Abstract
Considering the physics of Newton and of Leibniz, we are confronted with two different ways of explaining physical phenomena and with different kinds of concepts. Whether we speak about space, time, force, matter, vortices etc., their conceptions diverge.
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Notes
Here we are using an expression from M. Fichant: “[...], l’individualisation stylistique des configurations idéelles s’impose d’autant plus à l’attention de l’historien qu’il explore un corpus [le corpus leibnizien] essentiellement en devenir, dépôt d’un work in progress, dont les strates portent les tracent d’une genèse singulière.” in “De la puissance à l’action: la singularité stylistique de la dynamique” in Fichant Science et Métaphysique dans Descartes et Leibniz, Paris, PUF, 1998, 205.
I. Newton De Motu (1684), published in both Latin and English in I. Newton The mathematical papers of Sir I. Newton,éd. D.T. Whiteside, 8 vols., Cambridge, Cambr. Univ. Press, 1967–1981, vol VI, 30–75 [abbrev.MP].
I. Newton Philosophiae naturalis principia mathematica, Londres, 1687. The standard English translation has been I. Newton Mathematical principles of natural philosophy and his System of the world,. Eng. translation of 3e ed. by A. Motte (1729), rev. and edit. by F. Cajori, Berkeley, Univ. of California Press,re-ed. 1962. However, a new and very useful translation of the third edition now exists with some references to the first and second editions, I. Newton Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy, new translation by I.B. Cohen and A. Whitman, assisted by J. Budenz, preceded by “A Guide to Newton’s Principia”, by I.B. Cohen, Berkeley, Los Angeles, London, University of California Press, 1999. In our talk we only consider the first edition.
J. Conduitt Memorandum relating to Sr Isaac Newton given me by Mr Abraham Demoivre in Nor 1727, extracts published in Cohen [1971] Introduction to Newton’s Principia, Introd. vol to the ed. by Koyré and Cohen, Cambridge, Mass., Harvard Univ. Press, 1971; Cambridge, Cambridge Univ. Press, 1971; Cambridge, Mass, Harvard Univ. Press, 1978, 297–298.
I. Newton De motu sphaericorum corporum in Fluidis (1684) published in Latin and English in Unpublished Scientific Papers of Isaac Newton. A selection from the Portsmouth Collection in the University Library, Cambridge, ed. A.R. Hall et M. Boas-Hall, Cambridge Univ. Press, 1962, reed. 1978, 243–301. (abbrev [Hall and Hall]) Parts are published, but in Latin only in MP, VI, 74–80.
The fourth theorem concerns the demonstration of Kepler’s third law.
I. Newton De motu sphaericorum corporum in Fluidis (1684), in [Hall and Hall] 280.
I. Newton De motu sphaericorum corporum in Fluidis (1684), Law 4, “The common centre of gravity does not alter its state of motion or rest through the mutual actions of bodies. This follows from law 3” in [Hall and Hall] 267.
I. Newton De motu sphaericorum corporum in Fluidis (1684), Law 3, “The relative motions of bodies enclosed in a given space are the same whether that space is at rest or whether it moves perpetually and uniformely in a straight line without circular motion” in [Hall and Hall] 267.
Newton De motu sphaericorum corporum in Fluidis (1684), in [Hall and Hall] 281.
Newton De Gravitatione (1685), published in Latin and English in The Background to Newton’s Principia A Study of Newton’s Dynamical Researches in the Years 1664–1684,Oxford, 1965, 219–235. Abbrev. [Herivel] We follow here the interpretation of B.J.T Dobbs stating that the On Gravitation was written by Newton after On Motion of Spherical Bodies in Fluids but before another manuscript preparing the Principia,the On Motion of Bodies in uniformely yielding Media In his recent edition of Newton’s Principia,I.B. Cohen adopt this point of view. Dobbs, B.J.T (1991] The Janus faces og genius. The role of alchemy in Newton’s thought,Cambridge, NY, Melbourne, Cambridge Univ. Press, 1991, 138–146 and Cohen, I.B [1999] in “A Guide to Newton’s Principia” in Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy,new translation by I.B. Cohen and A. Whitman, assisted by J. Budenz, preceded by “A Guide to Newton’s Principia”,by I.B. Cohen, Berkeley, Los Angeles, London, University of California Press, 1999, 47, 56–60.
I. Newton De motu corporum in medijs regulariter cedentibus (early 1685), parts published in Latin and English in [Herivel] 304–320 and in MP,VI, 188–194.
I. Newton De motu corporum in medijs regulariter cedentibus (early 1685), in [Herivel] 310
G.W. Leibniz Sämtliche Schrii ten und Briefe,Darmstadt, Leibzig, Berlin, 1923-, II, i, 270 (abbrev. A)
G.W. Leibniz De arcanis motus et mechanica ad puram geometriam reducenda (1676) published in Latin only as beilage 4 (pp.201–205) in H.-J. Hess [1978] “Die unveroffentlichen naturwissenschaftlichen und technischen Arbeiten von G.W. Leibniz aus der Zeit seines Parisaufenhaltes. Eine Kurzcharkteristik”, Studia leibnitiana, suppl, vol. XVII Leibniz à Paris: Tome I, les sciences, Franz Steiner Verlag, Wiesbaden, 1978, 183–217.
G.W. Leibniz De arcanis (1676), “Quamadmodum in Geometria principium ratiocinandi sumi solet ab aequatione quae est inter totum et omnes partes; ita in Mechanicis cuncta pendent ab aequatione inter causam plenam et effectum integrum.” in Hess [1978] 203.
G.W. Leibniz De arcanis (1676), in Hess [1978] 203.
G.W. Leinbiz De corporum concursu (1678), published in Latin and French in Leibniz, La réforme de la dynamique, textes inédits,edition, presentation, translation into French and commentaries by M. Fichant, Paris, Vrin, 1994 (abbrev. [Fichant]).
For an analysis of this manuscript, see in particular the comments of M. Fichant in [Fichant] and of F. Duchesneau in Duchesneau, F. [ 1994 ] La dynamique de Leibniz, Paris, Vrin (Coll. Mathesis), 1994.
G.W. Leibniz De corporum concursu (1678), “Nempe vis in corpore non aestimanda est a celeritate et magnitudine corporis, sed ab altitudine ex qua decidit.” in [Fichant] 134 (Latin) and 269 (French).
G.W. Leibniz Libel/us Elementorum physicae and Cogitations de nova physica instauranda (1679), published in English in Leibniz Philosphical Papers and Letters, L.E. Loemker (ed.), Dordrecht, Boston, D. Reidel publ., 1969, 277–290 (abbrev. [Loemker]). Loemker dated these to 1682–84, but we follow here the datation of M. Fichant which proposes the date 1679 in Fichant [1993] Mécanisme et métaphysique: le rétablissement des formes substantielles (1679), Philosophie, 1993, 27–59.
G.W. Leibniz Libellus Elementorum physicae (1679) in [Loemker] 278.
G.W. Leibniz Cogitations de nova physica instauranda (1679), in [Loemker] 289.
G.W. Leibniz letter to the duke Johann-Friedrich automn 1679 A,1, ii, 225
G.W. Leibniz Discours de métaphysique (1686), we here use the English translation given in G.W. Leibniz Philosophical Essays edited and translated by R. Anew and D. Garber, Inianpolis and Cambridge, Hackett Pub1. Co., 1989, 35–68 (abrrev. AG)
For the Correspondance Leibniz-Arnauld, we also use the English translation given in AG However, this edition only gives extracts from the correspondance.
G.W. Leibniz Discours de métaphysique (1686), §18, in AG 51–52.
G.W. Leibniz Discours de métaphysique (1686), §18, in AG 51–52.
G.W. Leibniz Discours de métaphysique (1686), §21, in AG 53.
G.W. Leibniz De motus abstracti (1671) A, VI, ii, 258–276.
G.W. Leibniz letter to A. Arnauld on april 30 1687, in AG 86–87.
G.W. Leibniz Specimen dynamicum, published in Acta Eruditorum, april 1695.
G.W. Leibniz Système nouveau de la nature et de la communication des substances, published in Journal des Savants, June-July 1695.
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Simonsen, K. (2002). Concerning Some Philosophical Reasons for the Recourse to Mathematics in the Study of Physical Phenomena in the Thought of Newton and Leibniz. In: Heidelberger, M., Stadler, F. (eds) History of Philosophy of Science. Vienna Circle Institute Yearbook [2001], vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1785-4_5
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