4. THE CARRYING-OUT OF THIS PRINCIPLE.—From the very nature of the “number-principle,” it follows that its complete application to the province of the real, can only lead to a fruitless and empty symbolism. If we take numbers as even and odd, and still farther as finite and infinite, and apply them as such to astronomy, music, psychology, ethics, &c., there arise combinations like the following, viz.: one is the point, two are the line, three are the superficies, four are the extension of a body, five are the condition (_beschaffenheit_), &c.—still farther, the soul is a musical harmony, as is also virtue, the soul of the world, &c. Not only the philosophical, but even the historical interest here ceases, since the ancients themselves—as was unavoidable from the arbitrary nature of such combinations—have given the most contradictory account, some affirming that the Pythagoreans reduced righteousness to the number three, others, that they reduced it to the number four, others again to five, and still others to nine. Naturally, from such a vague and arbitrary philosophizing, there would early arise, in this, more than in other schools, a great diversity of views, one ascribing this signification to a certain mathematical form, and another that. In this mysticism of numbers, that which alone has truth and value, is the thought, which lies at the ground of it all, that there prevails in the phenomena of nature a rational order, harmony and conformity to law, and that these laws of nature can be represented in measure and number. But this truth has the Pythagorean school hid under extravagant fancies, as vapid as they are unbridled. The physics of the Pythagoreans possesses little scientific value, with the exception of the doctrine taught by Philolaus respecting the circular motion of the earth. Their ethics is also defective. What we have remaining of it relates more to the Pythagorean life, _i. e._ to the practice and discipline of their order than to their philosophy. The whole tendency of Pythagoreanism was in a practical respect ascetic, and directed to a strict culture of the character. As showing this, we need only to cite their doctrines concerning the transmigration of the soul, or, as it has been called, their “immortality doctrine,” their notion in respect of the lower world, their opposition to suicide, and their view of the body as the prison of the soul—all of which ideas are referred to in Plato’s Phædon, and the last two of which are indicated as belonging to Philolaus. SECTION VI THE ELEATICS.