  A third, somewhat obscure, but especially intriguing line of argument takes off from a position defended by Descartes in his Principles of Philosophy and touches on Leibniz’s work on the so-called  “Labyrinth of the Continuum.” In the Principles, Descartes had argued that (i) the world is a plenum, (ii) all motion  in a plenum must be circular, and (iii) such circular motion  presupposes the “infinite, or indefinite, division of the  various particles of matter” as they adjust and shift to  accommodate a continuous flow around bends and through narrows (AT  VIIIA.59/CSM 1:239). Concerning these propositions, Leibniz  approvingly remarks, “What Descartes says here is most  beautiful and worthy of his genius, namely, that every motion in  filled space involves circulation and that matter must somewhere be  actually divided into parts smaller than any given quantity” (L 393). But whereas Descartes had insisted only on the  “indefinite” division of “merely some part of  matter” (AT VIIIA.60/CSM 239) Leibniz pushes for a stronger  conclusion. Dismissing Descartes’s cautious “indefinite  division” as “being not in the thing, but in the  thinker,” he takes the argument to show that every part of  matter is actually infinitely divided (A VI.ii.264). Similarly,  rather than apparently restricting the infinite division of matter to some select moving parts, Leibniz maintains that every part of matter is everywhere moving, and so the sort of accommodation envisioned by  Descartes must occur everywhere (A. 6.3.565f; 6.3.58f). Thus, for  Leibniz, not only are some parts of matter actually infinitely  divided, but every part of matter is divided to infinity (Levey 1998, fn6)!