How coherent is Descartes' conception of vacuum in the Principles? Descartes' arguments attacking the possibility of vacuum are difficult to read and to understand because they reply to several distinct threads of discussion. I separate two strands that have received little careful attention: the scholastic topic of annihilation of space, particularly represented in Albert of Saxony, and the physical arguments concerning vacuum in Galileo that are also continued after the publication of the Principles in Pascal. The distinctness of the two (...) sorts of opponent accounts for Descartes' odd habit of summarily declaring vacuum "contradictory" in some contexts, while providing extended conceptual and physical arguments meant to establish its "impossibility" in others. In several passages late in the Principles, Descartes also considers the physical ramifications of "empty space," including a discussion of the appearance of a star, were an empty space situated at the center of the celestial vortex. I argue that the discussion allows for a sensible conception of space with extension, but without matter, quite adequate to the physical discussions of vacuum among Descartes' contemporaries. (shrink)