No CrossRef data available.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Euclidian Space and Absolute Space
Published online by Cambridge University Press: 02 April 2024
At first glance, the formulation of the principle of inertia—not. yet complete with Galileo, more precise with Gassendi, finally systematic with Newton—seems to constitute but one of the aspects of a process of deep transformations at the end of which traditional cosmology was replaced by various world systems. These transformations—or, to use a more classic term, this “ scientific revolution” —have been the object of numerous works, a list, of which would alone fill the pages of a thick volume. But the principle of inertia itself, a principle about which can be said without exaggeration that it expressed the essence of this revolution at the same time as it stimulated it, has perhaps not received all the attention it deserves. And especially the impact of this principle on Western culture has not been fully measured. True, Alexandre Koyré has always insisted on the fact that, by reducing movement to a state like that of the state of rest, the principle of inertia expressed a new vision of the world more than a scientific result. But his admirable analyses deal more with the slow advent of the priciple of inertia among the natural philosophers who preceded, accompanied and then followed Galileo than with the theological, philosophical and literary impact of this principle. Moreover, by examining this impact, we discover that it is necessary to make a distinction between Euclidian space and absolute space, a distinction which is frequently implicit with certain scientific historians, but, and this must be emphasized, is more often ignored.
1 Jean Starobinski, L'Oeil vivant, Paris, Ciallimard, p. 14.
2 Ibid., p. 129.
3 It is intentionally that I use the adjective "atomic." In analytical philosophy, atomic facts are expressed by atomic propositions which are independent from one another, just as the atoms of the Newtonian cosmos are independent one from another. Such independence necessarily implies perfect ontological stability: the atom, reflected by the atomic proposition, is only what it is (A=A). The consequence is that, inasmuch as the world is made up of atomic facts, it is without form, for every form is made up of elements which are both similar to themselves and distinct from themselves. In such a world nothing can be said— no more, in any case, than can be said of chaos or of a pile of stones. It is thus not surprising to see that the fundamental thesis of the first philosophy of Ludwig Wittgenstein (profoundly influenced by Bertrand Russell's logical atomism) is that it is impossible to say anything at all of the world as a totality. "Witt genstein's fundamental thesis is that it is impossible to say anything about the world as a whole." Bertrand Russell, "Introduction" to Ludwig Wittgenstein, Tractatus-Logico-Philosophicus, new transl., London, Routledge and Kegan Paul. 1961, p. xvii.
4 "The explicative force of theories resides essentially in the application of the postulate of identity in time… It is in virtue of this postulate that physical theories are dominated by the concept of discrete particles." Emile Meyerson, Jdentité et Réalité, Paris, Felix Alcan, 1908, p. 85. These are, of course, particles which remain perfectly identical to themselves, no matter what happens.
5 F. Bonamico, De Motu, I, V, c. xxxv, p. 503. Quoted by Alexandre Kovré, Etudes Galiléennes, Paris, Hermann, 1966, p. 25. Bonamico was Galileo's teacher.
6 Alexandre Koyré, Etudes Galiléennes, Paris, Hermann, 1966, p. 23, note 2.
7 Jacques Merleau-Ponty and Bruno Morando, The Rebirth of Cosmology, English transl., New York, Alfred A. Knopf, 1976, p. 77.
8 Etienne Gilson, L'Esprit de la philosophie médiévale, second revised edition, Paris, Jean Vrin, 1944, p. 65.
9 Jacques Merleau-Ponty, op. cit., p. 194.
10 André Malraux, "La lutte avec l'ange" in Les Noyers de l'Altenburg, Ge. neva, Albert Skira, 1945, p. 72.
11 On the theme of the solitary atom, the monadic life, see Ben Lazare Mijusko vic, Loneliness in Philosophy, Psychology and Literature, Assen (The Netherlands), Van Gorcum, 1979.
12 On desire as a power capable of reproducing substantial transformations in man, see Alexandre Kojève, Introduction à la lecture de Hegel, Paris, Gallimard, 1943 and, particularly, Gaston Fessard, De l'actualité historique, Paris, Desclée de Brouwer, 1959, volume 1, pp. 121-200. Hegelian philosophy was interested in the transformation or, better, the transsubstantiation of the vertical animal from the natural state into man. On the transformation of man into God (mysticism), see Evelyn Underhill, Mysticism, London, Methuen & Co. Ltd, 1911, and Alexan dre Koyré, Mystiques, spirituels, alchimistes du XVIe siècle allemand, Paris, Gallimard, 1971.
13 The work of Jean Baudrillard systematically explores these manners of identifying oneself to another through market mechanisms (symbolic exchange). See L'échange symbolique et la mort, Paris, Gallimard, 1976; Le système des objets, Paris, Gallimard, 1968.
14 René Descartes, Principia philosophiae, pars 2, art. 37.
15 "It is not in conformity to order nor beauty nor to the reason of creation that only a very small portion of matter enjoys, a vital principle or an immanent activity while the greatest perfection requires that the totality of matter be so endowed. Moreover, nothing says that there are not souls everywhere or at least something analogous, although dominant, and consequently, intelligent souls, such as human souls, cannot be everywhere." G.W. Leibniz, "De la Nature elle même, ou de la force inhérente aux choses créées et de leurs actions," in Opuscules philosophiques choisis, trad. Paul Schrecker, Paris, Hatier-Boivin, 1954, p. 106.
16 Fritjof Capra, "Le Tao de la physique," in Science et Conscience: Les deux lectures de l'univers, Paris, Stock, 1980, p. 45. Similarly Werner Heisenberg af firms, "… dass wir die Bausteine der Materie, die ursprünglich als die letzte objektive Realität gedacht waren, überhaupt nicht mehr ‘an sich' betrachten können … Das Ziel der Forschureg ist also nicht mehr die Erkenntnis der Atome …" Das Naturbild der heutigen Physik, Hamburg, Rowohlt, 1955, p. 18. Along the same lines, David Bohm stresses that "quantum theory shows that the attempt to describe and follow an atomic particle in precise detail has little meaning." Wholeness and the Implicate Order, London and Boston, Routledge and Kegan Paul, 1980; Paperback ed., 1982, p. 9. For the convergence between Aristotle and contemporary physics, see Patrick Suppes, "Aristotle's Concept of Matter and its Relation to Modern Concepts of Matter," Synthese, September 1974, 28:27-50. See also Theodore J. Kiesel, "The Reality of the Electron," Philosophy Today, Spring 1964, 8:56-64.
17 Martin Heidegger, Sein und Zeit, Halle, 1927, p. 64.
18 For the relation between metaphor and cosmology, see Joseph A. Mazzeo, Nature and the Cosmos: Essays in the History of Ideas, New York, Dabor Science Publications, 1977, pp. 28-30.
19 "The ideal of the Tractatus-Logico-Philosophicus was the mirror." Ernest Gellner, Words and Things, London, Victor Gollancz, 1959, p. 75. See also Hanna F. Pitkin, Wittgenstein and Justice, Berkeley and London, University of Califor nia Press, 1972, p. 27.
20 On the fragmentation of the universe in Wittgenstein, see William Barrett, The Illusion of Technique, New York, Anchor Press, Doubleday; Anchor Books, 1979, pp. 34-36.
21 Louis Vax, L'empirisme logique, Paris, P.U.F., 1970, p. 60. As for Jacques Bouveresse, he notes that "Wittgenstein's intention was to show … that it is completely strange to suppose that every time we speak we must first of all (in thought) have something to say." Le Mythe de l'intériorité, Paris, Editions de Minuit, 1976, p. 661. From a concept in which language refers the mind to atomic realities, that is to things identical to themselves, Wittgenstein moved to an exactly opposite concept in which there is no essence, not even a clear and distinct reflection of what the words evoke. The same rejection of language-mirror, -reflection, -essence or -significance is found in Nelson Goodman and Willard Quine. There are only manners of speaking or manipulations of symbols which cannot be reduced to precise definitions. This rejection of intuition and of the essence which corresponds to it belongs to the movement of increasing mistrust in the capacity which language has of bringing an essence out beyond its ap pearances. On this point existentialism and analytical philosophy coincide. This mistrust would be justified if language was only a reservoir of labels (each label corresponding to an essence). However, language is not just that, even if, under the pressure of acosmism, it has tended to be but that.
22 Walter Biemel, Le Concept du Monde chez Heidegger, Paris, Louvain, E. Nauwelaerts and Jean Vrin, 1950, p. 13. In another passage, Walter Biemel af firms that the spatiality of Dasein "cannot be compared to scientific space," p. 72.
23 For the relation between the body and the cosmos, see Victor Harris, All Coherence Gone, Chicago, The University of Chicago Press, 1949.
24 The principle of inertia is stated as follows: "Corpus omne perseverare in statu quo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum ille mutare." Isaac Newton, Philosophiae naturalis principia mathematica, London, 1687, "Axiomata sive Leges Motu," lex I, p. 12.
25 "He who had discovered the principle of inertia [Galileo] always refused to think of a straight inertial path, because it would have been ‘disorderly' …" Giorgio de Santillana, The Crime of Galileo, London, Heineman, 1958, p. 59.
26 The least that can be said is that Galileo is hardly interested in hypotheses which only preserve appearances or, as Cardinal Bellarmine said, explications ex suppositione: "Giudicai … comparir pubblicamente nel teatro del mondo, come testimonio di sincera verità…" Galileo Galilei, Dialogo sopra i due massimi sistemi del mondo (1632), in Opere, Turin, Franz Brunetti, 1969, p. 15. On this point see also Pierre Duhem, La Theovie Physique, second edition, Paris, Marcel Ri vière, 1914, p. 59.
27 "Nowhere, in fact, does Galileo ever state what the motion of a projectile would be if no forces were acting on it… Galileo regards the impetus as permanent but is unable to neglect the effects of gravity." Allen Franklin, The Principle of Inertia in the Middle Ages, Colorado, Colorado University Press, 1976, p. 60.
28 Emile Namer, L'Affaire Galilee, Paris, Gallimard et Julliard, 1975, p. 19.
29 Alexandre Koyré, Etudes Galiléennes, p. 174.
30 Frances Yates, Giordano Bruno and the Hermetic Tradition, London, Rout ledge and Kegan Paul, 1964, p. 297.
31 Emile Namer, Giordan Bruno, Paris, Seghers, 1966, p. 46. My underlining.
32 William Gilbert, De mundo nostro sublunari philosophia nova, Amsterdam, 1651, lib. I, cap. 28, p. 60. My underlining.
33 Quoted by Emile Namer, Giordano Bruno, Paris, Seghers, 1966, p. 30. My underlining.
34 On the facility with which animism and modern science can be merged and on the effort of the founders of our physics to free themselves of animism, see Robert Lenoble, Mersenne ou la naissance du mécanisme, Paris, Jean Vrin, 1943.
35 Petri Gassendi, De motu impresso a motore translato, Paris, 1641, c.xv, p. 59 and c.xvi, p. 62.
36 Quoted by Robert Lenoble, op. cit., p. 276.
37 Richard Westfall, "Newton and Absolute Space," Archives internationales d'histoire des sciences, April-June 1964, 67:121-132.
38 Robert Lenoble, op. cit., p. 276.
39 Isaac Newton, Philosophiae naturalis principia mathematica, London, 1687, p. 5.
40 George Berkeley, Principles of Human Knowledge, par. 110 in The Works of George Berkeley, Bishop of Cloyne, A. A. Luce and T. E. Jessop, eds., Edin burgh, I. Nelson, 1948, 2:89.
41 Max Jammer, Concepts of Space: The History of Theories of Space in Physics, 2nd ed., Cambridge, Mass., Harvard University Press, 1969, p. 101.
42 Berkeley, Works, vol. 4, p. 47.
43 Newton, Principia, p. 5.
44 On Henry More's influence on Newton, see Frank E. Manuel, A Portrait of Isaac Newton, Cambridge, Mass., Harvard University Press; New Republic Books, 1978, pp. 87, 334.
45 See Henry More, Enchiridium Metaphysicum sive de rebus incorporeis suc cinta et luculenta a dissertatio, Londini, 1671, cap. VI, 7, pp. 55-56.
46 Immanuel Kant, Gesammelte Werke, Berlin, Akademie Ausgabe, 1905, vol. 2, p. 13. My translation.
47 Alexis Philonenko, Qu'est-ce que s'orienter dans la pensée? Paris, Jean Vrin, 1959, p. 69.
48 See Bonamy Dobrée, English Literature in the Early Eighteenth Century, Oxford, Clarendon Press, 1959, pp. 499-500.
49 "Newton was delighted that his cosmology was thus presented [in the Boyle Lectures given by Richard Bentley] in relatively simple terms to vindicate God's active role in the world." Michael Hunter, Science and Society in Restoration England, Cambridge, Cambridge University Press, 1981, p. 184. See also James R. Jacob and Margaret Jacob, "The Anglican Origins of Modern Science: The Metaphysical Foundations of the Whig Constitution," ISIS, 1980, 71:251-267.
50 "If someone objects that we are unable to imagine an infinite universe, this I concede; contending nevertheless that we are able to understand it…" Un published Scientific Papers of Isaac Newton, A. Rupert Hall and Marie Boas Hall, eds., Cambridge, Cambridge University Press, 1962, p. 101.
51 Pierre Simon de Laplace, Exposition du système du monde, liv. V, chap. VI, in Oeuvres complètes, Paris, Gauthier-Villard, 1878-1912, vol. VI, p. 477.
52 François Arago, Oeuvres (Paris.: 1959), volume III, p. 456. Quoted by Jacques Merleau-Ponty, "Situation et rôle de l'hypothèse cosmogonique dans la pensée cosmologique de Laplace," Revue d'histoire des sciences, January, 1976, 29: 21-49.
53 In Die Mechanik in ihrer Entwicklung, Leipzig, 1833, Ernst Mach spoke of absolute space as a "Begriffsungetüme" (conceptual monster).
54 "In England, by the middle of the nineteenth century, it became clear that the concept of absolute space was useless in physical practice." Max Jammer, Concepts of Space, 2nd ed., Cambridge, Mass., Harvard University Press, 1969, p. 140.
55 Richard Westfall, "Newton and Absolute Space," Archives internationales d'histoire des sciences, April-June 1964, 67:121-132.
56 Alexis Philonenko, L'Oeuvre de Kant, Paris, Jean Vrin, 1969, vol. I, p. 73.
57 "Geometrization of space implies necessarily its infinitization: we cannot assign limits to Euclidean space." Alexandre Koyré, Newtonian Studies, Chicago, The University of Chicago Press; Phoenix Edition, 1968, p. 7, note 1.
58 Ronald Calinger, "Kant and Newtonian Science," ISIS, September 1979, 70: 349-362.
59 On this point see Herbert Butterfield, The Origins of Modern Science, rev. ed., New York, The Free Press, 1966, p. 177.
60 Friedrich Nietzsche, Die Fröhliche Wissenschaft, in Werke, Karl Schlechta, ed., Munich, Hanser, 1954-56, vol. 2, p. 127 (No. 125). My translation.
You have
Access