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The first approach is taken by more well-known Cartesians such as Geraud Cordemoy, Louis de la Forge, and Nicolas Malebranche; the second by Pierre-Sylvain Regis. For an overview of Cartesian philosophies see Desmond Clarke, Occult Powers and Hypotheses: Cartesian Natural Philosophy wilder Louis XIV (Oxford: Clarendon Press, 1989).
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For a study of de la Forge's version, see Steven Nadler, "The Occasionalism of Louis de la Forge," in Causation in Early Modern Philosophy, ed. Steven Nadler (University Park, PA: The Pennsylvania State University Press, 1993), 57-73.
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Finally, for a helpful discussion of the disagreement between Malebranche and Regis on this issue, see Tad Schmaltz, "Cartesian Causation: body-body interaction, motion, and eternal truths," Studies in History and Philosophy of Science 34 (2003): 737-62.
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I share Desmond Clarke's view that, even though Descartes introduces a new metaphysical account of matter that brings with it a new view of what counts as a scientific demonstration (and, I would add, what counts as a genuine cause), Descartes is still engaged in the same project as the Scholastics in that he is constructing a science rooted in metaphysics which makes possible demonstrative knowledge of the true causes found in nature. See, for instance, Desmond Clarke, "Descartes's Philosophy of Science," in The Cambridge Companion to Descartes, ed. John Cottingham (Cambridge: Cambridge University Press, 1992), 258-85.
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Martial Gueroult, "The Metaphysics and Physics of Force in Descartes," in Descartes: Philosophy, Mathematics and Physics, ed. Stephen Gaukroger (Sussex: Harvester Press, 1980), 196-229.
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Alan Gabbey, "Force and Inertia in the Seventeenth Century: Descartes and Newton," in Descartes: Philosophy, Mathematics and Physics, ed. Stephen Gaukroger (Sussex: The Harvester Press, 1980), 230-320.
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Garber, D.1
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and Daniel Garber, "How God Causes Motion: Descartes, Divine Sustenance and Occasionalism," in Descartes Embodied (Cambridge: Cambridge University Press, 2001), 189-220.
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Michael Della Rocca, "'If a Body Meet a Body': Descartes on Body-Body Causation," ["Body"] in New Essays on the Rationalists, ed. Rocco J. Gennaro and Charles Huenemann (Oxford: Oxford University Press, 1999), 48-81.
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While the divine legislator drops out of the picture for Hume, he employs essentially the same arguments against a necessary connection between cause and effect as does Malebranche. (See Nicolas Malebranche, "The Search For Truth," in Philosophical Selections, ed. Steven Nadler [Indianapolis: Hackett Publishing Company Inc., 1992], 94-96;
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Helen Hattab, "Conflicting Causalities: the Jesuits, their Opponents and Descartes on the Causality of the Efficient Cause" ["Conilicting Causalities"], in Oxford Studies in Early Modern Philosophy, vol. 1 (Oxford: Oxford University Press, 2003): 1-22;
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