Abstract
The overall goal of our investigation is to explore possible formulations of a Cartesian physics that can circumvent some of its well-known internal inconsistencies, such as those raised in Newton’s famous argument against Descartes’ theory of space and motion. However, in order to investigate the prospects of successfully devising such a response, we will need to explore further the details of Descartes’ laws of nature. While chapter 5 will investigate the origins and function of the Cartesian conservation law for “quantity of motion,” the present chapter will examine the conditions or stipulations that Descartes appended to his collision rules, as well as the specific character and content of Descartes’ hypotheses of matter and (material) substance. Up to this point, it has been largely assumed that Descartes’ laws, and his corresponding concept of matter, will present no special difficulties when transferred to a plenum setting (i.e., his matter-filled world). Yet, as will be shown, this marriage presents a number of obstacles that threaten to undermine Descartes’ entire project. I will argue, nevertheless, that many portions of Descartes’ major scientific treatise, the Principles of Philosophy, demonstrate that he was fully aware of, and capable of addressing, many of the difficulties brought to light by the conjunction of these seemingly incompatible partners, i.e., his quasi-absolutist natural laws and a plenum environment.
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Endnotes
The property of recovery of an original size and shape is the property that is termed elasticity.“ A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity (New York: Dover, 1944), 92. However, the term ‘elastic’ receives various interpretations. E. J. Aiton reasons, for example, that a body is elastic only if it rebounds in the opposite direction (while presumably recovering its initial shape) ”Descartes term ‘hard’chrw(133) cannot be equated with ‘elastic,’ since the hard bodies sometimes rebound and sometimes move together. E. J. Aiton, The Vortex Theory of Planetary
See, Miller and Miller, in Descartes, 1983, 64, fn. 44.3 He continues: “There is good reason for Descartes to have considered perfectly hard [solid], perfectly elastic bodies, for when soft and perfectly inelastic bodies collide the ‘quantity of motion’ is not conserved.” R. S. Woolhouse, Descartes, Spinoza, Leibniz: The Concept of Substance in Seventeenth Century Metaphysics (London: Routledge, 1993), p. 114. For a recent example of an “inelastically hard” reading, see, D. Garber, Descartes’ Metaphysical Physics ( Chicago: Chicago University Press, 1992 ), 357.
Rohault’s influential Cartesian text of the late seventeenth century provides a nice example of the contribution of bodily “volume” to quantity of motion: 4 If a body of two Cubic Feet runs through a Line sixty Foot long, it has twice as much Motion, as a Body of one Cubic Foot, which runs through the same Linechrw(133). J. Rohault, A System of Natural Philosophy, vol. 1 (written 1671), trans. J. Clarke and S. Clarke (1723), (New York: Johnson Reprint Corp., 1969), 43.
M. Gueroult, “The Metaphysics and Physics of Force in Descartes,” in Descartes: Philosophy, Mathematics, and Physics, ed. S. Gaukroger (Sussex: Harvester Press, 1980), 228, fn. 100.
A. Gabbey, “Force and Inertia in the Seventeenth Century: Descartes and Newton,” in Descartes: Philosophy, Mathematics, and Physics, ed. S. Gaukroger ( Sussex: Harvester Press, 1980 ), 245.
D. M. Clarke, Descartes’ Philosophy of Science (Manchester: Manchester University Press, 1982), 217. Clarke is certainly aware of the function of perfect solidity, however, as I will later comment. Another excellent discussion of the complexity of the factors influencing Descartes’ physics as regards collisions is P. McLaughlin, “Force, Determination, Impact”, in Descartes’ Natural Philosophy, ed. by S. Gaukroger, S. Schuster, and S. Sutton (London: Routledge, 2000). Many of McLaughlins conclusions, especially in section 4.2, parallel the conclusions reached below.
For a thorough comparison of Descartes’ and Newton’s theories of inertial motion, see, for example; A. Gabbey, 1980, 230–320.
As R. S. Westfall has pointed out, there is a great deal of ambiguity in Descartes’ use of the term “agitation.” Yet, Westfall agrees that this term seems to signify “momentum” (or quantity of motion, if its a scalar property) in the articles on the motions of stars in Pr III of the Principles. See, R. S. Westfall, The Concept of Force in Newton’s Physics ( London: MacDonald, 1971 ), 61–62.
This interpretation also accords with the separate role that surface area plays as regards vortex motions. In Pr III, surface area is responsible for the force exerted on an object while immersed within a circling mass of plenum particles, “because the larger [a body’s] surface is, the greater the quantity of matter acting against the surface (Pr III 121).”
Descartes’ account of “fluid” bodies seems also to confirm these conclusions. In Pr II 58, he remarks that many typical fluid bodies, such as air and water, put up great resistance to the rapid motions of bodies. Thus, in the collision rules, his ideal condition for the absence of plenum effects apparently translates into an appeal for a resistless “perfect fluid.” E. J. Aiton, 1972, 39–41, makes a similar observation.
Volume and surface area are two distinct quantities that can be easily confused as equivalent: For example, the volume of a sphere equals the cube of the radius times 4/3n, while its area equals the square of the radius times 4n.
D. M. Clarke is a notable exception. (1982, 213–221), for he correctly points out both the function of solidity and the elimination of surface area via the idealized conditions. However, Clarke fails to mention the crucial passages in Pr III of the Principles, especially Pr III 123 (see above). Thus he does not clearly draw together the three bodily properties of volume, quantity of matter, and surface area as utilized by Descartes.
For example, see: M. Jammer, Concepts of Mass in Classical and Modern Physics (Cambridge, Mass.: Harvard University Press, 1961), 60–61; R. J. Blackwell, “Descartes’ Concept of Matter”, in The Concept of Matter in Modern Philosophy (Notre Dame: U. of Notre Dame Press, 1963), 69, fn. 18; J. B. Barbour, Absolute or Relative Motion?, vol. 1, The Discovery of Dynamics (Cambridge: Cambridge University Press, 1989), 429; P. Damerow et al., Exploring the Limits of Preclassical Mechanics ( New York: Springer-Verlag, 1992 ), 76.
J. Carriero, “Comments on E. Slowik’s ‘Perfect Solidity, Quantity of Motion, and the Problem of Matter in Descartes’ Universe’ (an earlier version of the present paper),” which were both delivered at the American Philosophical Association Central Division Meeting, Chicago, Spring 1995.
In general, the erosion and wear of a body’s surface, which are rather complex phenomena, will result in a loss of kinetic energy. R. M. Brach, Mechanical Impact Dynamics: Rigid Body Collisions (New York: John Wiley & Sons), 119–120.
R. Descartes, The Philosophical Writings of Descartes, vol. 3, The Correspondence, eds. and trans. J. Cottingham, et al. (Cambridge: Cambridge University Press, 1991), 246–248. This point is raised by P. Damerow, et al., 1992, 102.
Leibniz was one of the first commentators to draw attention to this problem. See, G. W. Leibniz, “Critical Thoughts on the General Part of the Principles of Descartes,” in Leibniz: Philosophical Papers and Letters (Dordrecht: D. Reidel, 1969), 403–407. Moreover, a requirement for congruent contact surfaces can be found in work of another Cartesian, William Neile (1637–1670): “The whole square surface of the one [cube] meets in the same instant of time with the whole square surface of the other.” See, W. Neile, “Hypothesis of Motion,” in The Correspondence of Henry Oldenburg, Vol. 5, eds. A. R. Hall and M. B. Hall (Madison: University of Wisconsin Press, 1968), 519–524. This is also noted by P. Damerow, et al., 1992, 102.
See, W. L. Scott, The Conflict Between Atomism and Conservation Theory 1644–1860 (London: MacDonald, 1970 ), 14, 23.
G. de Cordemoy, Oeuvres philosophiques. P. Clair and F. Girbal, eds. (Paris: Presses Universitaires de France, 1968), 103–104; J. Rohault, 1969, 28; B. Spinoza, Ethics, Part I, Prop. 15., Demonstration, in Spinoza Opera, ed. by G. Gerhardt ( Heidelberg: C. Winter, 1925 ).
G. (Rodis-)Lewis, L’individualité selon Descartes. (Paris: J. Vrin, 1950), 45–57; D. Garber, 1992, 175–176; D. Des Chene, Physiologia: Natural Philosophy in Late Aristotelian and Cartesian Thought. ( Ithaca: Cornell University Press, 1996 ), 367–377.
S. V. Keeling, Descartes, 2nd ed. (Oxford: Oxford U. Press, 1968), 145; R. S. Woolhouse, 1993, 22–23, 55; W. E. Anderson, “Cartesian Motion”, in Motion and Time, Space and Matter: Interrelations in the History and Philosophy of Science, ed. by P. K. Machamer and R. G. Turnbull. (Columbus: Ohio State University Press, 1976), 202; G. Rodis-Lewis, L’oeuvre de Descartes. (Paris: J. Vrin, 1971), 548; D. Marshall, jr., Prinzipien der Descartes: Exegese. (Freiburg: Verlag Karl Alber, 1979), 5457. Listing all the commentators who accept the monist position, or at least find the notion of individual corporeal substance untenable, would take up nearly the entire length of this essay.
It should be noted that Descartes’ definition of substance, as “independence from other substances”, does not exactly correlate with substance as understood by many of the Scholastics, who often held a much more elaborate notion (e.g., Toletus). On this topic, see, D. Des Chene, 1996, chap. 3.
As G. Brown has argued, nevertheless, it may not be necessary to read the intimate correlation between extension and matter as a straightforward identity claim; “Mathematics, Physics, and Corporeal Substance in Descartes”, Pacific Philosophical Quarterly, 70 (1989), 281–302. This issue will be raised briefly below, although the identity of extension and matter, or lack thereof, will not affect the main arguments of this essay.
In his correspondence on this thought experiment, Descartes makes it clear that the removal of the body in the vessel results in the sides becoming “immediately” contiguous, but that there is no motion involved in this process (which would imply the contradictory state of affairs, for Descartes, of the sides moving into the empty space left behind). See, AT IV 109, AT II 482. Some commentators have failed to recognize this crucial distinction, and have accordingly posited motion to the sides of the vessel after the removal of the body: for example, J. Rohault, ibid., vol. 1, 28; and M. Jammer, Concepts of Space, 2nd ed. ( Cambridge, MA: Harvard U. Press, 1969 ), 43–44.
Spinoza is not a straight-forward Cartesian, of course, since many of his own ideas differ quite drastically from Descartes’ (especially on the metaphysical problem of dualism). Yet, their respective ideas concerning natural philosophy are similar enough to justify the general label.
G. W. Leibniz, “Letter to De Voider, May 13, 1699”, in G. W. Leibniz: Philosophical Papers and Letters, trans. and ed. by L. E. Loemker. ( Dordrecht: D. Reidel, 1970 ), 519.
M. Gueroult, “The Metaphysics and Physics of Force in Descartes”, in Descartes: Philosophy, Mathematics, and Physics, S. Gaukroger, ed. (Harvester Press: Sussex, 1980) 199. Gueroult’s full presentation of his argument appears in Descartes’ Philosophy Interpreted According to the Order of Reasons, Vol. II, trans. by R. Ariew ( Minneapolis: U. of Minnesota Press ), 63–74.
J. Bennett, “Spinoza’s Metaphysics”, in The Cambridge Companion to Spinoza, ed., D. Garrett. (Cambridge: Cambridge U. Press, 1996), 70–71. Interestingly, Bennett’s interpretation, which he dubs a “field” theory, is much in the spirit of later “supersubstantivalist” theories of space (i.e., where space is the only predicable substance; and thus objects are merely qualitatively/quantitatively distinct portions of space). Newton toyed with this idea in his early essay, De Gravitatione et aequipondio fluidorum, trans. and eds. A. R. Hall and M. B. Hall, in Unpublished Scientific Papers of Isaac Newton. (Cambridge: Cambridge U. Press, 1962), 139. We will return to this subject in chapter 6.
T. M. Lennon, The Battle of the Gods and Giants: The Legacy of Descartes and Gassendi. ( Princeton: Princeton University Press, 1993 ), 204–205.
AT VII 14. The Philosophical Writings of Descartes, Vol. II, trans. and ed. By J. Cottingham, R. Stoothoff, and D. Murdoch ( Cambridge: Cambridge U. Press, 1984 ), 10.
This problem with the modal thesis is raised by P. Hoffman, “The Unity of Descartes’ Man”, reprinted in The Rationalists, ed. by D. Pereboom ( Lanham: Rowman & Littlefield, 1999 ), 64.
Ironically, Descartes’ “empty vessel” argument can be seen as an early forerunner to the “hole” problem that plagued Einstein’s development of General Relativity, as well as recent formulations of substantivalist spacetime theories. See, J. Earman, World Enough and Space-Time. (Cambridge, MA: MIT Press, 1989), chap. 9.
E. Grosholz raises related difficulties, stressing that Descartes’ arguments against the vacuum can only work for finite, bounded vacua, and not necessarily against a vacuum that surrounds the material world: “Descartes and the Individuation of Physical Objects”, in Individuation and Identity in Early Modern Philosophy, ed. by K. F. Barber and J. J. E. Gracia (Albany: State U. of New York Press, 1994), 48–53. Also, Descartes’ term “indefinite” essentially functions as “infinite”, since it stands for a concept of which no limit can be conceived. Only God, however, is the proper subject of the “positive”-sounding designation, “infinite”, which lacks any sense of limit (Pr I 26–27 ).
E. Grosholz, Cartesian Method and the Problem of Reduction. ( Oxford: Clarendon Press, 1991 ), 68.
There were many sixteenth and seventeenth century Natural philosophers who did accept a theory with similar implications, such as F. Suarez, P. Fonseca, the Coimbra Jesuits, B. Amicus, and E. Maignan. These thinkers tried to accommodate both the notion of a finite extended world and an infinite (quasi-) non-extended void: i.e., an “imaginary” space that, while not possessing extension or dimensionality, had the capacity to receive extended bodies. Descartes’ theory of space rules out this option, for he interprets vacuum as an extended “nothing”, which is an impossible stateof-affairs (since “nothing” cannot be the subject of a property). Thus the actual existence of a plenum is impossible since extension must be a property of some thing (but this should not be taken to undermine the argument centered upon conceivability that will be advanced below). (Pr II 16) His substance-property dichotomy is clearly at work, here. (see, Pr I 56) On “imaginary” space theorists, see, E. Grant, Much Ado About Nothing: Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution. (Cambridge: Cambridge U. Press, 1981), chap. 7.
R. Florka has suggested to me that a better interpretation of the consequences of removing all of the space surrounding a body is that it would now fill all of extension: i.e., the body, say, a chair, would now assume the role of the “indefinitely” extended plenum, which is a better analogue to the case of the empty vessel, as examined above. Of course, the problem that would now arise is whether or not the object retains its identity after it becomes indefinite extension; since, if it is indefinitely extended, and thus has no boundary, in what sense can it still be referred to as a “chair”? Overall, both versions of individual material substance, i.e., Florka’s and my own, face the difficulty of coherently explaining the boundary, or surface, of these substances given their lack of contiguous neighbors, thus both approaches to this problem can be seen as complimentary. R. Florka, “Comments on Slowik’s `Descartes, Monism, and Individual Corporeal Substance”, presented at the American Philosophical Association Central Division Meeting, New Orleans, May 8, 1999.
M. Grene, Descartes. (Minneapolis: U. of Minnesota Press, 1985), 100101.
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Slowik, E. (2002). Matter and Substance in the Cartesian Universe. In: Cartesian Spacetime. International Archives of the History of Ideas / Archives Internationales d’Histoire des Idées, vol 181. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0975-0_5
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