In the Principle of the Axioms the argument turns on the nature of extensive quantity. Extensive quantity is defined as that in which the representation of the parts makes possible the representation of the whole. Kant again regards appearances as containing form and matter, the form being an intuition of space and time. Hence Kant says that all appearances contain, as regards their form, an intuition in space and time. The more philosophical difficulties centre in the successiveness of the transcendental synthesis. In the Aesthetic it was argued that times and spaces are known only as limitations of one infinite time and space; and consequently the original idea of infinite space and time must be a pure intuition, from which the concepts of temporality and spatiality are derived. The Principle of the Axioms is intended to show the objective validity of pure mathematics: it is our justification for applying pure mathematics to objects of experience.