(Adhort. ad Philos. p. 324, ed. Kiessling.) In this way a multitude of the most absurd
fictions took their rise -- such as that Apollo was his father; that his person gleamed with
a supernatural brightness; that he exhibited a golden thigh; that Abaris came flying to him
on a golden arrow; that he was seen in different places at one and the same time. (Comp.
Met. 1.5. p. 986.
12, ed. Bekker.) His disciples Dicaearchus, Aristoxenus, and Heracleides Ponticus had written
on the same subject. These writers, late as they are, are among the best from whom Porphyrius
and Iamblichus drew: their chief sources besides being legends and their own invention. Hence
we are reduced to admit or reject their statements mainly from a consideration of their
inherent probability, and even in that point of view it is not enough to look at each
separately, for if all the separately credible narratives respecting Pythagoras were supposed
true, they would extend the sphere and amount of his activity to an utterly impossible
extent. (Krische, de Societatis a Pythagora conditae Scopo politico.
Praef.; Brandis, Geschichte des Griech. Röm. Philosophie, p. 440 ;
Grote, Hist. of Greece, vol. iv. p. 540.)
That Pythagoras was the son of Mnesarchus, who was either a merchant, or, according to
others, an engraver of signets (Busir. p. 227, ed. Steph.). Others
called him a Tyrrhenian or Phliasian, and gave Marmacus, or Demaratus, as the name of his
father (Diog. Laert. l.c. ; Porph. Vit. Pyth. 1, 2;
Justin, l.c. 100.9), Pythagoras quitted Samos in the reign
of Polycrates, at the age of 40. According to Iamblichus he was 57 years of age in Fasti Hellen. s. a.
It was natural that men should be eager to know, or ready to conjecture the sources whence
Pythagoras derived the materials which were worked up into his remarkable system. And as, in
such cases, in the absence of authentic information, the conjectures of one become the belief
of another, the result is, that it would be difficult to find a philosopher to whom such a
variety of teachers is assigned as to Pythagoras. Some make his training almost entirely
Grecian, others exclusively Egyptian and Oriental. We find mentioned as his instructors
Creophilus (Iambl. Vit. Pyth. 9), Hermodamas (Porph. 2., l.c.), Thales (ibid.), Anaximander (ibid. Porph. l.c.), and Pherecydes of Syros (Aristoxenus and others in de Div. 1.49). The
Egyptians are said to have taught him geometry, the Phoenicians arithmetic, the Chaldeans
astronomy, the Magians the formulae of religion and practical maxims for the conduct of life
(Porph. l.c. 6). Of the statements regarding his Greek instructors, that
about Pherecydes comes to us with the most respectable amount of attestation.
It was the current belief in antiquity, that Pythagoras had undertaken extensive travels,
and had visited not only Egypt, but Arabia, Phoenicia, l.c. 11, 12; Iambl. l.c. 14, &c.) The journey to Babylon is
possible, and not very unlikely. That Pythagoras visited Egypt, may be regarded as more than
probable. Enough of Egypt was known to attract the curiosity of an inquiring Greek, and the
intercourse of Samos as well as other parts of Greece with that country is mentioned. (Porph. 7; Isocr. Busir. p. 227; Cic. de Fin. 5.27; l.c. p. 5 ;
Ritter, Gesch. der Pythagorischen Philosophie, p. 27.) According to one
account, of no great authority, and mixed up with much that is absurd and incredible,
Polycrates gave Pythagoras a letter of introduction to Amasis. (Gesch. der
Philos. vol. i. p. 363.) Even the doctrine of metempsychosis involves nothing which
compels us to look to Egypt or the East for its origin. It is rather one of the most obvious
sensualistic modes in which the continued existence of the soul could be conceived.
Pythagoras might have derived it quite as easily from Pherecydes as from the Egyptians.
Greater stress might be laid upon some external observances, such as the refraining from
eating beans and fish, were it not that doubt exists even with regard to these. (Aristoxenus
denied the fact of the interdiction of beans; see Gellius, N. A. 4.11.)
Nor, in any case, would initiation by the Egyptian priests be necessary to account for it. In
short, no foreign influence can be traced, which in any way illustrates or accounts for
either the philosophy or the institutions of Pythagoras. These exhibit only what might easily
have been developed by a Greek mind exposed to the ordinary influences of the age. Even the
ancient authorities point to a similar result in connecting the religious and ascetic
peculiarities of Pythagoras with the Orphic or Cretan mysteries (Iambl.100.25; Porph. 100.17;
Neither as to the kind and amount of knowledge which Pythagoras acquired, nor as to his
definite philosophical views, have we much trustworthy direct evidence.
Every thing of the kind mentioned by Plato and Aristotle is attributed not to Pythagoras, but
to the Pythagoreans. We have, however, the testimony of Heracleitus (de Anima,
1.3; l.c. vol. iv. p. 528, note.) Pythagoras is
said to have pretended that he had been Euphorbus, the son of Panthus, in the Trojan war, as
well as various other characters, a tradesman, a courtezan, &c. (Porph. 26; Non posse suav. vivi sec. Ep. p. 1094). There is a celebrated story of his
having discovered the arithmetical relations of the musical scale by observing accidentally
the various sounds produced by hammers of different weights striking upon an anvil, and
suspending by strings weights equal to those of the different hammers (Porph. in Ptol. Harms. p. 213; Harm. 1.2, p. 10, Meib.). The retailers of the story of course never took the trouble
to verify the experiment, or they would have discovered that different hammers do not produce
different sounds from the same anvil, any more than different clappers do from the same bell.
Discoveries in astronomy are also attributed to Pythagoras (l.c. 20 ; Iambl. l.c. 31, 140; Aelian, de Divin. 1.3, 46; Porph. l.c. 29.)
"In his prominent vocation, analogous to that of Epimenides, Orpheus, or Melampus, he appears
as the revealer of a mode of life calculated to raise his disciples above the level of
mankind, and to recommend them to the favour of the gods." (Grote, vol. iv. p. 529.)
No certainty can be arrived at as to the length of time spent by Pythagoras in Egypt or the
East, or as to his residence and efforts in Samos or other Grecian cities, before his removal
to Italy. Ritter is inclined to believe from the expressions of Herodotus that the secret
cultus or orgies of Pythagoras had gained some footing in Greece or Ionia, even before
Crotona became the focus of his influence (Gesch. der Phil. vol. i. p.
364, Gesch. der Pyth. Phil. p. 31). In the visits to various places in
Greece--Delos, Sparta, Phlius, Crete, &c. which are ascribed to him, he appears commonly
either in his religious or priestly character, or else as a law-giver (Iambl. l.c. 25; Porph. l.c. 17; Diog. Laert, 8.3, 13; Cic.Tusc. Qu. 5.3).
It is in the highest degree probable that the reason why Pythagoras removed to Crotona is
to be found in the unfavourable condition of his native country, while under the tyranny of
Polycrates, for the realisation of his schemes. Later admirers were content to believe that,
from the high estimation in which he was held by his fellow-citizens, he was so overburdened
with public duties, as to have no time to bestow upon philosophy, and so withdrew from Samos
(Iambl. 28; Porph. 9). The reason why he selected Crotona as the sphere of his operations, it
is impossible to ascertain from any existing evidence. All that is adduced on this head by K.
O. Müller (Dorians, 3.9.17, vol. ii. p. 189, &c.) is mere
conjecture, and is of the most unsatisfactory kind. Grote (vol. iv. p. 538) supposes that the
celebrity of Crotona for the cultivation of the art of medicine may possibly have had some
influence with him. That on his arrival there he speedily attained extensive influence, and
gained over great numbers to enter into his views, is all that can safely be affirmed in the
midst of the marvellous stories told by later biographers of the effects of his eloquent
discourses in leading the Crotoniates to abandon their luxurious and corrupting manner of
life and devote themselves to that purer system which he came to introduce. (Porph. 18;
Iambl. 37, &c.) His adherents were chiefly of the noble and wealthy classes. Three
hundred of these were formed into a select brotherhood or club, bound by a sort of vow to
Pythagoras and each other, for the purpose of cultivating the religious and ascetic
observances enjoined by their master, and of studying his religious and philosophical
theories. The statement that they threw all their property into a common stock has not
sufficient evidence to support it, and was perhaps in the first instance only an inference
from certain Pythagorean maxims and practices (comp. Cic. de Leg. 1.12,
de Off. 1.7; l.c. p. 27, &c.; Ritter, l.c. p. 39). That there
were several women among the adherents of Pythagoras is pretty certain. That any were members
of the club of 300 is not so probable. Krische (l.c. p. 45) considers
that these female Pythagoreans were only the wives and relations of members of the
brotherhood, who were instructed in some of the Pythagorean doctrines. These would doubtless
be mainly those connected with the religious part of his system. (Comp. Menage, Hist. de Mul. Philos.)
With respect to the internal arrangements and discipline of this brotherhood only a few
leading features seem to rest upon a basis of evidence and probability sufficient to warrant
our bestowing any attention upon them. All accounts agree that what was done and taught among
the members was kept a profound secret towards all without its pale. But we are also told
that there were gradations among the members themselves. It was an old Pythagorean maxim,
that every thing was not to be told to every body (Iamb. 31, l.c.), or Acustici, Mathematici, and
Physici (Gell. N. A. 1.9). Most of these divisions, however, presuppose
a more marked separation between the different branches of human knowledge, or between
philosophical training and political activity, than existed at that time. In the admission of
candidates Pythagoras is said to have placed great reliance on his physiognomical discernment
(Gell. l.c.). If admitted, they had to pass through a period of
probation, in which their powers of maintaining silence (Iambl. 94). That they had to maintain
silence for five years, and during the whole of that period were never allowed to behold the
face of Pythagoras, while they were from time to time exposed to various severe ordeals
(Iambl. 68), are doubtless the exaggerations of a later age. There is more probability in the
statement (Taurus, apud Gell. 1.9) that the period of noviciate varied
according to the aptitude which the candidates manifested for the Pythagorean discipline. As
regards the nature of the esoteric instruction to which only the most approved members of the
fraternity were admitted, some (e. g. Meiners, Gesch. der
Wissenschaften) have supposed that it had reference to the political views of
Pythagoras. Ritter (l.c. p. 47, &c.), with greater probability,
holds that it had reference mainly to the orgies, or secret religious
doctrines and usages, which undoubtedly formed a prominent feature in the Pythagorean system,
and were peculiarly connected with the worship of Apollo (Aelian, l.c. p. 37; Brandis, l.c. p. 432; Müller, Dorians, 3.9.17). The admission of women to Rhet. 1.14.2; Sext. Emp. 9.127. This was also one of the Orphic
precepts, de Esu Carn. pp. 993, 996, 997). It is, however, pointed out by Grote (vol.
iv. p. 533), that all the members cannot have been subjected to this prohibition ; Milo, for
instance, could not possibly have dispensed with animal food. The best authorities contradict
the statement. According to Ariston (ap. de Abst. 1.26 ; Iambl. 98). But temperance of
all kinds seems to have been strictly enjoined. It is also stated that they had common meals,
resembling the Spartan syssitia, at which they met in companies of ten (Iambl. 98; V.H. 14.18; Iambl. 197;
comp. Krische, l.c. p. 42). Iamblichus (96-101, apparently on the
authority of Aristoxenus) gives a long description of the daily routine of the members, which
suggests many points of comparison with the ordinary life of Spartan citizens. It is not
unlikely that many of the regulations of Pythagoras were suggested by what he saw in Crete
and Sparta. Among the best ascertained features of the brotherhood are the devoted attachment
of the members to each other, and their sovereign contempt for those who did not belong to
their ranks (Ariston. apud Iambl. 94, 101, &c., 229, &c.; comp.
the story of Damon and Phintias; Porph. 60; Iambl. 233, &c.). It appears that they had
some secret conventional symbols, by which members of the fraternity could recognise each
other, even if they had never met before (Schol. ad Arist. Nub. 611;
Iambl. 237, 238; Krische, pp. 43, 44). Clubs similar to that at Crotona were established at
Sybaris, Metapontum, Tarentum, and other cities of Magna Graecia.
The institutions of Pythagoras were certainly not intended to withdraw those who adopted
them from active exertion and social and political connections, that they might devote
themselves exclusively to religious and philosophical contemplations. Rather he aimed at the
production of a calm bearing and elevated tone of character, through which those trained in
the discipline of the Pythagorean life should exhibit in their personal and social capacities
a reflection of the order and harmony of the universe. But the question whether he had any
distinct political designs in the foundation of his brotherhood, has been variously answered.
It was perfectly natural, even without any express design on his part, that a club such as
the Three Hundred of Crotona should gradually come to mingle political with other objects,
and by the facilities afforded by their secret and compact organisation should speedily gain
extensive political influence, which, moreover, the political condition of Crotona, where the
aristocracy was with difficulty holding its ground, rendered more than usually easy. That
this influence should be decisively on the side of aristocracy or oligarchy, resulted
naturally both from the nature of the Pythagorean institutions, and from the rank and social
position of the members of the brotherhood. Through them, of course, Pythagoras himself
exercised a large amount of indirect influence over the affairs both of Crotona and of other
Italian cities. It does not appear however that he ever held any official rank, though we are
told that the senate urged him to accept the office of Prytanis. But we have no evidence that
the objects of Pythagoras were (as Krische, Müller, and others believe) from the first
predominantly political, or even that he had any definite political designs at all in the
formation of his club. That he intended to exhibit in Crotona the model of a pure Dorian
aristocracy (Müller, Dorians, 3.9.16), is a mere fancy (comp.
Grote, vol. iv. p. 545, note). It is true that the club was in practice at once "a
philosophical school, a religious brotherhood, and a political association" (Thirlwall, Hist. of Greece, vol. ii. p. 148), but there is nothing to show that "all
these characters appear to have been inseparably united in the founder's mind." Mr. Grote,
more in accordance with the earliest and best authority on the subject (Plato, de Rep. x. p. 600, comp. de Leg. vi. p. 782, who
contrasts Pythagoras, as the institutor of a peculiar mode of private life, with those who
exercised a direct influence upon public life), remarks, "We cannot construe the scheme of
Pythagoras as going farther than the formation of a private, select order of brethren,
embracing his religious fancies, ethical tone, and germs of scientific idea, and manifesting
adhesion by those observances which Herodotus and Plato call the Pythagorean orgies and mode
of life. And his private order became politically powerful because he was skilful or
fortunate enough to enlist a sufficient number of wealthy Crotoniates, possessing individual
influence, which they strengthened immensely by thus regimenting themselves in intimate
union" (Hist. of Greece, vol. iv. p. 544). The notion of Müller and
Niebuhr, that the 300 Pythagoreans constituted a kind of smaller senate at Crotona, is
totally without foundation. On the other hand, it seems quite as unfounded to infer from the
account that Pythagoras was the first to apply to himself the epithet Tusc. 5.3; life, and its analogy Aglaophamus, Orphica, lib.
ii. pp. 247, 698, 900. The resemblance in many respects of the Pythagorean brotherhood or
order to that founded by Loyola has been more than once pointed out.
It is easy to understand how this aristocratical and exclusive club would excite the
jealousy and hostility not only of the democratical party in Crotona, but also of a
considerable number of the opposite faction. The hatred which they had excited speedily led
to their destruction. The circumstances attending this event are, however, involved in some
uncertainty. In the hostilities which broke out between Sybaris and Crotona on the occasion
of the refusal of the Crotoniates (to which, it is said, they had been urged by Pythagoras)
to surrender some exiles of Sybaris, the forces of Crotona were headed by the Pythagorean
Milo [MILO]; and the other members of the brotherhood doubtless
took a prominent part. The decisive victory of the Crotoniates seems to have elated the
Pythagoreans beyond measure. A proposal (occasioned, according to the statement in
iAMBLICHUS, 100.255, by a refusal on the part of the senate to distribute among the people
the newly conquered territory of Sybaris; though this account involves considerable
difficulty; see Grote, l.c. c. p. 549) for establishing a more
democratical constitution, was unsuccessfully resisted by the Pythagoreans. Their enemies,
headed by Cylon and Ninon, the former of whom is said to have been irritated by his exclusion
from the brotherhood, excited the populace against them. An attack was made upon them while
assembled either in the house of Milo, or in some other place of meeting. The building was
set on fire, and many of the assembled members perished; only the younger and more active
escaping (Iambl. 255-259 ; Porph. 54-57; de Gen. Socr. p. 583).
Similar commotions ensued in the other cities of Magna Graecia in which Pythagorean clubs had
been formed, and kept them for a considerable time in a state of great disquietude, which was
at length pacified by the mediation of the Peloponnesian Achaeans (LYSIS; PHILOLAUS]. Still the Pythagoreans continued to exist as a sect, the members of which
kept up among themselves their religious observances and scientific pursuits, while
individuals, as in the case of Archytas, acquired now and then great political influence.
Respecting the fate of Pythagoras himself, the accounts varied. Some say that he perished in
the temple with his disciples (Arnob. ad v. Genes, i. p. 23), others
that he fled first to Tarentum, and that, being driven thence, he escaped to Metapontum, and
there starved himself to death (de Stoic. Rep. 37). His toinb
was shown at Metapontum in the time of Cicero (Cic. de Fin. 5.2).
According to some accounts Pythagoras married Theano, a lady of Crotona, and had a daughter
Damo, and a son Telauges; others say two daughters, Damo and Myia; but other notices seem to
imply that he had a wife and a daughter grown up, when he came to Crotona. (Bibl. Graec. vol. i. p.
772.)
For a considerable time after the breaking up of the clubs at Crotona and elsewhere great
obscurity hangs over the history of the Pythagoreans. No reliance can be placed on the lists
of them which later writers have given, as they have been amplified, partly through mere
invention, partly through a confusion between Pythagoreans and Italian philosophers
generally. The writings, or fragments of writings, which have come down to us under the names
of Archytas, Timaeus, Ocellus, Brontinus, &c., have been shown to be spurious.
Pythagorism seems to have established itself by degrees more and more in different parts of
Greece. About the time of Socrates, and a little later, we get some trustworthy notices of
Philolaus, Lysis, Cleinias, Eurytus, and Archytas. These men, and others who applied
themselves to the development of the Pythagorean philosophy, were widely different from the
so-called Pythagoreans of a later aee (from the time of Cicero onwards), who were
characterised by little except an exaggeration of the religious and ascetic fanaticism of the
Pythagorean system [APOLLONIUS TYANAEUS]. This Neo-Pythagorism was
gradually merged in the kindred mysticism of the Neo-Platonists.
When we come to inquire what were the philosophical or religious opinions held by
Pythagoras himself, we are met at the outset by the difficulty that even the authors from
whom we have to draw possessed no authentic records bearing upon the subject of the age of
Pythagoras himself. If Pythagoras ever wrote any thing, his writings perished with him, or
not long after. The probability is that he wrote nothing. (Comp. Plut. de
Alex. fort. p. 329; Porph. l.c. 57; Galen, de
Hipp. et Plat. Plac. 5.6.) The statements to the contrary prove worthless on
examination. Every thing current under his name in antiquity was spurious. (See Fabric. Bibl. Graec. vol. i. pp. 779-805; Ritter, Gesch. der Pyth.
Phil. p. 56.) It is all but certain that Philolaus was the first who published the Pythagorean doctrines, at any rate in a written form [PHILOLAUS]. Still there was so marked a peculiarity running through
the Pythagorean philosophy, by whomsoever of its adherents it was developed, and so much of
uniformitycan be traced at the basis even of the diversities which present themselves' here
and there in the views expressed by different Pythagoreans, as they have come down to us from
authentic sources, that there can be little question as to the germs of the system at any
rate having been derived from Pythagoras himself. (Brandis, l.c. p.
442.) The Pythagoreans seem to have striven in the main to keep their doctrine uncorrupted.
We even hear of members being expelled from the brotherhood for philosophical or other
heterodoxy; and a distinction was already drawn in antiquity between genuine and spurious
Pythagorism (Iambl. 81; Villois. Anecd. ii. p. 216;
Syrian. in Arist. Met. xii. fol. 71, b., 85, b.; Simplic. in Arist. Phys. fol. 104, b. ; Stob. Ecl. Phys. i. pp.
308, 448, 496). Aristotle manifestly regarded the Pythagorean philosophy as something which
in its leading features characterised the school generally. He found it, however, after it
had passed through a considerable period of development, in the hands of adherents of varying
tendencies. It was to be expected therefore that varieties should make their appearance
(comp. Arist. de Caelo, 3.1, at the end, with Met.
1.6). Nearly every thing that can be in any degree depended l.c. p. 62, &c.). On the philosophy of Archytas Aristotle had composed
a treatise in three books, which has unfortunately perished, and had instituted a comparison
between his doctrines and those of the Timaeus of Plato (
Pythagoras resembled greatly the philosophers of what is termed the Ionic school, who
undertook to solve by means of a single primordial principle the vague problem of the origin
and constitution of the universe as a whole. But, like Anaximander, he abandoned the physical
hypotheses of Thales and Anaximenes, and passed from the province of physics to that of
metaphysics, and his predilection for mathematical studies led him to trace the origin of all
things to number, this theory being suggested, or at all events
confirmed, by the observation of various numerical relations, or analogies to them, in the
phenomena of the universe. "Since of all things numbers are by nature the first, in numbers
they (the Pythagoreans) thought they perceived many analogies to things that exist and are
produced, more than in fire, and earth, and water; as that a certain affection of numbers was
justice; a certain other affection, soul and intellect ; another, opportunity; and of the
rest, so to say, each in like manner; and moreover, seeing the affections and ratios of what
pertains to harmony to consist in numbers, since other things seemed in their entire nature
to be formed in the likeness of numbers, and in all nature numbers are the first, they
supposed the elements of numbers to be the elements of all things" (Arist. Met. 1.5, comp. especially Met. 13.3). Brandis, who traces in the
notices that remain more than one system, developed by different Pythagoreans, according as
they recognised in numbers the inherent basis of things, or only the patterns of them,
considers that all started from the common conviction that it was in numbers and their
relations that they were to find the absolutely certain principles of knowledge (comp.
Philolaus, ap. Stob. Ecl. Phys. i. p. 458; Böckh, Philolaos, p. 62; Stob. l.c. i. p. 10 ; Böckh, l.c. p. 145, ad
v. Math. 7.92; Brandis, l.c. p. 442). Aristotle states the
fundamental maxim of the Pythagoreans in various forms, as, Met. 1.5); or,
Met. 1.6. p. 987. 24); nay, even that
numbers are things themselves (Ibid. p. 987. 28). According to Philolaus (Syrian. in Arist. Met. 12.6. p. 1080b. 16), is the "dominant and self-produced bond
of the eternal continuance of things." But number has two forms (as Philolaus terms them, ap.
Stob. l.c. p. 456; Böckh, l.c. p. 58), or
elements (Arist. Met. 1.5), the even and the odd, and a third, resulting
from the mixture of the two, the even-odd (l.c.) This third species is one itself, for it is both even and odd (Arist. l.c.
Another explanation of the l.c. p. 465, &c.). One, or unity, is
the essence of number, or absolute number, and so comprises these two opposite species. As
absolute number it is the origin of all numbers, and so of all things. (Arist. Met. 13.4. Gesch. der Phil. vol. i. p. 389).
These propositions, however, would, taken alone, give but a very partial idea of the
Pythagorean system. A most important part is played in it by the ideas of limit, and the unlimited. They are, in fact, the fundamental
ideas of the whole. One of the first declarations in the work of Philolaus [PHILOLAUS] was, that all things in the universe result from a
combination of the unlimited and the limiting (l.c. ;
Böckh, p. 49). From the unlimited were deduced immediately time, space, and motion
(Stob. Ecl.
Phys. p. 380; Simplic. in Arist. Phys. f. 98, b. ;
Brandis, l.c. p. 451). Then again, in some extraordinary manner they
connected the ideas of odd and even with the contrasted notions of the limited and the
unlimited, the odd being limited, the even unlimited (Arist. Met. 1.5,
p. 986a. 18, Bekker, comp. Phys. Ausc. 3.4, p. 203. 10, Bekker). They
called the even unlimited, because in itself it is divisible into equal halves ad infinitum,
and is only limited by the odd, which, when added to the even, prevents the division (Simpl.
ad Arist. Phys. Ausc. 3.4, f. 105; Brandis, p. 450, note). Limit, or
the limiting elements, they considered as more akin to the primary unity (Syrian. in Arist. Met. 13.1). In place of the plural expression of Philolaus
(Met. 1.8, p.
990, 1. 8, 13.3. p. 1091, 50.18, ed. Bekk.).
But musical principles played almost as important a part in the Pythagorean system as
mathematical or numerical ideas. The opposite principia of the unlimited and the limiting
are, as Philolaus expresses it (Stob. l.c. p. 458; Böckh, l.c. p. 62), "neither alike, nor of the same race, and so it would have
been impossible for them to unite, had not harmony stepped in." This harmony, again, was, in
the conception of Philolaus, neither more nor less than the octave (Brandis, l.c. p. 456). On the investigation of the various harmonical nical relations of the
octave, and their connection with weight, as the measure of tension, Philolaus bestowed
considerable attention, and some important fragments of his on this subject have been
prenumber served, which Böckh has carefully examined (l. c, p.
65-89, comp. Brandis, l.c. p. 457, &c.). We find running through the
entire Pythagorean system the idea that order, or harmony of relation, is the elements of the universe. (Arist. Met. 1.5. Elsewhere he speaks
as if the Pythagoreans generally did the same, Eth. Nic. 1.4, 2.5.)
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. 1.4);
the second, the row of the bad. Those in the second series were also regarded as having the
character of negation (Arist. Phys. 3.2). 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 synonymous (comp. Arist. Met. 1.5, 7, 13.4, Phys. 3.5).
To explain the production of material objects out of the 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 de Caelo, 3.1; comp. Alexand. Aphrod. quoted below),
the point being the in Arist. de prim. Phil. i. fol. 10, b.; Ritter, l.c. p. 404, note 3.) 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. Ecl. Phys. p. 308.) Two
geometrical points in themselves 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 explain very
well how corporeal substance is formed, and Ritter thinks that the
Pythagoreans perceived that this was the weak point of their system, and so spoke of the
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 which Ritter sets down
as that of the Pythagoreans is one which Aristotle mentions several times, and shows to be
inadequate to account 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,
3.1, after an elaborate discussion of the theory in question, 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 produce either body or weight (comp. Met.
13.3). Aristotle nowhere identifies the Pythagorean monads 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 (Mct. 12.6, p. 1080,
ed. Bekker). The Eel.
Phys. i. p. 380) that from the
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 metaphysics. He supposed "a primaeval principle without any actual determining
qualities whatever ; but including all qualities potentially, and manifesting 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 contrary to
each other-a primaeval something, whose essence it was to be eternally productive of
different phaenomena" (Grote, l.c. p. 518; comp. Brandis, l.c. p. 123, &c.). This he termed the Phys. fol. 6,
32). Both these terms hold a prominent position in the Pythagorean system, and we think there
can be but little doubt as to their parentage. The Pythagorean 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 determination of its
indefiniteness by the definiteness of number, which thus became the cause of all actual and positive existence (Met. 1.6). 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
qualitative definiteness in existing things, therefore, number is represented as their
inherent element, or even as the matter (Met. 1.5). But
both the Met. 12.6, 1.6, p. 987b. 22); the divine unity being the first principle and cause, and one, as the first of the limiting numbers and the element of all, being the basis of
positive existence, and when itself become possessed of extension (Met.
12.3, p. 1091a. 15) the element of all that possesses extension (comp. Brandis, l.c. p. 511, &c.). In its development, however, the Pythagorean system
seems to have taken a twofold direction, one school of Pythagoreans regarding numbers as the
inherent, fundamental elements of things (Arist. de Caelo, 3.1); another
section, of which Hippasus seems to have been the head, regarding numbers as the patterns
merely, but not as entering into the essence of things (Arist. Met. 1.6.
Though Aristotle speaks of the Pythagoreans generally here, there can be no doubt that the
assertion, in which the Greek commentators found a difficulty, should be restricted to a
section of the Pythagoreans. Comp. Iambl. in Nicom. Arithm. p. 11;
Syrian. in Arist. Met. xii. p. 1080b. 18; Simplic. in
Phys. f. 104, b.; Iambl. Pyth. 81; Stob. Ecl.
Phys. p. 302; Brandis, l.c. p. 444).
As in the octave and its different harmonical relations, the Pythagoreans found the ground
of connection between the opposed primary elements, and the mutual relations of existing
things, so in the properties of particular numbers, and their relation to the principia, did
they attempt to find the explanation of the particular properties of different things, and
therefore addressed themselves to the investigation of the properties of numbers, dividing
them into various species. Thus they had three kinds of even, according
as the number was a power of two (Arithm. 1.7, 8). In like manner they had three
kinds of odd. It was probably the use of the decimal system of notation
which led to the number ten being supposed to be possessed of
extraordinary powers. "One must contemplate the works and essential nature of number
according to the power which is in the number ten; for it is great, and perfect, and
all-working, and the first principle (Ed. Phys.
p. 8; Böckh, p. 139.) This, doubtless, had to do with the formation of the list of ten pairs of opposite principles, which was drawn out by some Pythagoreans
(Arist. Met. 1.5). In like manner the tetractys
(possibly the sum of the first four numbers, or 10) was described as containing the source
and root of ever-flowing nature (Carm. Aur. 1. 48). The number three was spoken of as defining or limiting the universe and all things,
having end, middle, and beginning, and so being the number of the whole
(Arist. de Caelo, 1.1). This part of their system they seem to have
helped out by considerations as to the connection of numbers with lines, surfaces, and
solids, especially the regular geometrical figures (Theolog. Arithm. 10,
p. 61, &c.), and to have connected the relations of things with various geometrical
relations, among which angles played an important part. Thus, according to Philolaus, the
angle of a triangle was consecrated to four deities, Kronos, Hades, Pan, and Dionysus; the
angle of a square to Rhea, Demeter, and Hestia; the angle of a dodecagon to Zeus ; apparently
to shadow forth the sphere of their operations (Procl. in Euclid. Elern.
i. p. 36 ; Böckh, l.c. p. 152, &c.). As we learn that he
connected solid extension with the number four (Theol.
Arithm. p. 56), it is not unlikely that, as others did (Nicom. Arithm. 2.6), he connected the number one with a point, two with a line, three with a surface (five he appropriated
quality and colour; to six life; to seven
intelligence, health, and light; to eight love, friendship,
understanding, insight (Theol. Arithin. l.c.). Others connected
marriage, justice, &c. with different numbers (Alex. Aphr. in Arist.
Met. 1.5, 13). Guided by similar fanciful analogies they assumed the existence of five elements, connected with geometrical figures, the cube being earth;
the pyramid, fire; the octaedron, air; the eikosaedron, water; the dodecaedron, the fifth
element, to which Philolaus gives the curious appellation of l.c. i. p. 10; Böckh, l.c. p. 161; comp. Plut. de Plac. Phil. 2.6).
In the Pythagorean system the element fire was the most dignified and
important. It accordingly occupied the most honourable position in the universe -- the
extreme (extreme they understood both the centre and the remotest region
(de Caelo, 2.13). The central fire Philolaus terms the hearth of the
universe, the house or watch-tower of Zeus, the mother of the gods, the altar and bond and
measure of nature (Stob. l.c. p. 488; Böckh, l.c. p. 94, &c.). It was the enlivening principle of the universe. By this fire
they probably understood something purer and more ethereal than the common element fire
(Brandis, l.c. p. 491). Round this central fire the heavenly bodies
performed their circling dance (counter-earth (l.c. p.
476). The space between the heaven of the fixed stars and the moon was termed l.c.). Philolaus assumed a
daily revolution of the earth round the central fire, but not round its own axis. The
revolution of the earth round its axis was taught (after Hicetas of Syracuse; see Plac. 3.13; Procl. in Tim. p. 281 )
: a combined motion round the central fire and round its own axis, by Aristarchus of Samos
(Plut. de Fac. Lun. p. 933). The infinite (in Phys. f. 108), not void space, but corporeal. The physical existence
of the universe, which in the view of the Pythagoreans was a huge sphere (Stob. l.c. p. 452, 468), was represented as a sort of vital process, time, space,
and breath (inhaled out of the l.c. p. 380; see Phys. Ausc. 4.6; Brandis, l.c. p. 476).
The intervals between the heavenly bodies were supposed to be determined according to the
laws and relations of musical harmony (Nicom. Harm. i. p. 6, 2.33; de Caelo
Schol. p. 496b. 9, 497. 11). Hence arose the celebrated doctrine of the harmony of the
spheres; for the heavenly bodies in their motion could not but occasion a certain sound or
note, depending on their distances and velocities; and as these were determined by the laws
of harmonical intervals, the notes altogether formed a regular musical scale or harmony. This
harmony, however, we do not hear, either because we have been accustomed to it from the
first, and have never had an opportunity of contrasting it with stillness, or because the
sound is so powerful as to exceed our capacities for hearing (Arist. de
Caelo, 2.9; Porph. in Harm. Ptol. 4. p. 257). With all this
fanciful hypothesis, however, they do not seem to have neglected the observation of
astronomical phaenomena (Brandis, l.c. p. 481).
Perfection they seemed to have considered to exist in direct ratio to the distance from the
central fire. Thus the moon was supposed to be inhabited by more perfect and beautiful beings
than the earth (Plut. de Plac. Phil. 2.30; Stob. l.c. i. p. 562; Böckh, l.c. p. 131). Similarly imperfect
virtue belongs to the region of the earth, perfect wisdom to the Met. 1.8; Alex. Aphrod. in
Arist. Met. 1.7, fol. 14, a.). The light and heat of the central fire are received by
us mediately through the sun (which, according to Philolaus, is of a glassy nature, acting as
a kind of lens, or sieve, as he terms it, Böckh, l.c. p. 124; Stob.
l.c. 1.26 ; Euseb. Praep. Evang. 15.23), and the
other heavenly bodies. All things partake of life, of which Philolaus distinguishes four
grades, united in man and connected with successive parts of the body, -- the life of mere
seminal production, which is common to all things; vegetable life; animal life; and intellect
or reason (Theol. Arithm. 4, p. 22; Böckh, p. 159.) It was only in
reference to the principia, and not absolutely in point of time, that the universe is a production ; the development of its existence, which was perhaps regarded
as an unintermitting process, commencing from the centre (Phil. ap. Stob. l.c. p. 360; Böckh, p. 90, &c. ; Brandis, p. 483); for. the universe is
"imperishable and unwearied; it subsists for ever; from eternity did it exist and to eternity
does it last, one, controlled by one akin to it, the mightiest and the highest." (Phil. ap.
Stob. Ecl. Phys. p. 418, &c. ; Böckh, p. 164, &c.) This
Deity Philolaus elsewhere also speaks of as one, eternal, abiding, unmoved, like himself
(Bockh, p. 151 ). He is described as having established both limit and the infinite, and was
'often spoken of as the absolute unity; always represented as pervading, though distinct
from, and presiding over the universe : not therefore a mere germ of vital development, or a
principium of which the universe was itself a manifestation or development; sometimes termed
the absolute good (Arist. Met. 13.4, p. 1091b. 13, Bekker), while,
according to others, good could belong only to concrete existences (Met.
11.7, p. 1072b. 31). The origin of evil was to be looked for not in the deity, but in matter,
which prevented the deity from conducting every thing to the best end (Theophr. Met. 9. p. 322, 14). With the popular superstition they do not seem to have
interfered, except in so far as they may have reduced the objects of it, as well as all other
existing beings, to numerical elements. (Plut. de Is. et Os. 10; Arist.
Met. 13.5.) It is not clear whether the all-pervading soul of the
universe, which they spoke of, was regarded as identical with the Deity or not (Cic. de Nat. Deor. 1.11). It was perhaps nothing more than the ever-working
energy of the Deity (Stob. p. 422; Brandis, p. 487, note n). It was from
it that human souls were derived (Cic. de Nat. Deor. 1.11, de Sen. 21). The soul was also frequently described as a number or harmony
(Plut. de Plac. 4.2; Stob. Ecl. Phys. p. 862 ;
Arist. de An. 1.2, 4); hardly, however, in the same sense as that
unfolded by Simmias, who had heard Philolaus, in the Phaedo of Plato (p. 85, &c.), with
which the doctrine of metempsychosis would have been totally inconsistent. Some held the
curious idea, that the particles floating as motes in the sunbeams were souls (Arist. de An. 1.2). In so far as the soul was a principle of life, it was supposed
to partake of the nature of the central fire (Theol. Arith. p. 22;
Böckh, p. 149; Tusc. 4.5), comes to much the same point. Even
animals, however, have a germ of reason, only the defective organisation of their body, and
their want of language, prevents its development (Plut. de Plac. 5.20).
The Pythagoreans connected the five senses with their five elements (Theol.
Arith. p. 27; Stob. l.c. p. 1104). In the senses the soul found
the necessary instruments for its activity; though the certainty of knowledge was derived
exclusively from number and its relations. (Stob. p. 8; Sext. Emp. ad v.
Math. 7.92.)
The ethics of the Pythagoreans consisted more in ascetic practice, and maxims for the
restraint of the passions, especially of anger, and the cultivation of the power of
endurance, than in scientific theory. What of the latter they had was, as might be expected,
intimately connected with their number-theory (Arist. Eth. Magn. 1.1,
Eth. Nic. 1.4, 2.5). The contemplation of what belonged to the pure and
elevated region termed wisdom, which was superior to virtue, the latter having to do
only with the inferior, sublunary region (Philol. ap. Stob. Ecl. Phys.
pp. 490, 488). Happiness consisted in the science of the perfection of the virtues of the
soul, or in the perfect science of numbers (Serm. xi. p. 165). Likeness to the
Deity was to be the object of all our endeavours (Stob. Eel. Eth. p.
64), man becoming better as he approaches the gods, who are the guardians and guides of men
(Plut. de Def. Or. p. 413; Plat. Phacd. p. 62, with
Heindorf's note), exercising a direct influence upon them, guiding the mind or reason, as
well as influencing external circumstances Ecl.
Phys. p. 206; Eth. Eud. 2.8); man's soul being a
possession of the gods, confined at present, by way of chastisement, in the body, as a
species of prison, from which he has no right to free himself by suicide (Plat. Phaed. p. 61; Cic. de Sen. 20). With the idea of
divine influence was closely connected that of the influence of daemons and heroes (de Is. et Os. p. 384;
Porph. Vit. Pyth. 30; Iambl. 64). Self-examination was strongly insisted
on (Cic. de Sen. 11). Virtue was regarded as a kind of harmony or health
of the soul (l.c.
p. 498, note 9). The transmigration of souls was viewed apparently in the light of a process
of purification. Souls under the dominion of sensuality either passed into the bodies of
animals, or, if incurable, were thrust down into Tartarus, to meet with expiation, or condign
punishment. The pure were exalted to higher modes of life, and at last attained to
incorporeal existence (Arist. de An. 1.2, 3; Aglaoph.
p. 893. What we find in Plato, Phaedr. p. 248b., and in Pindar, Thren. fr. 4, Olymp. 2.68, is probably in the main
Pythagorean). As regards the fruits of this system of training or belief, it is interesting
to remark, that wherever we have notices of distinguished Pythagoreans, we usually hear of
them as men of great uprightness, conscientiousness, and self-restraint, and as capable of
devoted and enduring friendship. [See ARCHYTAS; CLEINIAS; DAMON; PHINTIAS.]
For some account of the very extensive literature connected with Pythagoras, &c., the
reader is referred to Fabric. Bibl. Graec. vol. i. pp. 750-804. The
best of the modern authorities have been already repeatedly referred to.
Other figures named Pythagoras: Besides a Samian pugilist of the name of Pythagoras, who
gained a victory in Ol. 48, and who has been frequently identified with the philosopher,
Fabricius (l.c. p. 776, &c.) enumerates about twenty more
individuals of the same name, who are, however, not worth inserting.