§ [161]. There is, then, a "true order of going," and an order that leads from one to many, from thence to forms, from thence to morality, and from thence to the general objects of thought or the ideas. In the "Republic," where the proper education of the philosopher is in question, it is proposed that he shall study arithmetic, geometry, astronomy, and dialectic. Thus in each case mathematics is the first advance in knowledge, and dialectic the nearest to perfection. Most of Plato's examples are drawn from mathematics. This science replaces the variety and vagueness of the forms of experience with clear, unitary, definite, and eternal natures, such as the number and the geometrical figure. Thus certain individual things are approximately triangular, but subject to alteration, and indefinitely many. On the other hand the triangle as defined by geometry is the fixed and unequivocal nature or idea which such experiences suggest; and the philosophical mind will at once pass to it from these. But the mathematical objects are themselves not thoroughly understood when understood only in mathematical terms, for the foundations of mathematics are arbitrary. And the same is true of all the so-called special sciences. Even the scientists themselves, says Plato,

"only dream about being, but never can behold the waking reality so long as they leave the hypotheses they use unexamined, and are unable to give an account of them. For when a man knows not his own first principle, and when the conclusion and intermediate steps are also constructed out of he knows not what, how can he imagine that such a conventional statement will ever become science?"[330:9]

Within the science of dialectics we are to understand the connections and sequences of ideas themselves, in the hope of eliminating every arbitrariness and conventionality within a system of truth that is pure and self-luminous rationality. To this science, which is the great interest of his later years, Plato contributes only incomplete studies and experiments. We must be satisfied with the playful answer with which, in the "Republic," he replies to Glaucon's entreaty that "he proceed at once from the prelude or preamble to the chief strain, and describe that in like manner": "Dear Glaucon, you will not be able to follow me here, though I would do my best."

But a philosophical system has been projected. The real is that perfect significance or meaning which thought and every interest suggests, and toward which there is in experience an appreciable movement. It is this significance which makes things what they really are, and which constitutes our understanding of them. In itself it transcends the steps which lead to it; "for God," says Plato, "mingles not with men." But it is nevertheless the meaning of human life. And this we can readily conceive. The last word may transform the sentence from nonsense into sense, and it would be true to say that its sense mingles not with nonsense. Similarly the last touch of the brush may transform an inchoate mass of color into a picture, disarray into an object of beauty; and its beauty mingles not with ugliness. So life, when it finally realizes itself, obtains a new and incommensurable quality of perfection in which humanity is transformed into deity. There is frankly no provision for imperfection in such a world. In his later writings Plato sounds his characteristic note less frequently, and permits the ideal to create a cosmos through the admixture of matter. But in his moment of inspiration, the Platonist will have no sense for the imperfect. It is the darkness behind his back, or the twilight through which he passes on his way to the light. He will use even the beauties of earth only "as steps along which he mounts upward for the sake of that other beauty."

Aristotle's Hierarchy of Substances in Relation to Platonism.

§ [162]. We have met, then, with two distinct philosophical doctrines which arise from the conception of the absolute, or the philosopher's peculiar object: the doctrine of the absolute being or substance, and that of the absolute ideal or good. Both doctrines are realistic in that they assume reality to be demonstrated or revealed, rather than created, by knowledge. Both are rationalistic in that they develop a system of philosophy from the problem of philosophy, or deduce a definition of reality from the conception, of reality. There remains a third doctrine of the same type—the philosophy of Aristotle, the most elaborately constructed system of Greek antiquity, and the most potent influence exerted upon the Scholastic Philosophy of the long mediæval period. This philosophy was rehabilitated in the eighteenth century by Leibniz, the brilliant librarian of the court of Hanover. The extraordinary comprehensiveness of Aristotle's philosophy makes it quite impossible to render here even a general account of it. There is scarcely any human discipline that does not to some extent draw upon it. We are concerned only with the central principles of the metaphysics.

Upon the common ground of rationalism and realism, Plato and Aristotle are complementary in temper, method, and principle. Plato's is the genius of inspiration and fertility, Aristotle's the genius of erudition, mastery, and synthesis. In form, Plato's is the gift of expression, Aristotle's the gift of arrangement. Plato was born and bred an aristocrat, and became the lover of the best—the uncompromising purist; Aristotle is middle-class, and limitlessly wide, hospitable, and patient in his interests. Thus while both are speculative and acute, Plato's mind is intensive and profound, Aristotle's extensive and orderly. It was inevitable, then, that Aristotle should find Plato one-sided. The philosophy of the ideal is not worldly enough to be true. It is a religion rather than a theory of reality. Aristotle, however, would not renounce it, but construe it that it may better provide for nature and history. This is the significance of his new terminology. Matter, to which Plato reluctantly concedes some room as a principle of degradation in the universe, is now admitted to good standing. Matter or material is indispensable to being as its potentiality or that out of which it is constituted. The ideal, on the other hand, loses its exclusive title to the predicate of reality, and becomes the form, or the determinate nature which exists only in its particular embodiments. The being or substance is the concrete individual, of which these are the abstracted aspects. Aristotle's "form," like Plato's "idea," is a teleological principle. The essential nature of the object is its perfection. It is furthermore essential to the object that it should strive after a higher perfection. With Aristotle, however, the reality is not the consummation of the process, the highest perfection in and for itself, but the very hierarchy of objects that ascends toward it. The highest perfection, or God, is not itself coextensive with being, but the final cause of being—that on account of which the whole progression of events takes place. Reality is the development with all of its ascending stages from the maximum of potentiality, or matter, to the maximum of actuality, or God the pure form.

The Aristotelian Philosophy as a Reconciliation of Platonism and Spinozism.

§ [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.

Leibniz's Application of the Conception of Development to the Problem of Imperfection.