Materialist Mixed Mathematics: Hobbesian Optics, Natural Philosophy, and Politics

Marcus Adams

University of Pittsburgh

Abstract: 
When discussing Hobbes’s natural philosophy, there is no better place to start than his optics. Among his contemporaries, Hobbes’s optics was considered a rival to Descartes’s Dioptrique (1637). Mersenne’s inclusion of Hobbes’s optical treatise in Ballistica (1644) is part of the evidence for this claim, and Hobbes’s optical work was known to all of the key individuals working in 17th century optics. Given his general manner of self-appraisal, it is perhaps unsurprising that Hobbes saw his work in optics as monumental. In typical Hobbesian humility, in A Minute or First Draught of the Optiques (1646) Hobbes lauds his own contributions in optics as so significant that they would constitute the founding of a new science which would rival his work in political philosophy (Hobbes 1983, 622). For my purposes, however, Hobbes’s optics has special importance, for I argue that Hobbes’s work in optics provided him with a model for explanations outside of optics, not only for natural philosophy but for all of philosophy, including politics. First, I discuss Hobbes’s explicit treatment of the Aristotelian mixed mathematics tradition in De homine and in Anti-White. Next, I provide two case studies of explanations from Hobbes’s optics and natural philosophy: the first from De homine chapter 2 concerning why objects appear larger or smaller and appear in a location different from their actual location; and the second from De corpore chapter 25 concerning the explanation of sensation. I argue that these explanations are best understood as mixed mathematical explanations, and I show how viewing them in this way avoids some of the difficulties created by the two major positions in the literature, what I call the deductivist account (e.g., Peters 1967; Watkins 1973; Hampton 1986; Talaska 1988) and the disjointed account (e.g., Robertson 1886; Sorrel 1986; Taylor 1938; Warrender 1957). Finally, I consider some implications of this view for our understanding of Hobbes’s politics in the Leviathan by highlighting how it helps makes sense of the “Table of the Several Subjects of Science” in the 1651 edition of Leviathan chapter IX (English Works, volume III.72-73) and generally the connection between Leviathan Parts I and II.