stone. Let the stone be ground to dust, and the particle of dust is still a copy, another copy of the One.

The reader will bear in mind that we have only a few mystical expressions, such as, "Number is the principle of Things," handed down to us as the doctrines of a Thinker who created a considerable school, and whose influence on philosophy was undeniably immense. We have to interpret these expressions as we best can. Above all, we have to give them some appearance of plausibility; and this not so much an appearance of plausibility to modern thinkers as what would have been plausible to the ancients. Now, as far as we have familiarized ourselves with the antique modes of thought, our interpretation of Pythagoras is one which, if not the true, is at any rate very analogous to it; by such a logical process he might have arrived at his conclusions, and for our purpose this is almost the same as if he had arrived at them by it.

This history has but to settle two questions respecting Pythagoras: first, did he regard Numbers as symbols merely, or as entities? Second, if he regarded them as entities, how could he have arrived at such an opinion? The second of these questions has been answered in a hypothetical manner in the remarks just inade; but of course the explanation is worthless if the first question be negatived, and to that question therefore we now turn. If we are to accept the authority of Aristotle, the question is distinctly and decisively answered, as we have seen, in favor of the reality of Numbers. It is true that doubts are thrown on the authority of Aristotle, who is said to have misunderstood or misrepresented the Pythagorean doctrine; but when we consider the comprehensiveness and exactness of Aristotle's mighty intellect; when we consider further that he had paid more than his usual attention to the doctrines of the Pythagoreans, having written a special treatise thereon, we shall be slow to reject any statement he may make unless better evidence is produced; and where can better evidence be sought? Either we must accept Aristotle, or be silent on the whole matter; unless, indeed, we prefer-as

many prefer our own sagacity to his authority. It may be stated as a final consideration, that the view taken by the Stagirite is in perfect conformity with the opinions of Anaximander; so that given, the philosophy of the master, we might à priori deduce the opinions of the pupil.

The nature of this Work forbids any detailed account of the various opinions attributed to Pythagoras on subsidiary points. But we may instance his celebrated theory of the music of the spheres as a good specimen of the deductive method employed by him. Assuming that every thing in the great Arrangement (xidos), which he called the world, must be harmoniously arranged, and, assuming that the planets were at the same proportionate distances from one another as the divisions of the monochord, he concluded that in passing through the ether they must make a sound, and that this sound would vary according to the diversity of their magnitude, velocity, and relative distance. Saturn gave the deepest tone, as being the furthest from the earth; the Moon gave the shrillest, as being nearest to the earth.

It may be necessary just to state that the attempt to make Pythagoras a Monotheist is utterly without solid basis, and unworthy of detailed refutation.

His doctrine of the Transmigration of Souls has been regarded. as symbolical; with very little reason, or rather with no reason at all. He defined the soul to be a Monad (unit) which was self-moved. Of course the soul, inasmuch as it was a number, was One, i. e. perfect. But all perfection, in as far as it is moved, must pass into imperfection, whence it strives to regain its state of perfection. Imperfection he called a departure from unity; two therefore was accursed.

The soul in man is in a state of comparative imperfection.t It has three elements, Reason (vous), Intelligence (pv), and

* Aristot., De Animâ, i. 2.

+ Thus Aristotle expresses himself when he says that the Pythagoreans maintained the soul and intelligence to be a certain combination of numbers, τὸ δὲ τοιονδί (sc. τῶν ἀριθμῶν πάθος) ψυχὴ καὶ νοῦς. Metaph., i. 5.

Passion (uus): the two last man has in common with brutes; the first is his distinguishing characteristic. It has hence been concluded that Pythagoras could not have maintained the doctrine of transmigration, his distinguishing man from brutes being a refutation of those who charge him with the doctrine.* The objection is plausible, and points out a contradiction; but there is abundant evidence for the belief that transmigration was taught. The soul, being a self-moved monad, is One, whether it connect itself with two or with three; in other words, the essence remains the same whatever its manifestations. The One soul may have two aspects, Intelligence and Passion, as in brutes; or it may have the three aspects, as in man. Each of these aspects may predominate, and the man will then become eminently rational, or able, or sensual. He will be a philosopher, a man of the world, or a beast. Hence the importance of the Pythagorean initiation, and of the studies of Mathematics and Music.

"This soul, which can look before and after, can shrink and shrivel itself into an incapacity of contemplating aught but the present moment, of what depths of degeneracy is it capable! What a beast it may become! And if something lower than itself, why not something higher? And if something higher and lower, may there not be a law accurately determining its elevation and descent? Each soul has its peculiar evil tastes, bringing it to the likeness of different creatures beneath itself; why may it not be under the necessity of abiding in the condition of that thing to which it had adapted and reduced itself?"

In closing this account of a very imperfectly known doctrine, we have only further to exhibit its relation to the preceding philosophy. It is clearly an offshoot of Anaximander's doctrine,

* Pierre Leroux, De l'Humanité, i. 890-426.

+ Plato distinctly mentions the transmigration into beasts.-Phædrus, p. 45. And the Pythagorean Timæus, in his statement of the doctrine, also expressly includes beasts.-Timæus, p. 45.

Maurice, Moral and Metaphysical Philosophy.

which it develops in a more logical manner. In Anaximander there remained a trace of physical inquiry; in Pythagoras science is frankly mathematical. Assuming that number is the real invariable essence of the world, it was a natural deduction that the world is regulated by numerical proportions; and from this all the rest of his system followed as a consequence. Anaximander's system is but a rude and daring sketch of a doctrine which the great mathematical genius of Pythagoras developed. The Infinite of Anaximander became the One of Pythagoras. Observe that in neither of these systems is Mind an attribute of the Infinite. It has been frequently maintained that Pythagoras taught the doctrine of "a soul of the world." But there is no solid ground for the opinion, any more than for that of his Theism, which later writers anxiously attributed to him. The conception of an Infinite Mind is much later than Pythagoras. He only regarded Mind as a phenomenon; as the peculiar manifestation of an essential number; and the proof of this assertion we take to lie in his very doctrine of the soul. If the Monad, which is self-moved, can pass into the state of a brute or of a plant, in which state it successively loses its Reason (voữs) and its Intelligence (páv) to become merely sensual and concupiscible, does not this abdication of Reason and Intelligence distinctly prove them to be only variable manifestations (phenomena) of the invariable Essence? Assuredly; and those who argue for the Soul of the World as an Intelligence in the Pythagorean doctrine, must renounce both the doctrine of transmigration and the central doctrine of the system, the invariable Number as the Essence of things.

Pythagoras represents the second epoch of the second Branch of Ionian Philosophy; he is parallel with Anaximenes.

20

Translations from the 5th Chapter of Book I. of Aristotle's Metaphysics.

"In the age of these philosophers [the Eleats and Atomists], and even before them, lived those called Pythagoreans, who at first applied themselves to mathematics, a science they improved; and, having been trained exclusively in it, they fancied that the principles of mathematics were the principles of all things.

"Since numbers are by nature prior to all things, in Numbers they thought they perceived greater analogies with that which exists and that which is produced (ὁμοιώματα πολλὰ τοῖς οὖσι xai yıyvoμévois), than in fire, earth, or water. So that a certain combination of Numbers was justice; and a certain other combination of Numbers was Reason and Intelligence; and a certain other combination of Numbers was opportunity (xapós); and so of the rest.

"Moreover, they saw in Numbers the combinations of harmony. Since therefore all things seemed formed similarly to Numbers, and Numbers being by nature anterior to things, they concluded that the elements (roysia) of Numbers are the elements of things, and that the whole heaven is a harmony and a Number. Having indicated the great analogies between Numbers and the phenomena of heaven and its parts, and with the phenomena of the whole world (τὴν ὅλην διακόσμησιν), they formed a system; and if any gap was apparent in the system, they used every effort to restore the connection. Thus, since Ten appeared to them a perfect number, potentially containing all numbers, they declared that the moving celestial bodies (rà φερόμενα κατὰ τὸν οὐρανόν) were ten in number; but because only nine are visible they imagined (oo) a tenth, the Anticthone.

"We have treated of all these things more in detail elsewhere. But the reason why we recur to them is this-that we may learn from these philosophers also what they lay down as their