HOPOS Meets Descartes: Making Old Problems New Again

Mary Domski

University of New Mexico

Abstract: 
Over the past decade, increased attention to the history of philosophy of science has shed important light on the nuances and complexities that characterize early modern philosophy. Numerous studies, and numerous scholars, have shown us, on the one hand, that a comprehensive discussion of early modern thought must include consideration of the views espoused by practicing natural philosophers and mathematicians, such as Galileo, Boyle, Newton, and Huygens. On the other hand, and equally importantly, several other studies, and several other scholars, have shown us how our study of texts that are standardly placed in the early modern canon can be deepened, if not completely refashioned, when we remain sensitive to the scientific and mathematical commitments that inform what we are reading. And, yet, historians are well aware that understanding the interplay of science, mathematics, and philosophy in early modern thought is no straightforward matter precisely because we cannot, in any straightforward way, map our contemporary categories of “science”, “mathematics”, and “philosophy” onto the discourse of the seventeenth and eighteenth centuries. Figures such as Galileo and Descartes and Newton and Locke simply did not separate their study of natural objects, or even mathematical objects, from their philosophical and metaphysical views on God, causality, individuation, or the like. Thus, continuing our study of the history of early modern philosophy of science will involve, out of historical necessity, continued sensitivity to the complex threads that tie together the metaphysical, physical, and mathematical in the philosophies of that period. In this regard, much still remains to be done and, as I will urge in this paper, much remains to be gained. Building on the important work that has already been completed on the interplay of the physical and metaphysical in Descartes’s corpus, I aim to show how attention to Descartes’s mathematical commitments offers us a new perspective on his Meditations on First Philosophy. More specifically, by placing the Meditations in its proper mathematical context, I show that the infamous, oft-discussed problem of the Cartesian Circle can be refashioned, even dissolved, once we take heed of how Descartes’s view of mathematical reasoning informs his Third Meditation proof for the existence of God. I use my contextualized examination of this particular argument to illustrate how future study of early modern philosophy of science and mathematics can succeed in bringing new life to old philosophical problems, and in giving new direction to our study of early modern classics.