This paper looks at Euler’s and Maupertuis’ attempt to place mechanics on foundations different from Newton’s or Leibniz’s, via the principle of least action (PLA). I argue this episode shows how mathematization is not neutral with respect to ways the world can be.
Maupertuis claimed to ‘derive’ the PLA from a metaphysical principle, one asserting that Nature acts in the simplest, most efficient way. The PLA has interested philosophers because it is – controversially – billed as a continuing embodiment of final causes in physics. But the episode illustrates a phenomenon previously unnoticed by philosophers: the consequences for metaphysics of the mathematization of nature. When Maupertuis’ metaphysical principle was mathematized as a principle of mechanics, the PLA, it immediately faced formal challenges to its viability. Contra existing narratives, this re-emergence of teleology in physics was felled by novel means. The wider upshot is a new norm of consistent mathematical representability now constraining metaphysics.
