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    1. All three appeared in Königsberg in 1804 (when Kant died). A reprint in one volume, arranged by Alfons Hoffmann, was published in 1902, in Halle, at 2 marks.
    2. Over 2000 up to the time of Kant's death! What, then, may their number be to-day? (Cf. STUDIES ABOUT KANT, I, 469, edited by Von Vaihinger.)
    4. Cf. e.g. the Preface to the PROLEGOMENA.
    5. Concrete examples which might be adduced are: the atomic theory, the idea of gravitation, the metamorphic idea.
    6. This leading position did not last long: Comte is a Polytechnic teacher, Lotze a physician. Mill an official of the East India Company, Fechner a biologist, Spenser an engineer and sociologist, Hartmann an artillery officer, Wundt a physiologist, Nietzsche a Hellenist, etc.
    7. Vide Chamberlain, FOUNDATIONS OF THE NINETEENTH CENTURY, p. 736 et seq. [English edition: vol. ii, p. 241].
    10. Various passages in ANTHROPOLOGY.
    11. This and following passages are from EFFECT OF RECENT PHILOSOPHY.
    12. Vide Weimar edition, part II, 11, 377.
    13. “An attempt to establish a science of meteorology.“ See SELF-EXAMINATION, and CORRESPONDENCE BETWEEN GOETHE AND ZELTER, V, 381.
    15. Otto Harnack makes a notable exception to this in his book, GOETHE AT HIS ZENITH (1887). In Vaihinger's STUDIES ABOUT KANT, vols. I and II (1897, 1898), there is an extremely careful and documentarily exact compilation by Vorländer, entitled, HISTORICAL DEVELOPMENT OF GOETHE'S RELATION TO KANT. I particularly recommend perusal of the Appendix (II, 221 et seq.), where the exact allocation of


the passages marked by Goethe in his own copies shows how frequently and carefully he must have studied them. He even corrected several printer's errors with his own hand!
    16. LETTER TO JACOBI of 10th May, 1812.
    17. THE SORROWS OF WERTHER, letter of 10th May, of the first year.
    18. Conclusion of ANNALS, 1805.
    19. In his OBSERVATIONS ON THE EMOTIONS OF THE BEAUTIFUL AND SUBLIME, Kant says: “The Barbarians introduced a certain perverted taste, called the Gothic, which tended towards the grotesque.“ This prejudice was so widespread at that time as to require the profound perception of such a genius as Herder to penetrate the fog, and the enthusiasm of Goethe, when a youth, to defend Gothic art with success. Even Herder labelled everything Gothic as “grimacing and old women's tales“ before he had come into contact with Gothic art on his travels. (Cf. his DIARY OF TRAVEL of 1769, towards the end.)
    20. The splendid THIRD PILGRIMAGE TO ERWIN'S TOMB IN JULY, 1775, must not, however, be overlooked: “How many mists have been dispelled from before my sight, and yet thou hast not vacated thy throne in my heart, O all-pervading Love!“ (The MS. is in the series FROM GOETHE'S POCKET-BOOK, Weimar edition, 37, part I, 311 et seq.)
    22. TRAVELS IN ITALY, 8th October, 1786.
    24. WEIMAR EDITION, part I, 48, 249.
    27. VIEWS, PLANS, AND SOME DETAILS OF COLOGNE CATHEDRAL (Remarks on), 1823 to 1824.
    28. Vide LETTER TO ZELTER of 28, VIII, 1823, and the poem RECONCILIATION, dedicated to the pianist, Frau von Szymanowska in the TRILOGY OF PASSION.
    29. ANNALS, 1805.
    30. Part II, 173 et seq.
    31. The statement, to be found in most biographies, viz. that Kant first studied theology, is erroneous. He seems, however, to have intended for some time to study medicine. All the proofs have been collected in Benno Erdmann's MARTIN KNUTZEN AND HIS TIME, 1876, p. 133 et seq.


    33. Westminster Bridge was completed in 1750, and its size and beauty excited attention. It was demolished a century later, and replaced by another.
    34. Cf. Jachmann, IMMANUEL KANT AS SEEN IN HIS LETTERS, 1804, third letter.
    35. Reicke, KANTIANA, pp. 115, 149.
    39. The second lecture treats of Thought and Perception in detail, and the third one of the Senses and the Mind.
    40. HISTORY OF BOTANICAL STUDIES, final paragraph.
    41. Didactic portion of THE THEORY OF COLOUR, § 181.
    42. TENDENCY OF THIS WORK, etc. (in continuation of PLANT METAMORPHOSIS).
    43. I do not know whether the number of caudal vertebrae varies; in his admirable monograph, “The Cat, an introduction to the study of back-boned animals,“ 1881, Mivart says the cat has “about 20“; my cat has 16 caudal vertebrae, which, together with 7 cervical, 13 dorsal, 7 lumbar, and 3 pelvic vertebrae, total up to 46.
    44. Anatomical specialists, as far as feasible, avoid the expression “primitive vertebrae“ to-day, since this allegorical term so disturbs all experimental investigation of actual facts; they almost throughout use the words “primitive segments“ (1908).
    45. Schiller to Goethe, 23, VIII, 94.
    47. As Goethe, when discussing plants, principally employs the term “metamorphosis,“ and, when treating of animals, the words “transformative change“ or also “comparative anatomy,“ it might possibly be objected that I had connected things which bore no mutual relation. This objection would, however, be quite unfounded; Goethe laid especial stress on the identical character of his labours and the opinions he based thereon in all the departments of life. Thus, for example, in the ELUCIDATION OF THE APHORISTIC ESSAY 'NATURE,' he draws particular attention to the fact that he had undertaken the “Metamorphosis in the animal kingdom“ after “Plant Metamorphosis“; thus he makes a


MS. note in a draft of the HISTORY OF OSTEOLOGICAL STUDY: “Model for an Essay on Vegetable Metamorphosis“ (Weimar edition, II, 8, 362); thus in the essay REFLECTION AND RESULT, he applies the idea of simultaneous and successive transformation quite generally; thus, in § 3 of the LECTURES ON THE THREE FIRST CHAPTERS OF A DRAFT COMPARATIVE ANATOMY, he elaborates the same parallelism which I have here attempted to draw, and illustrates it by the same example of the vertebrae. He also gives a comprehensive survey of his study of organisms in his SUPPLEMENT TO THE COLOUR THEORY (first introduction), and partially regrets that the expression “metamorphosis“ should have been productive of some misconceptions. In the absence of further adducible proofs, this is sufficient.
    48. In the course of the following demonstration we will only examine the plant in so far as it is an annual, and develops uninterruptedly from the seed to full fruitage (PLANT METAMORPHOSIS, § 6). The essential theme of the whole book consists only of the so-called “flower“ of the angiosperms, and proof that its component parts are morphologically identical with their foliage, a fact much more satisfactorily established, from the scientific point of view, thirty years earlier, by Caspar Friederich Wolff, without the use of the misleading word “Metamorphosis.“ (Cf. his THEORY OF GENERATION, 1764, second tractate, § II, 79, 80, 81, where the THEORIA GENERATIONIS, of 1759, is further developed, and it is shown that “leaves, calices, blooms, pistils, seed-capsules, seeds, ... are essentially one and the same.“) The value of Goethe's little work does not — which is as often stupidly maintained as denied — consist in its importance to science, but its immortal significance lies in being the pioneer of the world of the eye. Goethe himself afterwards stated that the operculum was to be interpreted symbolically. (LETTER TO ZELTER of 14.X.1816.)
    49. Cf. Chamberlain, THE FOUNDATIONS OF THE NINETEENTH CENTURY, p. 781 et seq. [English edition: vol. ii, p. 296], and the mathematical digression in the third discourse (infra) in this book.
    51. THEORY OF COLOUR (didactic portion), § 622.
    53. Cf. Alfred Kirchhoff's valuable work, THE IDEA OF PLANT METAMORPHOSIS ACCORDING TO WOLFF AND GOETHE, Berlin, 1867 (in the annual report of the Louisenstadt Technical


School), p. 20. Albert Wiegaud's ANALYSIS AND HISTORY OF THE THEORY OF PLANT METAMORPHOSIS, Leipzig, 1846, supplies a philosophically shallow, yet useful, summary of the historical matter.
    54. ED. 1770, VINDOBONAE, p. 301.
    55. Goethe originally had the title HARMONIA PLANTARUM in his mind for his thoughts on plants (LETTERS TO KNEBEL, 18.viii.1787.)
    58. TRAVELS IN ITALY (second sojourn in Rome).
    60. TRAVELS IN ITALY (second sojourn in Rome, July, 1787, Account of).
    61. THE GROWTH OF NATURAL SCIENCE, sketch in the year 1821, Weimar edition, part II, 300.
    63. Kant discovers an analogy in the difference existing between “keen vision“ and “discriminative“ vision, with that between a “keen“ and a “musical“ ear (REFLECTIONS, I, 84).
    64. THEORY OF GENERATION, second tractate, § 5 et seq.
    65. This is expressed somewhat too decisively; because, firstly, historical developments are already hinted at by Grew, a century earlier than Wolff, and, moreover, a fully scientific basis for the said intuitive perceptions was not established till a century afterwards by Hugo von Mohl (1908).
    66. MORPHOLOGICAL STUDIES IN ITALY, the original material for observation and thought, which was first made accessible in the Weimar edition, part II, 7, 282.
    67. I quoted from TRAVELS IN ITALY; the exact words were contained in a letter of 8th June, 1787, to Frau von Stein, with a request to forward them to Herder (1908).
    68. In the only just published MS. material, Weimar edition, part II, 6, 318.
    70. Ibid.
    71. Actual “leaf-roots,“ so-called “Rhizoides,“ are actually present in the vegetable kingdom, but they are different morphologically from roots proper. (Cf. Goebel, ORGANOGRAPHY OF PLANTS, 1901, II, 444 et seq.).


    73. Cf. PURE REASON, second preface, p. xviii, 29.
    74. Goethe himself, who hates abstractions, admits: “Things are after all nothing but differences postulated and made by man“ (CONVERSATIONS, II, 181).
    77. For the sake of clearness of connection I here said “experience“ instead of “perceptions“ and was justified in doing so, because “perceptions make up the whole object of potential experience“ (PURE REASON, I, 95).
    78. LEÇONS SUR LES PHÉNOMÈNES DE LA VIE, 1878, I, 24, 63.
    79. FORMER INTRODUCTION TO MORPHOLOGY, Weimar edition, part 2, § 6, 317.
    80. In the edition of 1882, p. 3, Joh. Reinke, in his STUDIES FOR THE COMPARATIVE HISTORY OF THE EVOLUTION OF THE LAMINARACIAE (p. 7), also says: “Why should we shrink from saying that 'Laminaria saccharina' consists of a simple stem attached at its inferior end and of a leaf standing upright? ... I do not conceive the object of science to be the bolstering up of blind belief, but the making of ascertained facts clearly perceptible.“
    81. PURE REASON, V, 759. About twenty years earlier Kant had already said: “It is metaphysically so wide of the mark to say that the first thing known about an object is its definition, that to say it is the last thing is the truer of the two.“ (INVESTIGATION OF THE CLEARNESS OF THE PRINCIPLES OF NATURAL THEOLOGY AND ETHICS, 2nd observation.)
    82. INVESTIGATION OF THE CLEARNESS, ETC., 2nd obs., example.
    83. The conditional success of this, and its sufficiency for practical purposes only, can be gathered from Goebel's ORGANOGRAPHY OF PLANTS, p. 10 et seq.
    84. As early as 1849, Kölliker showed that in the cranium itself there are cutaneous osseous formations whose alleged similarity to vertebrae is merely superficial: but Huxley then proved that the so-called “Primordial cranium,“ from which the remaining bones proceed, is always produced uniformly and homogeneously. It is true that Gegenbaur's more recent segmental theory afterwards reinstated Oken's


and Goethe's vertebral theory in a restricted sense, because some analogy with a vertebra must necessarily be assumed to exist in every hypothetical segment (Metamer); but he who gives careful attention to § 103 in Gegenbaur's COMPARATIVE ANATOMY OF VERTEBRATE ANIMALS, and then still believes that actual things, and not merely scientific scholastics, are the matters under discussion, possesses that faith by which mountains can be moved, and which must fill every Trappist's heart with envy.
    85. THE LEPADS, 1824.
    86. INTER ALlA, p. 560.
    87. In the face of other authenticated sayings of Goethe's later years, some of which have been and still are to be quoted, I do not think that one mistake of Eckermann's can be altogether excluded. If, however, Goethe actually said “discovered,“ this would prove that he was only able to overcome his inborn and incarnate idea amidst the absolutely peaceful reflection consequent on literary effort.
    89. Vide supra, p. 21.
    90. THE PROBLEM AND THE REPLY. Goethe seems to have often felt the danger of his idea. The works only recently published contain some warnings at the most various times of his life. Thus Goethe, shortly after publication of the principal work, PLANT METAMORPHOSIS, 1790, began a “second attempt“ containing this direct admonition: “The misuse of this idea will entirely mislead us, and rather tend to retard than to advance the march of science.“ And in the aphoristic remarks which Goethe, to which he was incited by studying Decandolle's ORGANOGRAPHIE VÉGÉTALE, he points out that “that first idea, which we consider so valuable, may be of but little assistance, and might rather be a hindrance than a help with respect to the determination of many organisms“ (Weimar edition, part II, 6, 279 and 357.)
    91. LETTER TO ZELTER of 15.i.1813.
    92. Letter to Chancellor von Müller of 24.v.1828, as ELUCIDATION OF THE APHORISTIC ESSAY “NATURE.“


    99 ANNALS, 1810.



    1. In several passages; e.g. THE WORLD AS WILL AND PHENOMENON, vol. I, § 36.  Vol. II, chap. xiii; Parerga, II, § 35.
    2. According to a note in Hoefer's HISTOIRE DES MATHÉMATIQUES, 4 ed., p. 439, Roberval, a contemporary of Descartes', and a well-known mathematician, was aimed at by the silly saying. Of course, it is nothing but the spiteful invention of a joker.
    3. Since writing these words (in 1900), fuller study of Schopenhauer's methods of work has brought about very serious results. My attention being aroused by Hermann Cohen and August Stadler, I was convinced that intentional misquotation — although doubtless made under the influence of unconscious suggestion, yet not on that account less successful — is an absolute habit in his case; he makes prolific use of it in his criticism of Kantian philosophy; several proofs of this will be adduced in the last discourse. He goes to work in the same way in his disquisitions on mathematics, a fact of which Professor Alfred Pringsheim gave documentary proof in his academic Festival speech, “On the value and alleged worthlessness of mathematics“ (Munich, 1904, and with abridged references in the supplement to the Munich Allgemeine Zeitung, 14th and 16th March, 1904). In order to obtain decisive testimony for his depreciation of mathematics, he falsifies Baillet (Descartes' biographer); he falsifies Descartes, and also falsifies Georg Christian Lichtenberg. In this way he cunningly manages to make Descartes — one of the greatest men of mathematical genius of all time — and Lichtenberg — an eminent physicist and astronomer — appear to speak slightingly of mathematics. After a detailed exposure in Descartes' case, Pringsheim comes to this conclusion, viz.: “The fact that Schopenhauer, in spite of everything, dared to quote this great mathematician as one of his witnesses for the worthlessness of mathematics, must be said to be an unheard-of and in-


famous historical forgery“ (p. 18). For fuller information I refer the reader to the aforesaid Festival speech and also call his attention to the fact that the words quoted in Baillet's biography are almost word for word taken from Descartes RÈGLES POUR LA DIRECTION DE L'ESPRIT (éd. Cousin, XI, 218 et seq.), which neither Schopenhauer nor his authority, Hamilton, knew, and Pringsheim seems for the moment have overlooked.
    5. From Jean Paul Richter's edition of SCRITTI LETTERARI DI LEONARDO DA VINCI, § 653. (Quoted in future as R.)
    6. LEONARDO DA VINCI'S BOOK ON PAINTING, edited, translated, and explained by Heinrich Ludwig, 1882, § 16. (Quoted in future as L.) Here I once for all remark that I have in general taken the Italian text as I found it in the copies to hand, and it is therefore sometimes modernized and sometimes archaic and — according to the ideas of to-day — unorthographic.
    7. LES MANUSCRITS DE LEONARD DE VINCI DE LA BIBLIOTHÈQUE DE L'INSTITUT, PUBLIÉS PAR CHARLES RAVAISSON-MOLLIEN, F, folio 41 recto. The various MSS. are marked from A to M. (Quoted in future as R.M.)
    8. R.M., F, folio 5 recto. “There are many stars which are many times larger than the star which we call the earth.“ To the best of my knowledge no one has so far called attention to the fact that the expression molte stelle seems to prove that Leonardo believed not only in the actual size of the planets but also of the fixed stars, and thus showed himself greater in this respect than Copernicus.
    9. Cf. R.M., A, folio 64 recto, F, folio 41 recto, R., § 858, etc.
    10. R., §§ 848 and 850. Vide also the careful drawings of the interior anatomy of the heart in R.M., G, 1 verso, which prove that Leonardo's opinions were based on careful dissection.
    11. Vide chiefly Gabriel Séailles, LEONARDO DA VINCI L'ARTISTE ET LE SAVANT, Paris, 1892. Recently Marie Hertzfeld's book, LEONARDO DA VINCI, THINKER, INVESTIGATOR, AND POET, has appeared, containing a selection of his writings, and said to have a comprehensive introduction.
    12. Vide L., § 831, and generally the whole of part 6, DE LI ALBERI ET VERDURE, where there are acute observa-


tions on many of the complex questions with regard to ramifications, inflorescences, homodromy and heterodromy, etc., with which the nineteenth century has been occupied.
    16. Cf. supra, p. 97.
    18. I advise those who prefer to wander on different, concrete, paths, in order to arrive at the same result, to read Wilhelm Wundt's little book, AXIOMS OF PHYSIOLOGY AND THEIR RELATION TO THE PRINCIPLE OF CAUSALITY, 1886, where the historical origin and inevitable truth of the basic axiom: “all natural causes are causes of motion,“ are expounded with amazing clearness. The physiologist, Adolf Fick, also explains that the sense of space and the sense of time in combined operation create “a sense of velocity,“ in § 13 of his TEXTBOOK OF THE ANATOMY AND PHYSIOLOGY OF THE SENSE-ORGANS.
    19. Empty space would do just as well, if we only chose to conceive a continuity of interacting motions. — In a speech made at the Jubilee celebration of his fiftieth year of professorship, Lord Kelvin said: “I cannot suppress the conviction that we are on the road to a comprehensive idea of matter in which all its qualities will be regarded only as attributes of motion.“ (This quotation, as well as the one from Armstrong's book, is taken from the certainly reliable reports of the English periodical NATURE.) The physicists led the way, and now the chemists are already following in their footsteps. Ostwald, with respect to theoretical problems, one of the ablest living German chemists, defines as follows: “Matter is nothing but the sum of magnitudes of energy distinguishable in space“ (STUDY OF ENERGETICS, II, REPORTS AND PROCEEDINGS OF THE ROYAL SAXON SCIENTIFIC SOCIETY, 1892), and in his MAIN LINES OF INORGANIC CHEMISTRY, 1900, p. 19 et seq., he repudiates the hitherto usual expressions “conservation of substance“ or “conservation of matter“ and substitutes for these the idea “conservation of ponderability.“ For, as he says, by “matter“ one understands vaguely something endowed with all corporeal attributes, and this indeterminate something is better expressed by simple magnitudes of energy — that is, partly perceptible, and partly potential, motion.


    20. ON FANTASTIC VISUAL PHENOMENA, 1826, § 186 and § 188 (the latter is a misprint for 34).
    21. GOETHE AS NATURALIST, 1861. This excellent work must be recommended to all Goethe students even to this day.
    22. MECHANICS, vol. 59 of the Library of International Science, 3rd edition, 1897, p. 472 et seq.
    23. My brother, Basil Hall Chamberlain, points out that Mach's explanations are in general based on ignorance of the facts; for Chinese writing is in reality not ideography, and it is just this script which, more than any other in the world, is very fertile in suggestive side-values, and for its complete comprehension presupposes thorough familiarity with an extremely rich form of culture (1908).
    25. LETTERS TO ZELTER of 11.iv.1825; 10.vii.1828; 1.xi.1829.
    26. In KÜRSCHNER'S EDITION OF GOETHE, vol. 35, preface, p. 30. The sentence: “Goethe starts just where natural philosophy stopped short,“ is not perhaps very well chosen; natural philosophy neither leads up to Goethe, nor Goethe to natural philosophy; the slip of the pen might lead the inattentive to suppose so.
    28. HANDBOOK OF PHYSIOLOGICAL OPTICS, edition of 1867, p. 268.
    29. Whewell, the historian of the inductive sciences, also confesses his belief that everything in physical science depends principally on the definite and firm control of abstract ideas. (HISTORY OF THE INDUCTIVE SCIENCES, ed. 1857, I, 282).
    30. PRINCIPLES OF MECHANICS, Introduction, pp. 1 and 2.
    31. At the end of his days (towards 1830), Goethe expresses a similar view in his own way: “It will always on strict examination be seen that one presupposes what one finds, and finds that which is presupposed. The naturalist must not be ashamed as a philosopher to move this way and that in this oscillating system, and to make himself understood where the scientific world fails to come to a definite conclusion.“ (Weimar edition, part II, 6, 351.)
    33. The educated layman will find reliable scientific information about the theory of “electrons“ in Lorentz,


VISIBLE AND INVISIBLE MOTION, 1902, chap. VI. Aether is still the effective agency according to this theory, which is based on the vibration of the electrons and not of the aether, so that the idea is actually quite new. But I am of opinion that it is also very artificial and coarse, and therefore inadequate. (1908. For exact information about the views at present held by the most eminent physicists, I recommend in particular P. Lenard's Nobel-lecture ON KATHODIC RAYS, 1906.)
    34. Kant draws attention in his inimitably simple way to the fact that “dull, limited intellects“ are just those which, lacking a proper amount of understanding and original ideas, show a peculiar aptitude for becoming fitted to be specialists (v. PURE REASON, p. 173, Notes). Therefore, he says, “it is not unusual to come across very learned folk who allow their incorrigible want of power of judgment in the use of their knowledge to be apparent.“ We ought to learn how to discriminate between savant and savant as we do between priest and priest, and bestow our admiration and confidence only on the few truly eminent minds.
    36. The quotation (and inter alia, p. 31) is given literatim et verbatim; Helmholtz not infrequently makes use of such a peculiar construction as “Light differs from other light.“
    37. In the most favourable case a normal eye can discriminate from 160 to 165 shades within this limited scale. (Cf. Arthur König, COLLECT. DISC. ON PHYSIOLOG. OPTICS, 1903, p. 368).
    38. Cf. Höfler, PSYCHOLOGY, 1897, p. 115.
    39. By Adolf Wüllner, Edition of 1879.
    40. Helmholtz, LECTURES AND SPEECHES, Edition of 1884, I, 279.
    41. Cf. ON FANTASTIC VISUAL PHENOMENA, §§ 7, 10, 11. Clearly the assertion that “colour is length of vibration“ has not even as much value for knowledge of the nature of colour as the well-known saying of the man who was born blind, that he imagined red to be like the sound of a trumpet.
    42. This is also true of textiles. The dazzlingly white cloaks of certain Austrian uniforms turn dirty light yellow directly freshly fallen snow covers the ground. Cf. Goethe, COLOUR THEORY, § 690.
    44. COLOUR THEORY, introduction.


    46. Goethe also hazarded the thought that it might be “the same Ens,“ which now is manifest as light, now as magnetism, now as electricity and again as chemical action; I only refrained from quoting it in the text, because the actual words as given by Riemer seem doubtful. (LETTERS FROM AND TO GOETHE, etc., p. 302).
    47. Vide e.g. the splendid lecture by the ophthalmologist, Jacob Stilling, in the STRASSBURG GOETHE LECTURES, 1899 p. 147 et seq. Stilling justly says that what is to-day held to be most recent with respect to the colour-theory, means a return to Goethe. He says: “Goethe's theory of colour is more than saved“ [as also Classen in, ON KANT'S INFLUENCE UPON THE THEORY OF SENSE-PERCEPTION, 1866, p. 241, exclaimed “the physiological portion absolutely contains the foundations on which the most recent views are based.“] For looking at the physiologist, Rudolf Magnus' book, GOETHE AS NATURALIST, 1906, lectures 7 and 8, on page 258, one reads: “The physiological optical science of the nineteenth century traces directly its roots back to Goethe's theory of colour.“
    48. HUMAN UNDERSTANDING, IV, 7, § 11.
    50. The recklessness with which Darwin frequently treats facts is beginning to be increasingly recognised. I specially refer to Albert Fleischmann's book, THE THEORY OF DESCENT, 1901. And André Sanson's L'ESPÈCE ET LA RACE EN BIOLOGIE GÉNÉRALE, 1900 (v. e.g. p. 124), contains some quite brilliant instances, not only of false conclusions, but of very serious misstatements of fact.
    51. Cf. Descartes, in particular PRINCIPIA PHILOSOPHIAE, 1664, Kant, METAPHYSICAL PRIMER OF NATURAL SCIENCE, 1786, and Hertz, TREATISE ON THE PRINCIPLES OF MECHANICS IN THEIR NEW CONNECTION, 1894. Hertz really occupies the same standpoint as Descartes plus the profundity of mathematical thought, and the increased experience which two and a half centuries have brought in their train. I am convinced that, in the general view, the mechanical will carry off the palm of victory from the dynamic conception in the future as it has done in the past; for mediocre minds are as little sensible of the absurdity of their assumptions as the Congo black is of his belief that the medicine man can make the


rain come, and the former method has the advantage of having, with a few exceptions, stripped itself of all ideas, and being able to enjoy itself to the full in the field of mathematical abstractions, where every average brain, which has learnt to do some summing, is capable of following without the necessity actually thinking: whereas the dynamic conception is founded in geometrical ideas; however abstract the idea, it must needs still be real, and this — the spontaneous projection before the inner eye — is a demand to which only the minority respond.
    52. The energetic idea might, perhaps, be left unmentioned, it is obviously only intermediate. It is clear that those
physicists who form a third group, in so far as they only assume space and motion but not substance, belong to the dynamic school of thought.
    53. It is, however, always worth noting that the assumption of the physicists, which explains the colours of the prism from the assumed variation in velocity of vibratory duration (or colour), does not correspond with an unalterable mechanical law, according to which the velocity of propagation cannot possibly be dependent on wave-length. Such logical contradictions meet us in all the basic ideas of the so-called “exact sciences“; science properly passes on to the “order of the day“; but it is just here that the thinker finds the point of attachment for the weightiest intuitions with regard to the essential nature of human knowledge.
    54. Were our spirit of invention not so miserably undeveloped, and did not every happy inspiration act deterrently on the birth of additional inspiration, many other facts than prismatic calculation might be made the starting-point for a science of mathematical optics; but they would all agree, in that they originated in theories of motion and led to mathematical schemes.
    55. In this place I did not consider it suitable to mention “time“ as the second form of pure sensual perception, for reasons which can only be expounded at the close of the following discourse. But, for the attentive reader's benefit, I will here interpolate that which can only be made clear much later on towards the end of the book, viz.: that the idea of “pure perception“ is only a scientific abstraction (Cohen, KANT'S THEORY OF EXPERIENCE, part II, p. 320), or, in other words, a methodological assumption on which to base the comprehension of Reason. Pure perception can


in reality no more take place spontaneously and independently of experience than a sensual perception can take shape otherwise than in terms of space. The value of Kant's analysis is shown in its proved practical application, and e.g. eminently just here in the exact and quite intelligible possibility of discrimination it affords between Nature as Goethe saw her, and Nature as seen in the light of mathematical science.
    56. This is obvious to anyone familiar with the subject; I refer those in doubt to Classen, who, in his two books, PHYSIOLOGY OF THE SENSE OF SIGHT, 1876, and ON KANT'S INFLUENCE ON THE THEORY OF SENSE-PERCEPTION, 1886 proves the point in several passages, in spite of the unqualified respect he has for Helmholtz's undying services to science; on page 68 of the latter work, he shows that Helmholtz never knew the real sense in which Kant used the expression a priori; he confuses the “forms“ of perception and thought, without which we could neither see nor think, with intuitive knowledge and innate ideas. And, similarly, our entire psychological psychology — the highest reputations included — stands on the same level of a childish want of understanding. And, in addition, I refer to Ludwig Goldschmidt's KANT AND HELMHOLTZ, 1898, a book with which I, to my regret, only lately made acquaintance; those seriously interested will there find satisfactory information.
    58. COLOUR THEORY, Introduction.
    59. Cf. the experimental researches made by Shelford Bidwell and reported in the PROCEEDINGS OF THE ROYAL SOCIETY, vol. 60 et seq.
    60. SIEGE OF MAYENCE (towards end of).
    61. Leonardo, like the most modern of us moderns, added black and white (with, however, explicit restriction to their use in practice). I quote the chief passage: “I semplici colore sono sei, de' quali il primo è il bianco, benche alcuni filosophi non accettino il bianco ne'l nero nel numero de colori, perche l'uno è causa de colori, e l'altro n'è privatione. Ma pure perche il pittore non po fare sensa questi, noi li meteremo nel numero degli altri, e diremo il bianco in questo ordine essere il primo ne' simplici, e il giallo il secondo, e'l verde n'è'l terzo, l'azuro n'è'l quarto, e'l rosso n'è'l quinto, e'l nero n'è'l sesto“ (L., § 254). This view and arrangement of genuine colours is in precise correspondence with Goethe's theory. And, in


the same way as Goethe in his ATTEMPT TO DISCOVER THE ELEMENTS OF A THEORY OF COLOUR, §§ 1-16 (contained in Hempel's edition only, vol. XXXV, p. 49 et seq., and Weimar edition, part II, 5, 129 et seq.), set forth the reasons why black and white cannot be taken as real colours, and thus classified, Leonardo also devotes a particular section to “Perche'l bianco non è colore ma è in potentia recettiva d'ogni colore“, (R.M., F folio, 75 recto), in which the colour of white is essentially distinguished from others. If now, one considers the remaining numerous passages where Leonardo occasionally mentions green, for example, as a self or primary colour, which is admittedly in practice produced by a mixture of yellow and blue pigments, but solely because these already contain a certain quantity of green, and then, again, of red, and yellow, and blue, it cannot be denied that, although he is writing for painters, and therefore emphasizes the practical side, yet — in his own way — he actually has the idea of “primary colours“ and adheres to it very firmly. Professor Mach's remarks in opposition to Leonardo's (in the former's ANALYSIS OF SENSATION, 2nd ed., 1900, p. 51) turn out to be the merest sophisms; because the only true thing in them is that Leonardo did not commit the same error as himself, viz. of placing black and white in the same category of values as the other colours, an error from which he was saved by the keen truthfulness of his sense of sight. Leonardo is specially reproached with “making a hobby“ of research. Is, then, the “winter of our discontent“ an indispensable state of mind for the observation of Nature?
    62. SEQUEL TO COLOUR THEORY, § 4, COLOUR THEORY, § 705, etc.
    63. COLOUR THEORY, didactic part, introduction, § 696, etc. Even from the purely psychological point of view Goethe is right. Arthur König's investigations prove that the sensation of grey is caused by greatest dilution of visible Violet; if the dilution is lessened, the result is the sensation of blue, or the nearest approach to complete obscurity or entire absence of light (v. König, COLLECTED TREATISES ON PHYSIOLOGIC OPTICS, p. 354 et seq.).
    64. COLOUR THEORY, didactic part, § 523.
    65. Ibid., § 793.
    66. SOME GENERAL CHROMATIC PROPOSITIONS, Weimar edition, part II, 5, 93.
    67. COLOUR THEORY, introduction.


    68. COLOUR THEORY, didactic part, § 752.
    69. PRELIMINARY STUDIES TO THE PHYSIOLOGY OF PLANTS, Weimar edition, part II, 6, 302.
    70. All this is necessary for the fuller comprehension of the term “mathematics.“ To-day the term “universal mathematics“ is meant to convey every kind of definable deductive succession, without the necessity for taking into account number or substance (v. Whitehead, UNIVERSAL ALGEBRA, p. vi et seq.; details in the Plato lecture).
    71. The justification of this is shown in the following utterance by the famous French chemist, Berthelot: “C'est en vain que notre pensée s'efforce de représenter le monde par la superposition de lois simples, purement mathématiques‚ qui dans la realité ne se superposent que d'une façon incomplète, et ne se combinent jamais absolument. Un tel à peu près n'est pas dans la nature; il est dans la représentation que nous nous en faisons.“ (Lecture at the French Academy of Sciences on 22.xii.1896.)
    72. COLOUR THEORY, Introduction.
    74. Cf. Chamberlain, THE FOUNDATIONS OF THE NINETEENTH CENTURY, p. 775 et seq., 884. [English edition: vol. ii, p. 289 et seq., 420].
    75. Walter Pater, THE RENNAISSANCE (ch. on Leonardo da Vinci, p. 106).



    1. DE L'INFINITO, UNIVERSO E MONDI, 5. Dialogue (Lagarde edition, p. 399). “The harvest of the mind was gathered nowhere else than from this our own mind itself!“
    2. “No problem calls more vehemently for a solution than the problem of the nature and the limitations of human knowledge.... To me nothing seems more laughable than boldly to undertake to explain the mysteries of Nature without having once found out whether the mind of man is capable of receiving them.“ (RÈGLES POUR LA DIRECTION DE L'ESPRIT, § 8, XI, 245). Where not otherwise stated, all references are from Cousin's French edition, in XI vols., of Descartes' collected works, 1824-1826.
    3. DISCOURS DE LA MÉTHODE, part III, 1, 153.
    4. Cf. DISCOURS DE LA MÉTHODE, near the close of final part.
    5. Cf. the preface to the PRINCIPIA.
    6. If Kant, then, blames Descartes for his “conclusion by inference“ (PURE REASON, 422 and I, 355) it is due to misapprehension. I needed not in my lecture to touch upon the fact that the specialist will disagree with Descartes as to the present discussion being about the “idea,“ whereas, strictly speaking, “perception“ is the theme.
    7. Cf. also I, 202: “L'obscurité des distinctions et des principes dont ils se servent est cause qu'ils peuvent parler de toutes choses aussi hardiment que s'ils las savaient, et soutenir tout ce qu'ils en disent contre les plus subtils et les plus habiles, sans qu'on ait moyen de les convaincre.
    8. Cf. preface to the PRINCIPIA PHILOSOPHIAE.
    9. DIGRESSION SUR LES ANCIENS ET LES MODERNES; quoted from Sainte-Beuve, Port Royal, 4th ed., V, 354.
    10. It is interesting to note how this sworn foe to every philosophical world-concept, this insensate champion of an absolutely utilitarian, cut and dried, “Science,“ has remained so dear to the hearts of our specialists in philosophy. He is still always extolled in every philosophical text-book

as the founder of a New Era, whereas the naturalists have long since proved; firstly, that the Baconian method is not the method of exact natural investigation, and secondly, that recent methods of natural science were already practised in Bacon's times and led to brilliant results, but upon whichcalling to mind the life-work of Copernicus, Galileo, Harvey, Gilbert, etc. — Bacon poured ridicule, being, as he was, entirely incapable of so much as grasping even the essential of natural science. One need only, on this point, specially compare Justus Liebig's three works of the years 1863 and 1864 (printed in his SPEECHES AND TREATISES), to find them, once for all, conclusive, no matter whether our philosophers are satisfied or not. Goethe passed a delightful judgment on Francis Bacon: “He is the chief of all the Philistines, and, for that reason, they all agree with him“ (CONVERSATIONS 13.X.1907).
    11. Vide e.g. the Oeuvres Inédites published by Foucher de Careil, II, 171 et seq.
    12. Cf. Letters (1631) VI, p. 204; (1638) VII, 436-437; (1642) VIII, 567, and IX, 113; on Pascal, X, 344, 351.  I  have meanwhile been informed that in the BULLETINS DE L'ACADÉMIE ROYALE DE BELGIQUE, CLASSE DES LETTRES, 1889, pp. 632-644, G. Mouchamp drew attention to a hitherto unprinted letter, which incontestably proves that the idea of measuring barometric pressures emanated from Descartes, and that Pascal's experiment only followed the suggestion made by Descartes (cf. DEUTSCHE LITERATUR ZEITUNG, 2.vii.1902, Collection 1975). An expert points out the following fact to me, namely, that, according to L. Edinger, LECTURES ON THE CONSTRUCTION OF THE CENTRAL NERVE-ORGANS OF HUMAN BEINGS AND OTHER ANIMALS, 5th edition, p. 13, “the oldest pictures of cerebral convolutions and fibres are given in Descartes' TRACTATUS DE HOMINE, 1662.“
    13. The fact that people exist, who, like Mach (MECHANICS, 3rd edition, pp. 248, 275, etc.), would fain snatch this credit from Descartes, although even such narrow-minded and inveterate contemners of this great thinker such as Whewell (HISTORY OF THE INDUCTIVE SCIENCES, 3rd ed., II, 20 et seq.) would not have dared to commit such an outrage on historical truth, only deserves to be mentioned because it proves how little the real personality of Descartes, and its incomparable endowments and limitations are generally known. Nobody acquainted with Descartes' individuality will dream of com-

paring his achievements in the experimental establishment of actual facts with Galileo's; but, if Mach imagines he can wipe out Descartes' services to science with such a sentence as: “Descartes elaborated Galileo's ideas in his own fashion,“ he unconsciously falsifies history. Descartes' book LE MONDE was already ready for the press early in 1633 (vide the letters to Mersenne of March and April, and of 22nd July, 1633, VI, p. 224; 230, 236), and in this the so-called law of inertia or law of permanence is expressed with perfect clearness as the première règle (IV, p. 254 et seq.), as well as rectilinear motion (troisième règle, p. 259 et seq.), as the whole so-called “first Newtonian law“ (cf. also Clerk Maxwell, MATTER AND MOTION, § XVI). The law, too, of the quantity of motion (= mass multiplied by velocity) which even to-day continues to play so great a part in our mechanics, has its place in this early work (seconde règle). But Galileo's DISCORSI ET DIMONSTRAZIONE only appealed in 1638 and, as can be proved, Descartes only had his book about the Copernican system (published 1632) in his hands in August, 1634, and then only once for a single day on loan (v. letter to Mersenne of 14th August, 1634, VI, 247). And, furthermore, we should note that Descartes at least discovered the general principle of the law of gravitation independently of Galileo; he did not know it in June, 1631 (VI, 185); yet he was working at it then, and rejoices in 1634 when he finds the assumptions he has meanwhile made confirmed experimentally by Galileo (VI, 248). It is, however, in the teeth of the aberrations of worthy men like Whewell and Mach, consoling to observe that every man of undoubted genius — in the ranks, too, of physicists and mechanicians — such as Clerk Maxwell and Heinrich Hertz, appreciate the undying importance of Descartes at its proper value.
    14. I, 124; III, 21; and cf. letter of 15th April, 1630, in which he hopes to compose his system of the universe so,
qu'on le pourra lire en une après dinée“ (VI, 101).
    15. Even a Whewell admitted and proved that this discovery was indisputably and inalienably his own (I, ch. II, 280 et seq.) as against the attempts which, dating from early Newtonian days, were made to snatch the fame of this achievement from him in favour of some obscure specialist.
    17. Vide, e.g. vol. I, 204; III, 31; IV, 264, etc.
    18. Here I am only speaking of Descartes' philosophic

idea of God; otherwise our thinker was a lifelong anti-fanatical, yet true, son of the Church to which his ancestors held fast.
    19. Knowledge of the sections dealing with stellar motion, such as the third book of the PRINCIPIA, or the 5th chap. of LE MONDE, etc., are not sufficient for an understanding of Descartes' aetheric theory, which he sets up in full knowledge of its sharp opposition to atomism; the most important passages are those in which he treats of the nature of light, I mean the whole first section of the LA DIOPTRIQUE, and chap. XIV of LE MONDE; many important passages are contained in the correspondence, e.g. VI, 56, 104, 204 et seq., 278, 343 et seq., 355; VII, 241, 289; IX, 348, 351; vide also “Règle XII,“ XI, 277.
    20. Communicated by Foucher de Careil, LETTRES INÉDITES DE DESCARTES, II, 236.
    21. Here the formula runs thus: The quantity of energy in the universe is constant. Although we also speak of an energy of position or potential energy, and differentiate this from kinetic energy or the energy of motion, this only shows that Descartes' idea was so indispensable as to give us courage to confront all petty sophisms, and, as it were, to open an account with Nature as our banker; if now we skilfully operate with the “debit“ and “credit“ of the current account, the balance is always a true one; the mind of man can ask no more. Far as it may be from me to want, or even to be able, to write a learned book, I would yet like to protect a remark like the above against anticipated objections, and I do so by reference to the text-book on the PRINCIPLES OF MECHANICS, which is more inspired by genius than those of recent date written by Heinrich Hertz. Here we read in § 607: “The kinetic and the potential energies of a conservative system are to be distinguished, not by a difference in their nature, but only by the standpoint voluntarily assumed by our idea or the involuntary limitation of our knowledge as to the substantial quantities contained in the system. The same energy which can be called potential it a certain stage of our knowledge may have to be called kinetic when the point of view of our idea changes.“ Now, the specialist may perhaps object that these words only apply to what in mechanics are known as “conservative“ and not to “dissipative“ systems and that, strictly speaking, in Nature we only know the latter. But in that case I refer

him to § 665: “And, furthermore, the difference between conservative and dissipative systems and forces does not consist in Nature itself, but depends solely upon the voluntary limitation of our idea and the involuntary restriction of our knowledge of natural systems. If we consider all substances in Nature to be visible substances, every difference ceases to exist, and all natural forces can then be said to be 'conservative'. The latter assumption is the foundation of the natural science of energy of to-day, and although — pace the above — it is in our own power to determine what we wish to regard as being either potential or kinetic, the fact remains that in the idea 'energy' we must always understand two, and two quite different, forms of energy, for which we shall never succeed in finding one unambiguous definition“ (vide the book above referred to, § 26 of the Introduction. The idea of potential energy gains great clearness by Perrin's dictum: “L'énergie potentielle doit être regardée comme localisée dans l'éther“ (LES PRINCIPES, 1903, § 115).
    22. III, 506 et seq., 525; IV, 313 et seq.; V, 6 et seq.; 271 et seq.; VI, 345; VII, 241, 280, etc.
    23. II, 356; III, 507 et seq.; V, 64; IX, 377 et seq., etc.
    24. The hypothetical substance assumed by Descartes which he sometimes names “éther“ and more often “matière subtile,“ filling all space, must not be confused with the “aether“ of the ancients and the schoolmen — from Heraclitus to Bruno; in Descartes' case — and beginning with him — what is in question is a concrete scientific idea, and it corresponds in detail with Kant's definition of matter as being “that which pervades, penetrates, and sets the entire universe in motion.“ The most important passages in Descartes' works from which to gather accurate knowledge of his idea of aether are: TRAITÉ DE LA LUMIÈRE, chaps. II, XII, XIV, LA DIOPTRIQUE, I. Discours (this passage is particularly clear), LES MÉTÉORES, I. Discours, PRINCIPIA, II, § 18 et seq., III, from § 24 onwards, IV. There are also numerous enlightening remarks in the letters; special attention should be given to vols. VI, 278, 343 et seq.; VIII, 241, 289; IV, 348 et seq. It is interesting in this place to note that Lord Kelvin's latest expositions (at the British Association, Glasgow, 1901), with regard to the entire imponderability of aether, coincide exactly with those of Kant, whose doctrine was that aether must be thought of as being “imponderable, incompressible, incohesive, and inexhaustible.“ “It must,“

says Kant, “be a substance which has the quality of rendering ponderability possible in practice (Descartes!) without itself having any weight, — compressibility, without being subject to external pressure, — cohesion, without having any internal interdependence, — and, finally, an all-pervading substance which can neither be exhausted nor diminished and which fills the whole of space“ (TRANSITION, I, 122 et seq.). Lord Kelvin does not go quite so far as this, his whole attention is centred on Imponderability, and he says: “One cannot refuse to call ether matter, but it is not subject to the Newtonian law of gravitation. It is a distinct species of matter, which has inertia, rigidity, elasticity, compressibility, but not heaviness“ (Vide NATURE of 24th October, 1901, and also PHILOSOPHICAL MAGAZINE for August, 1901). But this admission of necessary absolute imponderability signifies an important and decisive step; a few years or perhaps, even a few months ago, laughter would have greeted a similar statement; all it meant was that aether was only very light indeed, and the thirst for more exact information was quenched with this soothing reply: “fifteen trillion times lighter than atmospheric air“; the idea of absolutely weightless “matter“ would have seemed nonsense to our materialist friends. Now, however, the mathematical physicists have spoken, and the other predicates postulated by Kant will soon follow; then only will aether really be “aether,“ for without this unsubstantial substance the human brain must utterly fail to construct matter which is matter — or in other words, a substantial universe. For the mind of man, as Kant has taught us already (v. p. 224, vol. I), legislates for Nature.
    25. HISTORY OF THE COLOUR THEORY, part IV, section “Renatus Cartesius.
    26. Vide Schlichting, GRAVITATION, A RESULT OF ETHERIC MOTION, 1892; P. Gerber, THE VELOCITY OF PROPAGATION IN GRAVITATION, 1905, V. Wellmann in ASTRONOMISCHE NACHRICHTEN, 1899, 148, and the ASTROPHYSICAL JOURNAL, 1902, p. 282 et seq., and cf. F. Ebner in the supplement to the ALLGEMEINE ZEITUNG, 1901, No. 288. Perrin (in other passages, p. 24) says of J. J. Thomson and Lorentz's most recent theories: “On se trouve avoir expliqué l'attraction universelle comme un résidu d'actions électriques.
    27. Ch. I, p. 49. What Hertz means to say is in complete

correspondence with the great basic Cartesian maxim: “Tous les corps qui sont au monde s'entretouchent“ (III, 329).
    28. In order to facilitate the full comprehension of these expositions it may not be superfluous here to quote the precise words of the three so-called “Newtonian Laws“ from the PRINCIPIA MATHEMATICA PHILOSOPHIAE NATURALIS. The first runs thus: “Everybody remains at rest, or continues at the same rate of rectilinear motion, unless forced to alter its condition by forces operating outside it.“ The second thus: “Change of motion is proportional to the effect of the directing force, and takes place in the direction of that straight line in which that force acts.“ The third thus: “Reaction is always opposed and equal to action, that is to say, the reciprocal actions of two bodies are always equal and in direct mutual opposition.“
    29. Vide Clerk Maxwell, MATTER AND MOTION, § 58.
    30. Vide Heinrich Hertz, PRINCIPLES OF MECHANICS, pp. 6—7, and cf. § 469 and § 470.
    31. Cf. § 37 et seq. in Book II of Descartes' PRINCIPIA, and especially LE MONDE, chap. 7.
    32. In discussing the law of inertia, Mach arrives at the conclusion that, in spite of its seeming simplicity, “this is very complex in its nature, because,“ he says, “it rests on inconclusive, and in fact, on never entirely conclusive, experience.“ This discovery troubles him quite considerably; for if the law of inertia once failed to adapt itself, the entire universe (or, at least, theoretical mechanics and the professors destined to expound them) would explode, and so he asks us “to practise a continual control of experience of this law.“ (MECHANICS, 3rd ed. pp. 231—232). One example will suffice to show where these anti-metaphysicians are likely to lead us; for, logically, Professor Mach would have to demand the institution of a permanent State Commission (whose language would of course be Chinese, which would have “continuously to control“ or check the statements that two and two make four. The law of inertia does not, however, in reality depend upon experience at all; it, on the contrary, first creates experience (vide p. 228, vol. I). As Poincaré (chap. I, p. 119) says: “L'expérience ne peut ni confirmer cette loi, ni la contredire.“ It is historically the spontaneous discovery of a genius in the art of perception; it can never be demonstrated from the physical standpoint, but — as Clerk

Maxwell, one of the greatest men of genius in physics of our century, has said — we must regard it as “the only possible scheme of a consistently — logical doctrine, establishing a relation between space and time, which the human mind has so far been able to conceive“ (MATTER AND MOTION, § XLI). All three of these basic ideas — matter, space, time — can only be arrived at on the metaphysical road.
    33. Helmholtz: Preface to Hertz's PRINCIPLES OF MECHANICS, p. xxi.
    34. “Tempus, spatium, locum et motum, ut omnibus notissima, non definio“ (quoted in German pace Wolff).
    35. The following note is not directly connected with the above, and is not intended either to enlighten or confirm: but I imagine that even at this early stage some reader will begin to get an inkling of Kant's metaphysical intuitive perception, which runs: “If space be regarded as a quality pertinent to things in themselves, then space and everything thereby conditioned, is a 'no-thing' “ (PURE REASON, 274). Additional light on the confusion of ideas underlying the assumption of “absolute space“ and “relative spaces“ capable of motion within the former, is given in METAPHYS. PRIN. NAT. SCI., I, 1, 2.
    36. A pure “science of numbers“ — be it said — can only be based on number in the abstract, i.e. algebra or reckoning by means of an alphabet; for a number is in reality the birth of a perception, whereas really pure mathematics have for their object relative magnitudes which only exist in thought, not only without form, but also without number. I ought, indeed, here to say “universal algebra“; but I would rather be found guilty of some slight inconsistency of expression than scare the reader by the use of phraseology unfamiliar to all but experts.
    37. This was not the place to enter into a war of words, and it is, moreover, always a pity to waste any time in fighting “clotted stupidity.“ No thoughtful mathematician ever doubted the “apriority“ of the geometrical view, and Descartes, who had not arrived at the philosophic conception of the essential nature of mathematics as the function of limitation (that is, limitation inwards, but not outwards!) and being possessed of a brilliantly mathematical brain, nevertheless makes merry over the folly of those who maintain that geometrical evidence is a proof of experimental experience. “Lorsque nous avons la première fois aperçu en

notre enfance une figure triangulaire tracée sur le papier, cette figure n'a pu nous apprendre comme il fallait concevoir le triangle géométrique, parcequ'elle ne le représentait pas mieux qu'un mauvais crayon une image parfaite. Mais d'autant que l'idée véritable du triangle était déjà en nous, et que notre esprit la pouvait plus aisément concevoir que la figure moins simple on plus composée d'un triangle peint, de là vient qu'ayant vu cette figure composée nous ne l'avons pas conçue elle-même, mais plutôt le véritable triangle“ (II, 290). Cf. especially the beginning of the fifth MEDITATION, and Gassendi's refutation of the objections thereto. A letter to Mersenne of 1st July, 1641, goes somewhat more deeply, and there Descartes explains that mathematics are in no way “built up on the phantoms of sense perceptions,“ but solely “sur les notions claires et distinctes de notre esprit; ce que savent assez ceux qui ont tant soit peu approfondi cette science“ (VIII, 529). H. Poincaré, the keenest-brained mathematical analyst of our own day, says: “On voit que l'expérience joue un rôle indispensable dans la genèse de la géometrie; mais ce serait une erreur d'en conclure que la géométrie est une science expérimentale, même en partie. Si elle était expérimentale, elle ne serait qu'approximative et provisoire. Et quelle approximation grossière! ... La notion de ces corps idéaux est tirée de toutes pièces de notre esprit, et l'expérience n'est qu'une occasion qui nous engage à l'en faire sortir“ (LA SCIENCE ET L'HYPOTHÈSE, p. 90).
    38. A small note, lest possible verbal obscurity endanger full comprehension. It is customary to call algebraic letters “symbols,“ but one is much inclined to give the name of “schemes“ to strictly geometrical figures — I did so myself above when speaking of painters. But from all that has been said, I hope that the reason why it is so particularly difficult to supply a pure nomenclature in matters mathematical will be readily grasped. Because a letter is a sign for a thought which can only become a “thing“ when aided by a perception, and the geometrical figure is a perception which, as Kant so strikingly observes, remains “blind“ until dominated and controlled by ideas. What value would there be, for example, in the evidence of these visible relations here given in the square of a+b, unless I schematised them in my thought? Here, in mathematics, the relations are so entirely unalloyed and spiritual, that, unless I symbolise my thoughts and schematise my perceptions, I can arrive at no

intuition. The use of the words “scheme“ and “symbol“ as used in mathematics can to this extent be justified; but they must only be so used with a critical consciousness of this relative connection.
    39. Herrmann Grassmann's THEORY OF EXTENSION in two revised editions, one of which appeared in 1844 (republished in 1894) and the other in 1862 (republished in 1895), is in all respects the most weighty work of recent date which treats of the truth so clearly apprehended by Descartes.
    40. Cf. XI, 278, as to the reciprocal relation between “intuition évidente“ and “déduction necessaire“ and its explanation.
    41. Vide MEDITATION, V, and RÉPONSE A GASSENDI (I, 310 and II, 289).
    42. There is not the least possible doubt as to the absolute correctness of the above interpretation, for elsewhere (XI, 298) Descartes says: “L'utilité des mathématiques est si grande, pour acquérir une science plus haute, que je ne crains pas de dire que cette partie de notre méthode n'a pas été inventée pour résoudre des problèmes mathématiques, mais plutôt que les mathématiques ne doivent être apprises que pour s'exercer à la pratique de cette méthode.“ Thus mathematics are not the method, but the method's “handmaiden.“ Even Goethe also recommends the mathematical method for general imitation in his essay EXPERIMENT AS THE MEDIUM BETWEEN OBJECT AND SUBJECT (Weimar edition, II, 11, 33 et seq.). Note also that Descartes revised the French translation of the above-mentioned work personally.
    43. Letter to the Duchess Palatine of 18th July, 1643, IX, 131.
    44. Respecting this, the right word has been said by Gibbon: “Syllogism is more effectual for the detection of error than for the investigation of truth“ (ROMAN EMPIRE, chap. 52).
    45. THE REPUBLIC, Book VII, 525—527.
    46. The subsequent digression into mathematics constituted an indispensable basis for the entire exposition, and preceded the original lecture itself. Now, in working it out, I tried my utmost to dispense with it. Those who feel an unconquerable aversion to the “boundary,“ and yet cannot trust the “railed ladder,“ although it is so constructed that every one can ascend it free from vertigo, may certainly skip what follows and make a connection again at p. 272.

The consequence, however, would be a sensible diminution in comprehension, although not a break in the sequence of thought.
    47. DISCOURS DE LA MÉTHODE, part 2.
    48. RÈGLE 18, ET SUIVANTES. The close relationship is here shown with Leonardo da Vinci, who also likes to symbolise all the operations of the science of numbers and prefers dealing with forms in place of figures. Leonardo's method of extracting the square root is pretty: “Divide a line of any length into as many parts as the number contains units; to these add a unit. Describe a circle of which this (lengthened) line is the diameter; erect a line, which shall intersect the circumference of the circle, at right angles to the diameter at one end; the length of this line is the required square root.“ Vide Ravaisson-Mollien, LES MANUSCRITS DE LEONARDO DA VINCI DE LA BIBLIOTHÈQUE DE L'INSTITUT, MS., A fol., 5 recto; and cf. MS. K fol., 75 et seq.
    50. Cf. Descartes, GÉOMÉTRIE, LIVRE PREMIÈRE, V, 315.
    51. Cf. the detailed explanation in Rule XIV of RÈGLES POUR LA DIRECTION DE L'ESPRIT, XI, 304.
    52. LETTER OF 20TH FEBRUARY, 1639, VIII, 103.
    53. Much interesting matter regarding Descartes is to be found in Cantor's LECTURES ON THE HISTORY OF MATHEMATICS, second ed., particularly in II, 749 et seq., 796 et seq., 856 et seq. Genuine appreciation of Descartes is neither to be expected nor found here; within each department the specialist speaks with a certain spitefulness of the services rendered by his “wonderful visitor.“
    54. Naturally meaning all which do not assume more than three dimensions in space.
    56. The reader is referred to my FOUNDATIONS OF THE NINETEENTH CENTURY, p. 908 et seq. [English edition: vol. ii, p. 450].
    57. “L'entendement pur“ often occurs in the letters as, e.g. V, IX, 130, where he even anticipates the Kantian application of the imaginative faculty; the expression “raison toute pure“ occurs in the first section of part III, 180, of the PRINCIPES; it is true that this work first appeared in Latin, and the Latin text only has the word “ratio,“ yet the French translation appeared several years before the death of Descartes, who revised it carefully, and which is

therefore authentic. (Cf. e.g. letter to the translator, Abbé Picot, of 17th February, 1654, which is misprinted in Cousin as 1643).
    58. Cf. PURE REASON, V, I, 393: “This gap in our knowledge (namely, the celebrated problem of the communion which exists between that which thinks and its extension in thought) can never be filled.“
    59. This is analysed with particular clearness and simplicity by Kant in his ANTHROPOLOGY, § 7: “With regard to the condition of ideas, my mind is either active and exercises power, or it is passive and exists in a state of receptivity. An intuition contains both these states of mind in combination.... Ideas, with respect to which the mind maintains an attitude of passivity, and by which, therefore, the subject is affected ... belong to the sensual, but those which contain mere action (thought), to the intellectual faculty of intuition.“
    60. “Bathos,“ the Inane, not “Pathos“ or passion.
    61. For simplicity's sake, I here said, “the higher mathematics,“ because the example I adduced is actually and historically connected with the inauguration of the higher mathematics; yet directly the matter is submitted to the test of metaphysics, it becomes obvious that there can be no mathematics independent of transcendental relativity: we should not know that two and two is four without perception, and neither can we know it through perception alone.
    62. The Greek word “categorie“ in no way denotes the relation which it is intended to cover. But in Kant's manuscript preparations for the CRITIQUE OF PURE REASON, we find the excellent expression, “Titel des Verstandes,“ or “title granted by Reason.“ His own note to this is: “Every perception must be subjected to a 'title granted by Reason,' because otherwise it would not be an idea at all, and no thought would be thereby conveyed. By means of such ideas we make use of phenomena, or, rather, ideas indicate the method by which we enlist phenomena into our service as the materials for our thought“ (POSTHUMOUS WORKS, I, 39 et seq.). I particularly recommend this name and its explanation to the general reader.
    63. Compiled (with some omissions) from PURE REASON, pp. 305—306 and 161. There is an important leading passage on Kant's interpretation of the categories in the lengthy

note to the preface of the METAPHYS. PRIMER OF NAT. SCI.; this passage should not escape the notice of any one desirous of knowing the true inwardness of the Kantian doctrine. I considered the enumeration of the categories unnecessary and even disturbing in the lecture; for I should have been led into a purely metaphysical region, whereas my object was to dwell upon the perceptive side of Kant's method of thought. Least of all concerned was I with the squabble about the number of pure abstract ideas. It is of no great consequence whether Goethe, at one time, distinguishes a single colour, and, at another, three or four primary colours; the formative principle itself is the decisive factor; the apparent contradictions in the evidence help the comprehension of a thought which evades logical analysis — i.e. of an idea (cf. p. 156). The fact that Kant adhered to twelve as being the number of possible root-ideas may perhaps have been an integral part of his character, deserving no more attention than Goethe's varying statements; but it might with greater probability be due to the accuracy and convenience of his method. The following statement may be quite sufficient for the layman. The logical judgments — on which every one of our ideas is based — can be gathered in groups of three each, with regard to “magnitude,“ “degree,“ “relativity,“ and “value.“ Kant's idea was simply this, viz. that each one of these twelve species of judgment, “inasmuch as applied to perceptions“ (!), must necessarily correspond with a special form of an ideal objective cognition, which form might be called a root concept, born of the “pan-idealising“ reasoning faculty, and incapable of further analysis: the ideas of unity, multitude, universality, underlie the idea of “magnitude“; those of reality, absence, limitation, underlie “degree“; those of persistence, causality, reciprocity that of “relativity“; those of potentiality (and impotentiality), existence (and non existence), necessity (and accidentality), that of “value.“ The first six of these twelve categories refer to objects, the other six to relations; the first three refer to objects in perception (extensive), the second three refer to objects in conception (intensive); the third refer to mutual relativity of objects (physical); the fourth to their relation to ourselves (psychical); consequently the first group stands for three “pure,“ the second, for three “empiric,“ the third, for three “objective,“ and the fourth for three “subjective,“ abstract or root-ideas. The table

below may possibly be of service in making the broad lines of the scheme perceptible.


    64. PURE REASON, § 16, p. 134 et seq. (with omission of two technical expressions which would only confuse the untrained reader).
    65. As Schiller says: “Nature is an idea in the mind itself, of which mind can form no idea“ (ON THE USE OF THE CHORUS IN TRAGEDY).
    66. This also corresponds with history; for the thought: “the world is my own phenomenon“ (born of a fatal misconception of Kantian philosophy), is many years older than the introduction of the Will as a basic metaphysical dogma. In sketches dating from an earlier period, the former theory may be found completely developed; yet at the side of the phenomenon stands, not the Will, but Consciousness. Then from this “consciousness“ grows the idea of an ordinary and a “better consciousness,“ which at first greatly resembles Goethe's terminological “higher consciousness“; now, this double consciousness leads to a “duplicity of the Will,“ to an affirmation and a negation, and the ideal assumption of the Will as the primary thing originates in these. Taken in connection with the explanations in the text, the following confession is especially valuable. On p. 724 of the MEMORABILIA, Schopenhauer says: “Thou shalt interpret Nature through thyself, not thyself through Nature. That is my revolutionary principle.“ This principle is word for word the repetition of Fichte's audacity. Now, as we have seen, according to Kant, the one is just as false as the other, just as meaningless and unreasoning and uncritical; Nature and

the Ego are not to be interpreted the one through the other, but by both taken in conjunction. At all events, this one short sentence proves that Schopenhauer is not among the true disciples of Kant.
    67. PURE REASON, 48, 54, etc. The “inner sense“ as Kant uses the words (v. Antimony II) is a special name for the Ego considered from the standpoint of perception, and therefore points, not to the sensual, but intellectual, side of the understanding.
    68. PURE REASON, p. 48 (fragmentarily).
    69. PURE REASON, pp. 49—50.
    70. Very long ago, William Rowan Hamilton called algebra “the science of pure time.“
    71. The following etymological fact is not without interest. The genuine German word for “straight line“ is “Zeile“ (Middle High German, Zil), and “Zeile“ has the same Germanic root as “Zeit.“ The Indo-Germanic root is “di,“ and it is an important point that the name of the Indian Goddess of limitless space was A-diti, or the “Time-less one“; space cannot be measured without Time; the Immeasurable, in the view of a metaphysically disposed people, is not immensity, but that which is beyond all possibility of measurement — that which lies outside both “Zeile“ and “Zeit.“ (According to Kluge, ETYMOLOGICAL DICTIONARY, and Wilke, GERMAN ETYMOLOGY.)
    72. CONFESSIONS, XI, 25.
    73. PRINCIPES, part I, § 57, p. 99. Tempus est nihil praeter modum cogitandi.
    74. Vide vol. I, p. 242. Even a mind like Schopenhauer's forms a similar judgment: “No human being has ever succeeded in getting a clear notion of this marvellous masterpiece of the schematisation of pure abstract thought“; he then helps us to get over the difficulty by assuring us that “the matter borders on the ridiculous,“ and that Kant's schematic doctrine is “altogether undemonstrable, and merely an arbitrary hypothesis“ (CRITICISM OF THE KANTIAN PHILOSOPHY, Works, II, 532 et seq., of the Brockhaus — and I, 573 et seq. of the Edition de luxe).
    75. Vide vol. I, pp. 87, 148, 243.
    76. Kant himself uses the word “symbol“ more or less in the same meaning as allegory, which was formerly not unusual (v. CRITIQUE OF POWER OF JUDGMENT, § 59; other

passages, CRITIQUE OF PURE REASON, end of 2nd chief part et seq.; Hartenstein ed., 1868, VIII, 541).
    77. Cf. the schematic diagram, p. 261 (vide Lord Redesdale's version).
    78. The chapter in THE CRITIQUE OF PURE REASON frequently referred to and entitled “Concerning Schematism.


    1. Thus, e.g. Francis Bacon of Verulam, who, in chap. I, Book IV, of DE AUGMENTIS SCIENTIARUM, rejects the Copernican hypotheses as inconsistent with the “principiis naturalis philosophiae recte positis.“ More fully detailed in DESCRIPTIO GLOBI INTELLECTUALIS, chap. 6.
    2. Vide DE L'INFINITO, introduction, and first dialogue, where it is said that only the least part, “picciola parte,“ of truth can be derived through sensual perception, whereas its actual life was in the mind (“nel mente in propria et viva forma“), is manifested in the syllogisms of the reason (“nell' intelletto per modo di principio o di conclusione“), and takes an active part in the conflict of thought (“nella ragione per modo di argumentatione e discorso“). Where not otherwise stated, all the quotations from Bruno's works in Italian are from the only authentic edition by Paul de Lagarde (Göttingen, 1888).
    3. Vide chap. 2, Book I, of METAPHYSICS.
    4. Cf. RIGVEDA, 10, 39, 2nd strophe, pace Geldner and Kaegi.
    5. RIGVEDA, 3, 62, 10. The noun-substantive “dhî,“ which is used in the two passages quoted certainly does not mean simple intuitive conception or thought, but a reverential conception, a devotional thought, also contemplation, absorption in sacred things, “Intuitive perception, wisdom, and piety conceived as a Unity.“ It is not, however, open to doubt that this dependent connection as above explained is legitimate; Agni, the real God of Light (the fire on the earth, the lightning in the clouds, the sun in the heavens), is simply called “medhâkâra,“ i.e. “The One Who causes Wisdom“ (RIGVEDA, 10, 91, 8). Thus everywhere we find the synonymity of Light and Knowledge. (According to oral and written statements by Professor Leopold von Schroeder. For proof of the undoubted genetic identity of the Hindu Agni and the Hellenic Apollo, the reader is referred to the same learned authority's study, too little noticed hitherto,

“Apollo-Agni,“ in the Journal of Comparative Etymology N.F. IX, 3 and 4).
    6. DE GL' HEROICI FURORI, towards the end of 4th dialogue of the first edn., Lagarde, p. 664.
    7. Cf. Deussen, THE VEDANTIC SYSTEM, p. 128, and Çankara, THE SÛTRAS OF THE VEDÂNTA (in Deussen's edition), p. 40.
    8. According to Zeller, PHILOSOPHY OF THE GREEKS, 5 A., I, 1, 191, the saying attributed to Aristotle: “Θαλης ωηδη πάντα πλήρη θεών είναι,“ is undoubtedly genuine.
    9. The quotations from Bruno's works in Latin are always taken from the editions by Fiorentino and Tocco.
    10. Vide THE DAY-VIEW AS OPPOSED TO THE NIGHT-VIEW, 1879, pp. 16 et seq., 64 et seq., etc., and cf. the excellent account of Fechner's life and doctrines given by Kurd Lasswitz, 1896, pp. 104, 132 et seq., 144 et seq., etc. The expression “day-view“ is meant to convey that all things are alive and “divinely inspired“ (or possessed of a soul), (p. 16), whereas the “night-view“ is the purely mechanical one which is mainly professed by natural scientists; a differentiation which reminds one of St. Augustin's “cognitio matutina“ and “cognitio vespertina.
    11. For instance, in the CORRESPONDENCE, VIII, 299, 581 et seq., 575, etc., there are particularly clear and dogmatically precise passages (besides the familiar ones in PASSIONS, the PRINCIPIA, and the MÉDITATIONS and RÉPONSES).
    12. Cf. Vâcaspatimiçra's MOONLIGHT OF THE SÂMKHYA-TRUTH in a German Translation by Richard Garbe, 1891, p. 104 et seq.
    13. Inter alia, p. 30.
    14. Inter alia, principally p. 106 et seq.
    15. DISCOURS DE LA MÉTHODE, part IV, 1, 158.
    16. Concerning the methodical importance of consictently differentiating between “the things of the mind“ and “natural things,“ cf. PURE REASON, 708 et seq.
    17. CATAPATHA-BRÂHMANA, 10, 3, 3, 6.
    18. Many years ago, J. J. Weber proved that this idea of the “Logos,“ so directly apparent in Heraclitus, playing such a great part later in Neo-Platonism and Gnosticism, and taken up by Christianity, in which its presence everywhere makes the impression of something exotic and unintellectualised, of something “not led up to“ — incontestably reached us by way of India; because this thought of “Vâc,“ as the

principle of creation which “was before God“ and “was with God“ and “by which all things were made“ (Gospel according to St. John, 1, 1 et seq.), is so characteristic of the Hindu mind as always to have had its place there from the Rigveda downwards until the present time, and persisted there, in spite of all the changes in philosophical concepts which have taken place. What this Logos — God's associate and, at the same time, God Himself, the Holy Ghost “who penetrates Heaven and Earth,“ and “bloweth as the wind, whither it listeth,“ “and no man knoweth whence it cometh or whither it goeth“ (RIGVEDA, 10, 125) — what this Logos may possibly mean, no human being will ever learn from the history of Christian dogma; to know this presupposes the most intimate acquaintance with the Hindu mind. History would be greatly simplified by this statement, which would be none the less entirely and literally true, viz. that the grand, but fatally one-sided, tendency of the Indo-Aryan mind finds its exact expression in the “Vâc-Logos“ idea; the tendency to give thought pride of place to perception; to prefer the “word“ above the “thing“; to “subject“ the subject to the object; and, translating this into terms of practical life, to put “speech“ above “action.“ The sublime conception of the breath of life as the creative agent of the universe gradually dissolved even the world by interpreting the naive mythological equation of “Thought“ with “Being,“ which exists exclusively in thought alone. Hegel made very great efforts to impose a similar system of philosophy during the last century. Cf. Weber's essay, INDIAN STUDIES, IX, 473 et seq., with regard to “Vâc“; also Deussen, GENERAL HISTORY OF PHILOSOPHY, I¹, 146 et seq. Cf. also Max Müller's opinion that originally Brahma was also called “the Word“: THREE LECTURES ON THE VEDÂNTA PHILOSOPHY, 1894, p. 147 et seq. The first chapter of Genesis in “God said: Let there be,“ etc., preserves a faint echo from the remotest past of the “Vâc-Logos“ myth, and Genesis was only composed at a very late, namely, in the post-exilic, period).
    19. Cf. Zeller, PHILOSOPHY OF THE GREEKS, I, 665 et seq., yet without laying the responsibility for my interpretation on this esteemed savant. The last passage: εν το σοφον μουνον λέγεσθαι ουκ εθέλει και εθέλαι Ζηυος ουνομα, is differently punctuated and interpreted by the various learned commentators on Heraclitus, yet Pfleiderer, Bernays, Schuster, Lassalle, Schleiermacher, and recently also Patrick

(THE FRAGMENTS OF THE WORK OF HERACLITUS OF EPHESUS, Baltimore, 1889, pp. 100 and 120) and Diels (THE FRAGMENTS OF THE PRE-SOCRATESIANS, 1903, p. 72) are in accord with the one thing I wished to accentuate in my lecture, and only Teichmüller (NEW STUDIES FOR THE HISTORY OF IDEAS, 1876 I, 127) dissents by translating: “The wisdom called Zeus would and would not only mean unity“ — not a very intelligent rendering, whereas the other one fits the Ephesian philosopher's system spontaneously. And also because it is of interest with regard to modern ideas, I will remark that another main scientific theory of Heraclitus, viz. that universal struggle is the ruling and formative principle (πόλεμος πατηρ πάντων) is undoubtedly borrowed directly from Iranian mythology. Soon afterwards Empedocles, with unusual strength of perception, changes this theory to one in which love and hate are the two leading principles of all motion. We clothe precisely the same myths, only applying them to richer material, to-day in the words “struggle for existence“ and “attraction and repulsion.“
    20. Cf. RIGVEDA, X, 129.
    21. Xenophon also somewhere says that Socrates “avoided going for walks, because nothing is to be learnt from trees and landscapes.“
    22. Cf. Schiaparelli, THE FORERUNNERS OF COPERNICUS IN ANTIQUITY, in the German translation appearing in the ALTPREUSSISCHE MONATSSCHRIFT, yearly vol. 1876.
    23. ACADEMICA, II, Book I, § 8.
    24. Vide chiefly METAPHYSICS, XII, 8. Thomas of Aquinas gives his adhesion to every word of this sequence of thought. He also thinks God is first and foremost the Prime Mover: “Oportet primum movens esse et hoc dicimus Deum“; this is the “Nous“ of Anaxagoras and nothing more. But besides this he comes to the same conclusion as Aristotle, namely, that every celestial body endowed with its proper motion is moved with a special “spirit“ (here called “angelus“), and that as many motions as there are in Heaven, so many motions — caused by the former — there must be on earth: “omnis motus inferiorum a motibus corporum coelestium causatur et ex virtute coelestium corporum haec inferiora formas et species consequentur“ (cf. COMPENDIUM, chap. 3 et seq., 126 et seq., etc.).
    25. “The circle is the original line, because (!) it is the simplest and most perfect“ (Aristotle, PHYSICS, VIII, 9).

    26. Strictly speaking, the auxiliary spheres, or so-called epicycles, are to be imagined as follows: A planet describes a smaller orbit; the (ideal) centre of this smaller circle meanwhile moves along the circumference of a larger (ideal) circle; the centre of this larger circle again moves along a still larger circumference, and so on.
    27. For “Varuna,“ cf. Leopold von Schroeder, INDIA'S LITERATURE AND CULTURE, p. 49 et seq., and the same learned man's so far unpublished work on ARYAN RELIGIONVaruna“ is a primitive Aryan idea very nearly evanescent in RIGVEDA to make room for more concrete images of God. For “asad,“ cf. Deussen's GENERAL HISTORY OF PHILOSOPHY, I, 198, 202.
    28. It will be observed that I introduce the word “organicism“ to denote a philosophic conception of the world, because I felt compelled to oppose a single word of similar formation to “atomism“ in order to express a theory which was just as opposed to atomism as the idea of an organism is to that of an atom.
    29. The method of discrimination between “mechanical“ and “dynamical,“ described in Kant's LETTERS, III, 33, is of great value.
    30. The Darwinians have to-day still further reduced their claims to logic. August Weismann, in his LECTURES ON THE THEORY OF DESCENT, vol. I, p. 213, states that flowers with funnel-shaped petals have bred bees with elongated probosces, and, on p. 217 of the same volume, he states that the said flowers “are produced by such insects“; and on p. 221 makes both these statements at once: “One may then, perhaps, say the flowers, in changing to this or that direction, produced certain kinds of visitors, but also conversely, that certain kinds of insects produced certain flowers.“ Of course one may “say“ what one pleases; it is a case of “bonnet blanc, blanc bonnet,“ or, as the English irreverently express it, “you pays your money and you takes your choice.“
    31. For example, ORIGIN OF SPECIES, chapter 2, last § before the Summary: “a number of species are now manufacturing ... many of the species already manufactured.“
    32. Inter alia, first §.
    33. This natural law of all living things, foreshadowed by Goethe, and called “the key of all formation“ in his poem “Athroismos,“ was first formulated explicitly by Cuvier in

his DISCOURS SUR LES RÉVOLUTIONS DE LA SURFACE DU GLOBE (p. 25 of the 1825 edition): “Tout être organisé forme un ensemble, un système unique et clos, dont les parties se correspondent mutuellement, et concurrent à la même action définitive par une réaction réciproque. Aucune de ses Parties ne peut changer sans que les autres changent aussi; et par conséquent chacune d'elles, prise séparément, indique et donne toutes les autres.
    34. These are those whom Goethe calls “die Umfassenden“ or “the comprisers“ (Weimar edition, 6, 302).
    36. ON MORPHOLOGY. Sequel, Section “Aphoristics.“
    37. HISTORY OF RECENT PHILOSOPHY, 2nd ed., I, 77. In the HEROICI FURORI (introduction), Bruno warns us against a too intensive absorption in the idea of unity at the expense of multiplicity; one would grow blind, says he, “da troppo alla contemplazione de l'unitá, che ne fura alla moltitudine“ (p. 617).
    38. On p. 163 of LA CENA DELLE CENERI, Bruno explains that stars are moved by an “indwelling principle which is the soul itself,“ and this soul is not only a “sensible“ but an “intellectual“ one, more so even than the human soul. “Muoveresi dumque la terra et gli altri astri secondo le proprie differenze locali dal principio intrinseco che è l'anima propria. Credete (disse Nundinio) che sii sensitiva questa anima? Non solo sensitiva, rispose il Nolano, ma anchè intellettiva; non solo intellettiva come la nostra, ma forse anchè più.
    39. ARTICULI ADVERSOS MATHEMATICOS, membrum 3, § 36 (I³, p. 26). It is very remarkable how he makes use of the one Universal Being as a foundation of innumerable unities. “Non igitur falsa, sed altior quam a triviali Peripaticorum sensu perceptibilis, fuit illa Xenophanis et Parmenidis sententia; 'Ens' unum, immobile, quod in rei veritate idem et principium et principiatum; sicut substantialiter praeter unitatem nihil est numerus; quod non est unum, nihil est; ergo unum est ens, unum et verum, multitudo vero relinquitur ut accidens, ut vanitas, ut non ens: ita intelliges ubi monadis vocem audies: 'sum quod es.' Ut ergo praeter monadem nihil est, praeter atomos et puncta nullum est quantum, ita et praeter minimi proportionem et definitionem nulla est mensura, nullus est geometra et nulla consequenter philosophia.“ Truly, an enviable dialectical genius! He assumes firstly that only absolute unity is Being, that multiplicity is a vain imagination,

is Non-existence and thence (ergo) deduces that “praeter atomos“ (atoms, plural) there can be nothing. It is easy to talk of contradiction here, but it is more interesting to note that such a sequence of thought discloses with mathematical certainty the exact point where the diagonal of his inwardly directed thought intersects his, so to say, no less inwardly directed, unsymmetrical vision, and, in opposition consequently to his thought, crosses the mind of Bruno.
    40. “Si ergo contemplatio naturae vestigia persequitur, et in minimo speculando consistat, et in mininium contemplando desinat oportet“ (DE TRIPLICE MINIMO, I, 4, note; Tocco ed., I³, p. 149). Bruno uses all kinds of terms for the atom which vary with his varying views of it: he names it “monas“ (monad, i.e. unity) when he considers it as something spiritual; “minimum“ when he wishes to say the least physical quantity; “punctum“ (a point) when discussing a geometrical system; “Unum“ (One) when treating of arithmetical computation .... Yet the differentiation is not very keenly maintained, and the idea of “atomos“ (or, as Bruno writes it “atomus“) is synonymous with the other terms as is proved by the passage in DE MINIMO, I, 2, so frequently quoted, viz. “Minimum substantia rerum est ... hinc monas, hinc atomus.
    41. DE ANIMA, Book I, chap. 2, towards the end.
    42. ... “censet imagines divinitate praeditas inesse universitati rerum“ ... (Cicero, DE NATURA DEORUM, I, 43).
    43. Cf. his ATOMIC THEORY.
    44. Vide the whole work DE L'INFINITO; e.g. p. 389: “Cotal spacio lo diciamo infinito, perche non è raggione, convenienza, possibilità, senso ò natura che debba finirlo; in esso sono infiniti mondi,“ etc.
    45 The passage in METAPHYSICS, V, 17, where Aristotle makes limitation and form synonymous is interesting: “Limit is the form of that which has magnitude“ (as translated by Bonitz, p. 108).
    46. Vide in particular PHYSICS, III, 7. Bruno's contrary view is pithily expressed as follows: “principium et fundamentum errorum omnium, tum in physica tum in mathesi, est resolutio continui in infinitum“ (DE TRIPLICI MINIMO ET MENSURA, I, 6, Tocco ed., I³, 153).
    47. One passage only, instead of several, on atoms and empty space: “ma philosophie ne réfute rien autre chose que cette philosophie creuse et subtile composée de vide et d'atomes,

qu'on a coutume d'attribuer à Démocnite et à Epicure, ou quelques autres qui lui ressemblent, et qui ne me regardent point du tout“ (letter of 27.xi.1637, VI, 338). In connection with this, cf. also especially § 202 of part 4 of the PRINCIPIA. Regarding the “forces,“ Descartes never tires of ridiculing those “who in this way ascribe little souls to substances“ and, for example “attribute gravity to things in much the same way as thought is an attribute of the human being“ (cf. e.g. Book IX, pp 104, 133).
    48. Cf. the fourth MEDITATION (ed. Cousin, I, 303), where on this point he says: “Je suis entièrement indifferent à le nier ou à l'assurer, ou bien même à m'abstenir d'en donner aucun jugement.“ And should it be objected that this is only a preliminary admission, which is entirely withdrawn in the sixth MEDITATION in favour of absolute dualism, I would refer the objector to the beautiful letter in vol. VIII, p. 586 et seq., where the same idea is developed many years afterwards.
    49. Haeckel's idea of the Universe signifies a relapse of the clumsiest kind into unadulterated mythology, clumsy, namely, because it goes to work not intuitively from force of imagination, but from ratiocination, and because — unlike the mythologies of simple-minded natural races — the hair-raising audacity of his similes, which harmonise no more with perception than they do with logic. This is neither poetry nor science nor philosophy, but a stillborn bastard of this unity.
    50. As against the assertion that Descartes' thought was solely directed outwardly, a hypercritical “literalist“ might object that he often spoke of Infinity in a manner more reminiscent of Bruno than of Aristotle. But real knowledge of Descartes shows that he champions Infinity only as being a necessary attribute of God — therefore from a purely theological point of view — but on the other hand, he sets up exactly the same distinction in science, which was afterwards developed by Kant in such a masterly fashion and by him critically applied, to distinguish the idea of an “Infintitum“ (Illimitable), and of an “Indefinitum“ (Unlimited). Bruno is indebted to Cardinal Cusa for the doctrine of Infinity, which he expounded with so much enthusiastic zeal, and it is precisely in opposition to Cusa that Descartes propounds his own contrary opinion: “Je ne dis pas que le monde soit infini, mais indéfini seulement; en quoi il y a une différence assez remarquable; car pour dire qu'une chose est infinie ou

doit avoir quelque raison qui la fasse connaître telle, ce qu'on ne peut avoir que de Dieu seul; mais pour dire qu'elle est indéfinie, il suffit de n'avoir point de raison par laquelle on puisse trouver qu'elle ait des bornes“ (letter of 6.vi.1647, X, 46. Cf. also OEUVRES INÉDITES, I, 67).
    51. HISTORY OF THE COLOUR-THEORY, part I, sec. 2, and part II, sec. 2.
    52. HISTORY OF THE COLOUR-THEORY, section “Renatus Cartesius.
    53. Vol. I, number 1‚ of the said periodical, p. 52.
    54. Cf. LO SPACCIO, p. 407, and in many other places.
    55. Several narrow-minded specialists thought it right to reproach me severely on account of this and some other similar passages, although the connection and the entire book quite plainly show that expressions such as “our mind is organised“ are only to be taken allegorically (1908).
    56. HISTORY OF MATERIALISM, Book II, sec. I, p. 376 of the 1881 edition.
    57. Conclusion of preface to PROLEGOMENA. The whole paragraph about the “indolence or stupidity“ of those who have the assurance to decide “metaphysical questions“ without even understanding the “true principles of criticism“ should be read.
    58. HISTOIRE DU PEUPLE D'ISRAEL, 13th ed., I, 49.
    59. Cf. LETTER TO LOUIS DE BALZAC of March, 1631, VI, 199.
    60. This connection was for long unsuspected, because Bruno's works could nowhere be obtained; even towards 1810 Goethe complained that they were not to be found (VIII, 189 et seq.); for a long while he seems only to have known that which was quoted in Bayle's DICTIONNAIRE, or six quite brief extracts in all (cf. Schöll, LETTERS AND ESSAYS BY GOETHE, p. 101). An edition compiled by Richard Wagner's uncle, Adolf Wagner, of the works in Italian only appeared in 1830; in Latin they have only been published within the last ten years.
    61. THE REPUBLIC, Book 7, 525—527.
    62. The fact that he treats only parts I and II of the PRINCIPIA, leaving out the entire “monde visible“ upon which Descartes lays special stress, is extremely significant of Spinoza's intellect. Kant, who cares but little for philosophers, did once give vent in a note to his disgust for Spinoza's “arrogance, which knew no limits,“ and showed up the

monstrosity of his mathematical method. Spinoza's philosophy seems to Kant the pure type of a method of thought which is in every particular opposed to genuine scientific critical analysis. (Cf. WHAT IS THE MEANING OF THOUGHT REGULATION?). Spinoza in general seems to be the only person against whom Kant, always so temperate and ready to recognise the merits of others, felt lifelong insuperable antipathy (cf. Professor Friedrich Heman's book on KANT AND SPINOZA in KANT STUDIES, vol. V, especially p. 291).
    63. The English philosopher, Jowett, the famous translator of Plato, very pertinently remarks: “The philosophical tenets of Spinoza taken in their entirety, may be described as the Jewish religion translated into the regions of abstraction“ (PLATO'S DIALOGUES, 3rd ed., II, 21). Spinoza's most recent biographer, J. Freudenthal, also establishes the fact that the impressions made by the specifically Jewish philosophy of religion adhered ineradicably in his mind (from an account of SPINOZA, HIS LIFE AND DOCTRINE, 1894, in the supplement of the MUNICH ALLGEMEINE ZEITUNG, 26, 7 1904).
    64. Cf. the AUTOBIOGRAPHY, ed. 1873, pp. 242 and 144.
    65. DE IMMENSO ET INNUMERABILIBUS, lib. V, cap. 12, v. 1 (Vol. 1², p. 154).
    66. 3rd ENNEAD, book 8, chap. 4.
    67. WORKS, 5th ed., 1837, III, 249.
    68. These excerpts from the preface to the PRINCIPIA in the original Latin text run: “Facile enim observatu est in Magistellis ipsos per eam (meaning 'philosophia vulgaris') rectae rationis minus reddi capaces, quam forent si eam nunquam attigissent .... Unde concluendum est, eos qui quamminimum didicerunt illorum ominum quae hactenus nomine Philosophiae insiquiri solent, ad veram percipiendam quammaxime esse idoneos ... quo plus in ea desudarunt, tanto solere ad verum percipiendum ineptiores esse.
    69. DE LA CAUSA, p. 277. “It is not formed nor capable of formation; it is not limited nor limitable; neither can it give form or definite shape to anything else.“
    70. Cf. ATTEMPT AT A GENERAL COMPARATIVE THEORY, Weimar edition, II, 7, 223, and in APHORISMS FOR MORPHOLOGY, 6, 216.
    71. I quote from Max Müller's English text: “There is one eternal Thinker, thinking non-eternal thoughts“ (THE UPANISHADS, II, 19). Cf. Max Müller's remarks to the

synonymous verse of the “Svetâsvatara-Upanishad“ in the same vol., p. 264, note 4, as to the entirely different gloss of the Hindu commentators which Deussen also accepts in the respective place in the UPANISHADS (5, Välli, strophe 13) (v. VEDANTIC UPANISHADS, p. 283).
    72. Analysed with special discrimination in the first edition of the CRITIQUE OF PURE REASON, first paragraph of  p. 370.
    73. “The false subtilities of the four syllogistic figures,“ § 5.
    75. As in contrast with the expert, the layman has to allege his proof of every statement, I here produce the passage referred to: “La veritá é quella entitá che non è inferiore á cosa alchuna; perche se vuoi fengere qualche cosa avanti la veritá, bisogna che stimi quella essere altro che veritá, et se la fingi altro che veritá, necesseriamente la intenderai non haver veritá in se et essere senza veritá, non essere vera; onde consequentemente é falsa, é cosa de niente, é nulla, é non ente. Lascio che niente puó essere prima che la veritá, se non é vero che quella via et sopra la veritá, et cotal vero essere non puó essere se non per la veritá. Cossi non puó essere altro insieme con la veritá et essere quel medesimo senza veritá; per cio che se per la veritá non é vero, non é ente, é falso, é nulla. Parimente  non puó essere cosa appressa la veritade; perche se é dopo lei, é senza lei, se é senza lei, non é vero, perche non liá la veritá in se; sará dumque falso, sará dumque niente. Dumque la veritá é avanti tutte le cose, et con tutte le cose, é dopo tutte le cose,“ etc. These words are the words of “Sophia“ or wisdom incarnate; I think this one passage will sufficiently indicate this intellect's “modernity“; one need perhaps but to place it side by side with Descartes' RÈGLES POUR LA DIRECTION to understand wherein the difference lies.
    76. Vide the SUMMA TERMINORUM METAPHYSICORUM in several places.
    77. Cf. ACROTISM, Art. XXI, 1¹, 117 et seq.
    78. The reader is referred to the index of names in Vorländer's edition of both these works. (N.B. — A principal passage in the CRITIQUE OF PURE REASON about Hume is entered under “Skeptiker“ and with the erratum, “p. 781,“ instead of 786.)

    80. Domenico Berti, VITA DI GIORDANO BRUNO DA NOLA 1868, p. 362 et seq.
    81. Original edition, 1804, p. 28; Alfons Hoffmann's edition, 1902, p. 17.
    82. Vide preface and appendix to the PROLEGOMENA (1783), “What is the meaning of thought-regulation?“ (1786);Concerning a discovery by which all fresh analysis of the reasoning faculty may be dispensed with by the use of an older one“ (1790); “On the recent adoption of a higher philosophical standard“ (1796); “Explanation with regard to Fichte's teaching of science“ (1799); “Letters,“ etc.
    83. THE ONLY POSSIBLE REASON, etc., part II, 5th consideration, § 2.
    84. Reicke, KANTIANA, p. 164.
    85. Also cf. the notes in the preface to these lectures, p. 5.
    87. INVESTIGATION OF THE SIGNIFICANCE OF THE PRINCIPLES, etc. (Introduction and Second Consideration to).
    88. In VIII, 624, of Hartenstein's edition of 1868.
    89. It is characteristic that Kant, on reaching Descartes, in his BRIEF SKETCH OF A HISTORY OF PHILOSOPHY (Logic, IV), makes no mention of the “cogito, ergo sum“ and other trivialities which still “pad“ our textbooks, but only lays stress upon this single thing, namely, that Descartes “contributed greatly to bring clearness into thinking by the establishment of the criterion of truth, which he considered to consist in the clarity and manifestation of intuitive knowledge.“
    90. Cf. e.g. SUMMA TERMINORUM METAPHYSICORUM, Tocco ed., 1¹, p. 113 et seq.
    91. Vide, inter alia, infra, and specially, DE IMAGINUM, SIGNORUM ET IDEARUM COMPOSITIONE, PRAEFATIO, 11³, p. 90.
    92. SUMMA TERMINORUM METAPHYSICORUM, Tocco ed., 14, 104.
    93. Bruno's connection with the Neo-Platonists is so close that he sometimes follows Plotinus page for page and simile for simile in his own finest works, of which fact one may be easily convinced by help of the notes to Lasson's German edition of DE LA CAUSA; see also Bartholomess, JORDANO BRUNO, II, 320: “Lorsqu'on compare Bruno avec les néoplatoniciens d'Alexandrie, il faut renoncer à citer, parcequ'il faudrait noter chaque page.“ But at first Bruno is connected

with the Lucretian doctrine in regard of spatial infinity and inhabited worlds without end, and with Cardinal Cusa, the chief instructor of his early years (who died 1464, nine years before Copernicus was born. Cf. hereon the Cardinal's DE DOCTA IGNORANTIA, Book 2, chap. 12, and the comprehensive book by J. F. Clemens, GIORDANO BRUNO AND NICHOLAS OF CUSA (1847, p. 142 et seq.). I must take this opportunity of calling attention to the fact that the books of Copernicus were not placed on the Index during Bruno's lifetime, and that Cusa's were held in the highest estimation. I therefore believe that Bruno was condemned by the Inquisition for heresy, pantheism, and defending sorcery, but not for philosophy and natural science. Two pamphlets among the lately discovered OPERA INEDITA by Bruno treat fully of magic and astrology; and these pamphlets are DE MAGIS ET THESES DE MAGIA, and DE MAGIA MATHEMATICA. Yet also in the works longest known, both in Italian (vide specially DE LA CAUSA, pp. 240, 237, and LO SPACCIO, pp. 530, 532) and in Latin (vide specially SIGILLUS SIGILLORUM, pp. 165, 197—199), there are plenty of passages in proof of Bruno's belief in magic, which is intimately connected with his entire conception of Nature. In the DE IMAGINUM, SIGNORUM ET IDEARUM COMPOSITIONE (Tocco ed., II³, 90), we read: “Ille qui in se videt omnia, quique est omnia idem .... Tunc ut possibile esset intelligere omnia, non esset atiam difficile omnia facere.“ In the SIGILLUS SIGILLORUM, he advocates the “transfusio virtutis ab una potentia in aliam“ (II², 176). Here it is interesting to recall that Roger Bacon composed a work, DE NULLITATE MAGIAE, three centuries earlier. None of those who know him will deny that Bruno was a “star“; but in such traits as these the difference between morning stars and stars of evening is brought to light. In this connection it is not unimportant to notice that even although Bruno was a Catholic not altogether free from ecclesiastical censure, he shows still less sympathy with the doctrines of the Reformation. In the great struggle about faith and works he stands with the Pope against Luther, and calls the latter's conception “una vana, bovina et asina fiducia,“ an idle, bovine and asinine belief! And he christens the Reformation, stock, lock and barrel, with the pet name “macchia del mondo,“ the plague and scandal of the earth, and prays God thus: “che le dissipe, disperda et annulle et spinga con qualsivolga forza, braccis et industria sino à la memoria del nome di

tanto pestîfero germe,“ to disperse, destroy, expel, and annihilate the Reformers, by any and every necessary force, weapons, and stratagems until even the memory of such a pestilential brood is wiped out of existence (LO SPACClO, 2ndo dialogo, I parte, pp. 462—468). This “religion of science“ evidently promised to be peculiarly tolerant.
    94. “... si Dio non é la natura istessa, certo é la natura de la natura (works in Italian, p. 533); Dio è vicino, con se et dentro di se, piu ch'egli medesimo esser non si possa; come quello ch'é anima de le anime, vita de le vite (p. 700) abbiamo dottrina di non cercar la divinitá rimossa da noi, se l'abbiamo appresso di noi, anzi di dentro più che noi medesimi siamo dentro arnoi (p. 128) .... Tutti sono principalmente, realmente et finalmente uno ente, una cosa medesima (p. 483).“ The first and last of these quotations are from SPACCIO DE LA BESTIA TRIONFANTE (3rd Dialogue, 2nd part, and 2nd Dialogue, 2nd part); the second from DE GL' HEROICI FURORI (2nd part, 1, 4), and the third from the CENA DELLE CENERI (1st Dialogue).
    95. “God is poured into the Reason by means of Nature; Reason climbs upward through Nature to God“ (DE TRIPLICI MINIMO, 1³, 136). Cf. DE LA CAUSA, PRINCIPIO ET UNO, p. 283 “... é una et medesima scala, per la quale la natura descende alla produttion de le cose, et l'intelletto ascende alla cognition di quelle; l'uno et l'altra da l'unitá procede all unitá....
    96. “L'anima de l'huomo é medesima in essenza specifica et generica con quelle de le mosche, ostreche marine et piante“ (CABALA DEL CAVALLO PEGASEO, p. 585).
    97. Vide all the beginning of 5th Dialogue of the DE LA CAUSA, where all the hundred repetitions in the Italian and Latin works are summarised and expounded with magnificent vigour.
    98. “Nomen unum omnia significans, Ratio una omnia considerans, omnia unus desiderans Appetitus“ (DE MONADE, chap. 2).
    100. DE GL' HEROICI FURORI (part I, 2nd Dialogue, p. 634).
    101. “... l'unitá é uno infinito implicito et l'infinito é la unitá explicita“ (LO SPACCIO, p. 454, and in many other places).
    102. “Nativitas est expansio centri, vita consistentia sphaerae, mors contractio in centrum“ (DE TRIPLICI MINIMO, 1, 3, note, Tocco ed., 1³, 143).

    104. BRIHADÂRANYAKA-UPANISHAD, 4, 4, 22 (inter alia, p. 479).
    105. MEISTER ECKHART, Sermon 98 (Pfeiffer ed., p. 316).
    106. “... dalla monade che é la divinitade, procede questa monade che é la natura, l'universo, il mondo, dove si contempla et specchia come il sole nella luna“ (DE GL'HEROICI FURORI, 2nd part, end of 2nd Dialogue, p. 724).

    107. Cf. DE IMMENSO, LIBER VIII, cap. 10 (1², 314); DE TRIPLICI MINIMO, part I, canto 4, vv. 18-19, and SUMMA TERMINORUM METAPHYSICORUM, 14, 73: “Deus est substantia universalis.... Sicut enim Natura est unicuique fundamentum entitatis, ita profundis naturae unius cujusque fundamentum est Deus.
    108. Once we find Bruno treading the Cartesian road: “evidens est, Deum non decipere nec decipi ... ita ... absque ulla haesitatione evidens esse censendum est, quidquid ille proponit credendum esse verum,“ etc. (14, 100). But he deduces no conclusion which might be profitable for the intuitional theory, but only the abstract axiom that Nature, which either itself is God, or Divine power manifest in things. (“aut Deus ipse, aut divina virtus in rebus ipsis manifestata“), will never be found out of harmony with the word of God or His will (“non opponitur verbo Dei,“ etc.), whereby we have again got to what Kant calls “babble.“
    109. ARTICULI ADVERSOS MATHEMATICOS, memb. 3, art. I, § 4, § 23. Kant, on the other hand, reminds us: “The simple (i.e. then, the Indivisible) ceases to be matter“; it follows also that it cannot supply any element for the construction of the visible universe.
    110. DE TRIPLICI MINIMO, notes to I, 6 (1³, pp. 151, 154). This work in particular (and before all the first book, DE MINIMI EXISTENTIA, and the third, INVENTIO MINIMI) ought to be studied for Bruno's THEORY OF THE MINIMUM, and DE MONADE NUMERO ET FIGURA, as well as the above-mentioned ARTICULI ANVERSOS MATHEMATICOS. The reader will find the most illuminating elucidations on this problem of infinite divisibility — a problem which, of course, only admits of metaphysical solution — in Kant, METAPHYS. PRIMER OF NATURAL SCIENCE, 2nd chief sect., 4th theorem, note 2.
    111. “Omnium corporum vis est in sphaera, omnis spherae vis est in circulo, omnis circuli vis in centro, vis omnis visibilium

est in invisibili. Minimum quantitate est virtute maximum, sicut potentia totius ignis in virtute scintillae ignis sita est. In minimo ergo, quod est absconditum ab oculis omnium, etiam sapientum et fortasse Deorum, vis omnis est; ideo ipsum est maximum omnium“ (ARTICULI ADVERSOS MATHEMATICOS, memb. 3, § 26. Tocco ed., 1³, 24).
    112. Transition from ELEM. METAPHYS., etc., I, 125. Cf. Çankara's expositions in the VEDANTIC SÛTRAS, II, 1, 29.
    113. PURE REASON, I, V, and II, 730. Kant himself briefly indicated the comparison of our reason with a sphere (in contrast with the one usually accepted, viz. “a wide plain of undefined extent“), inter alia, p. 790.
    114. PURE REASON, 784. Çankara, an intellect akin to Plato's and Kant's, who lived some thousand years before, wrote this: “It is matter of common knowledge that some teach one thing and some another from their reflective intuitions, and they greatly contradict each other. For that which one thinker maintains is perfect intuition is demolished by another, and the latter's again by a third, as every one knows“ (THE VEDANTIC SÛTRAS, translated by Paul Deussen, p. 277).
    115. Another remarkable passage runs thus: “Non est Deus vel intelligentia exterior circumrotans et circumducens; dignius enim illi — debet esse internum principium motus...“ (DE IMMENSO, V, 12, note, ed. Fiorentino, 1², 158).
    116. METAPH. PRIMER OF VIRTUE DOCTRINE, III, note to theorem 2.  And cf. PURE REASON, 404, 408, etc.
    117. “The soul cannot be mingled with the body...“ (DE ANIMA, 3, 4).
    118. PROLEGOMENA (Appendix 15). The reader will find the elementary distinction between the thing and the phenomenon, adapted for the use of the inexperienced, in CONVERSATIONS, 3rd sect., 3 title, on turning to § 7 of the ANTHROPOLOGY. The reader whose interest has been aroused by the previous lecture is, for the purpose of comparison with Kant, also advised to read the former's 3rd MEDITATION. Descartes is fully possessed of one-half of the intuitive analytical faculty: “Or la principale erreur et la plus ordinaire qui s'y puisse rencontrer consiste en ce que je juge que les idées qui sont en moi sont semblables ou conformes à des choses qui sont hors de moi...“; but, since he lacks the complementary discrimination of the Ego as being equally “phenomenon,“ he once more relapses into abstractions and dogmatic assertions.

    119. Cf. POSTHUMOUS PAPERS, I, 209; LETTERS, I, 129; PURE REASON, 533; idem, I, 359, etc.
    120. LETTER TO TIEFTRUNK of 5th April, 1798.
    121. The decisive importance of the “method“ of Kant's thought and system of philosophy will only be fully discussed in the final lecture.
    122. Cf. the preparation for this intuitive perception and the quotation from Schiller at the end of the previous lecture.


    1. Vide Jachmann, end of 8th letter.

    2. OBSERVATIONS ON THE FEELING OF THE BEAUTIFUL AND SUBLIME, Sec. III, towards the end and quite at the opening of Sec. II. For “they“ read “he“ in four places in the first quotation.
    3. From PHAEDRUS, 245 A.
    4. “Εις μιαν τε ιδεαν συνορωντα αχειν τα πολλαχη διεσπαρμενα...“ (PHAEDRUS, 265 D).
    5. “Plato is by nature a being possessed by Love above all, he is so unswervingly from the cradle to the grave; and as love is necessarily directed at first to visible things, this 'discipline in love' (his own expression is 'τα εροτικα') led to an exquisite development of the senses“ (PLATO AND PLATONISM, 1910, p. 134). Vide his REPUBLIC for the “τα του καλου εροτικα,“ 403 C.
    6. In the work by Pater referred to, cf. the entire chapter, THE GENIUS OF PLATO.
    7. SYMPOSIUM, 210-211, and cf. PHAEDRUS, 247 et seq. It is worthy of note how the presence of Love is glorified in the whole of Nature in the SYMPOSIUM, beginning with the physician, Eryxmachos, his praise of the prevailing concord of lifeless elements and forces, and ending with the premonitions of final intuitive truth in love and procreation, which Socrates puts into Diotima's mouth. In this connection every layman is strongly advised to read Rudolf Kassner's German version of these immortal masterpieces published by Diederich. This translation, in spite of some serious violence to the original, is so vivid and excellent in its literary style that it is more likely to inspire love and understanding than all the rest.
    8. THE RISE OF LATER AESTHETICISM, 1886, p. 357. Stein was unaware of the actual existence of a type “Dionysoplato“ and its wide dissemination; what interested him was the paradox that a drunken Dionysus could have been taken for an image of Plato; now, however, Egyptian records of


the Emperor Hadrian's time have shown that the Διονυσοπλατων was a well-known statue, based on a widely prevalent conception (cf. Supplement to the MUNICH ALLGEMEINE ZEITUNG of 26.ii.1903).
    9. More upon this point towards the final lecture's close.
    10. Cf. Eucken, HISTORY OF PHILOSOPHICAL TERMINOLOGY, 1879, p. 16 et seq.
    11. LETTERS ON THE FURTHERANCE OF HUMANITY, No. 79; according to the original form which was afterwards altered by Herder (COLLECTED WORKS, Suphan edition, XVIII, 324).
    12. 1804 edition, p. 193; von Hoffmann's edition, 1902, p. 410.
    13. THE PHAEDRUS, 249 C and D.
    14. Cf. Biedermann, GOETHE'S CONVERSATIONS, III, 200, and IX, 113. (Cf. also above, preface, p. 6.)
    15. Cf. POWER OF JUDGMENT, § 53 for exact text.
    16. Natorp, PLATO'S DOCTRINE OF THE IDEAL, p. 370. The best verdict on Aristotle known to me is in Schopenhauer's FRAGMENTS FOR A HISTORY OF PHILOSOPHY, § 5: “The greatest perspicacity united to circumspection, power of observation, versatility and lack of profundity, may be cited as the foundations of Aristotle's intellect. His philosophic view of the world is shallow, although carried out with much acumen.“
    17. In Hartenstein's complete edition, 1867, VIII, 794.
    18. Splendid proofs of his discrimination in delicate shades of verbal meaning occur in many works, as, for example, in the above-mentioned ESSAY ON DISEASES OF THE BRAIN (madness, silliness, stupid, dull, simple, foolish, etc.), and are particularly numerous in OBSERVATIONS ON THE FEELINGS OF THE BEAUTIFUL, etc., and in the ANTHROPOLOGY, as well as in the REFLECTIONS, published by Benno Erdmann.
    19. Cf. specially PHILEBOS, 65 A, in this connection.
    20. “The Good is beautiful“ (LYSIS, 216 D, SYMPOSIUM, 201 B, and in many other places). In this connection also cf. the REPUBLIC, Book III.
    21. METAPHYSICS, VII, 6, 1031 C, according to Bonitz.
    22. Plato's “Ideal of the Good“ is not a purely ethical abstraction, but this idea rather forms the central point of his metaphysics, and always increasingly so with the progress of his thought towards maturity, and denotes the final, supreme law of thought, the point from which thought, if it


can be called thought at all, “αυτος ο λογος,“ must originate; and yet these are metaphysical depths which cannot here be discussed. I refer the reader to Natorp, inter alia, pp. 183-196, although these marvellous expositions about the Good firstly as the finally ethical, secondly as the finally logical, and thirdly as the finally cosmic principle, do not in coy opinion seem to reach the absolutely lowest depths. With Plato “the Good“ frequently means the same as that which we to-day would call “purposivity.“
    23. THOUGHTS ABOUT GOETHE, 3rd ed., p. 161.
    24. “De mundi sensibilis atque intelligibilis forma et principiis“ is generally translated “about the form and the principles of the sensual and intellectual world“; I think the above version gives the true sense better.
    25. LETTERS, I, 117. The detailed plan of the work referred to will be found on p. 124, and hence it is obvious that the “phenomenology“ (sic) which certainly contained nothing but the critical analysis, was only considered to be the introductory part of the whole.
    26. Cf. also my FOUNDATIONS, p. 887 et seq. [English edition: vol. ii, p. 424].
    27. Cf. PURE REASON, 2 Preface, XXV, 9, 789, 823, 879, and REFLECTIONS, II, 40.
    28. Abridged from the CHARMIDES, 169 A.
    29. THEAITETOS, 184 C, D; and cf. Natorp, inter alia, p. 108. We read precisely the same thing in the KANSHITAKI-UPANISHAD, III, 8: “Not the form should be desired, but he who sees should be perceived; not the tone should be sought, but he who hears should be seen. (Deussen's version, p. 50.)
    30. Abridged from the REPUBLIC, 529.
    31. It is significant that precisely for this passage — for this thought, which could only have been expressed by this one man in the course of thousands of years — the authenticity of the SOPHIST should often have been, and still be, called in question by specialists. “Men of the most extensive learning can be very narrow-minded,“ says Kant.
    32. “Quae sunt, interrogas? Propria Platonis supellex est, ideas vocat....“ (EPISTOLA, LVIII).
    33. Vide ETHNOLOGICAL AND ETYMOLOGICAL JOURNAL, Vol. IV, pp. 403-464. The details, to which I refer above, are on p. 434 et seq.
    34. As examples, vide the THEAITETOS, 213 E, and the SOPHIST, 235 D.


    35. It may also well be that he (as e.g. PHAEDRUS, 265) conceives the “Idea“ species as the sum total of something clearly perceived and from that first separates the “Eide-genus,“ which caused some philologists, who were but little practised in investigating Nature, to translate Idea with genus, and Eidos with species, because they failed to grasp that although, logically, species is subordinate to genus, yet that in reality, as Plato here rightly says, firstly, “all things that are scattered must be comprised within a unity,“ before a separation into a particular genus can be undertaken. The method which is adopted in natural research is to comprise the various species not perhaps too strictly defined, within a certain genus, and not the other way about.
    36. “Eidos“ and “Idea“ are both derived from the word ειδω (resp. from eidemai and idein) which have the two meanings of “to see“ and “to know.“ This twofold meaning is inherent to the common Indo-Germanic root “wid,“ “which is probably latent from the beginning in the notion that knowledge has its origin on the sense of sight“; the original elemental quality of seeing is already very faint in the Sanskrit “veda“ and the German “wissen“ (to know, to wot), but in the Greek idiom the thought of vision predominates. Cf. Curtius, OUTLINES OF GREEK ETYMOLOGY, I¹, 82, and Kluge, ETYM. DIC. OF THE GERMAN LANGUAGE, under “wissen“). It is obvious how from the very beginning of things this word has a duplicate, combining and differentiative, or, in a word, a “critical,“ meaning.
    37. 253 D. The words in square brackets are auxiliary for the elucidation of the exact and undoubted meaning, which all the united Grecian sages would fail to extract from the translations made by Schleiermacher and Hieronymus Müller.
    38. The reader who is more practised in thinking is advised to read PURE REASON, 680 et seq., and especially 682, with regard to the distinction between genus and species (Eidos and Idea).
    39. Plato naturally anticipated this objection, and answered it in the PHAEDO, 100; according to him — and precisely in accord with Kant — we can, as a general proposition, only find that in the realm of thought of which we assume the existence.
    40. The word “εμμετρια“ (symmetry or balance) contains the idea “μετρον,“ the measure of confined speech, or


poetic rhythm, a fact not to be overlooked if the full beauty of the passage is to be understood.
    41. The THEAITETOS abridged, but literally so, from the three conjunctive passages, 157 A, 160 B, C, and 182 B. For the further comprehension of this leading idea of all critical analysis, cf. Kant's differentiation between a “defining“ and a “definable“ ego (PURE REASON, 407 et seq., and I, 402).
    42. Kant gives the example of the dog in PURE REASON, 180.
    43. Plato himself never succeeded in clearly describing the idea of “appearance,“ yet he sometimes suggests it as “phantasia“ or paraphrases it by the use of a verb, and says: “we say 'it appears' “ (“φαινεται ο λεγομεν,“ the SOPHIST, 264 B).
    44. Cf. also in the THEAITETOS, 193 et seq.
    45. Free, but actually accurate, paraphrastic interpretation of the PHAEDO, 75.
    46. The reader will find a further and very beautiful passage on the general value of antinomy in critical thought in the first paragraph of the Notes II to § 57 of THE POWER OF JUDGMENT.
    47. A modern zoologist with strictly empirical leanings writes: “Different sense-organs, when questioned with regard to the same object, give ... quite incommensurable answers. And as a matter of fact closer investigation reveals that congregation of all our phenomenal material of quite heterogeneous and quite incomparable sensations, which only acquires definition as a uniform object through apperception (the Ego)“ (J. von Uexküll, IN THE CONTEST FOR THE SOUL IN ANIMALS, S.A. from THE RESULTS OF PHYSIOLOGY, part II, 1902). I do not quote this as an argument or a justification, but only as a psychologico-empirical help for such as are still unpractised in critical thinking.
    48. With regard to this, Paul Natorp's epoch-making book, PLATO'S DOCTRINE OF THE IDEAL, AN INTRODUCTION TO IDEALISM, 1903, should be compared, especially for the comprehension of Plato. This work supplies a final conclusion, because it contains the entirely satisfactory conception of the leading metaphysical idea in addition to the “acribie“ which is philologically so indispensable to the critical treatment of the subject, the idea to which everything


leads, and from which everything proceeds. It is true that the publication of this work during the time occupied by the preparation of this lecture did not induce me to alter my view, yet I feel myself at the same time so enriched by having made its acquaintance, that a mere occasional reference would not suffice to give expression to the great obligation thereby conferred on me; on the contrary, I feel compelled to beg all who care to know Plato truly, to drink for themselves at this well of information.
    49. This is the exact literal meaning of the phrase, which is purposely kept vague in the TIMAEUS, 52 B.
    50. LES DILEMMES DE LA MÉTAPHYSIQUE PURE (1901) contains a novel and interesting view of the eternal antinomial problem by Renouvier.
    51. Kant says precisely the same thing (but as is usual with him, negatively instead of positively expressed) in a letter written in 1772. “The things of the world are neither alterable nor unalterable“ (LETTERS, I, 129).
    52. I once for all remark that in the following explanations I have in general used “force“ where, in accordance with the customary word employed to-day in the exact sciences, the more appropriate word would have been “energy.“ I have done so because experience taught me that an exotic term like “energy“ scares the layman, or induces him to imagine some bogy with magical powers; an idea expressed by a foreign term at once becomes an abstraction, whereas I strive to invest every thought with the greatest possible amount of perceptibility. And since, to the best of my knowledge, Robert Mayer never used the word “energy,“ and Helmholtz never saw any reason to change the title of his celebrated treatise ON THE CONSERVATION OF FORCE (die Erhaltung der Kraft) (published in 1847), but, as a matter of fact, repeated the same title in the lectures delivered in his later years, I boldly break away from the adoption of the scientific expression, the general use of which is otherwise perfectly justified. Strictly speaking, every single force is the effect and consequence of the abstract conception of energy as a constant quantity (cf. Helfenstein, THE FORMS OF ENERGY). Perhaps this formula may be more practical: “The human mind operates with hypothetical atoms when thinking of 'force,' but, when thinking of 'energy' (at all events as we regard it to-day), it dispenses with this assumption.“


    53. Newton in PRINCIPIA I, DEFINITIO 8, says: ... has vires (attractionem, impulsum, propensionem) non physice sed mathematice con sidero. Unde caveat lector, ne per hujusmodi voces cogitet me speciem vel modum actionis, causamve, aut rationem physicam alicubi definire, vel centris vires vere et physice tribuere, si forte aut “centra trahere,“ aut “vires centrorum esse dixero. In OPTICS (query 31), he says: “What I call attraction may be performed by impulse or by some other means unknown to me. I use that word here to signify only in general any force by which bodies tend towards one another, whatsoever be the cause.“
    54. Vide Weyhrauch's excellent publication, “The mechanics of heat in Robert Mayer's collected works, third edition revised and enlarged with historico-literary reports,“ 1893, p. 231 et seq.
    55. None have done more than Robert Mayer for the advancement of modern science; but it is eminently desirable that all professed naturalists and laymen should themselves follow the line of thought pursued by this great genius, instead of stamping their minds with an article of faith extracted from textbooks, which consists in the simultaneously mystic and materialistic dogma of the “conservation of force“; for they would then clearly there recognise for themselves the basis of his creative thought. In this connection, Robert Mayer says in the first essay, OBSERVATIONS ON THE FORCES OF INANIMATE NATURE, 1842, that it is impossible to prove that heat is transformed into motion or motion into heat; “he, however, prefers the hypothesis that heat is the result of motion, to the assumption of a cause without an effect and of an effect without a cause.“ He “prefers the assumption“! Here is a classically clear instance of an idea as an hypothesis for the explanation of phenomena as taught by Plato and held in abhorrence by Aristotle. And the second work in this connection, ORGANIC MOTION IN ITS RELATION TO CHEMICAL CHANGES, 1845, where he wishes to convince his opponents of the impossibility of the reduction of motion to nothing when its effect becomes imperceptible, but that, on the contrary, it must necessarily have been transformed into another equal and indestructible force, Mayer “relies upon“ the “law of thought“ as “an absolutely conclusive“ illustration; or, therefore, the idea as the law — which, of course, is the fundamental idea of the entire Platonic philosophy! This single example may stand for all


scientific formation. The significance of the precedent idea in Galileo's view can be just as plainly seen from several passages in his DISCORSI.
    56. Heinrich Hertz's Introduction to the PRINCIPLES OF MECHANICS is here especially recommended to all who desire to descend or ascend to profounder considerations.
    57. This quotation from Helmholtz occurs in the complete edition of LECTURES AND SPEECHES, 4th ed., I, 227. The sentence itself is explained by the addition: “All change in Nature consists in this, viz. that the force at work changes its form and place without any change taking place in its quantity. The universe is endowed with a store of working force which can neither be changed nor increased nor diminished by phenomenal transformation, and which sustains all processes of change within it.“ Now this is both popularly reasoned and expressed; and yet I think that we laymen might well be content with a formula which seemed sufficient for a Helmholtz.
    58. Here, too, in particular, cf. Hans Driesch's little book, BIOLOGY AS AN INDEPENDENT ELEMENTAL SCIENCE, 1893 in which this successful zoological experimentalist shows the current notion that life is the result of physico-chemical action, to be merely an empty phrase. “But phrases are ever more handy tools than thoughts“ (p. 48). That well-known physicist, Professor Tait, declares that the endeavour to trace the origin of life from matter and force is “simply unscientific“ and proves that the attempt to do so either sets aside (although, perhaps, unconsciously) all the Newtonian laws of motion as being false, and thus abolishes the entire natural mechanical system, or attaches a meaning to “matter “, which would render exact physical science impossible (Lecture printed in the CONTEMPORARY REVIEW, vol. 31, January, 1878, p. 298 et seq.).
    60. The whole of the second lecture in general may here be referred to. Vide also my FOUNDATIONS, Chap. IX, sections “Science“ and “Philosophy.“
    61. POPULAR LECTURES ON SCIENCE, 2nd ed., p. 225.
    62. DE L'ESPRIT, Discours I, cap. 4.
    63. Similarly Descartes in many places, e.g. PRINCIPIA II, § 16.
    64. Jean Perrin maintains that all the definitions hitherto


made of the so greatly belauded “energy“ amount to no more than the statement: quelque chose demeure constant, something or other persists unchanged. (TREATISE ON PHYSICAL CHEMISTRY, pt. I, THE PRINCIPIA, 1903).
    65. THE PRINCIPLES OF MECHANICS (Introduction to), p. 9. This is entirely in the style of Platonic thought. Natorp (inter alia, p. 265) thus condenses Plato's doctrine in the PARMENIDES, “Postulation is relation.“
    66. Turn, for instance, to C. von Nägeli, MECHANICO-PHYSIOLOGICAL THEORY OF THE DOCTRINE OF EVOLUTION, 1884, p. 83: “The origin of the organic from the inorganic is, in its essence, not a question of experience and experiment, but a fact based upon the law of the conservation of matter and force.“ “Fact“ as opposed to “experience“ is distinctly precious in the mouth of a professional natural scientist; the much-despised monks of the Middle Ages argued precisely thus. Max Verworn, on p. 125 of the 3rd ed., 1901, of his GENERAL PHYSIOLOGY, expresses a similar view with regard to the hypothesis that life is not identical with matter; this, says he, is “a bit of mysticism,“ and with profound wisdom adds: “Knowledge and mysticism are mutually exclusive.“ But if the assumption that life — the most evident to us of all phenomena — is an independent idea, is “a bit of mysticism,“ then the assumption of the altogether undefinable ideas of “matter“ and “force“ must at last be “religion.“ To such complete incapacity for thinking and seeing our science of to-day has come! (Cf. p. 89, vol. II.)
    67. It is of importance to understand clearly not only that a living being can only originate from a living being, but also that within each individual living body all the constituent parts of life — everything, therefore, which effects growth, nutrition, and the functions of life in general — are operative through the media of matter and force, but are themselves in their turn produced by definitely formed elements of life which again had their origin in identical elements. Nowhere, not even within the body itself, is there any “alchemical“ transformation of inorganic into organic substance. This fact was stated at the Viennese Scientific Academy, as long ago as 6th June, 1890, by Julius Wiesner, an investigator of well-known empirical bent, who summed up the result of all exact research as follows: “There is no such thing as spontaneous generation of organised


matter from dead substance,“ “progressive science has disproved all assertions of such a method of origin within an organised body itself“; on the contrary, “experience teaches us that everything organic proceeds from the inorganic.“ Thus science, based on sound observation, hunts spontaneous generation out of its last hiding-place. (More on this point is to be found in Wiesner's THE ELEMENTAL STRUCTURE AND GROWTH OF LIVING MATTER, published in 1893). And, finally, one of the greatest living physicists and cosmologists, Svante Arrhenius, has recently had the sense and the courage to say, “... In my opinion, enquiry into the origin of the earliest form of life stands on the same level as the question as to the origin of matter. We must gradually grow accustomed to the thought that forms of life have survived through all eternity, and could not therefore have had their origin in time ...“ (The UMSCHAU, or Review, 13.vi.1903, p. 485).
    68. Besides this, there are a few specialists — not, of course, taken very seriously by serious devotees of science — who are just now busying themselves with the ad oculos demonstration of the transition from crystallised forms into living organisms! The sight of crystals giving birth to their “young“ has been now vouchsafed unto us; the arrival upon the scene of the “homunculus“ cannot surely be now much longer delayed!
    69. All possible forms of crystallisation find their exhaustive mathematical expression in the single formula of the “Bravaisian law.“
    70. Cf. Tschermak's TEXTBOOK OF MINERALOGY, § 11.
    71. This even holds good of the individual atoms composing the molecules. Professor Sir Oliver Lodge upholds the view in a lecture, given by him on 5.ii.1903, that every atom of natron consists of 30,000 “electrons“ so infinitesimally small that — in proportion to their size — they are as far asunder from each other as the planets from their central suns, and the central suns from each other. “Our atomic science grows more like astronomy from day to day,“ says this learned electro-physicist; “we begin to question whether absolute magnitude has any definite meaning at all ... and whether the entire solar system is not itself merely an atom ...“
    72. “The elements,“ says Goethe, “are to be regarded as colossal foes with whom we must do eternal battle“ (Weimar edition, II, 12, 102).


    73. Cf. especially METAPHYSIC. PRIMER NAT. SCI., III, Theorem 3. Here Kant most clearly proves that “the possibility of establishing a science of Nature rests altogether on the law of inertia (as well as that of persistence),“ and that “directly one departs therefrom but a single step, one falls into Hylozoism (matter endowed with life) and so, therefore, into the death of all natural philosophy.“ The adepts in the doctrines of an Ernst Haeckel should reflect that their acceptation would imply nothing less than completest renunciation of all exact physical science.
    74. Concerning the stern necessity for such a reduction of all ideas (platonically speaking) to uniform ideas, cf. p. 202-203 of the 1902 edition of SCIENCE AND HYPOTHESIS by one of our most eminent contemporaneous mathematicians, namely, Poincaré: “Dans l'histoire du développement de la physique, on distingue deux tendances inverses ... l'unité ... et la variété.... Si c'est la première qui l'emporte, la science est possible.“ The entire distinction between the “variété“ given by observation and the “unité“ imperatively demanded by the intellect in its search for knowledge (and science), literally corresponds with Plato's discrimination and between, and correlation of δοξα and διανοια.
    75. Particularly clear in Heinrich Hertz, who thus defines force as “the intermediary link of thought between two forms of motion“ (INTRODUCTION, p. 34). It is observable that Hertz would prefer simply to say “motion“ in the place of “force“; but still the idea of transformation of one form of motion into another obtrudes itself, which, therefore, is to say that motion itself is again subject to impulse, and this thought is too essential not to require another term for its interpretation.
    76. More will be said on this point in the next lecture.
    77. SIXTY VEDANTIC UPANISHADS, translated by Paul Deussen, p. 851. Per contra, Kuno Fischer's version, viz.: “The subject is not in time, but time is in him,“ is obviously wrong; time is a mode of knowledge, not something which can be contained in some other thing.
    78. Kant probably anticipated this when he said: “The principle of life seems to be of an immaterial nature“ (DREAMS, I, i).
    79. THE PRIMARY FACTORS OF ORGANIC EVOLUTION, 1896 p. 482 et seq. It is more probable that death is a consequence of life than that the living is a product of the non-living. (A


view and intuition thus attained by way of pure empiricism must not on any account be confused with Fechner's “All-Being“ and “All-Consciousness“ as some of the readers of the first edition of 1908 happened to do.)
    80. And Alfred Wallace, the companion-founder of the theory of natural selection, with regard to the phenomenon of life also thinks: “There is in all this something quite beyond and apart from chemical changes....“ (DARWINISM, ed. 1889, p. 474 et seq. A pamphlet by R. Neumeister, a professor of physiological chemistry, entitled, CONSIDERATIONS OF THE ESSENTIALS OF THE PHENOMENA OF LIFE; A CONTRIBUTION TO THE IDEA OF PROTOPLASM, 1908, seems to me to deserve attention on account of the scientific profundity there displayed on the question which is here but slightly entered into. Its strictly technical polemics against the confused — and in reality almost criminally amateurish — ideas of Ostwald and Verworn are extremely gratifying. That genius, Otto Weininger, has condensed all that need here be said into one paradoxical dictum: “Chemistry can only be successfully encountered with the excrements of the living“ (RACE AND CHARACTER, 2nd edition, p. 429 et seq.).
    81. The zoologist, Prof. Rud. Burckhardt, recently spoke some words very well worth notice about the necessity of overcoming the tyranny of the cellular theory and “the erroneous generalisations of cellular phenomena“ (CONTRIBUTIONS TO THE HISTORY OF SYSTEMATISED BIOLOGY, 1903, p. sec. A. Proceedings of Nat. Soc., in Basle, XVI, 393. Vide also NATURE ET SCIENCES NATURELLES, 1904, chap. II, by Fréderic Houssaye), 1908. In his GENERAL BIOLOGY, 1906, Oscar Hertwig says: “The term 'cell' is really misleading; a speck of protoplasm, an 'elementary organism' is all that is now left by this definition (cf. pp. 8 and 9).
    83. With regard to the “unicellularism“ of the protozoa, the dissertations by Franz Leydig in 1864 (ON THE CONSTRUCTION OF THE ANIMAL BODY, p. 15 et seq.), are still very well worth reading and instructive.
    84. Cf. Claus, ZOOLOGY, sixth ed., 1897, p. 235.
    85. The pharynx is very beautifully illustrated in the RECORDS OF PROTIST RESEARCH, 1903, II, plate 3, fig. 6e and 8e.


    88. Turning over the pages of the RECORDS OF PROTIST RESEARCH attentively will show that the explanations given above apply not only to Infusoriae, but to all unicellular life, as soon as this is submitted to more stringent investigations. (Vide e.g. respecting the GREGARINAE — hitherto regarded as the ne plus ultra of simplicity — ANNUAL, 1904, vol. III, No. 3, p. 340 et seq).
    89. Cf. especially De Bary, MYCETOZOA (Myxomycetes), in his book, COMPARATIVE MORPHOLOGY AND BIOLOGY OF THE FUNGI, 1884, p. 453 et seq. Brief descriptions are found in every botanical handbook.
    90. Fritz Schaudinn, recognised as the foremost investigator of unicellular organisms, who unfortunately died prematurely, says in the ZOOLOGICAL YEAR-BOOKS, SECTION, ANATOMY AND ONTOGENESIS OF ANIMALS, vol. XIII, 1899-1900, p. 281: “More recent research about protozoa has proved how greatly complicated the relations may here be, how manifold may be the differences here presented in organisms apparently closely connected (i.e. mainly by organisms similar in external appearance; what, for instance, is not comprised within the Amoeba group!). Our astonishment constantly increases with what we perceive, the farther we penetrate into this unicellular world, as regards the differentiation and transformation which the single cell presents to our view.“ The UMSCHAU, or Review, of 28th March, 1908, contains reports of experiments made with infusoriae, which show that these do not, as hitherto assumed, take their food merely mechanically, but exercise a faculty of discrimination in their nourishment. “This result of research,“ it is inter alia said, “is also to be regarded as an uncommonly important contribution to the fact that the organism of the protozoa is far more complex than hitherto supposed.“
    91. “To standardise the meaning of cellular-growth ...“! Is this not mediaeval scholasticism to the nth power? Holy St. Crispin, ora pro nobis!
    92. Cf. also Lecture I, p. ? (58 in orig.).
    93. CRITICAL ANALYSIS OF THE POWER OF JUDGMENT, p. 315. I consider Ernst Mach's contrary view (vide MECHANIC, Ch. 5, § 1), to be mere hair-splitting; these antimetaphysicians


are all schoolmen from crown to heel, and differ from Occam and Duns Scotus only in the subjects of discussion and their appropriate terminology. It is as plain as the sun at noon that Kant does not use the word “mechanics“ in its restricted technical sense, but in its more extended meaning of everything which is motion or can be interpreted as motion, or — if one must needs insist on splitting hairs — everything which is in any way capable of numerical expression.
    94. Cf. the Bruno lecture, p. 368. The following explanations are complementary to what has there been said.
    95. Here, in view of the confusion produced by the use of the word “complicated,“ it might be well to quote Goethe's remark: “The most glorious thing in the mineralogical world is the simplest, and in the organized world it is the most complex. One sees, therefore, that both worlds have quite different tendencies, and that between them there is no graduated progressive scale whatever“ (CONVERSATIONS WITH ECKERMANN of 2, II, 1831).
    96. Formerly “organic“ and “mechanical“ had an identical meaning (cf. Eucken, ABSTRACT IDEAS OF THE PRESENT DAY, p. 156). Plato uses the term “organon“ to express “sense-instrumentality“ in the THEAITETOS (p. 185); in my opinion he attached no particular philosophic idea to the word.
    97. The great Buffon remarks: “C'est l'organisation qui fait proprement notre existence; la matière considérée sous ce point de vue, en est moins le sujet que l'accessoire“ (I, 426).
    98. Concerning purposivity as a “transcendental principle“ cf. POWER OF JUDGMENT, 361.
    99. A small book by the celebrated physicist, Sir Oliver Lodge, entitled LIFE AND MATTER, was published in London a few weeks after the first edition of the present book, which in almost the same words expressed the thought here developed. In the German translation (p. 104) just published (June, 1908) it says: “The view of life which I have attempted to utter above is that it is neither matter nor energy, nor even a combined function of them both, but that it must be placed in quite another scientific category.“ This exact investigator, therefore, arrived at a conclusion identical with my own, and his exposition supplements my own no less than mine forms a necessary complement to his (1908).


Society, 1902) and specially ON THE BIOLOGY OF LEAF-DISPOSITION (Central Journal of Biology, 1903, vol. XXIII, 209 et seq., 1908. The large, comprehensive book by the natural scientist referred to, THE ENJOYMENT OF LIGHT BY PLANTS, has in the meantime appeared (1907).
    101. The speech is printed in extenso in NATURE of 24.vii.1902.
    102. Vide THE STRUCTURE OF MAN AS EVIDENCE OF HIS PAST, 3rd ed., 1902, p. 217 et seq.
    103. I am indebted to Professor Leopold von Schroeder's lectures on OLD ARYAN RELIGION given at the University of Vienna, but which have not yet appeared in print, for this hint.
    104. Cf. Maspero, LES PEUPLES DE L'ORIENT CLASSIQUE, I, 155.
    105. Vide Teichmüller, STUDIES FOR THE HISTORY OF IDEAS, 1874, p. 63 et seq., besides historical textbooks.
    106. None the less, Kant elsewhere calls the usual evolutionary conception which is the modern scientific confession of faith, “the vulgar, shallow method of presentation“ (ON THE USE OF TELEOLOGICAL PRINCIPLES IN PHILOSOPHY, Rosenkranz edition, VI, 369).
    107. SUR UN ÉCRIT ANONYME, 19.iv.1772.
    108. In his excellent apologetic book, ON THE SIGNIFICANCE OF THE DARWINIAN PRINCIPLE OF NATURAL SELECTION (2nd edition, p. 227) one of the most capable and consistent champions of Darwinism, Professor Ludwig Plate, says: “The essential nature of natural selection ... is to be seen in this, namely, that by the separation of bodies capable and incapable of survival the purpose aimed at is progress towards perfection.“ Literally, then, as much as to say a continuous creation of the more from the less, or of something out of nothing.
    109. In this connection I point to Lessing's otherwise scarcely intelligible thought that its perfectibility is “the quality which alone renders persistence possible“ (XII, 148). Of course, the first necessity of all would be the scientific determination of that which is “like“ Nature and what not; we marvel to-day in childlike innocence of the baldest anthropomorphism at certain changes, — for instance, Darwin's pigeons — as at a miracle, albeit Nature herself instructs us that this means nothing to her, and although we also overlook other changes which, humanly speaking, seem to be minimal,


but which Nature herself fails to accomplish in aeons of time. Thus at this hour we are entirely unable to set up anything based on scientific reasoning about persistence or alteration of living forms; the necessary preparation is lacking, and is so because we are still in the dark about the problem itself.
    110. See further down.
    111. Plato already had this idea of the “Oneness of Life,“ and says that all animals stood in a relation of mutual reciprocity (the TIMAEUS, 30 D et seq.). It may seem questionable whether this unity will find its ideal expression in the mathematical formula of a differential equation, but I am of opinion that the indispensability of such a formula will sooner or later surely lead to its discovery. What is required is something which Kant calls a “regulative“ as opposed to a “constitutive“ idea, that is to say, an idea which points out the way for the inquisitive mind of man to take, and thus leads him on from discovery to discovery, but not an idea which claims the substantial weight of an ascertained fact, whereby thought is irremovably nailed fast. (Cf. PURE REASON, 715, and POWER OF JUDGMENT, in many passages.)
    112. Such was the impetus given by his doctrine that, even in Plato's lifetime and within his own school of thought, attempts were made at a “division into species“ (διαιρεσις ειδων. PHIL., 20 C). (Cf. Natorp, inter alia, p. 302.)
    113. In his ORIGIN AND PRINCIPLE OF SPECIES IN NATURAL HISTORY, p. 4, Nägeli draws attention to the fact that the earliest founders of systematisation — men like Caesalpinus and Tournefort — laid special stress on the importance of the genus, and treated species as a secondary thing; it was only later that any need was felt for precise definition of the idea “species.“ The entire question of the connection between individual, species, genus, type, and so forth, and particularly as regarded the number of relative views and the degree of abstraction, could not here be even suggested, much less gone into. Should I be spared, I hope to achieve this later on in detail in a THEORY OF LIFE.
    115. In his still readable HISTORY AND JUDGMENT OF ALL ZOOLOGICAL SYSTEMS (1811), Spix pithily names him “the cunning artist“ and opines: “He brings the light of day into the whole world of natural history“ (p. 92 and XVII). And Spix is very far indeed from being a follower of the system of the mighty Swede; he only speaks of his services


in determining the idea of “species.“ Yves Delage, too, a convinced evolutionist of our own times, refers to the incomparable merits of Linnaeus, and says that not a single present-day naturalist is capable of a similar accomplishment (HÉRÉDITÉ, p. 2).
    116. The most important of Linnaeus' works appeared between 1735-1775.
    117. Whereas, if properly put, the basic question of all systemisation would run: How comes it that, in spite of this idea of “species“ being a human invention, there are constant species in Nature?
    118. I would here briefly draw the reader's attention to the following connection: “species“ is an abstract idea (“l'éspèce est un mot abstrait,“ says Buffon, chap. LNE), whereas “form“ is an empiric perception; therefore “conservation of the species“ is a metaphysical thought, and “persistence of form“ an idea.
    119. The most recent formula runs thus: “Thus our own day has seen the solution of the great problem of how purpose can be born without the co-operation of purposive forces“ (Weismann, THEORY OF DESCENT, 1902, II, 441).
    120. Keen-witted David Hume asks: “I would fain know how an animal could subsist, unless its parts were so adjusted.“ (NATURAL RELIGION, 1st edition, p. 153).
    121. The words in italics are printed in a different fount of type in the original.
    123. THE FOUNDATIONS OF ZOOLOGY, 1898, p. 216. More than 10,000 species of animals alone are known from the Silurian epoch.
    124. One is involuntarily reminded of Goethe's “Satyros“:

“Learn how in no-thing
Confused was everything;
How the first thing surged up from no-thing
etc., etc.“

    125. It may perhaps be worth while to draw the reader's attention to the fact that the “fundamental biological law,“ so pompously blazoned forth to the wide world as Ernst Haeckel's discovery — the alleged repetition of racial history in the development of the individual — is a very old idea,


preached as an article of faith by most of the eighteenth-century natural philosophers. Bonnet uses the same word “Palingenesis“ in 1768 as Gegenbaur does to-day; in this case “hereditary transmission“ — namely, of thoughts — is very apparent. Erasmus Darwin, Schelling, Kielmeyer, and others express the same notion quite distinctly; Diderot at least hints at it in his PENSÉES SUR L'INTERPRÉTATION DE LA NATURE, ch. 58 (published in 1754), when he expounds the entire evolutionary doctrine. Meantime and independently of this enlightenment by dogma, true science was born. Karl Ernst von Baer, the founder of scientific embryology, is the discoverer of all those series of facts which that speculative intellect, Haeckel, recoined into his so-called “laws,“ whereas the indispensable complementary corollary of palaeontological facts and ideas is almost to be placed exclusively to the credit of the greatest genius who ever devoted the whole ardour of an extraordinarily powerful intellect to the service of natural research, I mean — Louis Agassiz. Only it must be said that both these men (of whom one died only in 1876, and the other only in 1873) disputed the correctness of the phantastic deductions drawn from the facts, and were never wearied of pointing out that in addition to the monstrosity of the hypothetical assumptions, an unconscious, perhaps, but none the less complete, falsification step by step of the facts was the consequence. (Cf. here also Karl Ernst von Baer's essay, ON THE DARWINIAN THEORY (more than ever deserving of perusal to-day, in vol. II of his collected speeches and essays.) The layman desiring to know how Haeckel partly suppresses and partly perverts facts in his famous genealogies, is particularly advised to read sect. 7 of ch. 3 of Louis Agassiz's DE LSPÈCE ET DE LA CLASSIFICATION EN ZOOLOGIE, also published in English as ESSAY ON CLASSIFICATION. Not less interesting is the classical booklet by Milne Edwards (the last of the race of great zoologists, deceased 1885), INTRODUCTION À LA ZOOLOGIE GÉNÉRALE, chap. VI of which contains a summary of all pertinent embryological facts and exposes the frivolity with which the perversion of the truth is effected under the pressure of suggestion paralysing the reason, and forms the foundation on which the entire Haeckelian edifice rests. Karl Camillo Schneider's HISTOLOGY, p. 182, also supplies some interesting corrections and additions from the most recent researches.
    126. A characteristic symptom of our modern intellectual


disease is the increasing tendency to relegate things to ever remoter and remoter origins. Thus, for instance, man was said to be descended from the ape; the anatomical impossibility of this is established to-day by a thousand reasons; moreover, the oldest simian skeletons known to us belong to the so-called “higher“ apes, whereas the so-called “lower“ apes only appear at a later period (vide Schwalbe in the NATURALIST CONGRESS, 1903); so now the formula is: Man is not directly descended from the ape, but both man and ape are descendants of a common ancestor unknown. And similar statements are made on every other page when we turn to Gegenbaur. We are always advised again and again to “assume an origin yet more remote.“ Thus it is, for instance, impossible to prove any connection between the mammalia and the reptilia; Gegenbaur, who must be better informed than any of his contemporaries, says so; but in spite of all such trifles, although they are recurrent warnings at every stage, the pretty little logical story, which makes everything so nicely “clear,“ is not willingly surrendered; all we need is the assumption of “primary reptilian conditions of which we have no knowledge“ (vide I, 67). And so it goes from page to page. And all the textbooks of the present day tell the same tale. Even professed Darwinians who have managed to keep some freedom of thought, find things getting beyond them; NATURE of 30.iv.1903 contains a keen criticism on Gegenbaur with a demonstration of the contradictions in which his rage for proving the truth of evolution in and out of season, involves him, written by the zoologist, H. Gadow. — 1908. The reader will find a highly interesting note by a specialist in Professor Karl Diener's essay PALAEONTOLOGY AND THE THEORY OF EVOLUTION in the “AUSTRIAN REVIEW,“ 1907, No. 3. “The extremely frequent uniformity of primitive characteristics with those of an advanced specialised fossilised type has two disconcerting consequences for the evolutionary doctrinaire. It compels him on the one hand to eliminate those types — which are precisely the most interesting and striking — from the ancestral line of recent formative groups, and to class them with extinct lateral branches, and on the other hand to place the departure of special formative groups from a common ancestral origin in an increasingly remote period of time. In each one of Haeckel's numerous genealogies one may observe that in the ancestry of the higher mammalia imaginary creatures almost always


take the place of direct ancestors, but that, on the other hand, those animals known in a fossilised condition, form the side branches, which become extinct, of that genealogical tree. It is most highly improbable that such genealogies should correspond with the relations actually existing in Nature.“
    127. Vide Dreyer, PENEROPLIS, A CONTRIBUTION TO BIOLOGICAL MORPHOLOGY AND THE PROBLEM OF SPECIES, 1898, p. 107. It is worthy of special note that a man like Dreyer, who has observed and described more than 25,000 specimens of the microscopic Radiolariae (radicipeds) and their very great variability of form, considers “the tenacious elasticity“ with which every living form asserts itself to be the basic phenomenon of life (p. 119). It was the same with Louis Agassiz, who undertook the task of carefully comparing 27,000 specimens of a snail singly, with the result that no two individuals out of the whole number were exactly alike, but also with the further undoubted result that the Linnaean conception of the “species“ was absolutely justified (DE L'ESPÈCE, p. 380). But, to prevent misconception, it must here be said that the question of permanent change of form and the transformation of the so-called Linnaean “species“ remains an open one, although the nonsensical dogmas of the theorisers on natural selection and descent may once for all be rejected. In this work I could not as much as even hint at my own views.
    128. Cf. e.g. Johannes Ranke's MAN, 2nd ed., II, from p. 471 to p. 483. Broca also says of certain races of the stone age: “they had in some of their traits attained the loftiest and noblest stages of human development“ (quoted in ANTHROPOLOGICAL ARCHIVES, 1904, I, No. 4, p. 185). In this connection it is not perhaps quite uninteresting to state that Cuvier and Agassiz both had unusually large skulls and strikingly intellectual features, whereas neither Lamarck nor Darwin were above the average in these respects.
    129. An excellent compilation of passages pertinent hereto is to be found in Auffahrt's THE PLATONIC IDEAL THEORY, 1883, p. 35 et seq.
    130. In addition cf. the THEAITETOS, 182 et seq., and the TIMAEUS, 27 et seq.
    131. In addition cf. PURE REASON, 266 et seq., where Kant proves that without the idea of “the persistent“ there can be no idea of time or even of change. “Only that which is permanent is subject to change.“


    132. Vide the illustration given by Heinrich Hertz, p. 133.
    133. In one passage Darwin refers to this, but, unfortunately, had never read Buffon himself, and always quotes him at second hand, or otherwise he would probably have hesitated at drawing some of the conclusions arrived at.
    134. This passage is in AMOEN. ACAD., VI, 296 (1763): “Suspicio est, quam diu fovi neque jam pro veritate indubia venditare audeo; sed per modum hypotheseos propono: quod scilicet omnes species ejusdem generis ab initio unam constituerit speciem ...“ (quoted from Von Baer, SPEECHES, II, 256, note, where the passage is given in full). Additional appropriate passages occur in Leydig's HORAE ZOOLOGICAE, 1902, p. 219 et seq. Thus, for instance, Linnaeus says of two kinds of “pheasant-eye narcissus,“ which are still considered separate species, “una ex altera orta.“ — 1908. I can now refer to my contribution to the Viennese Festival Souvenir, GOETHE, LINNAEUS, AND THE EXACT SCIENCE OF NATURE (vide in particular p. 233 et seq.).
    135. THE SLOTHS. Plato also believes in “infinite periods of time“ with infinite changes of form (vide LAWS, 676, and cf. with passage above quoted).
    136. In particular vide Wolff's experiments regarding the regeneration of the ophthalmic lens, and also cf. K. C. Schneider's VITALISM, p. 18.
    137. All the types extant to-day are present in the palaeolithic formations (vertebrates included); all that are wanting are the simplest, or, as one habitually says, the “lowest“ forms, but these are not calculated for conservation in this way, so that nothing can be deduced from their absence; neither have other types of construction than those now extant been found.
    138. Persistence from the earliest ages down to the present holds good not only of the few shells constantly quoted, such as Lingula, Terebratula, etc. — but of an ever-increasing number of newly discovered animals with an exceedingly complex anatomy. The persistence of the said species of shells is, indeed, all the more remarkable, because it is precisely this species of shells which change their form with extraordinary rapidity owing to the inconsiderable variations in the amount of salt, carbonic acid, lime, and the other components of salt water, so that it might almost be fair to assume that the palaeozoic ocean was identical in composition with that of to-day; yet the persistence of more complex forms of life is


of greater interest. Thus, for instance, we find many varieties of scorpions in the Silurian, and in the Carboniferous period there are numerous varieties of Arachnidae. According to an account given by Prof. Anton Fritsch at the Session of the Viennese Academy held on 7.xii.1903, 63 species of Arachnidae from palaeozoic strata are known to-day, belonging to 38 genera and 11 different families. In the year 1900, I saw in the South Kensington Museum in London, a recently discovered Sierra Leonian spider, Cryptostemma afzelii, which, in the opinion of experts, is almost quite identical with a specimen, Poliocherci punctata, from the coal strata of North America. Those who have any idea of the vast internal complexity of these animals, which possess a completely developed nervous system and extremely differentiated sex organs — especially in view of the ideas prevalent to-day — must necessarily be greatly surprised to find such an organised form as this persisting unchanged through the incalculable ages which separate us from the Carboniferous periods. If, however, it has not been persistent, but is of recent origin, this one fact completely shatters every evolutionary hypothesis, because, obviously, no degree of similarity can justify the deduction of consanguinity.
    139. The layman with a thirst for knowledge will find an excellent illustration in Fleischmann's ZOOLOGICAL TEXTBOOK, 1898, Plate III.
    140. Turning to whatsoever book we may on zoological anatomy, though couched in the most materialistic terminology, we always come upon the expression “idea“ (Gedanke) or its paraphrase as “type,“ “constructive plan,“ and so on. “Typus“ is borrowed from the Greek and signifies “model“ or pattern (“the type,“ says Goethe, “is the secret and unattainable pattern“). “Plan“ is French, and means “diagram or sketch.“ In both words, therefore, there is an implication of a sharpened, carefully combined, process of thought, although the foreign words may in some degree cause the basic fact of thought to escape the inattentive.
    141. “On my theory, unity of type is explained by unity of descent.“ (ORIGIN OF SPECIES, VI, last paragraph). “Conviction of a common organic descent has become the generally accepted starting-point for speculative research“ (Hugo de Vries, THE THEORY OF MUTATION, 1903, II, 664). It can be proved that if the adherents of the evolution


theory allowed this dogma to be doubted — a dogma by whose side all the articles of faith of the Roman church taken together are but child's play — the entire Tower of Babel of historic descent would collapse; because, once admitting a plurality of original germs, the immediate consequence, owing to the paucity of existing prototypes, is that community of origin cannot be deduced from similarity of organisation. That pioneer in botany, Joh. von Hanstein, made some excellent observations on this point twenty years ago on p. 303 et seq. of his little work PROTOPLASM, and Goethe's true instinct also rejected all such assumptions, because Nature always shows herself to be generous and even wasteful; even the human race, he says, is certainly not of common uniform origin (CONVERSATION of 6.x.1828). — 1908. Cf. also Hermann Friedmann, THE CONVERGENCE OF ORGANISMS, 1904, and F. Reinke, THE PHILOSOPHY OF BOTANY, p. 166, etc., for the development of kindred types through “convergence“ and not from a uniform origin.
    142. The corresponding Greek word “episteme“ is also derived from sta = to stand.
    143. Cf. Lecture II, p. 101 hereon.
    144. Vide REPUBLIC, 525 B and C, 527 B and D.E.
    145. Hereon cf. especially Whitehead, UNIVERSAL ALGEBRA, 1891: “Mathematics in its widest signification is the development of all types of formal, necessary, deductive reasoning.... The ideal of mathematics should be to erect a calculus to facilitate reasoning in connection with every province of thought or external experience, in which the succession of thoughts or events can be definitely ascertained and precisely stated. So that all serious thought which is not philosophy or inductive reasoning or imaginative literature, shall be mathematics developed by means of a calculus.... Such Algebras are mathematical sciences, which are essentially concerned with number or quantity ...“ (pp. vi-viii).
    146. The brochure by Th. Zeiher, THE BRAIN AND SPIRITUAL LIFE, p. 5 et seq., contains an interesting historical survey of the various theories of the ancients.
    147. MECHANISM AND VITALISM, 1902, p. 14.
    148. Cf. the statement on p. 153.
    149. Aristotle bears witness that Plato assigned “the intermediate place“ to mathematics (cf. Cohen, PLATO'S IDEAL DOCTRINE AND MATHEMATICS, 1879, p. 7).


    150. The most important passages bearing on Plato's schematic construction (in a connected exposition) occur at the close of Book VI of the REPUBLIC and the TIMAEUS, 51 D et seq. The technical expressions are partly divergent, but as the table below shows, correspond precisely in their division.

Republic Timaeus
4. νοησις. 4. νοησις.
3. διανοια. 3. λογος.
2. πιοτις. 2. δοξα.
1. εικασια. 1. αισθησις.

εικασια“ is a somewhat clearer sensual perception than “αισθησις,“ whereas with Plato “πιοτις“ always rather signifies the scientific edifice based on hypothesis than “δοξα,“ which is often absorbed in “dianoia.“ The latter expresses the pure mathematical constituents of reason, whereas '“Logos“ rather conveys the general conformability of all intellectual ideas. The development of the same schematic idea in PHILEBOS (23 and 27) is very remarkable, but not more so from the subjectively intuitive and critical, than from the objectively intuitive and critical point of view, and this results in the following series:

    4. αιτια — ideas as the cause.
    3. περας — that which defines.
    2. ξυμμιξις — the mingling of the limitative with the unlimited.
    1. απειρον — Infinity.

Regarded from the pure logical standpoint, so frequently preferred by Kant, the series would possibly be:

    4. “Original and creative reason.“
    3. The idea.
    2. Judgment.
    1. Phenomenon.

    151. SPACCIO (Preface to).
    152. DE LA CAUSA, PRINCIPIO ET UNO, Dialogue 5.
    153. It is obvious that Plato only speaks allegorically in the TIMAEUS in order to lay greater stress on the “organistic“ side of the dynamic conception of Nature as opposed to the idea of atomism. This differs essentially from what Kant in this respect says of the Cosmos, namely, that it

“must be regarded as an organic body of the very highest rank and kind“ (TRANSITION, etc., III, p. 85); for the present question is one of transcendent (not transcendental) speculations and an ordinance of abstract reason, not therefore of knowledge and science (cf. also POWER OF JUDGMENT, § 75).
    154. Inter alia, p. v.
    155. Cf. the SOPHIST, 250 B on the “third“: τριτον αρα τι παρα ταυτα το ον τη ψυχη τιθεν ...
    156. ON A RECENT ELEVATION OF TONE, etc. (Rosenkranz edition, I, 686; Hartenstein edition, 1867, VI, 477).
    157. Cf. e.g. POWER OF JUDGMENT, § 91, p. 457 et seq., and 462.



    1. CRITIQUE OF POWER OF JUDGMENT, Introduction, II, p. xix. Cf. also p. liii.

    2. Thus, for instance, Leo XIII, in the Encyclical DE STUDIIS SCRIPTURAE SACRE of the year 1893, and in a hundred other places at all times.
    3. Vide e.g. ETHICA, IV (Preface to).
    4. ETHICA, I, prop. 15 and 18: “omnia quae sunt per Deum concipi debent.“
    5. That is to say, it is the objective result to which the theoretic and the practical reason subjectively correspond; vide supra.
    6. For the extended definition of the idea “fact“ vide POWER OF JUDGMENT, § 91, p. 456.
    7. Kant's definition of “consciousness“: “Consciousness is the sole thing which turns phenomena into ideas“ (PURE REASON, I, 350).
    8. Vide e.g. PURE REASON, p. 564.
    9. SEVEN SMALL ESSAYS, Rosencranz and Schubert edition, IX¹, 269; Hartenstein edition, 1867, IV, 505.
    10. Vide e.g. LETTERS, I, 255, 316, 323.
    11. ON NATURAL SCIENCE IN GENERAL, Weimar edition, part II, XI, 161.
    12. This subject has already been taken into consideration from a more external point of view in the previous lecture (vide vol. I, p. 390).
    13. TRANSITION, etc., III, 393. The unabridged passage is: “Transcendental philosophy is the science of forms whereby to constitute oneself into a synthetic unity, made up of philosophy and thoughts“ (with the variation “to make oneself the object according to a principle“).
    14. Here the word “accidental“ is beyond all price!
    15. LETTRES, I, 157.
    16. PARERGA, I, Fragments for a History of Philosophy, § 3.


    17. Repeated in both volumes of his principal work and in the PARERGA.
    18. In addition, interesting explanations are to be found in Classen, Stadler, Cohen, and other authors. Cohen passed a severe sentence on chap. X, in particular in his book, KANT'S THEORY OF EXPERIENCE, with the heading, “Schopenhauer's objections to transcendental deduction,“ and concludes with the following words, which should be laid to heart: “In view of the esteem in which Schopenhauer is held, as being thoroughly conversant with, and an adherent of, the Kantian philosophy, I have considered it incumbent on me to go through his analysis of it seriatim; so that the persuasive assurance with which those unfounded judgments are given forth may at first become suspect, and then, by exacter comparison of that heart-searching instruction, recognised for what it really is, namely, mere obstinate wrangling about words of whose inner meaning their judge had not so much as an inkling.“ — 1908. To my regret I had not learnt of the existence of that meritorious brochure, SCHOPENHAUER'S RELATION TO KANT, by Raoul Richter, 1893.
    19. COMPLETE WORKS: Frauenstädt's edition, II, 510; Griesenbach's ed., I, 551. Schopenhauer deserves honourable mention for once writing down this truth: “Kant was endowed with a degree of clear and altogether individual circumspection such as has been granted to no other mortal besides“ (ON “UNIVERSITY“ PHILOSOPHY). But it remains an eternal puzzle how this statement is to be reconciled with the repeated assertions of “an incredible lack of reflective capacity.“
    20. MEMORABILIA, p. 671.
    21. LETTERS, I, 317; PURE REASON (Preface to), 2nd ed., xxxviii.
    22. It is possibly because “1788“ appears on the title page that this date is the one given for the publication of the CRITIQUE OF PURE REASON in all the works written upon it. Yet Kant has finished the book in the last days of June, 1787, and the publisher sends out copies as early as the first days of December following. (Cf. LETTERS, I, 467, 483, 487).
    23. For negative numbers only have their origin “through projection into space and linear conception.“ Whereas pure number is homologous with time, and therefore admits only of a single direction with the exclusion of possible reversion


— because it is impossible to ascend from the present into the past, and only direction into the future is admissible — I can just as well proceed in space from right to left as from left to right, and I denote the one by the sign + and the other by the sign -. (Cf. Conturat, DE L'INFINI MATHÉMATIQUE, 1896, p. 353 et seq.).
    24. Kant used essentially the same argument, though much more profoundly and clearly expressed, twenty years earlier in PURE REASON (p. 663 et seq.).
    25. Already a year before, in 1762, Kant had pointed out the basic idea of “synthetic judgments,“ which he here calls
“undemonstrable judgments,“ and of these he says: “Human intuition is full of such undemonstrable judgments“ (ON THE FALSE SUBTLETIES OF THE FOUR SYLLOGISTIC FIGURES, § 6, towards the end).
    26. Confirmation could have been furnished from many of the earlier works; I failed to adduce it, because what was quoted sufficed for my purpose.
    27. A young natural scientist and philosopher, Hermann von Kesserling, recently wrote me: “The whole of modern physical science is contained in Kant's TRANSITION, etc. And in the Festival Number of the KANT STUDIES of Feb. 12th, 1904, F. Heman makes a strong appeal for the recognition of the vast importance of these fragments which superficial historians have brought into such ill-repute.
    28. Karl Vogt compared the act of thinking to a secretion, such as bile or saliva!
    30. Hägerström, KANT'S ETHICS, 1903, p. 827.
    31. The explanation referred to is on p. 116 et seq. of the illustrated, and p. 158 et seq. of the unillustrated edition.
    32. This incongruity in Spinoza's basal assumption initially governs all the deductions supposed to be its consequences.
    33. Letter to Goethe of 28.x.1794.
    35. Cf. FOUNDATIONS, p. 730 et seq. [English edition: vol. ii, p. 233].
    36. Vide FOUNDATIONS, p. 793. [English edition: vol. ii, p. 311].
    37. REPORT OF THE ARRANGEMENT OF THE LECTURES IN THE WINTER SESSION, 1765-1766; the words in leaded text are so leaded in the original.
    38. Letter to Goethe of 9.vii.1796.


    40. Kant's German rendering of analytical and synthetical (vide PURE REASON, II).
    41. This fact is made very characteristically clear in a definition of experience found in the posthumous papers: “Experience is the continuous approximation of the sum total of empiric consciousness.“ (TRANSITION, etc., III, 605).
    42. Cf. Plato lecture, p. 20. Our anti-metaphysical empiricists have of late taken to praising an old idea currently known amongst the schoolmen as “lex parsimoniae naturae“ as a new discovery under various names. A shoddy idea, indeed! And this “economy of thought,“ of which Avenarius, Mach, and others make such a fuss to-day, seems to me not, perhaps, an altogether wrong, but a superficial and very “economic“ idea; it is scholasticism, not Nature. And, moreover, Kant had already disposed of this obvious construction (vide PURE REASON, 681).
    43. I here enter my caveat against possible misunderstanding, and refer to Heinrich Hertz: “We are neither justified in demanding simplicity a priori from Nature, nor in judging of what, in our interpretation of her, may be simple. But we can prescribe the images we form of her, inasmuch as these are our own individual creations“ (PRINCIPLES OF MECHANICS, introduction, p. 28). Yet it is not, however, a question of what we may demand, but of what we find; Hertz had the abstract assumptions of mathematical physicists in his mind; but both the investigator and the poet simultaneously see both exuberance and simplicity as the leading principles in the “style“ of Nature which is visible to the bodily eye.
    45. DIARIES, unabridged edition, III, 112.
    46. TRANSITION, etc., III, 405. The subject matter of the


text is mathematics and philosophy, which conjointly make up the possibility of an exact mechanical science of Nature in the Newtonian sense, in so far as they are reciprocally conditional — one as the abstract idea of pure perception, the other as the abstract idea of pure thought; yet what has been said is applicable without any limitation. (I have amended the erroneous singular “makes up“ to “make up“). Kant on the previous side of the same sheet says: “I entered upon my 79th year on 22nd of April“; so that this important formula can with certainty be dated as having been made between 22nd of April, 1802, and 22nd April, 1803.
    47. Cf. previous lecture.
    48. Vide Perrin, TRAITÉ DE CHIMIE PHYSIQUE, I, 179.
    49. In PURE REASON, p. 370, we read as follows: “The transcendental idealist can be ... an empiric realist, and, as he is called, a dualist“; then on p. 371: “Therefore the transcendental idealist is an empiric realist ...“ consequently the above phrase is a literally exact expression of Kantian thought.
    51. The aspect of the matter remains unchanged in spite of the fact that the same man who teaches us (2 A, p. 377, of his SYSTEM): “There is absolutely nothing outside or inside a human being which he can fully and completely (!) call his own except his Will,“ also assures us in his PHYSIOLOGICAL PSYCHOLOGY that “abstract Will“ is “a mere term,“ and “on being submitted to critical analysis dissolves in nothingness.“ Is then “gravitation“ anything but a word, a symbol? Is it intended to be anything else? Does not Newton expressly protect himself against every materialist interpretation of the term (vide vol. II, p. 282), and does the word, therefore, convey no meaning?
    53. Kant raised an energetic protest in advance against a “Philosophy of the Unknown.“ He concludes a lengthy exposition with these words: “Therefore the idea that any being can spontaneously operate purposively, yet without a purpose or aim implied in itself or its cause, is altogether imaginary sand vain, that is to say, devoid of any foundation in an existing object to which such an idea can correspond“ (ON THE USE OF TELEOLOGICAL PRINCIPLES).
    54. Cf. in particular PURE REASON, I, 118 et seq. § II


expresses, but still more strongly, exactly the same, because Kant was rightly careful to try and avoid entering the region of psychology, as now and again he happened to do in § I.
    55. Cf. LA SCIENCE ET L'HYPOTHÈSE, 1902, pp. 207 and 197.
    56. Many passages in the CRITIQUE OF PURE REASON but I, p. 706 et seq., in particular.
    57. PURE REASON in several passages, but specially I, 126 et seq.
    58. Briefly summarised, these judgments of the understanding on which all exact science is based are: (1) all perceptions are extensive magnitudes; (2) all sensations are intensive magnitudes; (3) potential experience consists in the idea formed by means of a necessary connotation of perceptions.
    59. One of the great services rendered by Hermann Cohen is the incontestable demonstration of the genesis of the tables of categories. On the categories themselves, cf. the third lecture, p. 252.
    60. The word “Nature“ is here used in the wider sense of an all-embracing “universe“ and as it has been used in our diagram, where it is opposed in thought to the idea of the “Ego“ as all-embracing reason (vide third lecture, p. 268). But “Nature,“ as has just been shown, may signify the material as opposed to the logical, or — and this is by no means the same thing — “Nature“ may be an idea of the theoretical reason, an abstraction of all laws as opposed to “freedom of the will.“ None but pedants can rail against this interchange of certain terms, for not only has it a base in history, but the one meaning is fused or incorporated with another; the word in this way — as before remarked — becomes an organ or instrument; it moves and carries us along with it. The same may be said of the word “reason.“ Reason, if it comprises theoretical and practical reason, is an idea transcendentally opposed to the idea “universe“; it then embraces all things, it becomes the Platonic “Noesis,“ the begetter of science and religion. But in the CRITIQUE OF PURE REASON, the subject matter treated is almost always theoretical reason in the more particular sense, and here the essential relation is altered. Here reason sometimes denotes the idea of the inclusively “rational“ (or pure thought) contrasted with the “empiric“ (PURE REASON, e.g. 863), and, consequently, comprises not


only the understanding, but at times also the formal part of sensuality, but more frequently “reason“ signifies the opposite to that complex unity, “mentality — sensuality“; this is the meaning which must be assumed throughout in this work, except where other definitions are expressedly given; sometimes, however, sensuality momentarily drops out of view, and the only remaining question is the distinction between the understanding which forms abstractions and the reason which creates ideas. He who — like too many so-called “learned“ men — only looks at the life-work of a Kant now and then may, of course, be easily misled by such things as these; but he who saturates himself with it will soon acquire the wisdom of not degrading the word to an algebraic sign — a proceeding which seems to be Professor Mach's ideal — but even of preserving its meaning as a plastic living reality in an organic connection with its entire contextual surroundings.
    61. Kant further says, in § 91 of POWER OF JUDGMENT: “God, freedom of the will, and the immortality of the soul are those problems whose solution is the final and sole aim of the entire armoury of metaphysics.“
    63. Here I naturally had only to allude quite generally to the distinction between “metaphysical“ and “transcendental.“ Attempted closer exposition would only have led to the most subtle processes of Kantian thought, especially in so far as Kant, in discussing the fundamental considerations about the a priori method, also discriminates between the pure formal “transcendental“ and the “metaphysical“ disquisitions, which latter rather regard the content of thought. I must refer the reader to Cohen as the best guide for the explanation of these intricate relations. Cohen also admits that Kant's presentation “suffers from the fundamental defect“ of not “surely and thoroughly“ sifting out the transcendental and the metaphysical separately (cf. KANT'S ESTABLISHMENT OF AN ETHICAL SYSTEM, 1877, p. 24 et seq., and KANT'S THEORY OF EXPERIENCE, 1885, p. 253 et seq., as well as 74, 99 et seq., 368, 583, etc.
    64. Vide e.g. Prof. Wenzel Hofman's very interesting brochure MOTION AND INERTIA, Vienna, 1904.
    65. LA SCIENCE ET L'HYPOTHÈSE, 1902, p. 141.
    66. Cf. the whole of the Leonardo lecture.


    68. ON PHILOSOPHY IN GENERAL, penultimate section.
    69. Justice can only be done to Wundt's great achievements by getting rid of the false impression conveyed in the title of his principal work; for in reality it does not deal with that monstrosity of thought “physiological psychology,“ but with “psychological physiology,“ that is to say, scientifically anatomical physiology, which gives appropriate and due weights to all phenomena of the alleged soul in the form of a continuous commentary.
    70. PRUSSIAN YEARBOOKS, February, 1904, p. 354.
    73. ANNALES, 1812; tome XIX, p. 76. It is common knowledge that the relations of the nervous system form the basis of his celebrated classification.
    74. It is everywhere stated that Descartes declared that the pineal gland was the seat of the soul. It were high time to put one's heel also on this confusion, engendered by superficial, lazy, and stupid, pygmies, which has been hawked about for centuries. Descartes is so far from declaring the pineal gland to be “the seat of the soul“ that he distinctly says: “Il est besoin de savoir que l'âme est véritablement jointe à tout le corps, et qu'on ne peut pas proprement dire qu'elle soit en quelqu'une de ses parties à l'exclusion des autres“ (LES PASSIONS DE L'AME, art. XXX). That ought to be sufficiently plain. In articles 31, 32, and 34, Descartes certainly develops the hypothesis that as the pineal gland is the only unpaired cerebral organ, it probably performs the particular function of creating uniformity, so that, perhaps (il me semble), the soul “exerce ses fonctions plus particulièrement que dans les autres parties.“
    76. J. v. Uexküll IN THE CONTEST FOR THE ANIMAL-SOUL, 1902, p. 24.
    77. Vide the Leonardo lecture, p. 139.
    78. “Weimar edition,“ 2nd sect., II, 162. The continuation of this significant dictum runs: “We are doubly 'between the devil and the deep sea.' Either we must


grant the object a plus quantity and forego our own subjective plus, or we must increase the subject by a plus and not take this into account.“ This one saying sufficiently proves how far from Spinoza and how near to Kant Goethe really was.
    79. I must note that Kant recognises and highly esteems a “rational psychology“ as being a means of exact discipline as soon as it relinquishes the brain-sick idea based on philosophic ignorance of founding a systematic and critico-analytic philosophy, and arrives at the perception that, quite conversely, it must itself be based on the critical analysis of intuition. For, as Kant remarks, it is ridiculous to believe that anything whatever can be decided as to the origin of experience before it has been settled in what experience consists. What would astronomy be without an antecedent theory of the laws of motion? But if we are in possession of a critical analysis and transcendental system of reason, then psychology may indeed be of some use, because “it can then search for the constituent elements, if not the principle of its potentiality, yet for the occasional causes of its procreation in experience itself“ (cf. PROLEGOMENA, § 21a, and PURE REASON, § 13, p. 116 et seq. The little book by Paul Natorp, INTRODUCTION TO PSYCHOLOGY BY THE CRITICAL METHOD, published by Mohr, at Freiburg, 1888, is an excellent preliminary to the study of psychology so understood, and is herewith strongly recommended to the reader.
    80. Every syllable of Kant's deserves careful attention, and I therefore here give the closer definition of the term “in Nature.“ If “substance“ is to be no more than a loose term for chaos, for Plato's μη ον, then its existence outside my own thought may be affirmed; but if “substance“ means a constituent part of a uniform universe, then its existence must be denied, for Nature is an idea of the reason, a regulative, constructive idea.
    81. The fine fellow who challenged us to lay ourselves across the rails didn't for a moment think that thoughts could be so hard, and objects so soft!
    82. As far as it is intended to affect Kant, among many passages sufficient to refute the constantly recurrent and stupid assertion, it needs only this one from p. 663 et seq. of PURE REASON, viz.: “The principle of deducing a cause from that which happens ... as an effect of that cause is a principle of the intuitive perception of Nature, not, however,


based on speculation ... the idea of a cause loses all meaning, when used merely speculatively, and no less so than this is the case with the accidental, whose objective reality could be intellectualised in concreto.“
    83. Vide ante omnia Jean Perrin, TRAITÉ DE CHIMIE PHYSIQUE, I, 1903, p. xiii et 108 et seq.
    84. PARERGA, On Philosophy, § 30.
    85. Cf. PURE REASON, 42 and elsewhere (especially 751). Kant — who in this respect always did too little rather than too much — developed this extremely subtle distinction, scarcely touched upon in his principal works, more fully towards the close of the first section of the polemical pamphlet CONCERNING A DISCOVERY, etc. Schopenhauer pays so little attention to the exact text in Kant as frequently to omit words when quoting him and, indeed, important words which he alone considers immaterial, and thus creates unintentionally false impressions. Every reader of Schopenhauer's criticism of Kantian philosophy is earnestly advised to submit all the references to word-for-word comparison with the original text.
    86. Vide in particular the beginning of ch. I, vol. II, of THE WORLD AS WILL AND PHENOMENON. Here almost every sentence, almost every word, is a challenge thrown to the critical, formal, systematic Platonic and Kantian idealist in favour of a dogmatic philosophy which is a combination of materialism and mysticism.
    87. Regarding the idea of “law“ vide especially PURE REASON, I, 126 et seq.
    88. A good expression which Mach once employs (v. p. 472).
    89. Considered thus, Plato's meaning in making space = substance (Timaeus) is made clear.
    90. Cf. many other passages, and in particular § 24 of PURE REASON.
    91. For further explanations cf. p. 206 et seq.
    92. The Schopenhauerian “Will“ as the thing per se and “root of the intellect“ stands exactly here.
    93. This idea, which is so very important for the Kantian system, is developed with particular clearness in PURE REASON, 522 et seq.
    94. The technical term “transcendental subject“ occurs also in Kant; it denotes the negative Ego per se, and forms the exact counterpart to the transcendental object. Thus e.g. PURE REASON, 404, and I, 355.


    95. Note on p. 1 of Preface to ON THE IDEA OF A SCIENTIFIC DOCTRINE. The following is textual: “A scientific doctrine might in the future decide this dispute in the direction of proving that our intuitive perception is not actually in direct relation through the medium of the idea, but perhaps indirectly through the medium of sensation caused by the thing in itself; that things are indeed idealised as phenomena, but felt as things in themselves.“ (The italicised words are italicised in the original).
    96. THE WORLD AS WILL AND PHENOMENON, vol. I, § 24. “If, now, all these considerations, even in abstracto, result in the clear and assured perception which everyone directly obtains in concreto, i.e. in feeling, namely, that the essence per se of his own phenomenon ... is the Will ... etc.“ It is only this application of reflective thought which hinders us from regarding the phenomenon as final, but it forms the transition to the “thing in itself.“ The whole paragraph should be read; every word of it is a flat contradiction of all the basic ideas of critical analysis.
    97. TRANSITION, etc., III, 554 and 555. In all these expressions the “thing in itself“ is obviously meant to convey the same idea as the “Ego per se.“ Cf. also in PURE REASON, 430: “It is impossible to see the Noumenon in oneself, because ...“
    98. “Nature and freedom of the Will are the two hinges of the portals of philosophy.“ (TRANSITION, III, 418).
    99. The Ego, in this sense of an entirely indefinable perception, is neither perception nor thought concept, neither phenomenon nor “thing per se“; neither is it, in any communicable, logically intelligible sense of the word, an “Ego,“ but only a something, an entity, akin as it were to an intangible element or “formless chaos,“ from which perception and thought proceed, a perception and a thought which immediately bifurcate into “I am“ and “the world is.“ (Cf. hereon PURE REASON, 422, and I, 381 et seq. and 402).
    100. PROGRESS, etc. (conclusion of No. II). The text has “Philodoxy“; yet as Kant himself translates “Philodox“ with “ratiocinator“ (“Vernunfts-Künstler“) (v. e.g. LOGIC, introduction, iii) I felt justified in introducing the more vigorous German word (viz. “Vernunfts-Künstelei“).
    101. FRAGMENTS FROM THE POSTHUMOUS PAPERS (Von Hartenstein edition, 1868, VIII, 621).


    103. Cf. the letter to Moses Mendelssohn of 8.iv.1766.
    104. WHAT IS THE MEANING OF THOUGHT-REGULATION? (last paragraph). In this connection one of that interesting English mystic, Blake's, sayings deserves mention, viz.: “The fool shall not enter into heaven be he ever so holy.“
    105. Cf. Spencer's AUTOBIOGRAPHY, ch. XVIII. The fact referred to above would be of but little intrinsic interest with respect to a thinker who raised ignorance to the dignity of a principle of life, and boasted of never once having had Locke's ESSAY ON THE HUMAN UNDERSTANDING in his hands; yet a beneficent destiny granted this active and sincere personality a lengthened term of life and, after he had survived his eightieth year, and the entire superb philosophic edifice in many volumes was complete, Spencer, in the repose and leisure of his closing days, at last came to see that the problem of the nature of space was not by any means futile (the consideration in question begins, “Old people must have many reflections in common“), and he now calls it “an ultimate question.“ And he now, with engaging simplicity, says: “There is one aspect of the Great Enigma to which little attention seems given, but which has of late years more frequently impressed me; I refer to the phenomena of Space“ (!) Then he appends a few short observations on the incomprehensibility of mathematical relations to this great discovery “to which little attention seems given“; “how does it happen that the blank form of things presents us with truths as incomprehensible as do the things it contains?“ and he goes on to speculate on the attributes of space as being qualities “innate, eternal, uncreated in its own being“; although the cosmos and its evolution must necessarily have had a beginning, there could have been no beginning of space, for space must have existed from all eternity; this spatial magnitude is “a thought too overwhelming to be dwelt upon“; and lastly this confession: “Of late years the consciousness that without origin or cause infinite Space has ever existed and must ever exist, produces in me a feeling from which I shrink...“ Comment would seem superfluous; but one might well express a wish that Spencer had gone on living for eighty years more, when it might probably have occurred to him that Time, too, of which he here speaks with such marvellous ingenuousness, is a problem which must be subjected to the critical analysis of its mode of perception. One seems to hear the stammering utterances of mankind in its infancy,


just beginning to think, and only most dimly conscious that the basic problem of all philosophy is the nature of intuitive perception itself. We may, however, from this example see whither dogmatic empiricism will lead us, if a thinker is sufficiently sincere and persistent to follow an empiric philosophic system consistently to the bitter end; he then, at the end of the nineteenth century, arrives at that point from which the earliest philosophers among the Hindus and Hellenes started many thousands of years ago. It is odd that it is just in the ranks of such people as these that we find such fanatical evolutionists; they themselves are but poor witnesses to the evolution of the intellect in Man. (The above quotations are from ULTIMATE QUESTIONS which make up the conclusion of Spencer's last book, FACTS AND COMMENTS, published in 1902).
    106. FRAGMENTS FROM THE POSTHUMOUS PAPERS, Rosencranz edition, XI, 237 et seq., Hartenstein edition, 1868, VIII, 622.
    107. Where this is not the case, as e.g. with that Nestor of the genuine appreciators of Kant's intellect, Hermann Cohen (Marburg), and with minds such as Stadler, Wernicke, and Hägerström, the form is so impenetrably scholastic as to meet with but little attention beyond the narrowest circles of scholastic thought. Only one non-expert, Ludwig Goldschmidt, has been for many years busily occupied in furthering a real comprehension of Kant in wider circles of people of education; Georg Simmel has recently joined the ranks with his delightful little book, SIXTEEN LECTURES ON KANT, 1904, and every one who honours Kant is earnestly advised to study it. And, of course, besides this Fr. A. Lange's HISTORY OF MATERIALISM should be a constant book of reference; in spite of the fact that much of what it contains about Kant is disputatious, this book none the less maintains its position as one of the most intellectual and instructive works in the range of German literature.
    108. With my own ears I heard, no longer ago than 1903, an “ordained public“ university professor announcing to a crowd of young High School boys, eager to learn, that Kant, when an old man, had lowered himself to demonstrate the abstract existence of God, freedom of the Will, and Immortality, under pressure brought to bear on him by the civil and ecclesiastical authorities, and under the lasting influence of his pietistic childhood and youthful schooldays,


“as this had been one of the duties incumbent on a professor of philosophy since the beginning of the Middle Ages.“ This last sentence may well show the caricature of Kantian thought gambolling in the brain of this state-installed instructor of youth, and what the riotous confusion of thought must have been in the brains of the gallant youths when the class broke up!
    109. This passage occurs two pages later than the one last quoted respecting the dangers of science.
    110. If without mentality and sensuality there could be such a thing as the faculty of reason, the distinction between a state of being and not-being would certainly not exist; yet Kant is not concerned with any such fantastic and unpresentable ideas, but only with still more clearly emphasising that which in reality does exist. The idea of duty originates in the conflict between reason and inclination; this conflict is a part of our essential nature; being, or life, leads us in one direction, how we ought to be, or live (i.e. duty), in another (cf. POWER OF JUDGMENT, § 76).
    111. Cf. the first lecture, p. 69.
    112. PURE REASON, 377, 383, and elsewhere. Analysed subsequently most plainly of all in POWER OF JUDGMENT, § 57, note 1, with keener discrimination between “abstract reason“ and “abstract understanding.“
    113. META. PRIMER OF THE THEORY OF VIRTUE, part II, deduction.
    114. POWER OF JUDGMENT, note to § 29. It has, since 24th April 1870, been a dogma of the Church of Rome that God “can with certainty be recognised in the world created by Him, by the natural light of human reason“ (Vatican Council, CONSTITUTIO DOGMATICA, CANONES II, 1). Kant, with regard to such hierarchical pretensions (which all confessions raise, but Rome alone clearly formulates) remarks: “This is called championing God's cause, although at bottom it may be nothing more than the cause of our overweening reason, which here overleaps its own barriers.“ (ON THE FAILURE OF ALL PHILOSOPHIC ATTEMPTS AT THEODICY).
    115. Vide notes 50 and 51.
    116. DIALOGUES CONCERNING NATURAL RELIGION, part IX. “Voluntary“ is, of course, wrong; such ideas are so involuntary as to call for a high degree of philosophical training to recognise them as non-existent facts. One such


word as this discloses the chasm which separates a Hume from a Kant. The attempts being made to-day to place Hume — who fully merits the warm words of great esteem and admiration which Kant also repeatedly expressed as being deserved — above Kant as the critical analyst of intuitive perception belong to that deliberate plan to mislead which calls for more than merely academic repudiation.
    117. This is the place for reference to the three possible kinds of Pantheism, which differ so greatly that the use of a single term often causes great confusion. 1. The idea “world“ is absorbed in the idea “God,“ the Universe is God (as the Indo-Aryans think, where God, like a spider, has spun the world out of his own body). 2. The idea “world“ absorbs the idea “God“ (modern Monism). 3. The ideas “God“ and “world“ are fused together into one still more remote and therefore still more incomprehensible, and still more impossible, hyper-abstract idea, which cannot be done without much painful infraction of logic as well as of ethical doctrine. (Bruno and, after Bruno, Spinoza).
    118. Hereon cf. the explanations on p. 358, vol. II.
    119. Cf. supra, p. 360, vol. II. The method is ever the same — the method of all exact science — je commence par supposer trouvée la chose cherchée; the hypothesis must be so constructed that all it includes is intelligible. Not to grasp this, is not to have taken the first step necessary in every branch of scientific knowledge.
    120. “Its“ refers to “causality of freedom of the will.“
    121. Meaning “unless we consider our will as being free.“
    123. Cf. METAPH. BASIS FOR ETHICS, § 2, I, in note to heading.
    124. We observe that this theory is maintained to-day by naturalists, e.g. by the zoologist, Karl Camillo Schneider.
    125. Cf. p. 296, vol. II, sqq.
    126. ON NATURAL SCIENCE IN GENERAL, Weimar edition, 2, § II, 145.
    127. According to Kant “the derivation (of morality) from a divine Supreme Will leads to a system of ethics in absolute opposition to morality“ (last heading of § 2 of METAPH. BASIS OF ETHICS).
    128. In another passage (almost at the close of METAPH.


BASIS OF ETHICS) it says that reasonable beings are an end in themselves.
    129. In METAPHYSICAL PRIMER OF THE THEORY OF VIRTUE, § 3, Kant instead of “person“ uses the term “reasonable natural being“ (“homo phenomenon“), and he denotes “personality“ by “a being endowed with inner (or spiritual?) freedom“ (“homo noumenon“).
    130. PRINCIPAL REASON, part I, I.B., 3rd sect. The words “in so far as it depends on the personality of the same“ mean that God's will is only said by us to be holy, inasmuch as he treats with his creatures as personalities, that is to say, as self-determining, purposive beings.
    131. CONCERNING PEDAGOGICS (Introduction to).
    132. FRAGMENTS, etc., Hartenstein edition, 1868, VII, 662.
    133. THE CONTEST OF THE FACULTIES, sect. 2, § 6.
    134. Cf. my FOUNDATIONS, pp. 44, 207 et seq.
    135. Lessing says the same thing word for word: “It is a superstition to say that historical belief is a duty, and necessary to salvation; because a belief in a mere historical statement is a belief devoid of the principle of life.“
    136. Cf. in particular also PURE REASON, 425 et seq. In this connection the little work by Alex. Wernicke, THE BASIS OF FAITH IN THE KANTIAN SYSTEM (monthly vol. of the Comenius Society, 1901, No. 3) deserves notice, although so decidedly one-sided in the stress laid upon the positive, and its depreciation of the negative.
    137. METAPH. BASIS OF ETHICS, § 2, 1, heading. The words in leaded type so appear in the original.
    138. That freedom of the Will is “in esse“ and not “in posse“ is the reason why it cannot be theoretically, ideally, and perceptibly grasped and represented. It is this intuitive perception — but imperfectly and uncritically developed in thought — which led Fichte, Schelling, Schopenhauer, and the most recent of our “Voluntarists“ to formulate their doctrine of the Will as the essential constituent of the Universe. Just as the theoretical reason makes itself objective in intangible “things“ (or realities), practical reason does so in the intangible Fata Morgana of a so-called “Will.“ The desire to interpret the whole of the Universe from one moiety of it can never attain the wished-for aim; moreover, in this attempted solution of the problem the cart is put before the horse; for to build up a philosophic conception of the universe originating in the Will corresponds precisely to the attempt


to construct it from “things“; Schopenhauer really goes to work in quite the same way as the materialists; he is the materialist of practical reason.
    139. Cf. also pp. 372, 381, with respect to God.
    140. All these Kantian dicta are taken from the last section of the POWER OF JUDGMENT.
    141. DE LA RÉCHERCHE DE LA VERITÉ, livre 3, partie 2, ch. 9, iv. In Malebranche the argument is directed only against the conception of God as “spirit.“
    142. MEISTER ECKHARDT, 99th sermon, Pfeiffer edition, p. 318 et seq.
    143. Inter alia, 56th sermon.
    144. RELIGION, etc., 4th St., part 2, § 3.
    145. ON A RECENT ELEVATION OF TONE, etc. (1796).
    146. In contrast, namely, with the pseudo-Semitic mythologies of Haeckel and Co.
    147. RELIGION, 4th St., part 2, p. 329. In the THEORY OF VIRTUE (deduction) it says: “Religion is the abstract idea of all duties as being Divine commands.“
    148. The reader's attention is drawn to the note made by Schiller on this passage.
    149. ON MAN'S AESTHETIC EDUCATION, 25th letter.
    150. Vide all the early part of this lecture.
    151. RELIGION, etc., preface to first edition, viii et seq.
    152. Hume, DIALOGUES CONCERNING NATURAL RELIGION, part I, towards the end.
    153. Vide RELIGION, etc., 4th St., part I, note to the first paragraph, for the exact text.
    154. Vide supra for the distinction between person and personality, p. 402, vol. II.
    155. Couturat, DE L'INFINI MATHÉMATIQUE, p. 299.
    157. Almost all of us are deprived of the freedom of our personality in our childhood; such things as, e.g. the exercises of the Jesuits have no other object than its deliberate and entire annihilation; and this is a far greater outrage on humanity than either murder or rape.
    159. Cf. my FOUNDATIONS, p. 195 et seq., p. 950 et seq.
    160. POWER OF JUDGMENT, § 32.
    161. RELIGION, etc., 4th St., part 2, § 2 and § 3, the latter with the glorious sub-title “OF PAPISTRY AS A TRAINING IN THE MOCK SERVICE OF THE PRINCIPLE OF GOODNESS.“


    162. ON THE PROVERBIAL SAYING: “ALL VERY WELL IN THEORY BUT NO GOOD IN PRACTICE,“ III, a brochure published in the same year (1793) as RELIGION, etc.
    163. Even now in the twentieth century, not many miles from the gates of Catholic Vienna, when “the stormy winds do blow“ the peasantry offer up “food“ to appease them in the shape of flour in great dishes, and similarly, on certain days in every year sacrifices are made to fire, so that it may continue its beneficent office and do no harm.
    165. “Christ has brought the kingdom of God nearer to earth; but he has been misunderstood; and in place of God's kingdom, the kingdom of the Priest has been established in our midst“ (REFLECTIONS, I, 213).

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