  Although how to best interpret Leibniz’s arguments for the ideality  of exact shape – and indeed how to best interpret his  admittedly paradoxical conclusion – remains open for debate,  the general idea here seems clear enough. While mechanistic physics  appeals to exact shapes like cubes and spheres, the actual  infinite division of matter reveals that these can be at best  approximations of the shapes of real bodies. For the shapes of real  bodies must – again at best – be infinitely complex since they are everywhere divided into bodies actually distinct in virtue  of their differing accommodating motions. Although Leibniz’s  conclusion is especially bold and enigmatic, it is nonetheless not  untypical for him in so far as it suggests that mechanism – carefully thought  through – points towards a radically different underlying metaphysical  reality. 