Such is Platonism. “Out of Plato,” says Ralph Waldo Emerson, “come all things that are still written and debated among men of thought.” He absorbed the learning of his times—of Greece from Philolaus to Socrates; then of Pythagoras in Italy; then what he could procure from Egypt and the East. He was so broad that all philosophy, European and Asiatic, was in his doctrines; and to culture and contemplation he added the nature and qualities of the poet.

The followers of Plato generally adhered strictly to his psychological theories. Several, however, like Xenocrates, ventured into bolder speculations. Speusippus, the nephew and successor of the great philosopher, was the author of the Numerical Analysis, a treatise on the Pythagorean numbers. Some of his speculations are not found in the written Dialogues; but as he was a listener to the unwritten lectures of Plato, the judgment of Enfield is doubtless correct, that he did not differ from his master. He was evidently, though not named, the antagonist whom Aristotle criticised, when professing to cite the argument of Plato against the doctrine of Pythagoras, that all things were in themselves numbers, or rather, inseparable from the idea of numbers. He especially endeavored to show that the Platonic doctrine of ideas differed essentially from the Pythagorean, in that it presupposed numbers and magnitudes to exist apart from things. He also asserted that Plato taught that there could be no real knowledge, if the object of that knowledge was not carried beyond or above the sensible.

But Aristotle was no trustworthy witness. He misrepresented Plato, and he almost caricatured the doctrines of Pythagoras. There is a canon of interpretation, which should guide us in our examinations of every philosophical opinion: “The human mind has, under the necessary operation of its own laws, been compelled to entertain the same fundamental ideas, and the human heart to cherish the same feelings in all ages.” It is certain that Pythagoras awakened the deepest intellectual sympathy of his age, and that his doctrines exerted a powerful influence upon the mind of Plato. His cardinal idea was that there existed a permanent principle of unity beneath the forms, changes, and other phenomena of the universe. Aristotle asserted that he taught that “numbers are the first principles of all entities.” Ritter has expressed the opinion that the formula of Pythagoras should be taken symbolically, which is doubtless correct. Aristotle goes on to associate these numbers with the “forms” and “ideas” of Plato. He even declares that Plato said: “forms are numbers,” and that “ideas are substantial existences—real beings.” Yet Plato did not so teach. He declared that the final cause was the Supreme Goodness—το ἀγαθόν. “Ideas are objects of pure conception for the human reason, and they are attributes of the Divine Reason.”[11] Nor did he ever say that “forms are numbers.” What he did say may be found in the Timæus: “God formed things as they first arose according to forms and numbers.”

It is recognized by modern science that all the higher laws of nature assume the form of quantitative statement. This is perhaps a fuller elaboration or more explicit affirmation of the Pythagorean doctrine. Numbers were regarded as the best representations of the laws of harmony which pervade the cosmos. We know too that in chemistry the doctrine of atoms and the laws of combination are actually and, as it were, arbitrarily defined by numbers. As Mr. W. Archer Butler has expressed it: “The world is, then, through all its departments, a living arithmetic in its development, a realized geometry in its repose.”

The key to the Pythagorean dogmas is the general formula of unity in multiplicity, the one evolving the many and pervading the many. This is the ancient doctrine of emanation in few words. Even the apostle Paul accepted it as true. “Εξ αυτοὺ, και δι᾽ αυτοῦ, και εις αυτὸν τὰ πάντα”—Out of him and through him and in him all things are. This, as we can see by the following quotation, is purely Hindu and Brahmanical:

“When the dissolution—Pralaya—had arrived at its term, the great Being—Para-Atma or Para-Purusha—the Lord existing through himself, out of whom and through whom all things were, and are and will be ... resolved to emanate from his own substance the various creatures” (Manava-Dharma-Sastra, book i., slokas 6 and 7).

The mystic Decad 1 + 2 + 3 + 4 = 10 is a way of expressing this idea. The One is God, the Two, matter; the Three, combining Monad and Duad, and partaking of the nature of both, is the phenomenal world; the Tetrad, or form of perfection, expresses the emptiness of all; and the Decad, or sum of all, involves the entire cosmos. The universe is the combination of a thousand elements, and yet the expression of a single spirit—a chaos to the sense, a cosmos to the reason.

The whole of this combination of the progression of numbers in the idea of creation is Hindu. The Being existing through himself, Swayambhu or Swayambhuva, as he is called by some, is one. He emanates from himself the creative faculty, Brahma or Purusha (the divine male), and the one becomes Two; out of this Duad, union of the purely intellectual principle with the principle of matter, evolves a third, which is Viradj, the phenomenal world. It is out of this invisible and incomprehensible trinity, the Brahmanic Trimurty, that evolves the second triad which represents the three faculties—the creative, the conservative, and the transforming. These are typified by Brahma, Vishnu, and Siva, but are again and ever blended into one. Unity, Brahma, or as the Vedas called him, Tridandi, is the god triply manifested, which gave rise to the symbolical Aum or the abbreviated Trimurty. It is but under this trinity, ever active and tangible to all our senses, that the invisible and unknown Monas can manifest itself to the world of mortals. When he becomes Sarira, or he who puts on a visible form, he typifies all the principles of matter, all the germs of life, he is Purusha, the god of the three visages, or triple power, the essence of the Vedic triad. “Let the Brahmas know the sacred Syllable (Aum), the three words of the Savitri, and read the Vedas daily” (Manu, book iv., sloka 125).

“After having produced the universe, He whose power is incomprehensible vanished again, absorbed in the Supreme Soul.... Having retired into the primitive darkness, the great Soul remains within the unknown, and is void of all form....

“When having again reünited the subtile elementary principles, it introduces itself into either a vegetable or animal seed, it assumes at each a new form.”