From the Closed World to the Infinite Universe: Notes

From the Closed World to the Infinite Universe, by Alexander Koyré, [1957], at sacred-texts.com

Notes

INTRODUCTION AND CHAPTER I

1. Cf. A. N. Whitehead, Science and the modern world, New York, 1925; E. A. Burtt, The metaphysical foundations of modern physical science, New York, 1926; J. H. Randall, The making of the modern mind, Boston, 1926; Arthur O. Lovejoy's classical Great chain of being, Cambridge, Mass., 1936, and my own Études Galiléennes, Paris, 1939.

2. The cosmos conception is only practically, that is, historically, linked together with the geocentric world-view. Yet it can be completely divorced from the latter as, for example, by Kepler.

3. The full story of the transformation of the space conception from the Middle Ages to modern times should include the history of the Platonic and Neoplatonic revival from the Florentine Academy to the Cambridge Platonists as well as that of the atomic conceptions of matter and the discussions about the vacuum following the experiments of Galileo, Torricelli and Pascal. But this would double the volume of this work and, besides, distract us somewhat from the very definite and precise line of development which we are following here. Moreover, for some of these problems we can refer our readers to the classical books of Kurd Lasswitz, Geschichte des Atomistik, 2 vols., Hamburg und Berlin, 1890, and Ernst Cassirer, Das Erkenntnisproblem in der Philosophie und Wissenschaft der neuen Zeit, 2 vols., Berlin, 1911, as well as to the recent works of Cornelis de Waard, L’expérience barométrique, ses antécédents et ses explications, Thouars, 1936, and Miss Marie Boas, "Establishment of the mechanical philosophy," Osiris, vol. x, 1952. See now Max Jammer, Concepts of space, Harvard Univ. Press, Cambridge, Mass., 1954, and Markus Fierz, "Ueber den Ursprung und Bedeutung von Newtons Lehre vom absoluten Raum," Gesnerus, vol. xi, fasc. 3 / 4, 1954, especially for the space conceptions of Telesio Pattrizzi and Campanella.

4. On the Greek conceptions of the universe cf. Pierre Duhem, Le système du monde, vol. i and ii, Paris, 1913, 1914; R. Mondolfo, L’infinito nel pensiero dei Greci, Firenze, 1934, and Charles Mugler, Devenir cyclique et la pluralité des mondes, Paris, 1953.

5. The MS of De rerum natura was discovered in 1417. On its reception and influence cf. J. H. Sandys, History of classical scholarship, Cambridge, 1908, and G. Hadzitz, Lucretius and his influence, New York, 1935.

6. The first Latin translation of Diogenes Laertius’ De vita et moribus philosophorum by Ambrosius Civenius appeared in Venice in 1475 and was immediately reprinted in Nürnberg in 1476 and 1479.

7. The atomism of the ancients, at least in the aspect presented to us by Epicurus and Lucretius—it may be that it was different with Democritus, but we know very little about Democritus—was not a scientific theory, and though some of its precepts, as for instance, that which enjoins us to explain the celestial phenomena on the pattern of the terrestrial ones, seem to lead to the unification of the world achieved by modern science, it has never been able to yield a foundation for development of a physics; not even in modern times: indeed, its revival by Gassendi remained perfectly sterile. The explanation of this sterility lies, in my opinion, in the extreme sensualism of the Epicurean tradition; it is only when this sensualism was rejected by the founders of modern science and replaced by a mathematical approach to nature that atomism—in the works of Galileo, R. Boyle, Newton, etc.—became a scientifically valid conception, and Lucretius and Epicurus appeared as forerunners of modern science. It is possible, of course, and even probable, that, in linking mathematism with atomism, modern science revived the deepest intuitions and intentions of Democritus.

8. Cf. René Descartes, "Lettre à Chanut," June 6, 1647, Oeuvres, ed. Adam Tannery, vol. v, p. 50 sq., Paris, 1903.

9. Nicholas of Cusa (Nicholas Krebs or Chrypffs) was born in 1401 in Cues (or Cusa) on the Moselle. He studied law and mathematics in Padua, then theology in Cologne. As archdeacon of Liège he was a member of the Council of Basel (1437), was sent to Constantinople to bring about a union of the Eastern and Western churches, and to Germany as papal legate (1440). In 1448 he was raised by Pope Nicholas V to the cardinalate, and in 1450 he was appointed Bishop of Britten. He died August 11, 1464. On Nicholas of Cusa cf. Edmond Vansteenberghe, Le Cardinal Nicolas de Cues, Paris, 1920; Henry Bett, Nicolas of Cusa, London, 1932; Maurice de Gandillac, La philosophie de Nicolas de Cues, Paris, 1941.

10. Cf. Ernst Hoffmann, Das Universum von Nikolas von Cues, especially the Textbeilage by Raymond Klibansky, pp. 41 sq., which gives the text of Nicholas of Cusa in a critical edition as well as the bibliography of the problem. The booklet of E. Hoffmann appeared as "Cusanus

[paragraph continues] Studien, I" in the Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Philosophisch-Historische Klasse, Jahrgang 19291930, 3. Abhandlung, Heidelberg, 1930.

11. Cf. De docta ignorantia, 1. ii, cap. ii, p. 99. I am following the text of the latest, critical, edition of the works of Nicholas of Cusa by E. Hoffmann-R. Klibansky (Opera omnia, Jussu et auctoritate Academiae litterarum Heidelbergensii ad codicum fidem edita, vol. i, Lipsiae, 1932). There is, now, an English translation of the De docta ignorantia by Fr. Germain Heron: Of learned ignorance by Nicholas Cusanus, London, 1954. I have, nevertheless, preferred to give my own translation of the texts I am quoting.

14. Ibid., p. 100 sq. It is to be remembered, however, that the conception of the relativity of motion, at least in the sense of the necessity to relate motion to a resting reference-point (or body) is nothing new and can already be found in Aristotle; cf. P. Duhem, Le mouvement absolu et le mouvement relatif, Montlignon, 1909; the optical relativity of motion is studied at length by Witello (cf. Opticae libri decem, p. 167, Basilae, 1572) and, even more extensively, by Nicole Oresme, (cf. Le livre du ciel et de la terre, ed. by A. D. Meuret and A. J. Denomy, C. S. B., pp. 271 sq., Toronto, 1943).

18. Cf. the famous passage of Virgil, Provehimur portu terraeque urbesque recedunt, quoted by Copernicus.

19. This famous saying which describes God as a sphaera cuius centrum ubique, circumferentia nullibi appears for the first time in this form in the pseudo-Hermetic Book of the XXIV philosophers, an anonymous compilation of the XIIth century; cf. Clemens Baemker, Das pseudohermetische Buch der XXIV Meister (Beiträge zur Geschichte der Philosophie und Theologie des Mittelalters, fasc. xxv), Münster, 1928; Dietrich Mahnke, Unendliche Sphaere und Allmittelpunct, Halle/Saale, 1937. In this Book of the XXIV philosophers, the above-mentioned formula forms the proposition ii.

20. He is, however, referred to by Giovanni Francesco Pico in his Examen doctae vanitatis gentium (Opera, t. ii, p. 773, Basileae, 1573) and Celio Calcagnini in his Quod coelum stet, terra moveatur, vel de perenni motu terrae (Opera aliquot, p. 395, Basileae, 1544); cf. R. Klibansky, op. cit., p. 41.

21. Cf. L. A. Birkenmajer, Mikolaj Kopernik, vol. i, p. 248, Cracow, 1900. Birkenmajer denies any influence of Nicholas of Cusa on Copernicus. On the medieval "forerunners" of Copernicus cf. G. McColley, "The theory of the diurnal rotation of the earth," Isis, xxvi, 1937.

23. Nicholas of Cusa's conception could be treated as an anticipation of that of Sir William Herschell; and even of more modern ones.

26. Ibid., p. 107. Once more, one could see in this conception of Nicholas of Cusa a prefiguration of the theory of the mutual attraction of the heavenly bodies.

29. Marcellus Stellatus Palingenius, whose true name was Pier Angelo Manzoli, born at La Stellata some time between 1500 and 1503, wrote, under the title of Zodiacus vitae, a didactical poem, which was printed in Venice (probably) in 1534, rapidly became extremely popular, especially among Protestants, and was even translated into English, French and German. The English translation (Zodiake of life) by Barnaby Goodge, appeared in 1560 (the first three books), and in 1565 the entire poem was printed. It seems that Palingenius was at a certain time suspected of heresy, but it was only 15 years after his death (he died in 1543) that, in 1558, the Zodiacus vitae was put on the Index librorum prohibitorum. Under Pope Paul II his bones were disinterred and burnt; cf. F. W. Watson, The Zodiacus Vitae of Marcellus Palingenius Stellatus: An old school book, London, 1908 and F. R. Johnson, Astronomical thought in Renaissance England, pp. 145 sq., Baltimore, 1937.

30. Zodiacus vitae, l. vii, Libra, ll. 497-99; Engl. transl., p. 118; cf. A. O. Lovejoy, The great chain of being, pp. 115 sq., Cambridge, Mass., 1936; F. R. Johnson, op. cit., pp. 147 sq.

35. Ibid., ll. 71-85 (transl., p. 229). The world-view of Palingenius is beautifully expressed by Edmund Spenser in his Hymn of heavenly beauty (quoted by E. M. W. Tillyard, The Elizabethan world picture, p. 45, London, 1943):

Far above these heavens which here we see, p. 281
Be others far exceeding these in light,
Not bounded, not corrupt, as these same be,
But infinite in largeness and in height,
Unmoving, incorrupt and spotless bright
That need no sun t’illuminate their spheres
But their own native light far passing theirs
And as these heavens still by degree arise
Untill they come to their first mover's bound,
That in his mighty compass doth comprise
And carry all the rest with him around;
So those likewise do by degree redound
And rise more fair till they at last arrive
To the most fair, whereto they all do strive.

CHAPTER II

2. Cf. Joachim Rheticus, Narratio prima. I am quoting the excellent translation of E. Rosen in his Three Copernican treatises, p. 147, New York, 1939.

3. F. R. Johnson, Astronomical thought in Renaissance England, pp. 24549, Baltimore, 1937; cf. A. O. Lovejoy, op. cit., pp. 109 sq.

4. John Donne, Anatomy of the world, First Anniversary (1611) ed., Nonesuch Press, p. 202. The disastrous effects of the seventeenth century's spiritual revolution have recently been studied with great care and some nostalgic regret by a number of scholars; cf. inter alia, E. M. W. Tillyard, The Elizabethan world picture, London, 1943; Victor Harris, All coherence gone, Chicago, 1949; Miss Marjorie H. Nicolson, The breaking of the circle, Evanston, Ill., 1950; S. L. Bethell, The cultural revolution of the XVIIth century, London, 1951. For a non-nostalgic treatment cf. A. O. Lovejoy, The great chain of being, and Basil Willey, The seventeenth century background, Cambridge, 1934.

5. Nicolaus Copernicus, De revolutionibus orbium coelestium, l. i, cap. viii.,

6. According to the mediaeval conception the central position of the earth is the lowest possible; only Hell is "lower" than our earthly abode.

7. For the pre-modern, that is, pre-telescopic astronomy, fixed stars possess a visible and even measurable diameter. Since, on the other hand, they are rather far away from us and in the Copernican conception even exceedingly far (cf. infra, pp. 92-9), their real dimensions must be extremely large.

8. Cf. Grant McColley, "The seventeenth century doctrine of a plurality of worlds," Annals of Science, i, 1936, and "Copernicus and the infinite universe," Popular Astronomy, xliv, 1936; cf. Francis R. Johnson, op. cit., pp. 107 sq.

13. Cf. Sir Walter Raleigh, The historie of the world, London, 1652, pp. 93 sq.; cf. Bethell, op. cit., pp. 46 sq.

15. Giordano Bruno understands them as teaching the infinity of the universe. I have already examined the case of Nicholas of Cusa; as for Lucretius, he asserts, indeed, the infinity of space and that of the worlds, but maintains the finiteness of our visible world and the existence of a limiting heavenly sphere, outside of which, but inaccessible to our perception, there are other identical or analogous "worlds." Anachronistically we could consider his conception as prefigurating the modern conception of island-universes dispersed in an infinite space, though with a very important difference: the Lucretian worlds are closed and not connected with each other.

16. Cf. Francis R. Johnson and Sanford V. Larkey, "Thomas Digges, the Copernican system and the idea of the infinity of the universe," The Huntington Library Bulletin, n. 5 (1934), and Francis R. Johnson, op. cit., pp. 164 sq.; cf. also A. O. Lovejoy, op. cit., p. 116.

18. A Perfit Description, sigs N 3-N 4; cf. Johnson-Larkey, pp. 88 sq.; Johnson, pp. 165-167.

19. A. O. Lovejoy, op. cit., p. 116. Giordano Bruno was born in Nola (near Naples) in 1548, became a Dominican in 1566, but, ten years later in 1576, on account of some rather heretical views held by him on transubstantiation and the Immaculate Conception, had to leave both the order and Italy. In 1579 he came to Geneva (where he could not stay), then to Toulouse, and to Paris (1581) where he lectured on the logical system of Raymundus Lullus (and wrote some philosophical works, i. e. De umbris idearum and a satiric comedy, Il Candelajo); in 1583 he went to England where he lectured and published some of his best works, such as La Cana de le Ceneri, De la causa, principio et uno and De l’infinito universo e mondi. From 1585 to 1592 Bruno wandered in Europe (Paris, Marburg, Wittenberg, Prague, Helmstadt, Zürich), publishing the De immenso et innumerabilibus in 1591. Finally, in 1592 he accepted an invitation to Venice. Denounced and arrested by the

[paragraph continues] Inquisition (in 1593), he was brought to Rome, where he remained imprisoned for seven years, until he was excommunicated and burnt at the stake on February 17, 1600. Cf. Dorothea Waley Singer Giordano Bruno, his life and thought, New York, 1950.

21. Cf. my Études Galiléenes, iii, p. ii sq., and "Galileo and the scientific revolution of the XVIIth century," The Philosophical Review, 1943.

22. Giordano Bruno, La Cena de le Ceneri, dial. terzo, Opere Italiane, ed. G. Gentile, vol. i, p. 73, Bari, 1907.

24. The De l’infinito universo e mondi was written in 1584; the De immenso et innumerabilibus, or to quote the full title, De innumerabilibus, immenso et infigurabili: sive de universo et mundis libri octo, in 1591. I shall base my exposition on the De l’infinito universo e mondi and quote it in the excellent recent translation of Mrs. Dorothea Waley Singer, adjoined to her Giordano Bruno, his life and work, New York, 1950. I shall give the reference first to the edition of Gentile (Opere Italiane, vol. i); then to Mrs. Singer's translation.

25. Bruno's space is a void; but this void is nowhere really void; it is everywhere full of being. A vacuum with nothing filling it would mean a limitation of God's creative action and, moreover, a sin against the principle of sufficient reason which forbids God to treat any part of space in a manner different from any other.

26. De l’inf. univ. e mondi, p. 309 sq., transl., p. 280; cf. De immenso . . . Opera Latina, vol. i, part i, p. 259.

29. The famous phrase "le silence éternel de ces espaces infinis m’effraye" does not express Pascal's own feeling—as is usually assumed by Pascal's historians—but that of the atheistic "libertin."

31. De l’inf. universo, p. 280 (transl., p. 250); cf. De immenso, i, 4, Opera, i, i, p. 214.

33. This very famous argument against the finitude of the universe—or of space—is a good example of the continuity of philosophical tradition and discussion. Giordano Bruno probably borrows it from Lucretius (De rerum natura, l. i, v. 968 sq.), but it was already widely used in the discussions of the XIII-XIVth centuries about the plurality of the worlds and the possibility of the void (cf. my paper quoted in chap. in, 40) and will be used by Henry More (cf. infra, p. 139) and even by Locke

[paragraph continues] (cf. An essay on human understanding, l. ii, §§13, 21). According to the Commentaire exégétique et critique of A. Ernout and L. Robin to their edition of the De rerun natura (p. 180 sq., Paris, 1925), the argument originates with Architas and is used by Endemios in his Physics (cf. H. Diels, Fragmente der Vorsocratiker, c. xxxv, A 24, Berlin, 1912). What is more important, it is to be found in Cicero, De natura deorum, i, 20, 54; cf. Cyril Bailey, Lucretius, De rerun natura, vol. ii, pp. 958 sq., Oxford, 1947.

35. Ibid., p. 283 (transl., p. 254); cf. Acrotismus Camoeracensis, Opera, i, i, pp. 133, 134, 140.

40. Ibid., p. 335 (transl., p. 304); cf. De immenso, Opera, i; i, p. 290; i, ii, p. 66.

47. G. Guillielmi Gilberti Colcestrensis, medici Londinensis, De magnete, magnetisque corporibus, et de magno magnete tellure physiologia nova, c. vi, cap. iii; pp. 215 sq., London, 1600; Gilbert's work was translated by P. Fleury Mottelay in 1892 and by Sylvanus P. Thompson in 1900. The Mottelay translation was reprinted in 1941 as one of "The Classics of the St. John's Program" under the title: William Gilbert of Colchester, physician of London, On the load stone and magnetic bodies and on the great magnet the Earth; cf. pp. 319 sq. According to J. L. E. Dreyer, A history of astronomy from Thales to Kepler, 2nd ed., New York, 1953, p. 348, Gilbert, in his posthumous work, De mundo nostro sublunari philosophia nova (Amstelodami, 1651), "appears to hesitate between the system of Tycho and Copernicus." This is not quite exact, since Gilbert, in contradistinction to Tycho Brahe, (a) asserts the rotation of the earth which Tycho Brahe rejects, and (b) denies the existence of a sphere of fixed stars, and even the finitude of the universe still taught by Brahe. Thus Gilbert tells us that though the majority of the philosophers placed the earth in the center of the world, there is no reason to do so (l. 2, cap. ii, De telluris loco, p. 115): "Telluris

vero globum in centro universi manentem omnis fere philosophorum turba collocavit. At si motum aliquem habuerit praeter diurnam revolutionem (ut nonnulli existimant) erronem etiam illam oportet esse; sin in suo sede volveretur tantum, non in circulo, planetarum ritu moveretur. Non tamen inde, aut ullis aliunde depromptis rationibus, certo persuadetur eam in universae rerum naturae centro, aut circa centrum, permanere." He adds, indeed (ibid., p. 117), that "Non est autem quo persuaderi possit in centro universi magis terram reponi quam Lunam, quam Solem; nec ut in motivo mundo horum unum in centro sit, necesse esse," and that, moreover, the world itself has no center (p. 119).

On the other hand, though he puts the sun and not the earth in the center of the moving world (p. 120): "locus telluris non in medio quia planetae in motu circulari tellurem non observant, tanquam centrum motionum, sed Solem magis," and tells us that the sun (p. 158) "maximam vim egendi et impellendi habet, qui etiam motivi mundi centrum est," he does not tell us outright that the earth belongs to this "moving world" of the planets.

Though he quotes Copernicus and even tells us that Copernicus erred in ascribing to the earth three motions, instead of two (around its axis and around the sun), the third one, that which, according to Copernicus, turned the axis of the earth in order to keep it pointing always in the same direction being not a motion at all, but lack of it (p. 165): "Tertius motus a Copernico inductus non est motus omnino, sed telluris est directio stabilis," he does not assert the truth of the heliocentric world-view.

He tells us, indeed (l. i, cap. xx, De vacuo separato), that the Aristotelian objections against the void are worthless, that things can just as well move in the void space as remain immobile in it and that the earth can very well be a planet and turn around the sun like the others; that, nevertheless, he does not want to discuss this question (l. i, cap. xx, De vacuo separato, p. 49): "Cujus rei veritatem sic habeto. Omnia quiescunt in vacuo posita; ita quies plurimis globis mundi. At nonnulli globi et infinitis viribus et actu aliorum corporum aguntur circa quaedam corpora, ut planetae circa Solem, Luna circa Tellurem et erga Solem.

"Quod si Sol in medio quiescit ut Canis, ut Orion, ut Arcturus, turn planetae, tum etiam tellus, a Sole aguntur in orbem, consentientibus propter bonum ipsis globorum formis: si vero tellus in medio quiescat (de cujus motu annuo non est huius loci disceptare) aguntur circa ipsam cetera moventia."

It is possible, of course, that Gilbert really considered that the discussion of the annual motion of the earth was out of place in a book

devoted to the development of a new philosophy of our sublunar world. Yet it is difficult to admit that, if he was fully convinced of the truth of the Copernican astronomy, he would so consistently avoid saying it, even when asserting its daily rotation, as, for instance in chap. VI of book II of the Philosophia nova (p. 135): "Terram circumvolvi diurno motu, verisimile videtur: an vero circulari aliquo motu annuo cietur, non hujus est loci inquirere." It seems, thus, that Gilbert was either not very much interested in the problem, or sceptical about the possibility to reach a solution and that he hesitated between an improved Copernicanism (such as Kepler's) and an improved Tycho Brah-ism (such as Longomontanus’).

CHAPTER III

1. In pointing out the analogy between Kepler's views and those of some modern scientists and philosophers of science I am not committing an anachronism: epistemology and logic are, indeed, nearly as old as science itself and empiricism or positivism are by no means new inventions.

2. The sun represents, symbolizes, and perhaps even embodies God the Father, the stellar vault, the Son, and the space in between, the Holy Ghost.

3. Cf. De stella nova in pede Serpentarii, cap. xxi, pp. 687 (Opera omnia, ed. Frisch, vol. ii, Frankofurti et Erlangae, 1859). The De stella nova was published in 1606.

9. A perfectly reasonable assumption, and quite analogous to that of contemporary astronomy, about the distribution of galaxies.

13. The sky being "above" us, the stars are "elevated" in respect to us; thus to place them at a greater distance from us (or the centre of the world) is to give them a greater "elevation."

15. The absence of stellar parallaxes imposes a minimum to the distance separating us from the fixed stars.

15a. Marcus Manilius, a Stoic, who lived in the Augustan age, author of a great astrological poem, Astronomicon libri quinque, which was edited by Regiomontanus in Nürnberg in 1473.

18. Two minutes is the magnitude of the visible diameter of a star for the unassisted eye.

24. J. Kepler, Dissertatio cum Nuntio Sidereo nuper ad mortales misso a Galileo Galilei, p. 490 (Opera omnia, vol. ii), Frankoforti et Erlangae, 1859. Wacherus = the Imperial Councillor Wackher von Wackenfels who was the first to inform Kepler about the discoveries of Galileo. Brutus = the Englishman Edward Bruce who was a partisan of Giordano Bruno and who, some years before (Nov. 5, 1603), sent to Kepler a letter (from Venice) in which he expressed his belief in the infinity of the world; according to Bruce fixed stars were suns surrounded by planets like our sun, and, like our sun, endowed with a rotational motion. Bruce's letter is quoted by Frisch, Opera omnia, vol. ii, p. 568, and published by Max Caspar in his edition of Kepler (Johannes Kepler, Gesammelte Werke, vol. iv, p. 450, München, 1938).

25. The fixed stars, as seen by a Galilean telescope, do not appear as light-points; they still have visible dimensions; cf. supra, p. 191.

26. Epitome astronomiae Copernicanae, liber i, pars ii, p. 136 (Opera omnia, vol. vi, Frankoforti et Erlangae, 1866).

the value of the old doubts about the possibility of an actually infinite world, and turned back to a finitist conception.

38. That is the conception ascribed by Plutarch (or Pseudo-Plutarch) to the Stoics.

40. Cf. my paper, "Le vide et l’espace infini au XIVème siècle," Archives d’histoire doctrinale et littéraire du Moyen-Age, xvii, 1949.

CHAPTER IV

1. Galileo Galilei, Sidereus nuncius . . . Venetiis, 1610; there is an English translation by E. S. Carlos, The sidereal messenger, London, 1880. Large parts of this translation are reprinted in Harlow Shapley and Helen E. Howarth, A source book in astronomy, New York, 1929. Though not using this translation I refer to it whenever possible. The expression Sidereus Nuncius was used by Galileo as meaning: the message of the stars. Yet Kepler understood it as meaning: the messenger of stars. This mistranslation became generally accepted and was corrected only in the recent edition of the Nuncius by Mrs. M. Timpanaro-Cardini, Florence, 1948.

2. Cf. Sidereus nuncius, pp. 59 sq. (Opere, Edizione Nazionale, v. iii, Firenze, 1892), Source book, p. 41.

3. On the discovery of the telescope cf. Vasco Ronchi, Galileo e il cannochiale, Udine, 1942, and Storia della luce, 2 ed., Bologna, 1952.

7. Galileo Galilei, Letter to Ingoli, p. 526. Opere, Ed. Naz., vol. vi, Firenze, 1896.

8. It is interesting to note that the conception according to which heavenly bodies are inhabited is referred to by Galileo as "commonly held."

11. Galileo Galilei, Dialogo sopra i due massimi sistemi del mondo (Opere, Ed. Naz., vol. vii), p. 44; Firenze, 1897; cf. also p. 333. The Dialogue is easily available now in the excellent modernization of the old Salusbury translation by Professor Giorgio di Santillana, Galileo Galilei, Dialogue on the great world systems, Chicago, 1953, as well as in the new translation by Stillman Drake, Galileo Galilei, Dialogue concerning the two

chief world systems, Ptolemaic and Copernican, Berkeley and Los Angeles, 1953.

15. Cf. Letter to Liceti, of February 10, 1640; Opere, vol. xviii, pp. 293 sq., Firenze, 1906.

16. Cf. R. Descartes, Principia philosophiae, part ii, §4, p. 42. (Oeuvres, ed. Adam Tannery, vol. viii, Paris, 1905.)

CHAPTER V

1. Cf. Miss Marjorie H. Nicolson, "The early stages of Cartesianism in England," Studies in Philology, vol. xxviii, 1929. Henry More accepted Cartesian physics, though only partially, and the Cartesian rejection of substantial forms, but he never abandoned his belief in the existence, and action, of "spiritual" agents in nature and never adopted the Cartesian strict opposition of matter—reduced to extension—to spirit, defined by self-consciousness and freedom. Henry More, accordingly, believes in animals 'having souls and in souls' having a non-material extension; cf. also Miss Nicolson's The breaking of the circle, Evanston, Ill., 1950.

2. These letters were published by Clersellier in his edition of the correspondence of Descartes (Lettres de M. Descartes où sont traittées les plus belles questions de la morale, de la physique, de la médecine et des mathématiques . . . Paris, 1657) and republished by Henry More

himself (with a rather angry preface) in his Collection of severall philosophical writings of 1662. I am quoting them according to the text of the Adam-Tannery edition of the works of Descartes (Oeuvres, vol. v, Paris, 1903).

4. In this work, written in 1646, he shows himself an enthusiastic follower of the Lucretian-Brunonian doctrine of the infinity of worlds; cf. Lovejoy, op. cit., pp. 125, 347.

5. On Gassendi see K. Lasswitz, op. cit., and R. P. Gaston Sortais, La philosophie moderne, depuis Bacon jusqu’à Leibniz, vol. ii, Paris, 1922; also Pierre Gassendi, sa vie et son oeuvre, Paris, 1955. Gassendi is not an original thinker and does not play any role in the discussion I am studying. He is a rather timorous mind and accepts, obviously for theological reasons, the finitude of the world immersed in void space; yet, by his revival of Epicurean atomism and his insistence upon the existence of the void, he undermined the very basis of the discussion, that is, the traditional ontology which still dominated the thought not only of Descartes and More but also of Newton and Leibniz.

7. In the Cartesian world vortices which surround fixed stars limit each other and prevent each other from spreading and dissolving under the influence of centrifugal force; if they were limited in number, and therefore in extension, then, first the outermost ones and then all the others would be dispersed and dissipated.

17. Ibid., p. 302. More's argument against Descartes is a re-edition of Plotinus’ argument against Aristotle.

22. Such was, in any case, the opinion of Pascal. Yet, after all, what is the God of a philosopher supposed to be if not a philosophical God?

26. At least, he started writing an answer—in August 1649—though he did not send it to Henry More.

28. It is possible, of course, that, as he went to Sweden on Sept. 1, 1649 and died there on Feb. 11, 1650, Descartes did not receive this last letter of Henry More.

29. Cf. my Essai sur les preuves de l’existence de Dieu chez Descartes, Paris, 1923, and "Descartes after three hundred years," The University of Buffalo Studies, vol. xix, 1951.

CHAPTER VI

1. Henry More has not received the monographical treatment to which he is undoubtedly entitled. On him, and on the Cambridge Platonists in general, cf. John Tulloch, Rational theology and Christian philosophy in England in the XVIIIth century, vol. ii, Edinburgh and London, 1874; F. J. Powicke, The Cambridge Platonists, London, 1926; J. H. Muirhead, The Platonic tradition in Anglo-Saxon philosophy, London, 1931; T. Cassirer, Die Platonische Renaissance in England und die Schule von Cambridge, Leipzig, 1932; English translation: The Platonic Renaissance in England and the Cambridge School, New Haven, 1953. Selections of the philosophical writings of Henry More (namely from The antidote against atheism, The immortality of the soul, and the Enchiridium metaphysicum in translation) were published in 1925 by Miss Flora J. Mackinnon with an interesting introduction, valuable notes, and an excellent bibliography: Philosophical writings of Henry More, New York, 1925. Cf. Marjorie Nicolson, Conway letters, the correspondence of Anna, Viscountess Conway, Henry More and their friends, 1642-1684, London, 1930; Markus Fierz, "Ueber den Ursprung und Bedeutung der Lehre Newtons vom absolutem Raum," Gesnerus, vol. xi, fasc. 3 / 4, 1954; Max Jammer, Concept of space, Harvard Univ. Press, Cambridge, Mass., 1954. Both Markus Fierz and Max Jammer seem to me to exaggerate the real influence of cabalist space conceptions on Henry More (and his predecessors). In my opinion, it was a typical

case of reprojection into the past of modern conceptions in order to back them up by sacred or venerable authorities; yet, as we know, misunderstanding and misinterpretation play an important part in the history of thought. It seems to me, moreover, that Fierz and Jammer themselves are not quite innocent of the sin of retroprojection, forgetting that space conceptions formed before the invention of geometry were not, and could not, be identical or even similar to the conceptions devised after this momentous event.

2. Henry More, An antidote against atheisme, or an appeal to the natural faculties of the minde of man, whether there be not a God, London, 1652; second ed. corrected and enlarged, London, 1655; third edition, corrected, and enlarged, "with an Appendix thereunto annexed," London, 1662. I am quoting this edition as given in Henry More's Collection of severall philosophical writings, London, 1662.

3. Henry More, The immortality of the soul, so farre forth as it is demonstrable from the knowledge of nature and the light of reason, London, 1669; second edition in the Collection of severall philosophical writings of 1662. It is this edition that I am quoting.

4. Henricus Morus, Enchiridium metaphysicum sive de rebus incorporeis succincta et luculenta dissertatio, Londini, 1671.

7. Cf. R. Zimmerman, "Henry More and die vierte Dimension des Raumes," Kaiserliche Akademie der Wissenschaften, Philosophisch-historische Klasse, Sitzungsberichte, Bd. 98, pp. 403-sq., Wien, 1881.

10. Axiom ix (b. i, c. ii, p. 19) tells us that "There are some Properties, Powers and Operations, immediately appertaining to a thing, of which no reasons can be given, nor ought to be demanded, nor the Way or Manner of the cohesion of the Attribute with the subject can by any means be fancied or imagined."

11. Cf. William Gilbert, De magnete, ch. xii, p. 308: "The magnetic force is animate, or imitates the soul; in many respects it surpasses the human soul while that is united to an organic body."

24. This definition is given by Descartes in the Principia philosophiae, part ii, §25.

CHAPTER VII

1. Cf. Nicolas Malebranche, Méditations chrétiennes, méd. ix, §9, p. 172, Paris, 1926. On Malebranche cf. H. Gouhier, La philosophie de Malebranche, Paris, 1925.

7. Cf. Malebranche, Correspondance avec J. J. Dortous de Mairan, ed. nouvelle, précédée d’une introduction par Joseph Moreau, Paris, 1947.

8. Cf., e. g., the already quoted book of E. A. Burtt, The metaphysical foundations of modern physical science, New York, 1925; second ed., London, 1932.

translated into English by Andrew Motte in 1729, the translation revised by Florian Cajori, p. 6, Berkeley, Calif., 1946.

18. Ibid., p. 7. The example of the sailor is discussed by Descartes in the Principia philosophiae, ii, 13, 32.

24a. Cf. Ernst Mach, The science of mechanics, Chicago, 1902, pp. 232 sq.; cf. also Max Jammer, op. cit., pp. 104 sq.; 121 sq.; 140 sq.

27. Ibid., book iii, The system of the world, prop. V, theorem VI, scholium, cor. III, p. 414.

29. As a matter of fact, they have been listed also by Boyle and Gassendi who, in contradistinction to Descartes, insist on impenetrability as an irreducible property of body distinct from mere extension.

30. Ibid., rule III, pp. 398 sq. The text I am referring to appeared in the second edition of the Principia; yet, as it represents the fundamental views of Newton which inspired his whole system, I feel it necessary to quote it here. On the difference between the first and the subsequent editions of the Principia, cf. my papers "Pour une édition critique des oeuvres de Newton," Revue d’Histoire des Sciences, 1955, and "Expérience et hypothèse chez Newton," Bulletin de la Société Française de Philosophie, 1956.

32. Cf. my Études Galiléennes. II, La loi de la chute des corps, and III, Galilée et la loi d’inertie.

[paragraph continues] Letter II (Jan. 17, 1692-93), p. 210, London, 1756; reprinted in Opera omnia, ed. by Samuel Horsley, 5 vols., London, 1779-85 (vol. iv, pp. 429-442), and also in the Works of R. Bentley, vol. in, London, 1838. I am quoting this edition.

36. Eight sermons preach’d at the Honourable Robert Boyle lecture in the first year MDCXCII, By Richard Bentley, Master of Arts, London, 1693. The first sermon proves The folly of atheism and . . . Deism even with respect to the present life, the second demonstrates that matter and motion cannot think, the third, fourth and fifth present A confutation of atheism from the structure of the human body, the sixth, seventh and eighth, forming the second part of the work, A confutation of atheism from the origin and frame of the world. I am quoting the last edition (Works, v. iii) of this book that has seen nine of them in English, and one in Latin (Berolini, 1696); cf. Part II, sermon VII (preached Nov. 7th, 1692), pp. 152 sq.

41. Letters from Sir Isaac Newton to the Reverend Dr. Bentley, Letter I, pp. 203 sq.

45. On the cosmical optimism of the XVIIIth century, cf. Lovejoy, op. cit., pp. 133 sq.; E. Cassirer, Die Philosophie der Aufklärung, Tübingen, 1932.

CHAPTER VIII

1. Joseph Raphson is chiefly known as the author of the violently pro-Newtonian Historia Fluxionum, sive Tractatus Originem et Progressum Peregregiae Istius Methodis Brevissimo Compendio (Et quasi synoptice) Exhibens, Londini, 1715.

2. Analysis Æquationum Universalis seu ad Aequationes Algebraicas Resolvendas Methodus Generalis et Expedita, Ex nova Infinitarum Serierum Methodo, Deducta et Demonstrata. Editio secunda cui accedit Appendix de Infinito Infinitarum Serierum progressu ad Equationum Algebraicarum Radices eliciendas. Cui etiam Annexum est De Spatio Reali seu Ente Infinito conamen Mathematico Metaphysicum, Authore

[paragraph continues] Josepho Raphson A. M. et Reg. Soc. Socio., Londini, 1702. The first edition of J. Raphson's work, without the above-mentioned appendices, appeared in 1697.

12. Ibid., Scholium, p. 76. On the space theories of the Cabala cf. Max Jammer, op. cit., pp. 30 sq.

CHAPTER IX

1. Strange as it may seem, the adjunction of these "queries," numbered 17 to 43, to the Latin edition of the Opticks in 1706 seems to have escaped the attention of Newton's historians who, usually, attribute these queries to the second (English) edition of 1617 of his Opticks. Thus, for instance, L. T. More, Isaak Newton, New York-London, 1934, p. 506, note: "A second edition (octavo) bears the advertisement 1717. It was published in 1718. . . . The number of new Queries added

begins with the seventeenth." Leon Bloch's La philosophie de Newton, Paris, 1908, is an honorable exception to the afore-mentioned rule; and today, Mr. H. G. Alexander, editor of The Leibniz-Clarke correspondence, Manchester University Press, 1956.

2. Philosophical principles of natural religion by George Cheyne, M. D. and F. R. S., London, 1705. The second edition of Cheyne's book, published under the title Philosophical principles of religion, natural and revealed, London, 1615, "corrected and enlarged," contains two parts: Part I, "containing the Elements of Natural Philosophy and the Proofs of Natural Religion arising from them," and a Part II, "containing the Nature and Kinds of Infinities, the Arithmetick and Uses, and the Philosophick Principles of Reveal’d Religion, now first published." Strangely enough the common title page, as well as that of the second part, bears the date 1715, whereas that of the first part, the date 1716. As a matter of fact, or at least according to David Gregory who held this information from Newton himself, it was the publication by Dr. Cheyne of his Fluxionum methodus inversa sive quantitatum fluentium leges generales, London, 1703 (rather sharply criticized by A. De Moivre in his Animadversiones in Dr. G. Cheyne's Fluxionum methodus . . . London, 1704), which prompted Newton to publish the Two treatises on the species and magnitudes of curvilinear figures, that is, The quadrature of curves and The enumeration of the lines of the third order; (cf. David Gregory, Isaak Newton and their circle, Extracts from David Gregory's Memoranda, edited by W. G. Hiscock, pp. 22 sq., Oxford, 1937). In the selfsame Memoranda under the date of December 21, 1705, we find also the following, very interesting passage (ibid., pp. 29-30): "Sir Isaak Newton was with me and told me that he had put 7 pages of Addenda to his Book of Lights and Colours in this new latin edition of it. He has by way of quaere explained the explosion of Gun powder, all the chief Operations of Chymistry. He has shewed that Light is neither a communication of motion nor of a Pressure. He inclines to believe it to be projected minute bodys. He has explained in those Quaerys the double Refraction in Iseland Crystall. His Doubt was whether he should put the last Quaere thus. What the space that is empty of bodies is filled with. The plain truth is that he believes God to be omnipresent in the literal sense. And that as we are sensible of Objects where their images are brought within the brain, so God must be sensible of every thing being intimately present with every thing: for he supposes that as God is present in space where there is no body, he is present in space where a body is also present. But if this way of proposing this his notion be too bold, he thinks of doing it thus. What cause did the Ancients assign of

[paragraph continues] Gravity. He believes that they reckoned God the Cause of it, nothing else, that is no body being the cause; since every body is heavy.

"Sir Isaak believes that the Rays of Light enter into the composition of most Natural Bodies that is the small particles that are projected from a lucid body in form of Rays. As plain this may be the case with most combustible, inflammable bodies." On the relations of light and matter according to Newton cf. Helène Metzger, Newton, Stahl, Boerhaave et la doctrine chimique, Paris, 1930.

3. Optice . . . l. iii, qu. 20, pp. 312 sq.; London, 1706; qu. 28 of the English edition; cf. I. Bernard Cohen's edition of the Opticks, New York, 1952, p. 369. As the English edition certainly gives the original text of Newton himself, I will quote this latter giving first the page numbers of the Latin, and then those of the afore-mentioned edition.

4. Ibid., pp. 322 sq.; pp. 375-76. The existence of various "impellent" and "repellent" forces acting between the "particles" of bodies is already asserted by Newton in the preface of the Principia.

11a. The reasoning is, of course, utterly false and it is rather astonishing that Newton could have made it and that neither he himself nor his editors noticed this falsehood.

CHAPTER X

1. George Berkeley, Principles of human knowledge, §110; p. 89 (The works of George Berkeley Bishop of Cloyne, ed. by A. A. Luce and T. E. Jessop, vol. i, Edinburgh, 1949).

[paragraph continues] Correspondence of Sir Isaak Newton and Professor Cotes . . . ed. J. Edleston, London, 1850, pp. 153 sq.): ". . . I think it will be proper [to] add something by which your book may be cleared from some prejudices which have been industriously laid against it. As that it deserts mechanical causes, is built upon miracles and recurrs to Occult qualities. That you may not think it unnecessary to answer such Objections you may be pleased to consult a Weekly Paper called Memoires of Literature and sold by Ann Baldwin in Warwick-Lane. In the 18th Number of ye second Volume of those Papers which was published May 5th, 1712, you will find a very extraordinary letter of Mr. Leibnitz to Mr. Hartsoeker which will confirm what I have said." Indeed, in this letter, dated Hanover, February 10, 1711, Leibniz who, as a matter of fact already had attacked Newton in his Théodicée (Essai de Théodicée, Discours de la Conformité de la Foi avec la Raison, §19, Amsterdam, 1710) assimilated the Newtonian gravity to an "occult quality," so "occult" that it could never be cleared up even by God. It is well known that neither Leibniz nor Huygens had ever accepted the Newtonian conception of gravitation, or attraction. Cf. René Dugas, Histoire de la mécanique au XXVII^e siècle, Neuchatel, 1954, cap. xii, Retour au Continent, pp. 446 sq. and cap. xvi, Réaction des Newtoniens, pp. 556 sq.

5. Cf. Mathematical principles of natural philosophy, translated into English by Andrew Motte in 1729. The translation revised . . . by Florian Cajori, General Scholium, pp. 543 sq., Berkeley, Cal., 1946.

12. Professor Cajori follows Andrew Motte in translating Newton's fingo by frame. It seems to be that the old term feign (used by Newton himself) is both more correct and more expressive.

17. Principles, p. 547. On the XVIIth century conception of "spirit" cf. E. A. Burtt, op. cit., and A. J. Snow, Matter and gravity in Newton's philosophy, Oxford, 1926.

CHAPTER XI

1. Wilhelmine Caroline, later Queen Caroline, was born Princess of Brandenburg-Anspach and in 1705 became the wife of George Augustus, Electoral Prince of Hanover. It was as Princess of Hanover that she became intimate with Leibniz; as Leibniz put it himself, she "inherited" him from Sophie Charlotte of Prussia.

2. Cf. "An extract of a letter written in November 1715," §§3 and 4, published in A Collection of papers, which passed between the late learned Mr. Leibnitz and Dr. Clarke. In the years 1715 and 1716 Relating to the Principles of Natural Philosophy and Religion. With an Appendix, pp. 3 and 5, London, 1717. Leibniz writes, of course, in French, and Clarke, in English. But he accompanies the publication of the originals by a translation of Leibniz's "papers" into English (probably made by himself) and of his own "replies" into French (probably made by the Abbé Conti). Moreover, he adds to the text a series of footnotes with references to relevant passages in Newton's writings. This polemic is now available in the excellent edition of G. H. Alexander, The Leibniz-Clarke correspondence, Manchester Univ. Press, 1956; cf. also René Dugas, La mécanique au XVII siècle, cap. xvi, §3, pp. 561 sq.

3. The choice of Dr. Samuel Clarke was rather obvious. Dr. Clarke, Rector of St. James’, Westminster, was not only a philosophical theologian—in 1704-5 he gave the Boyle Lectures—but also was former chaplain of Queen Anne, removed, to say the truth, from this charge for lack of orthodoxy (he was practically an Arian). However, after Queen Anne's death he became an intimate of Princess Caroline with whom, at her request, he had weekly philosophical conversations in which other gentlemen interested in discussing philosophical problems participated. Thus it was only natural that, as Des Maizeaux tells us in the preface to his own French re-edition of the Collection of papers (Recueil de diverses pièces sur la philosophie, la religion naturelle, l’histoire, les mathématiques etc., 2 vols., Amsterdam, 1720, p. II): "Madame la Princesse de Galles, accoutumée aux Recherches Philosophiques les plus abstraites et les plus sublimes fit voir cette Lettre à M. Clarke et souhaita qu’il y répondit. . . . Elle envoyait à M. Leibniz les Réponses de M. Clarke et communiquait à M. Clarke les nouvelles difficultés, ou les Instances de M. Leibniz." Indeed, Dr. Clarke as an intimate friend of Sir Isaac, and a Newtonian of long standing, could be relied upon to represent the philosophical views of his master.

In my opinion we must go even farther: it is utterly unconceivable that Clarke should accept the role of philosophical spokesman (and defender) of Newton without being entrusted by the latter to do it, nay, without having secured the collaboration of the great man, at least in the form of approval.

I am, thus, morally certain that Clarke communicated to Newton both Leibniz's letters and his own replies to them. It is indeed unthinkable that in the midst of his bitter fight with Leibniz about the priority of the invention of the calculus, Newton who "aided" both Keill and Raphson in their attacks against Leibniz, as he "aided" Des Maiseaux some years later in the preparation of his edition of the "Collection of papers" (the second volume of his edition carries the history of the calculus controversy by publishing translations of selected pieces of the Commercium epistolicum), should remain aloof and disinterested in the face of an assault upon his religious view and an accusation, practically, of atheism, by the selfsame Leibniz. As a matter of fact, the Princess of Wales informed Leibniz (Caroline to Leibniz, Jan. 10, 1716, in O. Klopp, Die Werke von Leibniz, Hanover, 1864-84, vol. xi, p. 71, quoted in The Leibniz-Clarke correspondence, Manchester Univ. Press, 1956, p. 193) that he was right in his supposition that these letters were not written without the advice of Newton. Strange as it may seem, the importance of Clarke's papers as representing literally the metaphysical views of Newton has never been recognized, with the result that their study was completely neglected by the historians both of Newton and of Leibniz. Thus, for instance, L. T. More, op. cit., p. 649: "It seems probable that Newton was even more exasperated by Leibniz's attack on the anti-Christian influence of the Principia than by the controversy over the invention of the calculus. To justify himself he guided Des Maizeaux in preparing for publication the long debate between Leibniz and Samuel Clarke on the religious significance of the Newtonian Philosophy. For this purpose he gave to the author the documents relating to the controversy, and assisted him in preparing an historical preface which reviewed the whole affair."

4a. As a matter of fact (cf. supra, p. 209) Newton, at least once, identified space with God's sensorium.

[paragraph continues] Sir Isaac Newton and Dr. Samuel Clarke were much nearer to Socinianism than to the teaching of the Established Church: neither of them, indeed, accepted the Trinitarian conception of God; they were both—as also John Locke—Unitarians; cf. H. McLachlan, The religious opinions of Milton, Locke and Newton, Manchester, 1941. On Newton's metaphysical and religious views, cf. Helène Metzger, Attraction universelle et religion naturelle, Paris, 1938, and E. W. Strong, "Newton and God," Journal of the History of Ideas, vol. xiii, 1952.

10. " Dr. Clarke's second reply," ibid., p. 41. Intelligentia supramundana, or more exactly, extra mundana, is an expression of Leibniz; cf. Théodicée, §217.

15. "Dr. Clarke's third reply," ibid., p. 77. Dr. Clarke uses the term "property" in his own "replies" as well as in the translation of Leibniz's "papers"—and one understands full well why he does not use the more correct one, "attribute": just because Leibniz has mentioned Spinoza. But Leibniz himself uses the term "attribute"; moreover the French translation of Clarke's "replies," reviewed and acknowledged by Clarke himself, uses "attribute" for "property."

16. Dr. Clarke's example is rather bad as, in this case, there would be a relative displacement of "our world" in respect to the fixed stars.

17. The use of the principle of inertia in the discussion of the old problem whether God can move the world in a straight line (cf. my paper quoted supra, cap. iii, n. 43) is rather ingenious.

25. Ibidem. Leibniz will mention Henry More in his fifth paper, n. 48: "To conclude. If the space (which the author fancies) void of bodies is not altogether empty: what is it then full of? Is it full of extended spirits perhaps, or immaterial substances, capable of extending and contracting of themselves; which move therein and penetrate each other without any inconveniency, as the shadows of two bodies penetrate one

another upon the surface of a wall? Methinks I see the revival of the odd imaginations of Dr. Henry More (otherwise a learned and well meaning man) and of some others who fancied that those spirits can make themselves impenetrable whenever they please."

31. We even have to suppose it if we want to link atomism with mathematical philosophy.

37. It is rather interesting to see Dr. Clarke use Henry More's famous concept and term.