Abstract
For many scholars, the publishing of Isaac Newton’s Principia in 1687 marks the beginning of a period of physics which they call the classical one.1 Yet it is questionable whether Newton’s “Mathematical Principles of Natural Philosophy”2 actually represent what is known as physics today. The Principia is a foundation for a mathematical philosophy of nature as viewed by Plato. If Physics is within the scope of this philosophy, then it also includes metaphysics, as a presupposed knowledge of the absolute, of space and time, of matter, force and motion, of cause and effect; read the Scholium that follows the eight definitions introduced at the beginning of the Principia.3 That is why physicists of the positivistic school of thought have had their problems with Newton since the time of George Berkeley and Ernst Mach,4 and why, as a result, many people are more familiar with the title than with the contents of the Principia.
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Notes
Cf. Eduard Jan Dijksterhuis, De mechanisering van het wereldbeeld, Amsterdam 1950
German trans, by H. Habicht, Die Mechanisierung des Weltbildes, Berlin 1956; reprint Berlin 1983, p.3.
Isaac Newton, Philosophiae Naturalis Principia Mathematica, in: Isaaci Newtoni Opera quae Exstant Omnia, Samuel Horsley ed., London 1779–1785;
German trans.: Mathematische Prinzipien der Naturlehre, J.Ph. Wolfers ed., Berlin 1872
Mathematische Grundlagen der Naturphilosophie, Ed Dellian ed., Hamburg 1987, in preparation.
S.Horsley ed., ibid. Vol.II p.6–12.
George Berkeley, Schriften über die Grundlagen der Mathematik und Physik, W. Breidert ed., Frankfurt a.M. 1985 = Suhrkamp Taschenbuch Wissenschaft No. 496, p. 210–243;
Ernst Mach, Die Mechanik in ihrer Entwicklung, repr. Frankfurt a.M. 1982, p. V.
Cf. Max Jammer, Concepts of Force, Cambridge/Mass., 1957, p. 166.
Immanuel Kant, Metaphysische Anfangsgründe der Naturwissenschaft, in: Kant’s gesammelte Schriften, Berlin 1911, Vol.IV p.468, 543.
This is still an open problem in quantum physics; cf. Gino Tarozzi A. van der Merwe eds., Open Questions in Quantum Physics, Dordrecht 1985.
Cf. Roger Cotes’s preface to the Second Edition of the Principia, London 1713, in S.Horsley ed., op. cit. Vol.II p.XIII-XXV.
Principia, definition 3; cf. S. Horsley ibid. p. 2. The problem that is discussed in this paper may have started in a sense from Andrew Motte’s translating of impetus as impulse in the Principia’s first English edition in 1729, thus cutting the connection between Newton and the impetus theory (Galileo, Leonardo da Vinci, Buridan).
Also Wolfgang Breidert ed., op.cit. p.48–55, and Max Jammer, Der Begriff der Masse in der Physik, Darmstadt 1981, p. 74, 75.
CF. von Weizsäcker, Aufbau der Physik, München 1985, p.234,243–45.
Cf. The banishment of the causa-effectus relation from mechanics (“Cet unique axiome vague & obscur”) by Jean le Rond d’Alembert, Traité de Dynamique, Paris 1758, Préliminaire, p. XI-XII.
Samuel Clarke, A Demonstration of the Being and Attributes of God, London 1705.
Cf. B.J.T. Dobbs, The Foundations of Newton’s Alchemy, Cambridge 1983, p. 193;
see also W. Windelband, Lehrbuch der Geschichte der Philosophie, H. Heimsoeth ed., Tübingen 1980, p.343–365 (§ 31 “Substanz und Kausalität”).
The phrase causa aequat effectum is actually a product of Leibniz’s own; cf. H.J. Heß, Die unveröffentlichen naturwissenschaftlichen und technischen Arbeiten von Leibniz; Studia Leibnitiana Suppl. Vol. 17 (1978), p. 183–205.
The phrase causa aequat effectum is actually a product of Leibniz’s own; cf. H.J. Heß, Die unveröffentlichen naturwissenschaftlichen und technischen Arbeiten von Leibniz; Studia Leibnitiana Suppl. Vol. 17 (1978). p.203.
Cf. the Scholium Generale at the end of the Principia’s book III (in S. Horsley op.cit. Vol. III, p. 174: “Et satis est quod Gravitas revera existat et agat secundum leges a nobis expositas…”).
Ibid. Vol. II p. 14. The axiom of the proportionality of cause and effect can be found in a little alterated formulation for instance in Jacques Rohault, Traité de Physique, Paris 1671, chapter V section 6–10; this book appeared in London in 1682 in a Latin translation, and was translated into English by John and Samuel Clarke in 1723.
Cf. Max Jammer, op.cit. (ref. 5) p. 130/1; Brian D. Ellis, Newton’s Concept of Motive Force, Journ. Hist. Ideas (23) 1962, p. 273
I. Bernard Cohen, The Newtonian Revolution, Cambridge 1980, p. 172
Richard S. Westfall, Force in Newton’s Physics, London 1972, p. 472;
Werner Kutschmann, Die Newtonsche Kraft, Wiesbaden 1983 = Studia Leibnitiana Sonderheft 12; E.J. Dijksterhuis, op.cit. p. 525.
Cf. especially Werner Kutschmann, Die Newtonsche Kraft, Wiesbaden 1983. p. 35.
Ernst Mach, Die Mechanik in ihrer Entwicklung, repr. Frankfurt a.M. 1982. p. 210.
But in this way it is treated by, for instance, Jürgen Mittelstrass, Neuzeit und Aufklärung, Berlin 1970, p. 288;
Steven Weinberg, Teile des Unteilbaren, Heidelberg 1984, p. 139, and Brockhaus Enzykopädie 1970 under “Kraft.”
Cf. Max Jammer, The Philosophy of Quantum Mechanics, New York 1974, p. 54: “The view that a formal identity between mathematical relations betrays the identity of the physical entities involved… harmonizes with the spirit of modern physics.… Physical entities which satisfy identical formalisms have to be regarded as identical themselves…”
Cf. Principia book III, regula philosophandi No. 3 and commentary; in S. Horsley, op.cit. Vol. III p. 2–3; James E. McGuire, Atoms and the Analogy of Nature: Newton’s third Rule of Philosophizing; Hist. Phil. Sci. I No. 1 (1970) p. 1.
Cf. James E. McGuire and Martin Tamny, Certain Philosophical Questions, Newton’s Trinity Notebook, Cambridge 1983, p. 134, 135.
Cf. Principia book I, Scholium after Lemma X (S. Horsley, op.cit. Vol. III p. 36), “Si quantitates indeterminatae diversorum generum conferanter inter se…” (my italics); cf. also John Wallis, Mechanica, London 1670, Proposition VII.
G.W. Leibniz, Brevis demonstratio erroris memorabilis Cartesii et aliorum..., Acta Eruditorum, March 1686.
Cf. Principia, Newton’s commentary to definition 4.
Cf. Principia in S. Horsley, op.cit. Vol. III p. 30,36.
So for instance Max Born, Die Relativitätstheorie Einsteins, Berlin 1984, p. 27;
see also I. Bernard Cohen, Newton’s Second Law and the Concept of Force in the Principia, in Robert Palter ed., The Annus Mirabilis of Sir Isaac Newton 1666–1966, Cambridge/Mass. 1970, p. 143.
Roger Cotes, Preface to the Principia’s Second Edition of 1713, in S. Horsley ed., op.cit. Vol. III p. XVI.
At the very beginning of the motion = “sub ipso motus initio,” as Cotes says, corresponding to Newton’s own formulation in the Principia, Lemma X.
This concept corresponds to the kinetic energy of analytical mechanics, expressed by mv 2 /2. The missing factor 1/2 was arbitrarily added only in 1829 by G. Coriolis because of better usage for integrations; see Max Jammer, Concepts of Force, op. cit. p. 166 footnote 12.
Newton himself called the Cartesian-Leibnizian method the “analysis of bunglers”; see Richard S. Westfall, Never at Rest, A Biography of Sir Isaac Newton, Cambridge 1980, p. 380.
Cf. Ed Dellian, Die Newtonische Konstante, Philosophia Naturalis (22) No. 3 (1985) p. 400
Ed Dellian, Experimental Philosophy Reappraised, Speculations in Science and Technology (9) No. 2 (1986) p. 135.
Cf. footnote 24 above.
Cf. Ed Dellian, On Cause and Effect in Quantum Physics, Speculations in Science and Technology, in print.
Samuel Clarke, A letter to Mr. Benjamin Hoadly F.R.S., Philosophical Transactions Vo. 35 (1727–1728), p. 381.
The connection of this equation with our mathematical expression for the equivalent inertial force could contribute to a mastering of the formal problems of modern physics, since the eq. E = (mv)c can very easily be demonstrated to be a desideratum in the foundation of quantum physics. Cf. also footnote 38.
Cf. Carolyn Merchant, The Death of Nature, German: Der Tod der Natur, München 1987.
B.J.T. Dobbs, op.cit. p. 212: “The universe lived again as Newton’s thought swung on towards the Principia in the 1680’s, for forces and active principles were everywhere.”
Cf. B.J.T. Dobbs, op.cit. p. 13.
More thoughtful physicists concede that such an understanding of modern physics is still missing. Cf. for instance Murray Gell-Mann (Nobel Price 1969), whom I. Bernard Cohen quotes as follows: “All of modern physics is governed by that magnificent and thoroughly confusing discipline called quantum mechanics, invented more than fifty years ago… Nobody understands it, but we all know how to use it and how to apply it to problems; and so we have learned to live with the fact that nobody can understand it.” (The Newtonian Revolution, op.cit. p. 147).
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Dellian, E. (1988). Inertia, the Innate Force of Matter: A Legacy from Newton to Modern Physics. In: Scheurer, P.B., Debrock, G. (eds) Newton’s Scientific and Philosophical Legacy. Archives Internationales D’Histoire des Idées / International Archives of the History of Ideas, vol 123. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2809-1_15
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