The Cartesian Natural Laws

• Edward Slowik
Chapter
Part of the International Archives of the History of Ideas / Archives Internationales d’Histoire des Idées book series (ARCH, volume 181)

Abstract

In chapter 1, it was necessary to briefly present Descartes’ theory of space and relational motion in order to better grasp the motivation underlying Newton’s argument against relationalism. If we intend to construct a Cartesian science immune to Newton’s problem, however, an in-depth examination of the details of Descartes’ natural philosophy is required. Only when all the components of the Cartesian theory have been revealed and their functions explained can the relationalist proceed to assemble a coherent version of Descartes’ theory. Before we can effectively study, or even construct, a Cartesian spacetime, moreover, it is necessary to investigate the origin and specific content of his views on force and material interaction. These ideas represent a sort of framework or foundation on which a Cartesian spacetime must be built. Among these ideas, the Cartesian laws of nature figure prominently; for they form the basis of all applications of Descartes’ relational theory of motion to the physical world. In this chapter, consequently, the content of the Cartesian natural laws will be analyzed in an attempt to uncover an effective means of resolving the dilemma imposed by Newton’s argument (although the working-out of any promising candidates will have to await Part III).

Keywords

Circular Motion Circular Path Inertial Motion Rectilinear Motion Impetus Theory
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Endnotes

1. 1.
One must be careful to distinguish the role of the Aristotelian “natural motions” in this synopsis: for example, the movements of the basic element “earth” towards the center of the universe, its “natural place,” constitutes one of these natural motions. In short, natural motions do not require an outside or foreign cause (i.e., an imposed force), because they originate from some sort of internal principle intrinsic to the body. Once a terrestrial body has reached its natural place, however, it will remain in a state of rest unless moved by an external force, a “violent motion.” Upon removal of this force, the body will once again seek its natural place.Google Scholar
2. 2.
See, J B. Barbour, Absolute or Relative Motion?, ibid., 196–203. I have also borrowed Barbour’s terminology, here (i.e., “pusher”). In addition, it should be noted that Aristotle did not embrace an impetus theory as later proposed by the Scholastics. He sought the cause of the violent motions (as opposed to the natural motions) in an outside, external agent continuously in contact with the moving body, but not contained within the body (e.g., a hand, the air). See, R. Sorabji, Matter, Space,and Motion (Ithaca: Cornell University Press, 1988), 220–227. On impetus theory, see A. Maier, On the Threshold of Exact Science, trans. by S. D. Sargent (Philadelphia: U. of Pennsylvania Press, 1982) chap. 4; and, J. E. Murdoch and E. D. Sylla, “The Science of Motion”, in Science in the Middle Ages, ed. by D. C. Lindberg (Chicago: University of Chicago Press, 1978) 206–265.Google Scholar
3. 3.
The apparent utilization of an “elasticity” type notion in Descartes’ theory of internal “resistance” will also be discussed in chapter 4. See, G. W. Leibniz, “Critical Thoughts on the General Part of the Principles of Descartes,” in G. W. Leibniz: Philosophical Papers and Letters (Dordrecht: D. Reidel, 1969) 383–412.Google Scholar
4. 4.
R. Descartes, The Philosophical Writings of Descartes, Vol.3, The Correspondence, eds. and trans. J. Cottingham, et al., (Cambridge: Cambridge University Press, 1991), 179.Google Scholar
5. 5.
One must be cautious in attributing a composite structure to determinations, however. Although Descartes will allow a determination to be decomposed into constituent parts, he is not willing to ascribe to these parts an independent ontological status separate from the single motion of the body. In other words, the component parts of the determination of a single motion are not to be confused with the determinations of the several component parts of a single motion. Since a body’s actual motion is not divisible, the component parts of its determination are only meaningful in relation to that one actual motion. For a lucid discussion of this distinction, see, P. Damerow, et al., Exploring the Limits of Preclassical Mechanics (New York: Springer-Verlag, 1992) 119–120.Google Scholar
6. 6.
R. Descartes, Optics, in The Philosophical Writings of Descartes, Vol.], eds. and trans. J. Cottingham, R. Stoothoff, D. Murdoch (Cambridge: Cambridge University Press, 1984), 159. In this example, the ball travels more slowly after penetrating the sheet since it has transferred to it some of its quantity of motion.Google Scholar
7. 7.
For a thorough discussion of the development of this problematic theory, see, D. Garber, Descartes’ Metaphysical Physics (Chicago: University of Chicago Press, 1992), 234–248.Google Scholar
8. 8.
For a thorough discussion of the philosophical importance of these concepts in the Early Modern period, see, R. Ariew and A. Gabbey, “The Scholastic background”, in The Cambridge History of Seventeenth Century Philosophy,Vol 1 (Cambridge: Cambridge University Press, 1998), 425454.Google Scholar
9. 9.
R. Descartes, Objections and Replies, in The Philosophical Writings of Descartes, Vol.2, eds. and trans. J. Cottingham, R. Stoothoff, D. Murdoch (Cambridge: Cambridge University Press, 1984), 298.Google Scholar
10. 10.
In actuality, the stone retains its position within the rotating sling due to a balance of the tangential centrifugal force and the centripetal pull of the hand towards the circle’s center.Google Scholar
11. 11.
Or, better yet, “center-fleeing” motions/tendencies, to avoid the philosophical implications of the modern understanding of the term “centrifugal”.Google Scholar
12. 12.
Westfall suggests that this aspect of Descartes’ hypothesis is one of the last conceptual remnants of the Aristotelian/Scholastic theory of “natural circular motion” (i.e., a form of circular “inertia” that the Medievals commonly believed the motion of the planets to represent). R. Westfall, The Concept of Force in Newton’s Physics (London: MacDonald, 1971), 82. Nonetheless, Descartes’ theory only ascribes a single component of a body’s “striving” to a circular path (at an instant). Given the combination of all the tendencies towards motion, the body will not move in a circular inertial motion if unconstrained (as demonstrated in the case of Descartes’ stone upon release from the sling). See section 3.4.Google Scholar
13. 13.
See, for example, R. Westfall 1971, 187–188.Google Scholar
14. 14.
15. 15.
See, for example, D. Garber 1992, 293–299; A. Gabbey, “Force and Inertia in the Seventeenth Century: Descartes and Newton.” in Descartes: Philosophy, Mathematics and Physics, ed. Stephen Gaukroger (Sussex: Harvester Press, 1980) 230–320; G. Hatfield, “Force (God) in Descartes’ Physics”, Studies in History and Philosophy of Science, 10 (1979): 113–140; and M. Della Rocca, “’If a Body Meets a Body’: Descartes on Body-Body Causation”, in New Essays on the Rationalists,R. J. Gennaro and C. Huenemann, eds. (Oxford: Oxford University Press, 1999).Google Scholar
16. 16.
It should be noted that Gabbey’s interpretation of Cartesian force is rather complex and involves numerous additional postulates. For instance, Gabbey also understands force as a consequence of God’s sustaining creative act (which grounds all existing things), and as a mode of body comparable to the closely related modes of “existence” and “duration.” See, Gabbey 1980, 236–238.Google Scholar
17. 17.
Besides their generally wrong predictions, there are numerous inconsistencies in Descartes’ collision rules. On e of the first and best critiques of these rules belongs to Leibniz 1969, 383–412.Google Scholar
18. 74.
19. 18.
That is, by declaring these states intrinsically or fundamentally “opposite” or “contrary” (as it can be interpreted from the French or Latin), Descartes reasons that motion and rest are mutually exclusive phenomenon that cannot transform or change into the one another when isolated from external influences. For a complete discussion of the role of the Scholastic logic of contraries in Descartes’ natural philosophy, see, P. Damerow, et al., 1992, 82–91.Google Scholar
20. 19.
See, e.g., M. Clagett, The Science of Mechanics in Middle Ages (Madison: University of Wisconsin Press, 1959) chap. 3–4; and, E. Grant, Planets, Stars,& Orbs: The Medieval Cosmos, 1200–1687 (Cambridge: Cambridge University Press, 1994) chap. 18.Google Scholar
21. 20.
For a nice discussion of the various influences on Descartes’ natural philosophy, see, S. Gaukroger, Descartes: An Intellectual Biography (Oxford: Oxford University Press, 1995), and, W. R. Shea, The Magic of Numbers and Motion: The Scientific Career of René Descartes (Canton, Mass.: Science History Publications, 1991).Google Scholar
22. 21.
Galileo Galilei, Letters on the Sunspots, trans. by S. Drake, in Discoveries and Opinions of Galileo (New York: Anchor, 1957) 113–114. For a recent discussion of these issues, see, W. Hooper, “Inertial Problems in Galileo’s Preinertial Framework”, in The Cambridge Companion to Galileo, P. Machamer, ed. (Cambridge: Cambridge University Press, 1998) 146–175.Google Scholar
23. 22.
I. Beeckman, Journal, I, C. de Waard edition (The Hague: M. Nijhoff, 1939) 24.Google Scholar
24. 23.
J Herival, The Background to Newton’s ‘Principia’ (Oxford: Oxford University Press, 1965) 47, 54. Westfall also points out this misreading of Descartes’ theory; 1971, 93–94, fn. 49.Google Scholar
25. 24.
W. R. Shea 1991, 281–282.Google Scholar
26. 25.
The concept of “solidity” in Cartesian natural philosophy is quite complex. See, chapter 4 for an attempt to clarify this, and related, notions.Google Scholar