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.]

[Side-note: Music of the Spheres.]

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,[40] 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.[41]

[Footnote 40: Playfair observes (in his dissertation on the Progress of Natural Philosophy, p. 87) respecting Kepler--"Kepler was perhaps the first person who conceived that there must be always a law capable of being expressed by arithmetic or geometry, which connects such phenomena as have a physical dependence on each other". But this seems to be exactly the fundamental conception of the Pythagoreans: or rather a part of their fundamental conception, for they also considered their numbers as active forces bringing such law into reality. To illustrate the determination of the Pythagoreans to make up the number of Ten celestial bodies, I transcribe another passage from Playfair (p. 98). Huygens, having discovered one satellite of Saturn, "believed that there were no more, and that the number of the planets was now complete. The planets, primary and secondary, thus made up twelve--the double of six, the first of the perfect numbers."]

[Footnote 41: Aristot. De Coelo, ii. 9; Pliny, H.N. ii. 20.

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

[Side-note: Pythagorean list of fundamental Contraries--Ten opposing pairs.]

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[42] 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.[43] 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.[44]

[Footnote 42: Aristot. Metaphys. [Greek: G]. 2, p. 1004, b. 30. [Greek: ta\ d' o)/nta kai\ tê\n ou)sian o(mologou=sin e)x e)nanti/ôn schedo\n a(/pantes sugkei=sthai.]]

[Footnote 43: Aristot. Metaphys. A. 5, p. 986, a. 22. He goes on to say that Alkmæon, a semi-Pythagorean and a younger contemporary of Pythagoras himself, while agreeing in the general principle that "human affairs were generally in pairs," ([Greek: ei)=nai du/o ta\ polla\ tô=n a)nthrôpi/nôn]), laid down pairs of fundamental contraries at random ([Greek: ta\s e)nantio/têtas ta\s tuchou/sas])--black and white, sweet and bitter, good and evil, great and little. All that you can extract from these philosophers is (continues Aristotle) the general axiom, that "contraries are the principia of existing things"--[Greek: o(/ti ta)na/ntia a)rchai\ tô=n o)/ntôn].

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

[Footnote 44: Theophrast. Metaphys. 9. Probably the recognition of one dominant antithesis--[Greek: To\ E(/n--ê( a)o/ristos Dua\s]--is the form given by Plato to the Pythagorean doctrine. Eudorus (in Simplikius ad Aristot. Physic. fol. 39) seems to blend the two together.]

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,[45] 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,[46] which they seem to have diligently cultivated, we have not sufficient information to determine with certainty.

[Footnote 45: Aristot. Metaph. A. 5, p. 985, b. 23. [Greek: oi( Puthagorei=oi tô=n mathêma/tôn a)psa/menoi _prô=toi tau=ta proê/gagon_, kai\ e)ntraphe/ntes e)n au)toi=s ta\s tou/tôn a)rcha\s tô=n o)/ntôn a)rcha\s ô)|ê/thêsan ei)=nai pa/ntôn.]]

[Footnote 46: Concerning the Pythagorean doctrines on Harmonics, see Boeckh's Philolaus, p. 60-84, with his copious and learned comments.]

[Side-note: Eleatic philosophy--Xenophanes.]

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.[47] He composed, and recited in person, poems--epic, elegiac, and iambic--of which a very few fragments remain.

[Footnote 47: Karsten. Xenophanis Fragm., s. 4, p. 9, 10.]

[Side-note: His censures upon the received Theogony and religious rites.]

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."[48] Dissatisfied with much of the customary worship and festivals, Xenophanes repudiated divination** altogether, and condemned the extravagant respect shown to victors in Olympic contests,[49] 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.[50] 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.[51]

[Footnote 48: Xenophanis Fragm. 5-6-7, p. 39 seq. ed. Karsten; Clemens Alexandr. Strom. v. p. 601; vii. p. 711.]

[Footnote 49: Xenophan. Fragm. 19, p. 60, ed. Karsten; Cicero, Divinat. i. 3, 5.]

[Footnote 50: Xenophanis Fragment. 34-35, p. 85, ed. Karsten; Aristotel. Rhetoric. ii. 23; Metaphys. A. 5, p. 986, b. 19.]

[Footnote 51: Xenoph. Frag. 1-2, p. 35.

[Greek: Ou)=los o(ra=|, ou)=los de\ noei=, ou)=los de t' a)kou/ei.]

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

[Side-note: His doctrine of Pankosmism, or Pantheism--The whole Kosmos is Ens Unum or God--[Greek: E(\n kai\ Pa=n]. Non-Ens inadmissible.]

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."[52] 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.[53] Non-Ens he pronounced to be an absurdity--an inadmissible and unmeaning phrase.

[Footnote 52: Timon, fragment of the Silli ap. Sext. Empiric. Hypot. Pyrrh. i. 33, sect. 224.

[Greek: o)/ppê ga\r e)mo\n no/on ei)ru/saimi, ei)s e(\n tau)to/ te pa=n a)nelu/eto, pa=n de o)\n ai)ei\ pa/ntê a)nelko/menon mi/an ei)s phu/sin i)/stath' o(moi/an].

[Greek: Ai)ei\] here appears to be more conveniently construed with [Greek: i)/stath'] not (as Karsten construes it, p. 118) with [Greek: o)/n].

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

[Footnote 53: Theophrastus ap. Simplikium in Aristotel. Physic. f. 6, Karsten, p. 106; Arist. Met. A. 5, p. 986, b. 21: [Greek: Xenopha/nês de\ prô=tos tou/tôn e(ni/sas, o( ga\r Parmeni/dês tou/ton le/getai mathêtê/s,--eis to\n o(/lon ou)/ranon a)poble/psas to\ e(\n ei)=nai/ phêsi to\n theo/n.]]

[Side-note: Scepticism of Xenophanes--complaint of philosophy as unsatisfactory.]

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."[54]

[Footnote 54: Xenophan. Fragm. 14, p. 51, ed. Karsten.

[Greek: kai\ to\ me\n ou)=n saphe\s ou)/tis a)nê\r ge/net' ou)/de tis e)/stai ei)dô\s, a)mphi\ theô=n te kai\ a)/ssa le/gô peri\ pa/ntôn; ei) ga\r kai\ ta\ ma/lista tu/choi tetelesme/non ei)pô\n, au)to\s o(mô=s ou)k oi)=de; do/kos d' e)pi\ pa=si te/tuktai].

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.

[Side-note: His conjectures on physics and astronomy.]

Without attempting to define the figure of the Earth, he considered it to be of vast extent and of infinite depth;[55] 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.[56] He supposed that the sun, moon, and stars were condensations of vapours exhaled from the Earth, collected into clouds, and alternately inflamed and extinguished.[57]

[Footnote 55: Aristot. De Coelo, ii. 13.]

[Footnote 56: Xenophan. Fragm. p. 178, ed. Karsten; Achilles Tatius, [Greek: Ei)sagôgê\] in Arat. Phænom. p. 128, [Greek: ta\ ka/tô d' e)s a)/peiron i(ka/nei].

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.]

[Footnote 57: Xenophanes Frag. p. 161 seq., ed. Karsten. Compare Lucretius, v. 458.

"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."]

[Side-note: Parmenides continues the doctrine of Xenophanes--Ens Parmenideum, self-existent, eternal, unchangeable, extended,--Non-Ens, an unmeaning phrase.]

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.[58] 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.[59] Parmenides conceived Ens not simply as existent, but as self-existent, without beginning or end,[60] as extended, continuous, indivisible, and unchangeable. The Ens Parmenideum comprised the two notions of Extension and Duration:[61] 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.[62]

[Footnote 58: Parmenid. Fr. v. 29.]

[Footnote 59: Parm. Frag. v. 40, 52-56.

[Greek: to\ ga\r au)to\ noei=n e)sti/n te kai\ ei)=nai. A)lla\ su\ tê=s d' a)ph' o(dou= dizê/sios ei)=rge no/êma, mêde/ s' e)/thos polu/peiron o(do\n kata\ tê/nde bia/sthô, nôma=|n a)/skopon o)/mma kai\ ê)chê/essan a)kouê\n kai\ glô=ssan; kri=nai de\ lo/gô| polu/dênin e)/legchon e)x e)me/then rhêthe/nta.]]

[Footnote 60: Parm. Frag. v. 81.

[Greek: au)ta\r a)ki/nêton mega/lôn e)n pei/rasi desmô=n e)sti\n, a)/narchon, a)/pauston], &c.]

[Footnote 61: Zeller (Die Philosophie der Griech., i. p. 403, ed. 2) maintains, in my opinion justly, that the Ens Parmenideum is conceived by its author as extended. Strümpell (Geschichte der theor. Phil. der Griech., s. 44) represents it as unextended: but this view seems not reconcilable with the remaining fragments.]

[Footnote 62: Parm. Frag. v. 102.]

[Side-note: He recognises a region of opinion, phenomenal and relative, apart from Ens.]

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.[63] Nothing is really generated or destroyed, but only in appearance to us, or relatively to our apprehension.[64] In like manner we perceive plurality of objects, and divide objects into parts. But Ens is essentially One, and cannot be divided.[65] 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[66]) 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.

[Footnote 63: Parm. Frag. v. 96.

[Greek: ----e)pei\ to/ ge moi=r' e)pe/dêsen Oi)=on a)ki/nêton tele/thein tô=| pa/nt' o)/nom' _ei)=nai_, O)/ssa brotoi\ kate/thento, pepoitho/tes ei)=nai a)lêthê=, gi/gnesthai/ te kai\ o)/llusthai, ei)=nai/ te kai\ ou)ki\, kai\ to/pon a)lla/ssein, dia/ te chro/a phano\n a)mei/bein;