Here under follows the transcription of the Notes-section of Houston Stewart Chamberlain's Immanuel Kant, published by John Lane, The Bodley Head, 1914.
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See also the reviews of this book:
Kant in the 20th century. Review in the London Times Literary Supplement, 1914
Kritische Urteile über Chamberlain's Kant. Collection of reviews in german, 1909
 
 

VOLUME I page
INTRODUCTORY 3
GOETHE 13
LEONARDO 101
DESCARTES 197
BRUNO 311




VOLUME II
PLATO 3
KANT 169
NOTES 415
INDEX 513

415
NOTES

416
(Blank page)

417
NOTES TO GOETHE

    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.)
    3. DE LA NATURE DE L'HOMME.
    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].
    8. THOUGHTS ABOUT OPTIMISM.
    9. WHAT IS THE MEANING OF THOUGHT-REGULATION?
    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.
    14. CORRESPONDENCE BETWEEN GOETHE AND STATE COUNCILLOR SCHULTZ, p. 385.
    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

418 NOTES TO GOETHE
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.)
    21. ON GERMAN ARCHITECTURE, 1823.
    22. TRAVELS IN ITALY, 8th October, 1786.
    23. OLD GERMAN PAINTINGS IN LEIPZIG, 1814.
    24. WEIMAR EDITION, part I, 48, 249.
    25. TREASURES OF ART ON THE RHINE, MAIN, AND NECKAR, 1814—1815.
    26. ON GERMAN ARCHITECTURE, 1823.
    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.

419 NOTES TO GOETHE
    32. SOME IDEAS ON THE REAL APPRECIATION OF LIVING FORCES, preface, § 7.
    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.
    36. THE HAPPY EVENT.
    37. THE SENSE OF SIGHT, OBJECTIVELY CONSIDERED.
    38. CONTRIBUTION TO KNOWLEDGE OF BOHEMIAN MOUNTAINS, letter to Herr Leonhard.
    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.
    46. TIBIA AND FIBULA.
    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

420 NOTES TO GOETHE
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.
    50. PRINCIPES DE PHILOSOPHIE ZOOLOGIQUE.
    51. THEORY OF COLOUR (didactic portion), § 622.
    52. PLANT METAMORPHOSIS, § 69.
    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

421 NOTES TO GOETHE
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.)
    56. ON FANTASTIC VISUAL PHENOMENA, § 181.
    57. PLANT METAMORPHOSIS.
    58. TRAVELS IN ITALY (second sojourn in Rome).
    59. PLANT METAMORPHOSIS, § 73.
    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.
    62. IMPORTANT ADVANCE.
    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.
    69. EFFECT OF MODERN PHILOSOPHY.
    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.).
    72. LECTURES ON THE FIRST THREE CHAPTERS OF THE

422 NOTES TO GOETHE
DRAFT OF A GENERAL INTRODUCTION TO COMPARATIVE ANATOMY, II, 1796.
    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).
    75. PLANT METAMORPHOSIS, § 120.
    76. PRINCIPES DE PHILOSOPHIE ZOOLOGIQUE.
    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

423 NOTES TO GOETHE
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.
    88. LECTURES ON THE FIRST THREE CHAPTERS OF THE DRAFTS OF THE GENERAL INTRODUCTION TO COMPARATIVE ANATOMY, STARTING FROM OSTEOLOGY, II (Weimar edition, A. 2, § 8, 71).
    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.“
    93. IMPORTANT ADVANCE THROUGH A SINGLE WITTY AND SIGNIFICANT WORD.

424 NOTES TO GOETHE
    94. THE PROBLEM AND THE REPLY.
    95. THE KAMMERBERG NEAR EGER.
    96. THE ONLY POSSIBLE REASON FOR PROVING THE EXISTENCE OF GOD, part II.
    97. HISTORY OF MY BOTANICAL STUDIES
    98. MORE ABOUT MATHEMATICS AND MATHEMATICIANS.
    99 ANNALS, 1810.


425
NOTES TO LEONARDO

    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-

426 NOTES TO LEONARDO
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.
    4. INSTRUCTION IN MAKING MEASUREMENTS WITH THE CIRCLE AND T-SQUARE, 1538, folio A. 1.
    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-

427 NOTES TO LEONARDO
tions on many of the complex questions with regard to ramifications, inflorescences, homodromy and heterodromy, etc., with which the nineteenth century has been occupied.
    13. LETTER TO LODOVICO IL MORO (R. II, 396).
    14. ON MATHEMATICS AND THEIR ABUSE.
    15. MORE ABOUT MATHEMATICS AND MATHEMATICIANS.
    16. Cf. supra, p. 97.
    17. APHORISMS ON NATURAL SCIENCE.
    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.

428 NOTES TO LEONARDO
    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).
    24. ON MATHEMATICS AND THEIR ABUSE.
    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.
    27. In the essay, ON ERNST STIEDENROTH'S PSYCHOLOGY.
    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.)
    32. DISCOURS PRÉLIMINAIRE DU TRAITÉ DE DYNAMIQUE, 1st paragraph.
    33. The educated layman will find reliable scientific information about the theory of “electrons“ in Lorentz,

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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.
    35. PRINCIPLES OF MECHANICS, p. 15.
    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.
    43. RECHERCHE DE LA VÉRITÉ PAR LES LUMIERES NATURELLES, ed. Cousin, XI, 370.
    44. COLOUR THEORY, introduction.

430 NOTES TO LEONARDO
    45. THE ONLY POSSIBLE REASON FOR PROVING THE EXISTENCE OF GOD, 4, II.
    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.
    49. THOUGHTS ON REASON, SUPERSTITION, AND INFIDELITY.
    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

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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

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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.
    57. TIBIA AND FIBULA.
    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

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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.

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    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.
    73. CRITICISM OF HERDER'S IDEAS ON THE PHILOSOPHY OF HISTORY.
    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).


435
NOTES TO DESCARTES

    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

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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 which — calling 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-

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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.
    16. RÉFLEXIONS ET MAXIMES, No. 279.
    17. Vide, e.g. vol. I, 204; III, 31; IV, 264, etc.
    18. Here I am only speaking of Descartes' philosophic

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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

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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,“

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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

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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

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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

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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

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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.

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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.
    49. MAXIMS AND REFLECTIONS ON ART.
    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.
    55. RÉFLEXIONS SUR LA MÉTAPHYSIQUE DU CALCUL INFINITÉSIMAL, 4th ed., 1860, p. 7.
    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

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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

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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 mig