And as little, or rather still less, would it be just to deny to the age all love—if, at least, an enthusiasm which readily and cheerfully makes the greatest sacrifices be a part of love. Consequently, I can not concur with the opinion which will not concede to the age in which we live the least spark of hope. Even though many of its expectations—as being at least precipitate or wholly immaterial—as being founded, in short, on naught—have terminated in naught, and even in their desired fulfillment, must have ended in a nullity—still we dare not, therefore, throw aside all higher, holier, and diviner hope. For in this we feel every earthly expectation, so far as it is real and well-grounded, will receive its final accomplishment, being realized to a degree surpassing all that we had ever ventured to look for. And even if dark clouds are again gathering on the horizon, and if to many an observer, whose position in the political world affords him a wide and distant prospect of society, the dangers menacing our own generation seem still more fearful and terrible even than those which have but scarcely passed away; still there is no need of despair. Rather, taught by past experience in like fearful circumstances, and recognizing in this lesson of experience a teaching higher than man’s, we will, even though our fears be fulfilled in the worst and most awful form, regard it all as probably forming, if not a necessary, yet certainly a most salutary crisis of transition to a higher state of divine hope. To this divine hope it is sufficient for me thus briefly to have alluded. For whatever I have at any time in my past life attempted—it may be feebly and inadequately—to give expression to, and all that it is my object to convey to my present respected auditory, and all that hereafter I shall have to say in this world, has had and will have no other end or object than to point to and to preach this sacred and eternal hope of a true, not merely earthly, but profoundly new era, and of a spiritual life advancing in it toward the perfection of majesty and glory. To gain a full assurance for such a hope, and to establish it to the best of my power firmly and immovably among the actuating motives of life, has ever been and will always be my first and dearest wish.

But still, though the poet’s distich, in its immediate reference to our own days, requires to be greatly qualified, I would, nevertheless, venture to apply it to art. At least, it admits of such an application; though in this case likewise it must undergo some restriction and limitation. As passed even on the present condition of art, the sentence is harsh, if not unjust. If, however, there ever was or should be a time of which, if not strictly and absolutely, yet generally and on the whole, it could with truth be asserted, that the existing condition of art “had neither faith nor love,” then might we go on confidently to add the inference, “How then should hope remain for it?”

I must once again repeat it: such a sentence, if applied to German art in our own days, would be both harsh and unmerited. If, however, art—which itself is nothing but the significant hieroglyphics, the deeply-moving and elevating song of eternal hope—should have for its basis, instead of a true and unwavering faith, one merely artificial and self-imposed, or at best, the unreal faith of feeling, fugitive and transitory, and unable to stand the fiery trial—if, too, love, instead of being deep-felt and profound, be but the cuckoo-note of a fashionable admiration, unthinkingly caught up and repeated without nature; then the harsh sentence we have just quoted, together with its sad inference, finds a due application. At least, it is so far applicable as it is true that in this sad deficiency of living faith and earnest love, we can alone discover an explanation of what otherwise seems so strange in the history of art within the recent century. If, after many a truly noble beginning, the further development and result corresponded but little and most imperfectly with the expectations that had at first been excited—if, with truly great talents and rare endowments of genius, so much has fallen to the ground, like imperfect blossoms, without maturing any useful and lasting intellectual fruits—it was simply because art was deficient in this its firmest basis. And partly it was, also, because she mistook and was unable to take her proper position in the times, or even if she did understand, was too weak to retain it by an abiding feeling of love. For the true position of art must not be misunderstood, nor the natural order of things reversed, if it is truly to flourish, and the age itself is not to be deprived of, or checked and disturbed in, its true enjoyment of it. True art and poetry are the beautiful crown, the promising blossoms, yea, the very flowers of hope, on the nobly-grown tree of humanity, as it widely expands itself in rich and marvelous intellectual development. But it can not also be its root; and if any where it pretends or desires to be such, there assuredly some strange perversion must exist, or some profound and essential defect must have led to so singular a pretension.

We hear, no doubt, in horticulture, of inverted trees, whose heads being placed in the ground, strike root and grow, while the natural root freely develops itself into branches and leaves. The experiment so successful with plants can not be imitated in mental matters without fearful peril. Here the blossoming crown, if reversed, will not take root, and never bear real and genuine fruit. No! an absolutely æsthetic foundation is insufficient even for this life, and much more so, then, for the next. Of the origin of life and the world, a mere poetical view of things can give but a specious and cleverly-evasive account; but as good as none of that of hope, of which, in such a case, it must wholly have lost the clew. If, then, that which is at most but the bright morning tint of hope should seek to keep back the sun, or would set itself up for the true luminary, then—supposing it for a moment to be possible—it would itself soon lower into dark clouds, and instead of the longed-for splendor of the full and glorious daylight, a dull, gray sky would cover the whole earth. This intrinsic weakness often betrays itself in poetry (and frequently, also, in other spheres of human invention), by what at any rate appears to be an inflated display, which, instead of concealing, does but create a suspicion of a deep internal hollowness. What I allude to may take two forms. Sometimes it manifests itself in an excessive luxuriousness—often we might call it a very deluge—of the most unintelligible exaggerations of sacred feelings, such as I regret occasionally to observe in our modern school of poetry. At other times it comes forward in an equally lavish and boundless prodigality of wit and raillery; sometimes, too, a serious humor lurks in the wit, while a mocking parody makes sport with the very humor, or a still loftier tone of irony, from its height of spiritual exaltation, soars above both wit and humor, and the whole work itself—nay, above all besides, and even the very universe. It is in this one-sided preponderance, and in the absoluteness with which reason or fancy is allowed to take a decided but exclusive direction, that the first cause lies of that alienation already mentioned as subsisting between men of a purely æsthetical temperament and poetical nature, who on the one side judge of every thing by the rules of taste, and the men of practical reason on the other, whose only standard is utility. This estrangement is only too apparent in real and actual life, where in the degree which we have supposed, and by the methods ordinarily pursued, it is utterly irreconcilable. They stand, indeed, as fully estranged from each other, and as hostile, as two wholly different races. And in this light a well-known savant, at the close of the last century, seems really to have regarded them, since, on the whole face of the earth, he saw only two races—noble-minded, elegant, and tasteful Celts, and dull, ordinary, and stupid Mongols. Here, however, I must repeat my previous remark, that, in these days at least, by far the greater danger is to be apprehended from an absolute ascendency of reason. For the rationalizing system of thought which results from such one-sidedness, is not confined merely to the schools and their scientific theories, but it too often extends its pernicious consequences, and its fatal and debasing influence, over the whole range of public and social life. On the other hand, the slight aberrations of taste, or (if they most be accounted such) the little extravagances of genius, may always be easily and promptly reduced within due limits, especially in an age like our own, so thoroughly pervaded with a correct feeling of art.

To give a solid basis to the whole of life, a firm internal conviction is necessary. It must be a deeper feeling than any that a mere aspiration, however beautiful, or any poetical visions of enthusiastic hope, or even that irony which exalts itself above both, can ever give. Now, for the attainment of this inward certainty and irrefragable science of life and truth, pure thought, though it does not form the only road, is, nevertheless, in every case a necessary agent, whose co-operation is indispensable. In the further prosecution, therefore, of our pursuit of the science of life, as deducible from the very notion of the consciousness, according to that theory of it which we have been developing, thought, in and by itself, must now, as we hinted in our first sketch, form the subject of a special inquiry. But here the principal thing to be guarded against is, the delusion that philosophy must aim at the rigor of mathematical certainty, and a mode of proof derived, on such an hypothesis, from that science, by a servile copying of its method; for, often as this has been attempted, it has never as yet led to a felicitous result. This misconception in the domain of science is something like to what it would be if in poetry, from an undue consideration of music, the mere play of tones—the rhyme and rhythm—which do indeed contribute to the ornateness of its figurative investiture, should be held to be the very essence of the art. Or, to take another illustration, it is much the same as if, with some of the more recent English poets, we should wish to make picturesquely descriptive poetry to be a peculiar species; whereas in truth it forms, or has a tendency to degenerate into, a mere faulty mannerism.

You will remember that I explained a notion to be a conception completely determined, both inwardly and outwardly (i.e., in extent and comprehension), according to the mathematical dimensions of number, measure, and weight. But this, perhaps, is the only mathematical formula that in the domain of philosophy is universally applicable. And even as such it only applies to the notion as a standard and fundamental idea by which we may judge of the correctness of its formation, and the completeness of its division into its several organic parts, or lower genera and species. It is no use further for the combination of the several notions into entire scientific periods and conclusions; for we may regard every complete system of science and speculative thought as some such perfect period and syllogism. But with regard to the notion and its object, it is unquestionably of the highest importance to determine whether it be absolutely simple or compound. If the latter, it may suggest many questions. If double, it may fall into an intrinsic contrariety, or be involved in a twofold want of harmony. If it numbers three constituents, we may have to inquire whether in its triple energy it enjoys a living unity of operation; or if possessed of four opposite directions, it may be involved in binary contrarieties and double discord; or, again, we might have to inquire whether the essential accession of some fifth element forms the living center to hold together and reunite the four which otherwise are divergent and apart; or whether the whole in triple couplets, or a double trine, forms a six; or whether seven arise from the union of a trine and quartain, either in the world of thought, or the realities of life and outward experience; and again, eight may be a double square in the one or the other relation; or yet once more, we may have to inquire whether in the still advancing inward reckoning and development of life, nine arise from a thrice repeated triple energy. And lastly, whether all these first elementary numbers are in various ways perfected and combined together in the decade.

Rightly understood, the Pythagorean theory of numbers—however unintelligible its single statements may appear, when detached from the general context—is perhaps as little devoid of foundation as the Platonic doctrine of anamnesis. The latter I have endeavored to justify, by explaining it in a better sense than it is ordinarily taken; the former, however, from a deficiency of original and genuine historical authorities, it is far more difficult to judge of correctly and impartially. In the first place, the Pythagoreans as a body stand very far indeed above the ordinary standard of the Grecian intellect and enlightenment; for Plato was but a single great mind, and stood almost alone even in the Socratic school.

The degradation of the female sex, though founded on the habits as well as political institutions of the rest of Greece, was decried by these earnest and deep-thinking men, who, in their reform, adopted quite an opposite sentiment. And if in their measures for its removal something seems still to be desiderated, and even something to be blamed, both defects arise chiefly from their having fallen into the other extreme of error, by proposing to give to woman a culture too decidedly masculine, and seeking to establish it as the rule of their new society. Women were concurrent and co-ordinate members of the governing body of the Pythagorean league, and an essential element of the splendid aristocracy of merit in this new model of life and society; which, however, as clashing too directly with the inveterate habits of their countrymen, soon provoked a revolution, and was entirely overthrown. It was, however, from this source that Plato, and also Socrates, chiefly derived their respect for highly-gifted women and their general view of the female sex; which in a degree, though very imperfectly, anticipated the purer Christian notion both of it and human nature, possessing on the whole a right but vague notion of the true dignity of both.

With respect to the theory of numbers in this ancient philosophy, and its true and simple sense, we have the following remarks to make. There is, we know, a certain chronological feeling by means of which the skillful physician strives, with acute and often happy conjecture, to determine the impending crisis of disease and its probable termination. There is also a similar tact which enables the experienced politician to measure the under-current of the rapid flow of mundane events—to feel the pulse of life as it beats in its thronging and quickly-passing incidents. In both cases, however, we feel that it is no infallibly certain and perfectly omniscient oracle—for none such is to be found in the whole range of the human mind. Neither is it any prophetical forecasting—not to speak of any pre-destined necessity. It must be regarded as a delicate and sensitive tact, which may deceive, but whose perceptions subsequent results most frequently prove to be correct. Now, of somewhat similar nature to this, there is a kind of immediate, searching, arithmetical glance into the internal and essential numerical relations of things in general, and also of all the objects of nature and phenomena of life, which does unquestionably form an essential element in every innate talent for scientific thinking. In some such simple sense as this we may understand the Pythagorean doctrine of intrinsic life-numbers in things and their manifold relations. Under such limitations we may adopt it, or at least allow its validity. And at any rate we must admit that it was an advance (or at least the first step thereto) in scientific thought, to be able, by this way of regarding things, to count, in the analysis of them or their notions, up to ten, or even to fifteen or more.

Thus, then, as regards the general notions (but only in regard to these), the mathematical view and method may be profitably applied to philosophy. In any case it is highly important, and indeed essential, for the correct formation of notions (and also for the complete division of them into their organic members, whatever may be the sphere to which they belong), that we should be able to determine the true inner number, both of them and their objects, since on this number the right quantity and weight of any one notion relatively to others, whether kindred or distinct, and especially to the whole, most intimately depends.