Pythagoras had long devoted his intellectual adoration to the lofty idea of order, which seemed to reveal itself to his mind, as the presiding genius of the serene and silent world. He had, from his youth, dwelt with delight upon the eternal relations of space, and determinate form, and number, in which the very idea of proportion seems to find its first and immediate development, and without the latter of which (number), all proportion is absolutely inconceivable. To this ardent genius, whose inventive energies were daily adding new and surprising contributions to the sum of discoverable relations, it at length began to appear as if the whole secret of the universe was hidden in these mysterious correspondences.
In making this extensive generalization, Pythagoras may, on his known principles, be supposed to have reasoned as follows: The mind of man perceives the relations of an eternal order in the proportions of space, and form, and number. That mind is, no doubt, a portion of the soul which animates and governs the universe; for on what other supposition shall we account for its internal principle of activity--the very principle which characterizes the prime mover, and can scarce be ascribed to an inferior nature? And on what other supposition are we to explain the identity which subsists between the principles of order, authenticated by the reason and the facts of order which are found to exist in the forms and multiplicities around us, and independent of us? Can this sameness be other than the sameness of the internal and external principles of a common nature? The proportions of the universe inhere in its divine soul; they are indeed its very essence, or at least, its attributes. The ideas or principles of Order which are implanted in the human reason, must inhere in the Divine Reason, and must be reflected in the visible world, which is its product. Man, then, can boldly affirm the necessary harmony of the world, because he has in his own mind a revelation which declares that the world, in its real structure, must be the image and copy of that divine proportion which he inwardly adores. [441]
[Footnote 441: ][ (return) ] It is an opinion which goes as far back as the time of Plato, and even Pythagoras, and has ever since been widely entertained, that beauty of form consists in some sort of proportion or harmony which may admit of a mathematical expression; and later and more scientific research is altogether in its favor. It is now established that complementary colors, that is, colors which when combined make up the full beam, are felt to be beautiful when seen simultaneously; that is, the mind is made to delight in the unities of nature. At the basis of music there are certain fixed ratios; and in poetry, of every description, there are measures, and correspondencies. Pythagoras has often been ridiculed for his doctrine of "the music of the spheres;" and probably his doctrine was somewhat fanciful, but later science shows that there is a harmony in all nature--in its forms, in its forces, and in its motions. The highest unorganized and all organized objects take definite forms which are regulated by mathematical laws. The forces of nature can be estimated in numbers, and light and heat go in undulations, whilst the movements of the great bodies in nature admit of a precise quantitative expression. The harmonies of nature in respect of color, of number, of form, and of time are forcibly exhibited in "Typical Forms and Special Ends in Creation," by M'Cosh.
Again, the world is assuredly perfect, as being the sensible image and copy of the Divinity, the outward and multiple development of the Eternal Unity. It must, therefore, when thoroughly known and properly interpreted, answer to all which we can conceive as perfect; that is, it must be regulated by laws, of which we have the highest principles in those first and elementary properties of numbers which stand next to unity. "The world is then, through all its departments, a living arithmetic in its development, a realized geometry in its repose." It is a κόσµος (for the word is purely Pythagorean)--the expression of harmony, the manifestation, to sense, of everlasting order.
Though Pythagoras found in geometry the fitting initiative for abstract speculation, it is remarkable that he himself preferred to constitute the science of Numbers as the true representative of the laws of the universe. The reason appears to be this: that though geometry speaks indeed of eternal truths, yet when the notion of symmetry and proportion is introduced, it is often necessary to insist, in preference, upon the properties of numbers. Hence, though the universe displays the geometry of its Constructor or Animator, yet nature was eminently defined as the µίµησις τῶν ἀριθµῶν--the imitation of numbers.
The key to all the Pythagorean dogmas, then, seems to be the general formula of unity in multiplicity:--unity either evolving itself into multiplicity, or unity discovered as pervading multiplicity. The principle of all things, the same principle which in this philosophy, as in others, was customarily called Deity, is the primitive unit from which all proceeds in the accordant relations of the universal scheme. Into the sensible world of multitude, the all-pervading Unity has infused his own ineffable nature; he has impressed his own image upon that world which is to represent him in the sphere of sense and man. What, then, is that which is at once single and multiple, identical and diversified--which we perceive as the combination of a thousand elements, yet as the expression of a single spirit--which is a chaos to the sense, a cosmos to the reason? What is it but harmony--proportion--the one governing the many, the many lost in the one? The world is therefore a harmony in innumerable degrees, from the most complicated to the most simple: it is now a Triad, combining the Monad and the Duad, and partaking of the nature of both; now a Tetrad, the form of perfection; now a Decad, which, in combining the four former, involves, in its mystic nature, all the possible accordances of the universe. [442]
The psychology of the Pythagoreans was greatly modified by their physical, and still more, by their moral tenets. The soul was ἀριθµὸς ἑαυτὸν κινῶν--a self-moving number or Monad, the copy (as we have seen) of that Infinite Monad which unfolds from its own incomprehensible essence all the relations of the universe. This soul has three elements, Reason (νοῦς), Intelligence (φρήν), and Passion (θυµός). The two last, man has in common with brutes, the first is his grand and peculiar characteristic. It has, hence, been argued that Pythagoras could not have held the doctrine of "transmigration." This clear separation of man from the brute, by this signal endowment of reason, which is sempiternal, seems a refutation of those who charge him with the doctrine.
In the department of morals, the legislator of Crotona found his appropriate sphere. In his use of numerical notation, moral good was essential unity--evil, essential plurality and division. In the fixed truths of mathematical abstractions he found the exemplars of social and personal virtue. The rule or law of all morality is resemblance to God; that is, the return of number to its root, to unity, [443] and virtue is thus a harmony.
[Footnote 442: ][ (return) ] That is, 1+2+3+4=10. There are intimations that the Pythagoreans regarded the Monad as God, the Duad as matter, the Triad as the complex phenomena of the world, the Tetrad as the completeness of all its relations, the Decad as the cosmos, or harmonious whole.
[Footnote 443: ][ (return) ] Aristotle, "Nichomachian Ethics," bk. i. ch. vi.