## Quasi-Causality and Causality in the Principia: Newton’s Method

Against Descartes’ admission of algebraic curves into mathematical practice, Newton’s Principia urges a return to the Euclidean paradigm where geometry is a part of ‘general mechanics’ and geometric objects are the results of quasi-causal motions (e.g. the rectilinear motion of a point generates a line segment). This position borrows from Isaac Barrow’s idea that real definitions of geometric curves may postulate the mechanical causes (tracing mechanisms) of their generation. Though the Principia is deliberately divided into mathematical (Books I and II) and physical (Book III) portions, Newton clearly views this quasi-causal conception of mathematics as central to his method in deriving universal gravity in Book III. But how are the mechanical quasi-causes generating mathematical curves related to the physical causes generating real motions? I offer a reading connecting the two halves of the Principia – mathematical and physical – by illustrating how the success of Newton’s method of successive approximations in Book III may depend upon some quasi-causal features of his conception of mathematics. In particular, I try to connect the plurality of possible tracing mechanisms to Newton’s implicit taxonomy of measures of centripetal force.

Bio:

Adwait Parker is a 6th year PhD student in Philosophy writing a dissertation on the relation of Kant’s theory of space to Newtonian and Cartesian conceptions of motion. He obtained a BA from The University of Chicago and an MA from Paris I Panthéon-Sorbonne.