Abstract
In the opuscule De primae philosophiae emendatione notione substantiae (1694), Leibniz mentions that he has devoted a special science, dynamics, to the notion of force, and that this methodological elaboration clarifies the metaphysics of substance.1 To a certain extent this assertion causes problems. The scientific papers published by Leibniz up to that time do not support this claim to have founded a science of dynamics. Certainly, since the Brevis demonstratio erroris memorabibis cartesii (1686), Leibniz had been working to invalidate demonstratively the Cartesian principle of the conservation of quantity of motion. He proposes as an alternative a new measure of the motive force which would be conserved in mechanical exchanges, a measure based on the estimate of absolute force (potentia absoluta) or living force (vis viva), expressed by the product mv 2. Since then, a stormy quarrel with the Cartesians concerning the possibility of deducing the new principle as foundation of the system of the laws of nature had broken out2. But on what basis was Leibniz able to claim that he had founded a science of dynamics? One factor in the answer to this question emerges from a more careful examination of the appeals to the a priori method of demonstration which appear progressively in his unpublished work and in certain exchanges of letters, in particular with De Volder, Johann Bernouilli, and Christian Wolff. Our ambition here will be limited to presenting some reasons which militate in favor of such a re-examination, then to initiate the process of analysis through a study of the first part of the Dynamica de potentia (1689-90) where recourse to the a priori method is first sketched.
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Notes
Die philosophische Schriften von G.W. Leibniz,, ed. C. I. Gerhardt, (GP), Iv, p. 469: “Cujus rei ut aliquem gustum dem, dicam interim, notionem virium seu virtutis (quam Germani vocant Krafft, Galli la force) cui ego explicandae peculiarem Dynamices scientiam destinavi, plurimum lucis afferre ad veram notionem substantiae intelligendam,”
On the significance of the controversy concerning “living forces” (forces vives), cf. Carolyn Iltis, “Leibniz and the Vis viva Controversy,” Isis, 62 (1971), pp. 21-35; George Gale, “Leibniz1 Dynamical Metaphysics and the Origin of the Vis Viva Controversy,” Systematics, 11 (1973), pp. 184-207; David Papineau, “The Vis Viva Controversy,” in: R.S. Woolhouse (Ed.), Leibniz: Metaphysics and the Philosophy of Science, Oxford:Oxford Uniyersity Press, 1981, pp. 139-156.
Cf. Louis Couturat, La Logique de Leibniz, Olms: Hildesheim, 1969, chap. VI, L’ encyclopédie; chap. VI, La science générale; Francois Duchesneau, “Leibniz and the Philosophical Analysis of Science,” Logic, Methodology and Philosophy of Science, Amsterdam: Elsevier Science Publishers, 1989, pp. 609-624.
Cf. De ipse natura sive de vi insita actionibusque Creaturarum, pro Dynamicis suis confirmandis illustrandisque (1698) GP, IV, pp. 505–506: “Cujus inter alia indicium insigne praebet fundamentum naturae legum, non petendum ex eo, ut conservetur eadem motus quantitas, uti vulgo visum erat, sed potius ex eo, quod necesse est servari eandem quantitatem potentiae potentiae actricis, imo (quod pulcherrima ratione evenire deprehendi) etiam eandem guantitatem actionis motricis...”
Martial Gueroult, Leibniz, Dynamique et métaphysique, Paris: Aubier Montaigne, 1967, pp. 110–153.
Cf. the declarations relative to the mixed propositions in the Nouveaux essais sur l’entendement humain, 4.11.14 G.W.Leibniz. Sämtliche Schriften and Briefe, VI vi, 446-447, and those which concern the status of physics in 4.12.10:, ibid, 453-454 “I remain agreed that the whole of physics will never be a perfect science for us, but we will not lack the ability to have some sort of physical science; and indeed we already have some samples of it. For example, Magnetology can pass for such a science, for making little of suppositions founded in experience, we are able to demonstrate as a result of it a number of phenomena which are as reason leads us to believe.”
Cf. Hide Ishiguro, “Leibniz on Hypothetical Truths,” in: Michael Hooker (ed.), Leibniz: Critical and Interpretive Essays, Manchester: Manchester University Press, 1982, pp. 90–102; François Duchesneau, “Leibniz et les hypothèses de physique,” Philosophiques, 9 (1982), pp. 223-238.
Mathematische Schriften von G.W. Leibniz, ed. par C.I. GerHardt (GM), VI, Pp. 281–514. I have translated the quoted passages into English.
Cf. Michel Fichant, “La ‘reforme’ leibnizienne de la dynamique d’après des textes inédits,” Akten des II. internationalen Leibniz-Kongresses. Bd 2. Wissenschaftstheorie und Wissenschaftsgeschichte. Wiesbaden: F. Steiner, 1974, pp. 195–214; “Les concepts fondamentaux de la mécanique selon Leibniz en 1676,” in A. Heinekamp (ed.), Leibniz à Paris (1672-1676), Wiesbaden: F. Steiner, 1978, I, pp. 219-232.
Cf. on this point, Pierre Costabel, Leibniz et la dynamique. Les textes de 1692. Paris: Hermann, 1960.
The same is true of the analyses of Gerd Buchdahl in his book Metaphysics and the Philosophy of Science. Oxford: Blackwell, 1969, chap. VII. Leibniz: Science and Metaphysics, pp. 388–469.
GM, VI, p. 349.
GM VI, p. 283.
GM, VI, pp. 289–290.
GM VI, p. 282.
GM, VI, p. 292.
GM, IV, p. 320: “Movetur vel in motu est A, cui quidquid inest homogenum seu comparabile B, aliquod punctum habet ut E, quod per unius ejusdemque temporis quamcunque partem in eodem loci puncto non est.”
GM VI, p. 323.
GM VI, p. 330.
GM VI, p. 341.
GM VI, pp. 341–342.
GM VI, pp. 345–346.
GM VI, p. 346.
GM VI, p. 348.
GM VI, p. 349.
GM VI, p. 355.
GM VI, p. 355.
GM VI, p-356.
GM VI, p. 359: “Actionum aestimatio composita est ex aestimatione effectuum seu longitudinum et velocitatem; sed longitudines sunt in ratione composita temporum et velocitatum; ergo actiones sunt in consideratione composita ex simplice temporum et duplicata velocitatum. Ergo si tempora sint aequalia, actiones sunt in consideratione duplicata velocitatum; sed haec consideratio...”
GM VI, p. 357: “Si aequales sint materiae quantitates, et tempora actionum aequalis, actiones motuum formales erunt in duplicata ratione velocitatum vel longitudinum motus.”
GM, VI, p. 358.
GM, VI, p. 359.
GM, VI, p. 359.
GM, VI, p. 362.
GM, VI, p. 364.
GM, VI, p. 367.
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Duchesneau, F. (1991). The Sense of the a Priori Method in Leibniz’s Dynamics. In: Brittan, G.G. (eds) Causality, Method, and Modality. The University of Western Ontario Series in Philosophy of Science, vol 48. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3348-7_5
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