Descartes' Kinematics

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Notes

1. Descartes' collision rules are given in the Principles of Philosophy (Dordrecht and London: Kluwer Academic Publishers, 1991), Part II §§45–52 and are discussed at some length in Richard J. Blackwell ‘Descartes’ Laws of Motion', Isis 57 (1966), pp.220–34 and Daniel Garber's Descartes' Metaphysical Physics (Chicago and London: The University of Chicago Press, 1992), Chapter 8.

2. There are three levels effectively involved in the dispute: a discussion over the general principle of conservation, a dispute over specific laws and an argument over the impact rules. Effectively whilst the controversy was primarily conducted in relation to impact rules, this cannot be really grasped in lieu of an articulation of the basis of the general conservation principle and its relation to the laws of nature in Cartesian physics. Hence this piece is offered as a propaedeutic to discussion of the dispute over the relationship between laws of nature and rules of impact. For a view of the vis viva dispute that partially responds to the questions guiding my general approach see David Papineau, ‘The Vis Viva Controversy: Do Meanings Matter?’, Studies in the History and Philosophy of Science 8:2 (1977), pp.111–42.

3. For an argument to the effect that Leibniz's initiation of the vis viva controversy was a decisive spur towards the development of his denial of transeunt causation and development of pre‐established harmony see George Gale, ‘The Concept of “Force” and Its Role in the Genesis of Leibniz’ Dynamical Viewpoint’, Journal of the History of Philosophy, 26:1 (1988), pp.45–66 and for a discussion of the importance of Leibniz for the distinction of dynamics from kinematics see Richard S. Westfall's Force in Newton's Physics: The Science of Dynamics in the Seventeenth Century (New York: American Elsevier, 1971), Chapter 6.

4. See for example L.J. Beck's The Method of Descartes (Oxford: Clarendon Press, 1952), Stephen Gaukroger's Cartesian Logic: An Essay on Descartes' Conception of Inference (Oxford: Clarendon Press, 1989) and Bernard Williams' Descartes: The Project of Pure Inquiry (New York and London: Penguin, 1978).

5. René Descartes, Œuvres de Descartes, ed. Charles Adams and Paul Tannery (Paris: Vrin, 1996), vol. X, p.381; The Philosophical Writings of Descartes, vol.1, ed. Cottingham, Stoothoff, Murdoch and Kenny (Cambridge: Cambridge University Press, 1985), p.21.

6. In the course of discussing Rule 14 Descartes also adds that ‘the business of human reason consists almost entirely in preparing for this operation’ of comparing two or more things with each other.

7. For a discussion of the importance of this notion of simple natures and its role in the Meditations see J. L. Marion, Cartesian Questions, trans. J.L. Kosky (Chicago and London: University of Chicago Press, 1999), Chapter 3 and see also Brian E. O'Neil, ‘Cartesian Simple Natures’, Journal of the History of Philosophy, 10:2 (1972), pp. 161–81.

8. René Descartes, Principles of Philosophy, I § 48, p.21–22. Here and throughout citations from René Descartes' Principles of Philosophy are from the translation by V.R. Miller and R.P. Miller.

9. René Descartes, Principles of Philosophy, I § 51, p.23.

10. René Descartes, Principles of Philosophy, I § 53, p.23–24.

11. René Descartes, Principles of Philosophy, I § 65, p.29–30.

12. René Descartes, Principles of Philosophy, II § 19, p.48.

13. René Descartes, Principles of Philosophy, II § 23, p.50.

14. René Descartes, Principles of Philosophy, II § 24, p.50.

15. René Descartes, Principles of Philosophy, II § 24, p.50

16. René Descartes, Principles of Philosophy, II § 25, p.51.

17. For an extended discussion of the varieties of ways local motion could be understood see Alan Gabbey's ‘New Doctrines of Motion’, in The Cambridge History of Seventeenth Century Philosophy, ed. Daniel Garber and Michael Ayers, 2 vols (Cambridge and New York: Cambridge University Press, 1998) vol. 1, pp.553–623.

18. René Descartes, Principles of Philosophy, II § 26, p.13–14.

19. Modes are described in Principles I 56 as that by which ‘the substance is affected or altered’ although there are some technical questions concerning how Descartes distinguishes modes from attributes: see the letter of 1645–46 where he addresses this question (Œuvres de Descartes, vol. IV, pp.348–50 and The Philosophical Writings of Descartes, vol.3, ed. Cottingham, Stoothoff, Murdoch and Kenny (Cambridge: Cambridge University Press, 1991), pp.279–81).

20. René Descartes, Principles of Philosophy, II § 28, p.52–53.

21. René Descartes, Principles of Philosophy, II § 29, p.53.

22. So on my account the rationale for the account of ‘proper’ movement is not an avoidance directly of Copernicanism as Westfall suggests but rather a placing of it within its correct frame of reference by means of accounting for what makes the discussion of frames of reference appropriate.

23. René Descartes, Principles of Philosophy, II § 31, p.54–55.

24. René Descartes, Principles of Philosophy, II § 31, p.54–55.

25. René Descartes, Principles of Philosophy, II § 14, p.45–46.

26. For quite a different account of the basis of Descartes' distinction between the vulgar and the proper account of movement see Daniel Garber's Descartes' Metaphysical Physics, pp.157–72.

27. René Descartes, Principles of Philosophy, II § 36, p.57–58.

28. René Descartes, Principles of Philosophy, II § 23, p.50.

29. Unless one sees this the response to Descartes' principle of conservation can be swift. Thus for example the translators of the Principles argue in a footnote to II § 36 that Descartes has only here proved that the total quantity of something must be conserved, not what that quantity has to consist in. This would be right if the appeal to the divine principles had a role separate from those enumerated here. That separate role would be one that should have intended to show a ground for the specific type of quantity conserved in nature. However Descartes does not need to appeal to the divine principles to do this as the role of simple natures in his argument has already filled that role so that the appeal to divine principles is effectively restricted to fulfilling the point of initiating movement and conserving its quantity where these twin points are grounded on what is previously established.

30. Gerd Buchdahl, Metaphysics and the Philosophy of Science: The Classical Origins Descartes to Kant (Oxford: Basil Blackwell, 1969), p.148. Buchdahl goes on to describe this principle as an example of what he, following Arthur Pap, calls a ‘functional a priori’. See Arthur Pap, The A Priori in Physical Theory (New York: King's Crown Press, 1946). It is also worth pointing out however that Brian E. O'Neil in ‘Cartesian Simple Natures’ presents a strong case for viewing Descartes as implicitly committed through the doctrine of simple natures to a version of the synthetic a priori hence indicating a closer link to the accounts of Buchdahl and Pap.

31. René Descartes, Principles of Philosophy, II § 37, p.59.

32. René Descartes, Principles of Philosophy, II § 37, p.59.

33. The role of appeals to contradiction in the description of the principles of nature in Descartes is a subject worthy of further analysis in relation to the question articulated by Buchdahl and O'Neil in the previous note about the forms of a priori analysis required in explanatory discussion of phenomena.

34. Peter Damerow et al., Exploring the Limits of Preclassical Mechanics (New York: Berlin and London Springer‐Verlag, 1992), p.76.

35. This has the clear result that air is characterized as a primary resistant power. The closest statement Descartes makes to this effect is when considering how its compression can provide a motor for machines (Principles IV § 47) where it is indicated to have the ability to ‘spring’.

36. René Descartes, Œuvres de Descartes, vol. X, p. 417; The Philosophical Writings of Descartes, vol.1, p.43. See also the succeeding discussion where Descartes writes: ‘when we consider things in the order that corresponds to our knowledge of them, our view of them must be different from what it would be if we were speaking about them in accordance with how they exist in reality’ (Œuvres de Descartes, vol. X, p.418; The Philosophical Writings of Descartes, vol. I, p.44).

37. René Descartes, Principles of Philosophy, II § 39, p.60–61.

38. René Descartes, Principles of Philosophy, I § 55, p.24.

39. René Descartes, Principles of Philosophy, II § 40, p.61–62.

40. René Descartes, Œuvres de Descartes, vol. II, pp.543–44; The Philosophical Writings of Descartes, vol. 3, p.135.

41. René Descartes, Œuvres de Descartes, vol. V, pp.342; The Philosophical Writings of Descartes, vol. 3, p.372.

42. For some quite different reasons for denying the equivalence of quantity of motion with quantity of action see §3 of Kant's ‘Thoughts on the True Estimation of Living Forces’, in Kant's Gesammelte Schriften ‐ Werke vol. 1, ed. W. Dilthey et al. (Berlin: Akadmie, 1900), p.18.

43. In fact Leibniz never denies that the quantity of motion is preserved, just that it is the only or most important thing conserved in the world.

44. René Descartes, Principles of Philosophy, II § 43, p.63.

45. Gary C. Hatfield, ‘Force (God) In Descartes’ Physics', Studies in the History and Philosophy of Science, 10:2 (1979), pp.113–40 (p. 126). Hatfield's general argument is however intended to be one showing that Descartes' metaphysical position is an occasionalist one. For an argument in opposition to this see Michael Della Rocca, ‘“If A Body Meet A Body”: Descartes on Body‐Body Causation’, in New Essays on the Rationalists eds. R.J. Gennaro and C. Huenemann (Oxford and New York: Oxford University Press, 1999), pp.48–81.

46. The question of whether Descartes' position is an occasionalist one has not thereby been decided however and would be the subject of a separate study.

47. This analysis obviously requires supplementation by historical‐philosophical investigation into Leibnizian dynamics although it also indicates some methodological guidelines for such supplementary investigation.