Jeffrey McDonough

Confronting the threat of a Spinozistic necessitarianism, Leibniz insists that not all possible substances are compossible—that they can't all be instantiated together—and thus that not all possible worlds are compossible—that they can't all be instantiated together. While it is easy to appreciate Leibniz's reasons for embracing this view, it has proven difficult to see how his doctrine of incompossibility might be reconciled with the broader commitments of his larger philosophical system. This essay develops, in four sections, a novel solution to the "puzzle of incompossibility." The first section frames the difficulty more carefully and briefly argues that the two dominant strategies developed by Leibniz's commentators fail to solve it fully insofar as they require simply abandoning one or another of its motivating commitments. The second and third sections show how Leibniz's guiding analogy of a geometrical packing or tiling problem may be applied to solve the puzzle of incompossibility in the context of finite and infinite worlds composed of extended corporeal substances. Finally, the fourth section shows how the strategy of Leibniz's packing analogy might be applied even in the context of a thoroughly idealist metaphysics in which the only true substances are nonextended, mindlike "monads." The essay concludes by drawing some connections between Leibniz's thinking about the puzzle of incompossibility and the development of his views concerning the status of corporeal substances and extended bodies. CiteULike Connotea Del.icio.us Digg Reddit Technorati What's this?

In this paper I argue that the hoary theological doctrine of divine concurrence poses no deep threat to Leibniz’s views on theodicy and creaturely activity even as those views have been traditionally understood. The first three sections examine respectively Leibniz’s views on creation, conservation and concurrence, with an eye towards showing their sys­tematic compatibility with Leibniz’s theodicy and metaphysics. The fourth section takes up remaining worries arising from the bridging principle that conservation is a continued or continuous creation, and argues that they can be allayed once two readings of the prin­ciple are distinguished. What emerges from the discussion as a whole is, I hope, a clearer picture of Leibniz’s views on the nature of monadic causation, his understanding of the relationship between divine and creaturely activity, and his position with respect to later medieval and early modern debates over secondary causation

The Dioptrique, often translated as the Optics or, more literally, as the Dioptrics is one of Descartes’ earliest works. Likely begun in the mid to late 1620’s, Descartes refers to it by name in a letter to Mersenne of 25 November 1630 III, 29). Its subject matter partially overlaps with Descartes’ more foundational project The World or Treatise on Light in which he offers a general mechanistic account of the universe including the formation, transmission, and reception of light. Although Galileo’s condemnation by the Church prompted Descartes to abandon, in 1633, his plans for publishing The World, he continued in the ensuing years to vigorously pursue a number of scientific projects, including projects related to his work in optics. He was eventually persuaded to publish three essays highlighting some of his discoveries together with an introductory essay concerning “the method for rightly directing one’s reason and searching for truth in the sciences” . As one of those essays, Descartes’ Dioptrics finally appeared in print together with the Discourse on Method, the Meteorology and the Geometry in the summer of 1637 in a French language edition. It was republished in a Latin edition in 1644. The subject matter of the Dioptrics may be thought of as covering three main topics and is formally divided by Descartes into ten chapters or “discourses”. The first main topic concerns the nature of light and the laws of optics. In the first discourse, Descartes invites his readers to.