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or relations. Noting the symmetry, using the complementary classes, and observing that, whether we have x, or X, the symmetry of relation is not altered, we say that all seven propositions can be brought under the two forms XY=0, XY>0; where the first expresses a relation of total exclusion, the second a relation of partial inclusion, between two classes. The relation XY=0, if both classes are taken positively, becomes xy=0, and may be read in any of the forms. No x's are y's; no y's are a's; all x's are not-y's; all y's are not-x's.
Similarly the relation xy>0 may be read in either of the forms: some x's are y's; some y's are x's. In each of the forms XY=0, XY>0, X may be taken to represent x or , and Y to represent y or y. These two, then, are the only kinds of simple relations; it being understood that æ may be substituted for X, or y for Y; so that the example ży=0 (all y's are x's) is the same kind of relation as xy=0); and wy>(some y's are not-x's) is the same kind of relation as
All propositions which have either the subject or predicate unaffected by the symbol v, “ some,” can be brought under the first form ; the remaining propositions fall under the second form.
Now, the premises of every categorical syllogism are two propositions having a common tèrm. Taking X and 2 for the extremes, and Y for the middle term, the only combinations of premises are:
1. XY=0, ZY=0.
And of these there are only two which give rise to a conclusion or relation between the extreme terms.
As regards the negative cases, this is at once seen to be so;, thus, xy=0, zy=0 (no x's are y's, no z's are y's), leads to no conclusion in regard to the positive terms, x, z.
As regards the positive cases the conclusions may be easily proved to be valid hy general symbolical reasoning. Thus, whatever Y may be, we know Y=Yx+Yx; but in case 2, since XY=0 .. Y=Y.. But also we are given ZY>0, therefore substituting, we have ZYÃO.. ZĪ0.
Again, X2=XZy+XZy always; but in 4 a factor of XZY, namely, Xy, is equal to nought, and a factor of XZy, namely, Zy, is equal to nought; therefore, X2=0+0=0.
The logical signification of each step is obvious.
Still further, these two forms, the only forms which give a conclusion, differ only in the quantity of Z, which does not affect the reasoning, formally considered, in the slightest, since one of the original terms, say Z or vZ, may be allowed to enter unchanged into the conclusion. The seeming difference of form where in the second premise the y's seem to be of different quality, as do the x's in the conclusion, is produced by the fact that in translating ZY>O into an equation, the quality of Y is unchanged, for it gives - some Z's are Y's, v2=vY; while in translating Zy=0 into like form, the quality of y is changed, since it gives “ all Z's are y's,” Z=vy. This is a particular case used as a diagram in the general demonstration, enabling us to see that if A is used to represent z and vZ, the general form to which we have apodeictically reduced all categorical Syllogism may be written, .
Thus we have demonstrated that a conclusion can be reached in every instance where two or more of the four terms contained in the two premises are universal, and that, too, whatever be the variation of the terms as to quality. When but one of the four terms is universal, a conclusion can be reached in all cases (and in those only) where the universal term is the middle term in one of the propositions, and the middle term in the other proposition is of the same quality — that is, positive when the universal term is positive, and negative when the universal term is negative, or where the propositions can be reduced to that form.
NOTES AND DISCUSSIONS.
THE MORAL PURPOSE OF TOURGUÉNEFF.
The nineteenth century is peculiarly an age of philosophy, using the word in its widest sense as embracing both empirical and speculative science. Such expressions as “the philosophy of George Eliot,”: “the social views of Dickens,” “Goethe's theory of culture,” are current phrases. The novel reflects this phase of modern life as it does others.
Tourguéneff has the largest audience of any foreign writer; the question of the moral attitude of his art is, therefore, one of some interest. That most of the Russian novelist's books have for their central idea a moral question is apparent on the first glance. The - Journal of a Sportsman" is a tremendous picture of the degradation of the serfs reacting on the masters; “Smoke" etches the corrupting tendencies of a false civilization ; " Dimitri Roudine” draws in deep lines the uselessness of a philosophy which does not solidify its aspirations into deeds; “ Fathers and Sons” lays bare the weakness of the old Russian culture and the barbarism of the new; while his latest work, “ Virgin Soil,” still further develops the suicidal madness of Nihilism. But though these are moral questions, they are treated in so purely an artistic manner that the reader feels the moral more a deduction of his own than an intention of the author, and thus Tourguéneff is usually regarded rather as an artist than a moralist. Is he? Does he select his themes simply because they are effective, or does he show the evils which he draws in order that men, seeing their danger, may avoid it?
To answer this question one must consider his work as a whole. The first impression it makes is that of somber breadth. The atmosphere has the still intensity which precedes a thunder-storm; the figures start out of the shadows. They seem at first mere outlines, landscape figures; but as we look longer the details appear in preraphaelite distinctness — the landscape is only a background. Tourguéneff has been called a realist, but he has nothing of that passion for the sordid which distinguishes the French realistic school. From underrating the object and importance of the mean, the French school has rushed into the other extreme of worshiping it. To Flaubert, Zola, and the rest, a base soul is an acceptable study. They follow it through all its devious windings; with actual zest they analyze its moral squalor, its ignoble hopes, its repulsive pleasures, its degrading ambitions. Disease, say this school, is as real as health ; we paint the real — we take disease. They take it exclusively; they paint it with the minute fidelity of Van Ostade, and they show a genuine delight in their work. Now, Tourguéneff has not a hint of any such feeling. When it comes to him to picture crime or misery, the crime or misery is pictured frankly ; but the author shows no pleasure in his work. These things are facts which have their bearing on other facts, therefore they must be shown— not for themselves. Baseness is never the main motive of Tourguéneff. He draws his heroes on a large scale. They are often weak, but seldom contracted or mean. And this is even more noticeable with regard to his women. Tourguéneff's good women have a broad magnanimity of nature which puts to shame the conventional type of the novelists — the woman who sacrifices herself, like an angel, for her lover, and is spitefully unjust to her rival. Tourguéneff's best women are tender, faithful, and strong. Liza and Tania have a sense of justice which includes the women who have wronged them, as well as the men they love. Pure Realism has never achieved anything like these two characters. Indeed, their fundamental principle is deliberate preference of the good before the evil; not because it will bring happiness, even though it brings suffering — simply because it is the good. This seems to these clever Frenchmen an idea impossible to recognize, much more to apprehend. This breadth of scope and grandeur of motive is visible in all Tourguéneff's plots. They deal with those great principles of human action which underlie all our civilization and all our life. Here, perhaps, may be traced his German training. As a young man, Tourguéneff spent three years in Berlin, studying the Hegelian philosophy. He says himself, modestly, that he has no philosophical mind; “I see, and I describe what I see.” Yet every artist has, of necessity, some theory of the aims and processes of art, whether he formulate it or not.
Hegel taught that the object of art was “to reveal truth under sensuous forms.” This theory is equally opposed to the servile imitation of the realists, which, by showing only a part, is false to the whole, and the cramping of art into a moral mold of the moralists. An artist is at liberty to have a moral purpose if he choose, but he must use it as an artist and not as a moralist. "I see, and I describe what I see.” The man who, no matter for what noble purpose he may work, illustrates his moral by improbable goodness and impossible vice, betrays art. He has it on his conscience if he omit or add a shade. Tourguéneff has adopted Hegel's philosophical method. He assumes as true everything asserted of his subject, and then by its self-contradictions evolves the truth. He has also adopted Hegel's prescription of grand motives and a national atmosphere. There is a manifest probability that he has the German's theory of the object of Art, as well as the processes.
But as we examine more closely our first impression, we notice the atmosphere of gloom which settles down on every grand motive or noble character. This it is which makes the critics style Tourguéneff a disciple rather of Schopenhauer than of Hegel. The author's entire " aloofness” (to use a phrase of Coleridge) deepens the feeling. Hegel prescribes complete repose in art, and, since a novel must be founded on collision, the sense of repose is only to be attained by the unity of the work, and the author's freedom from those stormy emotions which he describes.
Such a passionless style gives to literature a touch of the eternal calm of sculpture. Possibly, to obtain this calm, something of color and life is sacrificed. In cases where the current of the story bears the frail beings who live in it to destruction, the spectacle of the author impassively surveying them from the bank gives a certain sensation of coldness.
Tourguéneff never pities, and he never preaches. His - Journal of a Sportsman” deals with the same subject as that of “Uncle Tom's Cabin,” but it is impossible to imagine a stronger contrast to the moral gush of that excellent book. He is so impartial that he seems indifferent. He does not choose pleasant themes, nor does he ever shrink from following them “ to the bitter end."
This indifference shows sometimes like actual cruelty. He seems to excite the reader's interest merely that he may the better lacerate his feelings. It is something like persuading a boy to take off his jacket so as to thrash him with more effect.
Tourguéneff draws a fine nature — young, generous, ardent — and then, by a series of temptations, deliberately pulls it down and leaves it writhing in the dust, despising itself and perforce despised by the reader. He flings a great passion on a proud spirit and crushes it. He pits an honest man against an egotist with as small manners as