Geometry as Spiritual Exercise
Geometry as Spiritual Exercise
This chapter studies one set of exercises Descartes deemed propaedeutic to a better life and better knowledge—his famous, if too little known, geometry—and examines his Geometry of 1637, on its own terms, using his repetitive statements of its purpose, its contents, and its foundation. In his writings from the 1620s until his death, he asserted regularly that mathematics is an exercise, perhaps the best that we have to practice thinking well. Taking this claim seriously helps to clarify problematic aspects of Descartes' geometry and philosophy of mathematics. Looking at both his mathematics and his understanding of its purpose, we will escape a long tradition of equating the subject Descartes aimed to create through his exercise with the so-called Cartesian and modern subjects.
Keywords: Descartes, mathematics, philosophy, Geometry
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