Chasles’ Philosophy of Duality

In this chapter, I present the thesis that Chasles’ foundational programme is not restricted to geometry and physics, but it also concerns philosophy in its epistemological and ontological aspects. Dualisms became the creed of Chasles’ philosophy. The basis of this idea derived from the principle of duality, born in projective geometry and extended by Chasles to several aspects of mechanics and philosophy. The chapter is divided into five sections. In the first one, I offer a reading of how Chasles interpreted duality within projective geometry. In this context, the principle of continuity, which Chasles reformulated as principle of contingent relations, plays a prominent role. In the second section, the decisive role of duality in geometry and physics is discussed. The third section regards the extension of this principle to philosophy and the interpretations offered by Chasles in this regard. As Steiner was something like an alter ego for Chasles with regard to projective geometry, Poinsot was an analogous figure with respect to physics and to the philosophy of duality. Therefore, in the fourth section a comparison between Poinsot’s and Chasles’ ideas on duality is developed. Final considerations on Chasles’ concept of duality close the chapter.