In this chapter we discuss Leibniz’s appropriation of the Scholastic term “syncategorematic” to characterize any actually infinite multiplicity of things, taken distributively, not as a collection. We show how this conception coheres with his prior denial of infinite number, and does not connote a merely potential infinite (which Leibniz never advocates). We then discuss Leibniz’s various strategies in his mature writings for justifying his use of infinitesimals and infinites, and, finally, his justification for the rules of his differential algorithm itself.