§ 163. To understand the virtue of this philosophy as a basis for the reconciliation of different interests, we must recall the relation between Plato and Spinoza. Their characteristic difference appears to the best advantage in connection with mathematical truth. Both regarded geometry as the best model for philosophical thinking, but for different reasons. Spinoza prized geometry for its necessity, and proposed to extend it. His philosophy is the attempt to formulate a geometry of being, which shall set forth the inevitable certainties of the universe. Plato, on the other hand, prized geometry rather for its definition of types, for its knowledge of pure or perfect natures such as the circle and triangle, which in immediate experience are only approximated. His philosophy defines reality similarly as the absolute perfection. Applied to nature Spinozism is mechanical, and looks for necessary laws, while Platonism is teleological, and looks for adaptation and significance. Aristotle's position is intermediate. With Plato he affirms that the good is the ultimate principle. But this very principle is conceived to govern a universe of substances, each of which maintains its own proper being, and all of which are reciprocally determined in their changes. Final causes dominate nature, but work through efficient causes. Reality is not pure perfection, as in Platonism, nor the indifferent necessity, as in Spinozism, but the system of beings necessary to the complete progression toward the highest perfection. The Aristotelian philosophy promises, then, to overcome both the hard realism of Parmenides and Spinoza, and also the supernaturalism of Plato. [Sidenote: Leibniz's Application of the Conception of Development to the Problem of Imperfection.]