622 PYTHAGORAS. regulating principle of the whole universe. Some of the Pythagoreans (but by no nneans all, as it appears) drew out a list of ten pairs of opposites, which they termed the elements of the universe. (Arist. Afet. i. 5. Elsewhere he speaks as if the Pythagoreans generally did the same, Elk. Nic. i. 4, ii. 5.) These pairs were — Limit and the Unlimited. Odd and Even. One and Multitude. Right and Left. Male and Female. Stationary and Moved. Straight and Curved. Light and Darkness. Good and Bad. Square and Oblong. The first column was that of the good elements (Arist. Eth. Nic. i. 4) ; the second, the row of the bad. Those in the second series were also re- garded as having the character of negation (Arist. r/iys. iii. 2). These, however, are hardly to be looked upon as ten pairs of distinct principles. They are rather various modes of conceiving one and the same opposition. One, Limit and the Odd, are spoken of as though they were synony- mous (comp. Arist. Met. i. 5, 7, xiii. 4, Ph^s. iii. 5). To explain the production of material objects out of tlie union of the unlimited and the limiting, Ritter {Gesch. der Pyth. Phil, and Gesch. der Phil. vol. i. p. 403, &c.) has propounded a theory which has great plausibility, and is undoubtedly much the same as the view held by later Pythagorizing mathematicians ; namely, that the ainipov is nei- ther more nor less than void space, and the Trepai- vovTa points in space which bound or define it (which points he affirms the Pythagoreans called monads or units, appealing to Arist. de Caelo, iii. 1 ; comp. Alexand. Aphrod. quoted below), the point being the dpxn or principium of the line, the line of the surface, the surface of the solid. Points, or monads, therefore are the source of material existence ; and as points are monads, and monads numbers, it follows that numbers are at the base of material existence. (This is the view of the matter set forth by Alexander Aphrodisiensis in Arist. de prim. Phil. i. fol. 10, b. ; Ritter, I. c. p. 404, note ?>.) Ecphantus of Syracuse was the first who made the Pythagorean monads to be corporeal, and set down indivisible particles and void space as the principia of material existence. (See Stob. Eel. Phys. p. 308.) Two geometrical points in them- selves would have no magnitude ; it is only when they are combined with the intervening space that a line can be produced. The union of space and lines makes surfaces ; the union of surfaces and space makes solids. Of course this does not ex- plain very well how corporeal substance is formed, and Ritter thinks that the Pythagoreans perceived that this was the weak point of their system, and 80 spoke of the aneipov, as mere void space, as little as they could help, and strove to represent it .IS something positive, or almost substantial. But however plausible this view of the matter may be, we cannot understand how any one who compares the very numerous passages in which Aristotle speaks of the Pythagoreans, can suppose that his notices have reference to any such system. The theory wln'ch Ritter sets down as that of the PYTHAGORAS. Pythagoreans is one which Aristotle mentions several times, and shows to be inadequate to ac- count for the physical existence of the world, but he nowhere speaks of it as the doctrine of the Pythagoreans. Some of the passages, where Ritter tries to make this out to be the case, go to prove the very reverse. For instance, in De Caelo, iii. ], after an elaborate discussion of the theory in ques- tion, Aristotle concludes by remarking that the number-theory of the Pythagoreans will no more account for the production of corporeal magnitude, than the point-line-and-space- theory which he has just described, for no addition of units can pro- duce either body or weight (comp. Met. xiii. 3). Aristotle nowhere identifies the Pythagorean mo- nads with mathematical points ; on the contrary, he affirms that in the Pythagorean system, the monads, in some way or other which they could not explain, got magnitude and extension {Met. xii. 6, p. 1080, ed. Bekker). The Kevov again, which Aristotle mentions as recognised by the Pythagoreans, is never spoken of as synonymous with their aireipov ; on the contrary we find (Stob. Eel. Phys. i. p. 380) that from the aireipou they deduced time, breath, and void space. The fre- quent use of the term irepas, too, by Aristotle, instead of TrepaiVoi'Ta, hardly comports with Ritter's theory. There can be little doubt that the Pythagorean system should be viewed in connection with that of Anaximander, with whose doctrines Pythagoras was doubtless conversant. Anaximander, in his attempt to solve the problem of the universe, passed from the region of physics to that of meta- physics. He supposed " a primaeval principle without any actual determining qualities whatever; but including all qualities potentially, and manifest- ing them in an infinite variety from its continually self-changing nature ; a principle which was nothing in itself, yet had the capacity of producing any and all manifestations, however contrar}'^ to eacli other — a primaeval something, whose essence it was to be eternally productive of different ph.ieno- mena" (Grote, I. c. p. 518 ; comp. Brandis, /. c. p. 123, &c.). This he termed the aireipou ; and he was also the first to introduce the term dpx^ (Simplic. in Arist. Phys. fol. 6, 32). Both these terms hold a prominent position in the Pythago- rean system, and we think there can be but little doubt as to their parentage. The Pythagorean direipop seems to have been very nearly the same as that of Anaximander, an undefined and infinite something. Only instead of investing it with the property of spontaneously developing itself in the various forms of actual material existence, they regarded all its definite manifestations as the de- termination of its indefiniteness by the definiteness of num,()er, which thus became the cause of all actual and positive existence (tovs dpiO/xoxis alrlovs elvai ToTs diWois ttjs ovalas^ Arist. Met. i. 6). It is by numbers alone, in their view, that the objective becomes cognisable to the subject ; by numbers that extension is originated, and attains to that definiteness by which it becomes a concrete body. As the ground of all quantitative and quali- tative definiteness in existing things, therefore, number is represented as their inherent element, or even as the matter (oAv)-, as well as the passive and active condition of things (Arist. Met. i. 5). But both the Trepaluovra and tlie d-rrcipov are re- ferred to a higher unity, the absolute or divine
