CHAPTER I.

PLATO.

PRE-SOKRATIC PHILOSOPHY.

CHAPTER I.

SPECULATIVE PHILOSOPHY IN GREECE, BEFORE AND IN THE TIME OF SOKRATES.

The life of Plato extends from 427-347 B.C. He was born in the fourth year of the Peloponnesian war, and he died at the age of 80, about the time when Olynthus was taken by the Macedonian Philip. The last years of his life thus witnessed a melancholy breach in the integrity of the Hellenic world, and even exhibited data from which a far-sighted Hellenic politician might have anticipated something like the coming subjugation, realised afterwards by the victory of Philip at Chæroneia. But during the first half of Plato's life, no such anticipations seemed even within the limits of possibility. The forces of Hellas, though discordant among themselves, were superabundant as to defensive efficacy, and were disposed rather to aggression against foreign enemies, especially against a country then so little formidable as Macedonia. It was under this contemplation of Hellas self-acting and self-sufficing--an aggregate of cities, each a political unit, yet held together by strong ties of race, language, religion, and common feelings of various kinds--that the mind of Plato was both formed and matured.

In appreciating, as far as our scanty evidence allows, the circumstances which determined his intellectual and speculative character, I shall be compelled to touch briefly upon the various philosophical theories which were propounded anterior to Sokrates--as well as to repeat some matters already brought to view in the sixteenth, sixty-seventh, and sixty-eighth chapters of my History of Greece.

To us, as to Herodotus, in his day, the philosophical speculation of the Greeks begins with the theology and cosmology of Homer and Hesiod. The series of divine persons and attributes, and generations presented by these poets, and especially the Theogony of Hesiod, supplied at one time full satisfaction to the curiosity of the Greeks respecting the past history and present agencies of the world around them. In the emphatic censure bestowed by Herakleitus on the poets and philosophers who preceded him, as having much knowledge but no sense--he includes Hesiod, as well as Pythagoras, Xenophanes, and Hekatæus: upon Homer and Archilochus he is still more severe, declaring that they ought to be banished from the public festivals and scourged. The sentiment of curiosity as it then existed was only secondary and derivative, arising out of some of the strong primary or personal sentiments--fear or hope, antipathy or sympathy,--impression of present weakness,--unsatisfied appetites and longings,--wonder and awe under the presence of the terror-striking phenomena of nature, &c. Under this state of the mind, when problems suggested themselves for solution, the answers afforded by Polytheism gave more satisfaction than could have been afforded by any other hypothesis. Among the indefinite multitude of invisible, personal, quasi-human agents, with different attributes and dispositions, some one could be found to account for every perplexing phenomenon. The question asked was, not What are the antecedent conditions or causes of rain, thunder, or earthquakes, but Who rains and thunders? Who produces earthquakes? The Hesiodic Greek was satisfied when informed that it was Zeus or Poseidon. To be told of physical agencies would have appeared to him not merely unsatisfactory, but absurd, ridiculous, and impious. It was the task of a poet like Hesiod to clothe this general polytheistic sentiment in suitable details: to describe the various Gods, Goddesses, Demigods, and other quasi-human agents, with their characteristic attributes, with illustrative adventures, and with sufficient relations of sympathy and subordination among each other, to connect them in men's imaginations as members of the same brotherhood. Okeanus, Gæa, Uranus, Helios, Selênê,--Zeus, Poseidon, Hades--Apollo and Artemis, Dionysus and Aphroditê--these and many other divine personal agents, were invoked as the producing and sustaining forces in nature, the past history of which was contained in their filiations or contests. Anterior to all of them, the primordial matter or person, was Chaos.

Hesiod represents the point of view ancient and popular (to use Aristotle's expression) among the Greeks, from whence all their philosophical speculation took its departure; and which continued throughout their history, to underlie all the philosophical speculations, as the faith of the ordinary public who neither frequented the schools nor conversed with philosophers. While Aristophanes, speaking in the name of this popular faith, denounces and derides Sokrates as a searcher, alike foolish and irreligious, after astronomical and physical causes--Sokrates himself not only denies the truth of the allegation, but adopts as his own the sentiment which dictated it; proclaiming Anaxagoras and others to be culpable for prying into mysteries which the Gods intentionally kept hidden. The repugnance felt by a numerous public, against scientific explanation--as eliminating the divine agents and substituting in their place irrational causes,--was a permanent fact of which philosophers were always obliged to take account, and which modified the tone of their speculations without being powerful enough to repress them.

Again in the beginning of the second book of the Meteorologica, Aristotle contrasts the ancient and primitive theology with the "human wisdom" which grew up subsequently: [Greek: Oi( a)rchai=oi kai\ diatri/bontes peri\ ta\s theologi/as--oi( sophô/teroi tê\n a)nthrôpi/nên sophi/an] (Meteor, ii. i. p. 353, a.)]

Even in the sixth century B.C., when the habit of composing in prose was first introduced, Pherekydes and Akusilaus still continued in their prose the theogony, or the mythical cosmogony, of Hesiod and the other old Poets: while Epimenides and the Orphic poets put forth different theogonies, blended with mystical dogmas. It was, however, in the same century, and in the first half of it, that Thales of Miletus (620-560 B.C.), set the example of a new vein of thought. Instead of the Homeric Okeanus, father of all things, Thales assumed the material substance, Water, as the primordial matter and the universal substratum of everything in nature. By various transmutations, all other substances were generated from water; all of them, when destroyed, returned into water. Like the old poets, Thales conceived the surface of the earth to be flat and round; but he did not, like them, regard it as stretching down to the depths of Tartarus: he supposed it to be flat and shallow, floating on the immensity of the watery expanse or Ocean. This is the main feature of the Thaletian hypothesis, about which, however, its author seems to have left no writing. Aristotle says little about Thales, and that little in a tone of so much doubt, that we can hardly confide in the opinions and discoveries ascribed to him by others.

Pherekydes, Epimenides, &c., were contemporary with the earliest Ionic philosophers (Brandis, Handbuch der Gesch. der Gr.-Röm. Phil., s. 23).

According to Plutarch (Aquæ et Ignis Comparatio, p. 955, init.), most persons believed that Hesiod, by the word Chaos, meant Water. Zeno the Stoic adopted this interpretation (Schol. Apollon. Rhod. i. 498). On the other hand, Bacchylides the poet, and after him Zenodotus, called Air by the name Chaos (Schol. Hesiod. Theogon. p. 392, Gaisf.). Hermann considers that the Hesiodic Chaos means empty space (see note, Brandis, Handb. d. Gesch. d. Gr.-Röm. Phil., vol. i., p. 71).]

It is stated by Herodotus that Thales foretold the year of the memorable solar eclipse which happened during the battle between the Medes and the Lydians (Herod. i. 74). This eclipse seems to have occurred in B.C. 585, according to the best recent astronomical enquiries by Professor Airy.]

The next of the Ionic philosophers, and the first who published his opinions in writing, was Anaximander, of Miletus, the countryman and younger contemporary of Thales (570-520 B.C.). He too searched for an [Greek: A)rchê/], a primordial Something or principle, self-existent and comprehending in its own nature a generative, motive, or transmutative force. Not thinking that water, or any other known and definite substance fulfilled these conditions, he adopted as the foundation of his hypothesis a substance which he called the Infinite or Indeterminate. Under this name he conceived Body simply, without any positive or determinate properties, yet including the fundamental contraries, Hot, Cold, Moist, Dry, &c., in a potential or latent state, including farther a self-changing and self-developing force, and being moreover immortal and indestructible. By this inherent force, and by the evolution of one or more of these dormant contrary qualities, were generated the various definite substances of nature--Air, Fire, Water, &c. But every determinate substance thus generated was, after a certain time, destroyed and resolved again into the Indeterminate mass. "From thence all substances proceed, and into this they relapse: each in its turn thus making atonement to the others, and suffering the penalty of injustice." Anaximander conceived separate existence (determinate and particular existence, apart from the indeterminate and universal) as an unjust privilege, not to be tolerated except for a time, and requiring atonement even for that. As this process of alternate generation and destruction was unceasing, so nothing less than an Infinite could supply material for it. Earth, Water, Air, Fire, having been generated, the two former, being cold and heavy, remained at the bottom, while the two latter ascended. Fire formed the exterior circle, encompassing the air like bark round a tree: this peripheral fire was broken up and aggregated into separate masses, composing the sun, moon, and stars. The sphere of the fixed stars was nearest to the earth: that of the moon next above it: that of the sun highest of all. The sun and moon were circular bodies twenty-eight times larger than the earth: but the visible part of them was only an opening in the centre, through which the fire or light behind was seen. All these spheres revolved round the earth, which was at first semi-fluid or mud, but became dry and solid through the heat of the sun. It was in shape like the section of a cylinder, with a depth equal to one-third of its breadth or horizontal surface, on which men and animals live. It was in the centre of the Kosmos; it remained stationary because of its equal distance from all parts of the outer revolving spheres; there was no cause determining it to move upward rather than downward or sideways, therefore it remained still. Its exhalations nourished the fire in the peripheral regions of the Kosmos. Animals were produced from the primitive muddy fluid of the earth: first, fishes and other lower animals--next, in process of time man, when circumstances permitted his development. We learn farther respecting the doctrines of Anaximander, that he proposed physical explanations of thunder, lightning, and other meteorological phenomena: memorable as the earliest attempt of speculation in that department, at a time when such events inspired the strongest religious awe, and were regarded as the most especial manifestations of purposes of the Gods. He is said also to have been the first who tried to represent the surface and divisions of the earth on a brazen plate, the earliest rudiment of a map or chart.

Anaximander conceived [Greek: to\ a)peiron] as infinite matter; the Pythagoreans and Plato conceived it as a distinct nature by itself--as a subject, not as a predicate (Aristotel. Physic. iii. 4, p. 203, a. 2).

About these fundamental contraries, Aristotle says (Physic. i. 4, init.): [Greek: oi( d' e)k tou e(no\s e)nou/sas ta\s e)nantio/têtas e)kkri/nesthai, ô(/sper A)naxi/mandro/s phêsi]. Which Simplikius explains, [Greek: e)nantio/tête/s ei)si, thermo\n, psuchro\n, xêro\n, u(gro\n, kai\ ai( a)/llai], &c.

Compare also Schleiermacher, "Ueber Anaximandros," in his Vermischte Schriften, vol. ii. p. 178, seq. Deutinger (Gesch. der Philos. vol. i. p. 165, Regensb. 1852) maintains that this [Greek: e)/krisis] of contraries is at variance with the hypothesis of Anaximander, and has been erroneously ascribed to him. But the testimony is sufficiently good to outweigh this suspicion.]

Eudêmus, in his history of astronomy, mentioned Anaximander as the first who had discussed the magnitudes and distances of the celestial bodies (Simplikius ad Aristot. De Coelo, ap. Schol. Brand, p. 497, a. 12).]

A doctrine somewhat like it is ascribed even to Thales. See Alexander's Commentary on Aristotel. Metaphys. i. p. 983, b. 17.

The reason here assigned by Anaximander why the Earth remained still, is the earliest example in Greek philosophy of that fallacy called the principle of the Sufficient Reason, so well analysed and elucidated by Mr. John Stuart Mill, in his System of Logic, book v., ch. 3, sect. 5.

The remarks which Aristotle himself makes upon it are also very interesting, when he cites the opinion of Anaximander. Compare Plato, Phædon, p. 109, c. 132, with the citations in Wyttenbach's note.]

The third physical philosopher produced by Miletus, seemingly before the time of her terrible disasters suffered from the Persians after the Ionic revolt between 500-494 B.C., was Anaximenes, who struck out a third hypothesis. He assumed, as the primordial substance, and as the source of all generation or transmutation, Air, eternal in duration, infinite in extent. He thus returned to the principle of the Thaletian theory, selecting for his beginning a known substance, though not the same substance as Thales. To explain how generation of new products was possible (as Anaximander had tried to explain by his theory of evolution of latent contraries), Anaximenes adverted to the facts of condensation and rarefaction, which he connected respectively with cold and heat. The Infinite Air, possessing and exercising an inherent generative and developing power, perpetually in motion, passing from dense to rare or from rare to dense, became in its utmost rarefaction, Fire and Æther; when passing through successive stages of increased condensation it became first cloud, next water, then earth, and, lastly, in its utmost density, stone. Surrounding, embracing, and pervading the Kosmos, it also embodied and carried with it a vital principle, which animals obtained from it by inspiration, and which they lost as soon as they ceased to breathe. Anaximenes included in his treatise (which was written in a clear Ionic dialect) many speculations on astronomy and meteorology, differing widely from those of Anaximander. He conceived the Earth as a broad, flat, round plate, resting on the air. Earth, Sun, and Moon were in his view condensed air, the Sun acquiring heat by the extreme and incessant velocity with which he moved. The Heaven was not an entire hollow sphere encompassing the Earth below as well as above, but a hemisphere covering the Earth above, and revolving laterally round it like a cap round the head.

Cicero, Academic. ii. 37, 118. "Anaximenes infinitum aera, sed ea, quæ ex eo orirentur, definita."

The comic poet Philemon introduced in one of his dramas, of which a short fragment is preserved (Frag. 2, Meineke, p. 840), the omnipresent and omniscient Air, to deliver the prologue:

The general principle of cosmogony, involved in the hypothesis of these three Milesians--one primordial substance or Something endued with motive and transmutative force, so as to generate all the variety of products, each successive and transient, which our senses witness--was taken up with more or less modification by others, especially by Diogenes of Apollonia, of whom I shall speak presently. But there were three other men who struck out different veins of thought--Pythagoras, Xenophanes, and Herakleitus: the two former seemingly contemporary with Anaximenes (550-490 B.C.), the latter somewhat later.

Of Pythagoras I have spoken at some length in the thirty-seventh chapter of my History of Greece. Speculative originality was only one among many remarkable features in his character. He was an inquisitive traveller, a religious reformer or innovator, and the founder of a powerful and active brotherhood, partly ascetic, partly political, which stands without parallel in Grecian history. The immortality of the soul, with its transmigration (metempsychosis) after death into other bodies, either of men or of other animals--the universal kindred thus recognised between men and other animals, and the prohibition which he founded thereupon against the use of animals for food or sacrifice--are among his most remarkable doctrines: said to have been borrowed (together with various ceremonial observances) from the Egyptians. After acquiring much celebrity in his native island of Samos and throughout Ionia, Pythagoras emigrated (seemingly about 530 B.C.) to Kroton and Metapontum in Lower Italy, where the Pythagorean brotherhood gradually acquired great political ascendancy: and from whence it even extended itself in like manner over the neighbouring Greco-Italian cities. At length it excited so much political antipathy among the body of the citizens, that its rule was violently put down, and its members dispersed about 509 B.C. Pythagoras died at Metapontum.

Though thus stripped of power, however, the Pythagoreans still maintained themselves for several generations as a social, religious, and philosophical brotherhood. They continued and extended the vein of speculation first opened by the founder himself. So little of proclaimed individuality was there among them, that Aristotle, in criticising their doctrine, alludes to them usually under the collective name Pythagoreans. Epicharmus, in his comedies at Syracuse (470 B.C.) gave occasional utterance to various doctrines of the sect; but the earliest of them who is known to have composed a book, was Philolaus, the contemporary of Sokrates. Most of the opinions ascribed to the Pythagoreans originated probably among the successors of Pythagoras; but the basis and principle upon which they proceed seems undoubtedly his.

Some passages of Aristotle, however, indicate divergences of doctrine among the Pythagoreans themselves (Metaphys. A. 5, p. 986, a. 22). He probably speaks of the Pythagoreans of his own time when dialectical discussion had modified the original orthodoxy of the order. Compare Gruppe, Ueber die Fragmente des Archytas, cap. 5, p. 61-63. About the gradual development of the Pythagorean doctrine, see Brandis, Handbuch der Gr.-R. Philos. s. 74, 75.]

The problem of physical philosophy, as then conceived, was to find some primordial and fundamental nature, by and out of which the sensible universe was built up and produced; something which co-existed always underlying it, supplying fresh matter and force for generation of successive products. The hypotheses of Thales, Anaximander, and Anaximenes, to solve this problem, have been already noticed: Pythagoras solved it by saying, That the essence of things consisted in Number. By this he did not mean simply that all things were numerable, or that number belonged to them as a predicate. Numbers were not merely predicates inseparable from subjects, but subjects in themselves: substances or magnitudes, endowed with active force, and establishing the fundamental essences or types according to which things were constituted. About water, air, or fire, Pythagoras said nothing. He conceived that sensible phenomena had greater resemblance to numbers than to any one of these substrata assigned by the Ionic philosophers. Number was (in his doctrine) the self-existent reality--the fundamental material and in-dwelling force pervading the universe. Numbers were not separate from things (like the Platonic Ideas), but fundamenta of things--their essences or determining principles: they were moreover conceived as having magnitude and active force. In the movements of the celestial bodies, in works of human art, in musical harmony--measure and number are the producing and directing agencies. According to the Pythagorean Philolaus, "the Dekad, the full and perfect number, was of supreme and universal efficacy as the guide and principle of life, both to the Kosmos and to man. The nature of number was imperative and lawgiving, affording the only solution of all that was perplexing or unknown; without number all would be indeterminate and unknowable."

Ibid., Aphorism 105-107:--"Arithmetic is the science of the second idea, or that of time or motion, or life. It is therefore the first science. Mathematics not only begin with it, but creation also, with the becoming of time and of life. Arithmetic is, accordingly, the truly absolute or divine science; and therefore every thing in it is also directly certain, because every thing in it resembles the Divine. Theology is arithmetic personified."--"A natural thing is nothing but a self-moving number. An organic or living thing is a number moving itself out of itself or spontaneously: an inorganic thing, however, is a number moved by another thing: now as this other thing is also a real number, so then is every inorganic thing a number moved by another number, and so on ad infinitum. The movements in nature are only movements of numbers by numbers: even as arithmetical computation is none other than a movement of numbers by numbers; but with this difference--that in the latter, this operates in an ideal manner, in the former after a real."]

According to Plato, as well as the Pythagoreans, number extended to ten, and not higher: all above ten were multiples and increments of ten. (Aristot. Physic. iii. 6, p. 203, b. 30).]

The first principle or beginning of Number, was the One or Monas--which the Pythagoreans conceived as including both the two fundamental contraries--the Determining and the Indeterminate. All particular numbers, and through them all things, were compounded from the harmonious junction and admixture of these two fundamental contraries. All numbers being either odd or even, the odd numbers were considered as analogous to the Determining, the even numbers to the Indeterminate. In One or the Monad, the Odd and Even were supposed to be both contained, not yet separated: Two was the first indeterminate even number; Three, the first odd and the first determinate number, because it included beginning, middle, and end. The sum of the first four numbers--One, Two, Three, Four = Ten (1 + 2 + 3 + 4) was the most perfect number of all. To these numbers, one, two, three, four, were understood as corresponding the fundamental conceptions of Geometry--Point, Line, Plane, Solid. Five represented colour and visible appearance: Six, the phenomenon of Life: Seven, Health, Light, Intelligence, &c.: Eight, Love or Friendship. Man, Horse, Justice and Injustice, had their representative numbers: that corresponding to Justice was a square number, as giving equal for equal.

By [Greek: a(rmoni/a], Philolaus meant the musical octave: and his work included many explanations and comparisons respecting the intervals of the musical scale. (Boeckh, p. 65 seq.)]

The number Five also signified marriage, because it was a junction of the first masculine number Three with the first feminine Two. Seven signified also [Greek: kairo\s] or Right Season. See Aristotel. Metaphys. A. 5, p. 985, b. 26, and M. 4, p. 1078, b. 23, compared with the commentary of Alexander on the former passage.]

The Pythagoreans conceived the Kosmos, or the universe, as one single system, generated out of numbers. Of this system the central point--the determining or limiting One--was first in order of time, and in order of philosophical conception. By the determining influence of this central constituted One, portions of the surrounding Infinite were successively attracted and brought into system: numbers, geometrical figures, solid substances, were generated. But as the Kosmos thus constituted was composed of numbers, there could be no continuum: each numerical unit was distinct and separated from the rest by a portion of vacant space, which was imbibed, by a sort of inhalation, from the infinite space or spirit without. The central point was fire, called by the Pythagoreans the Hearth of the Universe (like the public hearth or perpetual fire maintained in the prytaneum of a Grecian city), or the watch-tower of Zeus. Around it revolved, from West to East, ten divine bodies, with unequal velocities, but in symmetrical movement or regular dance. Outermost was the circle of the fixed stars, called by the Pythagoreans Olympus, and composed of fire like the centre. Within this came successively,--with orbits more and more approximating to the centre,--the five planets, Saturn, Jupiter, Mars, Venus, Mercury: next, the Sun, the Moon, and the Earth. Lastly, between the Earth and the central fire, an hypothetical body, called the Antichthon or Counter-Earth, was imagined for the purpose of making up a total represented by the sacred number Ten, the symbol of perfection and totality. The Antichthon was analogous to a separated half of the Earth; simultaneous with the Earth in its revolutions, and corresponding with it on the opposite side of the central fire.

A poet calls the tetraktys (consecrated as the sum total of the first four numbers 1 + 2 + 3 + 4 = 10) [Greek: pêgê\n a)ena/ou phu/seôs rhizô/mat' e)/chousan]. Sextus Empiric. adv. Mathemat. vii. 94.]

Aristot. Metaph. N. 3, p. 1091, a. 15. [Greek: phanerô=s ga\r le/gousin] (the Pythagoreans) [Greek: ô(s tou= e(no\s sustathe/ntos--eu)thu\s to\ e)/ggista tou= a)pei/rou o(/ti ei(lketo kai\ e)perai/neto u(po\ tou= pe/ratos].

Aristot. Physic. iv. 6, p. 213, b. 21. [Greek: Ei)=nai d' e)/phasan kai\ oi( Puthago/reioi keno/n, kai\ e)peisie/nai au)to\ tô=| ou)ra/nô| e)k tou= a)pei/rou pneu/matos, ô(s a)napne/onti; kai\ to\ keno/n, o(\ diori/zei ta\s phu/seis, ô(s o)/ntos tou= kenou= chôrismou= tinos tô=n e)phexê=s kai\ tê=s diori/seôs, kai\ tou=t' ei)=nai prô=ton e)n toi=s a)rithmoi=s; to\ ga\r keno\n diori/zein tê\n phu/sin au)tô=n]. Stobæus (Eclog. Phys. i. 18, p. 381, Heer.) states the same, referring to the lost work of Aristotle on the Pythagorean philosophy. Compare Preller, Histor. Philos. Gr. ex Font. Loc. Context., sect. 114-115.]

The inhabited portion of the Earth was supposed to be that which was turned away from the central fire and towards the Sun, from which it received light. But the Sun itself was not self-luminous: it was conceived as a glassy disk, receiving and concentrating light from the central fire, and reflecting it upon the Earth, so long as the two were on the same side of the central fire. The Earth revolved, in an orbit obliquely intersecting that of the Sun, and in twenty-four hours, round the central fire, always turning the same side towards that fire. The alternation of day and night was occasioned by the Earth being during a part of such revolution on the same side of the central fire with the Sun, and thus receiving light reflected from him: and during the remaining part of her revolution on the side opposite to him, so that she received no light at all from him. The Earth, with the Antichthon, made this revolution in one day: the Moon, in one month: the Sun, with the planets, Mercury and Venus, in one year: the planets, Mars, Jupiter, and Saturn, in longer periods respectively, according to their distances from the centre: lastly, the outermost circle of the fixed stars (the Olympus, or the Aplanes), in some unknown period of very long duration.

Martin (in his Études sur le Timée de Platon, vol. ii. p. 107) and Gruppe (Die Kosmischen Systeme der Griechen, ch. iv.) maintain that the original system proposed by Pythagoras was a geocentric system, afterwards transformed by Philolaus and other Pythagoreans into that which stands in the text. But I agree with Boeckh (Ueber das Kosmische System des Platon, p. 89 seqq.), and with Zeller (Phil. d. Griech., vol. i. p. 308, ed. 2), that this point is not made out. That which Martin and Gruppe (on the authority of Alexander Polyhistor, Diog. viii. 25, and others) consider to be a description of the original Pythagorean system as it stood before Philolaus, is more probably a subsequent transformation of it; introduced after the time of Aristotle, in order to suit later astronomical views.]

The revolutions of such grand bodies could not take place, in the opinion of the' Pythagoreans, without producing a loud and powerful sound; and as their distances from the central fire were supposed to be arranged in musical ratios, so the result of all these separate sounds was full and perfect harmony. To the objection--Why were not these sounds heard by us?--they replied, that we had heard them constantly and without intermission from the hour of our birth; hence they had become imperceptible by habit.

See the Pythagorean system fully set forth by Zeller, Die Philosophie der Griechen, vol. i. p. 302-310, ed. 2nd.]

Ten was, in the opinion of the Pythagoreans, the perfection and consummation of number. The numbers from One to Ten were all that they recognised as primary, original, generative. Numbers greater than ten were compounds and derivatives from the decad. They employed this perfect number not only as a basis on which to erect a bold astronomical hypothesis, but also as a sum total for their list of contraries. Many Hellenic philosophers recognised pairs of opposing attributes as pervading nature, and as the fundamental categories to which the actual varieties of the sensible world might be reduced. While others laid down Hot and Cold, Wet and Dry, as the fundamental contraries, the Pythagoreans adopted a list of ten pairs. 1. Limit and Unlimited; 2. Odd and Even; 3. One and Many; 4. Right and Left; 5. Male and Female; 6. Rest and Motion; 7. Straight and Curve; 8. Light and Darkness; 9. Good and Evil; 10. Square and Oblong. Of these ten pairs, five belong to arithmetic or to geometry, one to mechanics, one to physics, and three to anthropology or ethics. Good and Evil, Regularity and Irregularity, were recognised as alike primordial and indestructible.

This axiom is to be noted as occupying a great place in the minds of the Greek philosophers.]

The arithmetical and geometrical view of nature, to which such exclusive supremacy is here given by the Pythagoreans, is one of the most interesting features of Grecian philosophy. They were the earliest cultivators of mathematical science, and are to be recognised as having paved the way for Euclid and Archimedes, notwithstanding the symbolical and mystical fancies with which they so largely perverted what are now regarded as the clearest and most rigorous processes of the human intellect. The important theorem which forms the forty-seventh Proposition of Euclid's first book, is affirmed to have been discovered by Pythagoras himself: but how much progress was made by him and his followers in the legitimate province of arithmetic and geometry, as well as in the applications of these sciences to harmonics, which they seem to have diligently cultivated, we have not sufficient information to determine with certainty.

Contemporary with Pythagoras, and like him an emigrant from Ionia to Italy, was Xenophanes of Kolophon. He settled at the Phokæan colony of Elea, on the Gulf of Poseidonia; his life was very long, but his period of eminence appears to belong (as far as we can make out amidst conflicting testimony) to the last thirty years of the sixth century B.C. (530-500 B.C.). He was thus contemporary with Anaximander and Anaximenes, as well as with Pythagoras, the last of whom he may have personally known. He composed, and recited in person, poems--epic, elegiac, and iambic--of which a very few fragments remain.

Xenophanes takes his point of departure, not from Thales or Anaximander, but from the same ancient theogonies which they had forsaken. But he follows a very different road. The most prominent feature in his poems (so far as they remain), is the directness and asperity with which he attacks the received opinions respecting the Gods--and the poets Hesiod and Homer, the popular exponents of those opinions. Xenophanes not only condemns these poets for having ascribed to the Gods discreditable exploits, but even calls in question the existence of the Gods, and ridicules the anthropomorphic conception which pervaded the Hellenic faith. "If horses or lions could paint, they would delineate their Gods in form like themselves. The Ethiopians conceive their Gods as black, the Thracians conceive theirs as fair and with reddish hair." Dissatisfied with much of the customary worship and festivals, Xenophanes repudiated divination** altogether, and condemned the extravagant respect shown to victors in Olympic contests, not less than the lugubrious ceremonies in honour of Leukothea. He discountenanced all Theogony, or assertion of the birth of Gods, as impious, and as inconsistent with the prominent attribute of immortality ascribed to them. He maintained that there was but one God, identical with, or a personification of, the whole Uranus. "The whole Kosmos, or the whole God, sees, hears, and thinks." The divine nature (he said) did not admit of the conception of separate persons one governing the other, or of want and imperfection in any way.

Plutarch ap. Eusebium, Præp. Evang. i. 8; Diogen. Laert. ix. 19.]

Though Xenophanes thus appears (like Pythagoras) mainly as a religious dogmatist, yet theogony and cosmogony were so intimately connected in the sixth century B.C., that he at the same time struck out a new philosophical theory. His negation of theogony was tantamount to a negation of cosmogony. In substituting Ens Unum--one God for many, he set aside all distinct agencies in the universe, to recognise only one agent, single, all-pervading, indivisible. He repudiated all genesis of a new reality, all actual existence of parts, succession, change, beginning, end, etc., in reference to the universe, as well as in reference to God. "Wherever I turned my mind (he exclaimed) everything resolved itself into One and the same: all things existing came back always and everywhere into one similar and permanent nature." The fundamental tenet of Xenophanes was partly religious, partly philosophical, Pantheism, or Pankosmism: looking upon the universe as one real all-comprehensive Ens, which he would not call either finite or infinite, either in motion or at rest. Non-Ens he pronounced to be an absurdity--an inadmissible and unmeaning phrase.

It is fair to presume that these lines are a reproduction of the sentiments of Xenophanes, if not a literal transcript of his words.]

It was thus from Xenophanes that the doctrine of Pankosmism obtained introduction into Greek philosophy, recognising nothing real except the universe as an indivisible and unchangeable whole. Such a creed was altogether at variance with common perception, which apprehends the universe as a plurality of substances, distinguishable, divisible, changeable, &c. And Xenophanes could not represent his One and All, which excluded all change, to be the substratum out of which phenomenal variety was generated--as Water, Air, the Infinite, had been represented by the Ionic philosophers. The sense of this contradiction, without knowing how to resolve it, appears to have occasioned the mournful complaints of irremediable doubt and uncertainty, preserved as fragments from his poems. "No man (he exclaims) knows clearly about the Gods or the universe: even if he speak what is perfectly true, he himself does not know it to be true: all is matter of opinion."

Compare the extract from the Silli of Timon in Sextus Empiricus--Pyrrhon. Hypot. i. 224; and the same author, adv. Mathemat. vii. 48-52.]

Nevertheless while denying all real variety or division in the universe, Xenophanes did not deny the variety of human perceptions and beliefs. But he allowed them as facts belonging to man, not to the universe--as subjective or relative, not as objective or absolute. He even promulgated opinions of his own respecting many of the physical and cosmological subjects treated by the Ionic philosophers.

Without attempting to define the figure of the Earth, he considered it to be of vast extent and of infinite depth; including, in its interior cavities, prodigious reservoirs both of fire and water. He thought that it had at one time been covered with water, in proof of which he noticed the numerous shells found inland and on mountain tops, together with the prints of various fish which he had observed in the quarries of Syracuse, in the island of Paros, and elsewhere. From these facts he inferred that the earth had once been covered with water, and even that it would again be so covered at some future time, to the destruction of animal and human life. He supposed that the sun, moon, and stars were condensations of vapours exhaled from the Earth, collected into clouds, and alternately inflamed and extinguished.

This inference from the shells and prints of fishes is very remarkable for so early a period. Compare Herodotus (ii. 12) who notices the fact, and draws the same inference, as to Lower Egypt; also Plutarch, De Isid. et Osirid. c. 40, p. 367; and Strabo, i. p. 49-50, from whom we learn that the Lydian historian Xanthus had made the like observation, and also the like inference, for himself. Straton of Lampsakus, Eratosthenes, and Strabo himself, approved what Xanthus said.]

"per rara foramina, terræ Partibus erumpens primus se sustulit æther Ignifer et multos secum levis abstulit ignis . . . . Sic igitur tum se levis ac diffusilis æther Corpore concreto circumdatus undique flexit: . . . . Hunc exordia sunt solis lunæque secuta."]

Parmenides, of Elea, followed up and gave celebrity to the Xenophanean hypothesis in a poem, of which the striking exordium is yet preserved. The two veins of thought, which Xenophanes had recognised and lamented his inability to reconcile, were proclaimed by Parmenides as a sort of inherent contradiction in the human mind--Reason or Cogitation declaring one way, Sense (together with the remembrances and comparisons of sense) suggesting a faith altogether opposite. Dropping that controversy with the popular religion which had been raised by Xenophanes, Parmenides spoke of many different Gods or Goddesses, and insisted on the universe as one, without regarding it as one God. He distinguished Truth from matter of Opinion. Truth was knowable only by pure mental contemplation or cogitation, the object of which was Ens or Being, the Real or Absolute: here the Cogitans and the Cogitatum were identical, one and the same. Parmenides conceived Ens not simply as existent, but as self-existent, without beginning or end, as extended, continuous, indivisible, and unchangeable. The Ens Parmenideum comprised the two notions of Extension and Duration: it was something Enduring and Extended; Extension including both space, and matter so far forth as filling space. Neither the contrary of Ens (Non-Ens), nor anything intermediate between Ens and Non-Ens, could be conceived, or named, or reasoned about. Ens comprehended all that was Real, without beginning or end, without parts or difference, without motion or change, perfect and uniform like a well-turned sphere.

In this subject Ens, with its few predicates, chiefly negative, consisted all that Parmenides called Truth. Everything else belonged to the region of Opinion, which embraced all that was phenomenal, relative, and transient: all that involved a reference to man's senses, apprehension, and appreciation, all the indefinite diversity of observed facts and inferences. Plurality, succession, change, motion, generation, destruction, division of parts, &c., belonged to this category. Parmenides did not deny that he and other men had perceptions and beliefs corresponding to these terms, but he denied their application to the Ens or the self-existent. We are conscious of succession, but the self-existent has no succession: we perceive change of colour and other sensible qualities, and change of place or motion, but Ens neither changes nor moves. We talk of things generated or destroyed--things coming into being or going out of being--but this phrase can have no application to the self-existent Ens, which is always and cannot properly be called either past or future. Nothing is really generated or destroyed, but only in appearance to us, or relatively to our apprehension. In like manner we perceive plurality of objects, and divide objects into parts. But Ens is essentially One, and cannot be divided. Though you may divide a piece of matter you cannot divide the extension of which that matter forms part: you cannot (to use the expression of Hobbes) pull asunder the first mile from the second, or the first hour from the second. The milestone, or the striking of the clock, serve as marks to assist you in making a mental division, and in considering or describing one hour and one mile apart from the next. This, however, is your own act, relative to yourself: there is no real division of extension into miles, or of duration into hours. You may consider the same space or time as one or as many, according to your convenience: as one hour or as sixty minutes, as one mile or eight furlongs. But all this is a process of your own mind and thoughts; another man may divide the same total in a way different from you. Your division noway modifies the reality without you, whatever that may be--the Extended and Enduring Ens--which remains still a continuous one, undivided and unchanged.

v. 75:--

ei)/ ge ge/noit', ou)k e)/st'; ou)d' ei)/ po/te me/llei e)/sesthai; tô=s ge/nesis me\n a)pe/sbestai, kai\ a)/pistos o)/lethros.]]

Aristotel. Metaphys. A. 5, p. 986, b. 29, with the Scholia, and Physic. i. 2, 3. Simplikius Comm. in Physic. Aristot. (apud Tennemann Geschichte der Philos. b. i. s. 4, vol. i. p. 170) [Greek: pa/nta ga/r phêsi (Parmeni/dês) ta\ o)/nta, katho\ o)/nta, e(n e)sti/n]. This chapter, in which Tennemann gives an account of the Eleatic philosophy, appears to me one of the best and most instructive in his work.]

"Expansion and duration have this farther agreement, that though they are both considered by us as having parts, yet their parts are not separable one from another, not even in thought; though the parts of bodies from which we take our measure of the one--and the parts of motion, from which we may take the measure of the other--may be interrupted or separated."--Locke, Essay on the Human Understanding,