characteristica tone which the epic and

the drama also strike, and which breathes about the works of the arts of visible representation themselves like a universal, fragrant odor of the soul; for here spirit and soul will speak to spirit and soul through all their images.

DIVISION: We come now to the division necessary to be established for the further and more precisely developing investigation of this third great realm of art. The fundamental idea of the Romantic in its internal unfolding lies in the following three separate moments or elements:

1. The Religious, as such, constitutes the first circle, of which the central point is given in the history of redemption in the life, death, and resurrection of Christ. Introversion ( Umkehr) here assumes importance as the chief characteristic. The spirit assumes an attitude of hostility toward, and overcomes, its own immediacy and finitude, and through thus rendering itself free it attains to its infinity, and absolute independence in its own sphere.

2. Secondly, this independence passes out of the abstract divine of the spirit, and also leaves aside the elevation of finite man to God, and passes into the affairs of the secular world. Here at once it is the individual (Subjekt), as such, that has become affirmative for itself, and has for the substance of its consciousness, as also for the interest of its existence, the virtues of this affirmative individuality, namely, honor, love, fidelity, and valor— that is, the aims and duties which belong to Romantic Knighthood.

3. The content and form of the third division may be summed up, in general, as Formal Independence of Character. If, indeed, personality is so far developed that spiritual independence has come to be its essential interest, then there comes, also, to be a special content, with which personality identifies itself as with its own, and shares with it the same independence, which, however, can only be of a formal type, since it does not consist in the substantiality of its life, as is the case in the circle of religious truth, properly speaking. But, on the other hand, the form of outer circumstances and situations, and of the development of events, is indeed that of freedom, the result of which is a reckless abandonment to a life

of capricious adventures. We thus find the termination of the Romantic, in general, to consist in the accidentality both of the external and of the internal, and with this termination the two elements fall asunder. With this we emerge from the sphere of art altogether. It thus appears that the necessity which urges consciousness on to the attainment of a complete comprehension of the truth demands higher forms than Art is able in anywise to produce..

STATEMENT AND REDUCTION OF SYLLOGISM.

BY GEORGE BRUCE HALSTED.

At the basis of Logic stands the conception of class, the formation of general notions, the use of a word to denote the objects possessing a common attribute-e. g., Geometer.

This assumes our ability to contemplate these objects apart from any or all others.

From this group we may select again those of them which belong to some other defined class, and so on.

We will represent classes by letters of the alphabet. Suppose a represents "men," and z, "geometers." Then z would naturally be read "men geometers," and will mean such individuals of the class men as belong also to the class geometers. By an easy extension we take in all adjectives. Suppose y means French, or the class French things; then xyz will mean all Frenchmen who are geometers.

We see that the order in which we select the classes is indifferent, in the sense that it gives the same result whatever order is taken.

In our example, if we first select geometers, then men, then French, we see that our final result, zxy, geometers who are Frenchmen, or yzx, French geometers who are men, should give the same final class of individuals. In ordinary language we use the position of words sometimes as a help toward expressing our meaning, but in this notation for Logic such help

is not needed. If we represent by x and z any two classes, known or unknown, we may generalize this law of the combination of classes, and express it by writing xz=zx.

We use the sign of equality to express, in the most general way, identity of individuals, coexistence of qualities, or equality of numbers.

The above equation, then, expresses the fact that logical multiplication is Commutative.

In using the word multiplication, and, further on, other terms of the common algebra of number, it is not even necessary to claim the slightest analogy between numerical multiplication and our process of logical combination. We are completely justified simply because their symbolic expressions are the same and subject to the same formal law.

But suppose we take as a class "all things," or the universe, or, much better, "the universe of discourse," and combine this with any other class, as x. We see that this does not change x in value; that ux=xu=x, whatever may be. Have we in the common algebra of number a symbol possessing formally this property? This leads us to represent the universe of discourse by unity, by the simple arithmetical figure 1.

Again, it is indifferent whether from a group of objects considered as a whole we select the class x, or whether we divide the group into two parts, select the x's from them separately, and then connect the results in one aggregate conception. That is, x (y+2)=xy+xz=(y+z) x, or logical multiplication is doubly distributive with reference to addition.

All substances outside of, or not belonging to or included in, a class may be considered together as forming another class, which is the negative of the first. In logic, by not-x or non-x we mean all the universe except x. The negative is a remainder, gained by the subtraction of the positive from the universe; x and non-x are the opposites under a given universe. So the term "not-gold" will apply to everything in the universe except what is truly gold. Representing "except" by the minus sign, we have, for example, non-gold-everything except gold=1—g, and so with any class.