This is the whole of the Pythagorean philosophy taken generally. We now

have to come to closer quarters, and to consider the determinations,

or universal significance. In the Pythagorean system numbers seem

partly to be themselves allied to categories—that is, to be at

once the thought-determinations of unity, of opposition and of the

unity of these two moments. In part, the Pythagoreans from the

very first gave forth universal ideal determinations of numbers as

principles, and recognized, as Aristotle remarks (Metaph. I. 5), as

the absolute principles of things, not so much immediate numbers in

their arithmetic differences, as the principles of number, _i.e._ their

rational differences. The first determination is unity generally, the

next duality or opposition. It is most important to trace back the

infinitely manifold nature of the forms and determinations of finality

to their universal thoughts as the most simple principles of all

determination. These are not differences of one thing from another,

but universal and essential differences within themselves. Empirical

objects distinguish themselves by outward form; this piece of paper

can be distinguished from another, shades are different in colour,

men are separated by differences of temperament and individuality.

But these determinations are not essential differences; they are

certainly essential for the definite particularity of the things,

but the whole particularity defined is not an existence which is in

and for itself essential, for it is the universal alone which is the

self-contained and the substantial. Pythagoras began to seek these

first determinations of unity, multiplicity, opposition, &c. With him

they are for the most part numbers; but the Pythagoreans did not remain

content with this, for they gave them the more concrete determinations,

which really belong to their successors. Necessary progression and

proof are not to be sought for here; comprehension, the development

of duality out of unity are wanting. Universal determinations are

only found and established in a quite dogmatic form, and hence the

determinations are dry, destitute of process or dialectic, and

stationary.

a. The Pythagoreans say that the first simple Notion is unity

(_μονάς_); not the discrete, multifarious, arithmetic one, but identity

as continuity and positivity, the entirely universal essence. They

further say, according to Sextus (adv. Math. X. 260, 261): “All

numbers come under the Notion of the one; for duality is one duality

and triplicity is equally a ‘one,’ but the number ten is the one chief

number. This moved Pythagoras to assert unity to be the principle of

things, because, through partaking of it, each is called one.” That

is to say, the pure contemplation of the implicit being of a thing

is the one, the being like self; to all else it is not implicit,

but a relationship to what is other. Things, however, are much more

determined than being merely this dry “one.” The Pythagoreans have

expressed this remarkable relationship of the entirely abstract one

to the concrete existence of things through “simulation” (_μίμησις_).

The same difficulty which they here encounter is also found in Plato’s

Ideas; since they stand over against the concrete as species, the

relation of concrete to universal is naturally an important point.

Aristotle (Metaph. I. 6) ascribes the expression “participation”

(_μέθεξις_) to Plato, who took it in place of the Pythagorean

expression “simulation.” Simulation is a figurative, childish way of

putting the relationship; participation is undoubtedly more definite.

But Aristotle says, with justice, that both are insufficient; that

Plato has not here arrived at any further development, but has only

substituted another name. “To say that ideas are prototypes and that

other things participate in them is empty talk and a poetic metaphor;

for what is the active principle that looks upon the ideas?” (Metaph.

I. 9). Simulation and participation are nothing more than other names

for relation; to give names is easy, but it is another thing to

comprehend.

b. What comes next is the opposition, the duality (_δυάς_), the

distinction, the particular; such determinations have value even now in

Philosophy; Pythagoras merely brought them first to consciousness. Now,

as this unity relates to multiplicity, or this being-like-self to being

another, different applications are possible, and the Pythagoreans

have expressed themselves variously as to the forms which this first

opposition takes.

(_α_) They said, according to Aristotle (Metaph. I. 5): “The elements

of number are the even and the odd; the latter is the finite” (or

principle of limitation) “and the former is the infinite; thus the

unity proceeds from both and out of this again comes number.” The

elements of immediate number are not yet themselves numbers: the

opposition of these elements first appears in arithmetical form rather

than as thought. But the one is as yet no number, because as yet it is

not quantity; unity and quantity belong to number. Theon of Smyrna[42]

says: “Aristotle gives, in his writings on the Pythagoreans, the reason

why, in their view, the one partakes of the nature of even and odd;

that is, one, posited as even, makes odd; as odd, it makes even. This

is what it could not do unless it partook of both natures, for which

reason they also called the one, even-odd” (_ἀρτιοπέριττον_).

(_β_) If we follow the absolute Idea in this first mode, the opposition

will also be called the undetermined duality (_ἀόριστος δυάς_). Sextus

speaks more definitely (adv. Math. X. 261, 262) as follows: “Unity,

thought of in its identity with itself (_κατ̓ αὐτότητα ἑαυτῆς_), is

unity; if this adds itself to itself as something different (_καθ̓

ἑτερότητα_), undetermined duality results, because no one of the

determined or otherwise limited numbers is this duality, but all are

known through their participation in it, as has been said of unity.

There are, according to this, two principles in things; the first

unity, through participation in which all number-units are units,

and also undetermined duality through participation in which all

determined dualities are dualities.” Duality is just as essential a

moment in the Notion as is unity. Comparing them with one another, we

may either consider the unity to be form and duality matter, or the

other way; and both appear in different modes. (_αα_) Unity, as the

being-like-self, is the formless; but in duality, as the unlike, there

comes division or form. (_ββ_) If, on the other hand, we take form

as the simple activity of absolute form, the one is what determines;

and duality as the potentiality of multiplicity, or as multiplicity

not posited, is matter. Aristotle (Met. I. 6) says that it is

characteristic of Plato that “he makes out of matter many, but with him

the form originates only once; whereas out of one matter only one table

proceeds, whoever brings form to matter, in spite of its unity, makes

many tables.” He also ascribes this to Plato, that “instead of showing

the undetermined to be simple (_ἀντὶ τοῦ ἀπείρου ὡς ἑνός_), he made of

it a duality—the great and small.”

(_γ_) Further consideration of this opposition, in which Pythagoreans

differ from one another, shows us the imperfect beginning of a table

of categories which were then brought forward by them, as later on by

Aristotle. Hence the latter was reproached for having borrowed these

thought-determinations from them; and it certainly was the case that

the Pythagoreans first made the opposite to be an essential moment in

the absolute. They further determined the abstract and simple Notions,

although it was in an inadequate way, since their table presents a

mixture of antitheses in the ordinary idea and the Notion, without

following these up more fully. Aristotle (Met. I. 5) ascribes these

determinations either to Pythagoras himself, or else to Alcmæon “who

flourished in the time of Pythagoras’ old age,” so that “either Alcmæon

took them from the Pythagoreans or the latter took them from him.” Of

these antitheses or co-ordinates to which all things are traced, ten

are given, for, according to the Pythagoreans, ten is a number of great

significance:—

1. The finite and the infinite.

2. The odd and the even.

3. The one and the many.

4. The right and the left.

5. The male and the female.

6. The quiescent and the moving.

7. The straight and the crooked.

8. Light and darkness.

9. Good and evil.

10. The square and the parallelogram.

This is certainly an attempt towards a development of the Idea of

speculative philosophy in itself, _i.e._ in Notions; but the attempt

does not seem to have gone further than this simple enumeration.

It is very important that at first only a collection of general

thought-determinations should be made, as was done by Aristotle; but

what we here see with the Pythagoreans is only a rude beginning of the

further determination of antitheses, without order and sense, and very

similar to the Indian enumeration of principles and substances.

(_δ_) We find the further progress of these determinations in Sextus

(adv. Math. X. 262-277), when he speaks about an exposition of the

later Pythagoreans. It is a very good and well considered account of

the Pythagorean theories, which has some thought in it. The exposition

follows these lines: “The fact that these two principles are the

principles of the whole, is shown by the Pythagoreans in manifold ways.”

א. “There are three methods of thinking things; firstly, in accordance

with diversity, secondly, with opposition, and thirdly, according

to relation. (_αα_) What is considered in its mere diversity, is

considered for itself; this is the case with those subjects in which

each relates only to itself, such as horse, plant, earth, air, water

and fire. Such matters are thought of as detached and not in relation

to others.” This is the determination of identity with self or of

independence. (_ββ_) “In reference to opposition, the one is determined

as evidently contrasting with the other; we have examples of this in

good and evil, right and wrong, sacred and profane, rest and movement,

&c. (_γγ_) According to relation (_πρός τι_), we have the object

which is determined in accordance with its relationship to others,

such as right and left, over and under, double and half. One is only

comprehensible from the other; for I cannot tell which is my left

excepting by my right.” Each of these relations in its opposition,

is likewise set up for itself in a position of independence. “The

difference between relationship and opposition is that in opposition

the coming into existence of the ‘one’ is at the expense of the

‘other,’ and conversely. If motion is taken away, rest commences; if

motion begins, rest ceases; if health is taken away, sickness begins,

and conversely. In a condition of relationship, on the contrary, both

take their rise, and both similarly cease together; if the right

is removed, so also is the left; the double goes and the half is

destroyed.” What is here taken away is taken not only as regards its

opposition, but also in its existence. “A second difference is that

what is in opposition has no middle; for example, between sickness and

health, life and death, rest and motion, there is no third. Relativity,

on the contrary, has a middle, for between larger and smaller there

is the like; and between too large and too small the right size is

the medium.” Pure opposition passes through nullity to opposition;

immediate extremes, on the other hand, subsist in a third or middle

state, but in such a case no longer as opposed. This exposition shows

a certain regard for universal, logical determinations, which now and

always have the greatest possible importance, and are moments in all

conceptions and in everything that is. The nature of these opposites

is, indeed, not considered here, but it is of importance that they

should be brought to consciousness.

ב. “Now since these three represent three different genera, the

subjects and the two-fold opposite, there must be a higher genus over

each of them which takes the first place, since the genus comes before

its subordinate kinds. If the universal is taken away, so is the kind;

on the other hand, if the kind, not the genus, for the former depends

on the latter, but not the contrary way.” (_αα_) “The Pythagoreans have

declared the one to be the highest genus of what is considered as in

and for itself” (of subjects in their diversity); this is, properly

speaking, nothing more than translating the determinations of the

Notion into numbers. (_ββ_) “What is in opposition has, they say, as

its genus the like and the unlike; rest is the like, for it is capable

of nothing more and nothing less; but movement is the unlike. Thus

what is according to nature is like itself; it is a point which is not

capable of being intensified (_ἀνεπίτατος_); what is opposed to it is

unlike. Health is like, sickness is unlike. (_γγ_) The genus of that

which is in an indifferent relationship is excess and want, the more

and the less;” in this we have the quantitative relation just as we

formerly had the qualitative.

ג. We now come for the first time to the two opposites: “These three

genera of what is for itself, in opposition and in relationship,

must now come under”—yet simpler, higher—“genera,” _i.e._

thought-determinations. “Similarity reduces itself to the determination

of unity.” The genus of the subjects is the very being on its own

account. “Dissimilarity, however, consists of excess and want, but both

of these come under undetermined duality;” they are the undetermined

opposition, opposition generally. “Thus from all these relationships

the first unity and the undetermined duality proceed;” the Pythagoreans

said that such are found to be the universal modes of things. “From

these, there first comes the ‘one’ of numbers and the ‘two’ of numbers;

from the first unity, the one; from the unity and the undetermined

duality the two; for twice the one is two. The other numbers take their

origin in a similar way, for the unity over moves forward, and the

undetermined duality generates the two.” This transition of qualitative

into quantitative opposition is not clear. “Hence underlying these

principles, unity is the active principle” or form, “but the two is

the passive matter; and just as they make numbers arise from them, so

do they make the system of the world and that which is contained in

it.” The nature of these determinations is to be found in transition

and in movement. The deeper significance of this reflection rests in

the connection of universal thought-determinations with arithmetic

numbers—in subordinating these and making the universal genus first.

Before I say anything of the further sequence of these numbers, it

must be remarked that they, as we see them represented here, are pure

Notions. (_α_) The absolute, simple essence divides itself into unity

and multiplicity, of which the one sublates the other, and at the same

time it has its existence in the opposition. (_β_) The opposition has

at the same time subsistence, and in this is found the manifold nature

of equivalent things. (_γ_) The return of absolute essence into itself

is the negative unity of the individual subject and of the universal

or positive. This is, in fact, the pure speculative Idea of absolute

existence; it is this movement: with Plato the Idea is nothing else.

The speculative makes its appearance here as speculative; whoever does

not know the speculative, does not believe that in indicating simple

Notions such as these, absolute essence is expressed. One, many, like,

unlike, more or less, are trivial, empty, dry moments; that there

should be contained in them absolute essence, the riches and the

organization of the natural, as of the spiritual world, does not seem

possible to him who, accustomed to ordinary ideas, has not gone back

from sensuous existence into thought. It does not seem to such a one

that God is, in a speculative sense, expressed thereby—that what is

most sublime can be put in those common words, what is deepest, in

what is so well known, self-evident and open, and what is richest, in

the poverty of these abstractions.

It is at first in opposition to common reality that this idea of

reality as the manifold of simple essence, has in itself its opposition

and the subsistence of the same; this essential, simple Notion of

reality is elevation into thought, but it is not flight from what is

real, but the expression of the real itself in its essence. We here

find the Reason which expresses its essence; and absolute reality is

unity immediately in itself. Thus it is pre-eminently in relation

to this reality that the difficulties of those who do not think

speculatively have become so intense. What is its relation to common

reality? What has taken place is just what happens with the Platonic

Ideas, which approximate very closely to these numbers, or rather

to pure Notions. That is to say, the first question is, “Numbers,

where are they? Dispersed through space, dwelling in independence in

the heaven of ideas? They are not things immediately in themselves,

for a thing, a substance, is something quite other than a number:

a body bears no similarity to it.” To this we may answer that the

Pythagoreans did not signify anything like that which we understand

by prototypes—as if ideas, as the laws and relations of things,

were present in a creative consciousness as thoughts in the divine

understanding, separated from things as are the thoughts of an artist

from his work. Still less did they mean only subjective thoughts in our

consciousness, for we use the absolute antithesis as the explanation of

the existence of qualities in things, but what determines is the real

substance of what exists, so that each thing is essentially just its

having in it unity, duality, as also their antithesis and connection.

Aristotle (Met. I. 5, 6) puts it clearly thus: “It is characteristic of

the Pythagoreans that they did not maintain the finite and the infinite

and the One, to be, like fire, earth, &c., different natures or to have

another reality than things; for the Infinite and the abstract One

are to them, the substance of the things of which they are predicated.

Hence too, they said, Number is the essence of all things. Thus they

do not separate numbers from things, but consider them to be things

themselves. Number to them is the principle and matter of things, as

also their qualities and forces;” hence it is thought as substance, or

the thing as it is in the reality of thought.

These abstract determinations then became more concretely determined,

especially by the later philosophers, in their speculations regarding

God. We may instance Iamblichus, for example, in the work _θεολογούμενα

ἀριθμητικῆς_, ascribed to him by Porphyry and Nicomachus. Those

philosophers sought to raise the character of popular religion, for

they inserted such thought-determinations as these into religious

conceptions. By Monas they understood nothing other than God; they also

call it Mind, the Hermaphrodite (which contains both determinations,

odd as well as even), and likewise substance, reason, chaos (because it

is undetermined), Tartarus, Jupiter, and Form. They called the duad by

similar names, such as matter, and then the principle of the unlike,

strife, that which begets, Isis, &c.

c. The triad (_τριάς_) has now become a most important number,

seeing that in it the monad has reached reality and perfection. The

monad proceeds through the duad, and again brought into unity with

this undetermined manifold, it is the triad. Unity and multiplicity

are present in the triad in the worst possible way—as an external

combination; but however abstractly this is understood, the triad

is still a profound form. The triad then is held to be the first

perfect form in the universal. Aristotle (De Cœlo I. 1) puts this

very clearly: “The corporeal has no dimension outside of the Three;

hence the Pythagoreans also say that the all and everything is

determined through triplicity,” that is, it has absolute form. “For

the number of the whole has end, middle, and beginning; and this

is the triad.” Nevertheless there is something superficial in the

wish to bring everything under it, as is done in the systematization

of the more modern natural philosophy. “Therefore we, too, taking

this determination from nature, make use of it in the worship of the

gods, so that we believe them to have been properly apostrophized

only when we have called upon them three times in prayer. Two we call

both, but not all; we speak first of three as all. What is determined

through three is the first totality (_πᾶν_); what is in triple form

is perfectly divided. Some is merely in one, other is only in two,

but this is All.” What is perfect, or has reality, is its identity,

opposition and unity, like number generally; but in triplicity this

is actual, because it has beginning, middle, and end. Each thing is

simple as beginning; it is other or manifold as middle, and its end

is the return of its other nature into unity or mind; if we take this

triplicity from a thing, we negate it and make of it an abstract

construction of thought.

It is now comprehensible that Christians sought and found the Trinity

in this threefold nature. It has often been made a superficial reason

for objecting to them; sometimes the idea of the Trinity as it was

present to the ancients, was considered as above reason, as a secret,

and hence, too high; sometimes it was deemed too absurd. But from the

one cause or from the other, they did not wish to bring it into closer

relation to reason. If there is a meaning in this Trinity, we must try

to understand it. It would be an anomalous thing if there were nothing

in what has for two thousand years been the holiest Christian idea; if

it were too holy to be brought down to the level of reason, or were

something now quite obsolete, so that it would be contrary to good

taste and sense to try to find a meaning in it. It is the Notion of the

Trinity alone of which we can speak, and not of the idea of Father and

Son, for we am not dealing with these natural relationships.

d. The Four (_τετράς_) is the triad but more developed, and hence with

the Pythagoreans it held a high position. That the tetrad should be

considered to be thus complete, reminds one of the four elements, the

physical and the chemical, the four continents, &c. In nature four

is found to be present everywhere, and hence this number is even now

equally esteemed in natural philosophy. As the square of two, the

fourfold is the perfection of the two-fold in as far as it—only having

itself as determination, i.e. being multiplied with itself—returns

into identity with itself. But in the triad the tetrad is in so far

contained, as that the former is the unity, the other-being, and

the union of both these moments, and thus, since the difference, as

posited, is a double, if we count it, four moments result. To make this

clearer, the tetrad is comprehended as the _τετρακτύς_, the efficient,

active four (from _τέτταρα_ and _ἄγω_); and afterwards this is by the

Pythagoreans made the most notable number. In the fragments of a poem

of Empedocles, who originally was a Pythagorean, it is shown in what

high regard this tetraktus, as represented by Pythagoras, was held:

“If thou dost this,

It will lead thee in the path of holy piety. I swear it

By the one who to our spirit has given the Tetraktus,

Which has in it eternal nature’s source and root.”[43]

e. From this the Pythagoreans proceed to the ten, another form of this

tetrad. As the four is the perfect form of three, this fourfold, thus

perfected and developed so that all its moments shall be accepted as

real differences, is the number ten (_δεκάς_), the real tetrad. Sextus

(adv. Math. IV. 3; VII. 94, 95) says: “Tetraktus means the number

which, comprising within itself the four first numbers, forms the most

perfect number, that is the number ten; for one and two and three and

four make ten. When we come to ten, we again consider it as a unity

and begin once more from the beginning. The tetraktus, it is said,

has the source and root of eternal nature within itself, because it

is the Logos of the universe, of the spiritual and of the corporeal.”

It is an important work of thought to show the moments not merely to

be four units, but complete numbers; but the reality in which the

determinations are laid hold of, is here, however, only the external

and superficial one of number; there is no Notion present although

the tetraktus does not mean number so much as idea. One of the later

philosophers, Proclus, (in Timæum, p. 269) says, in a Pythagorean

hymn:—

“The divine number goes on,”...

“Till from the still unprofaned sanctuary of the Monad

It reaches to the holy Tetrad, which creates the mother of all that

is;

Which received all within itself, or formed the ancient bounds of all,

Incapable of turning or of wearying; men call it the holy Dekad.”

What we find about the progression of the other numbers is more

indefinite and unsatisfying, and the Notion loses itself in them. Up to

five there may certainly be a kind of thought in numbers, but from six

onwards they are merely arbitrary determinations.

2. _Application of the System to the Universe_. This simple idea and

the simple reality contained therein, must now, however, be further

developed in order to come to reality as it is when put together and

expanded. The question now meets us as to how, in this relation, the

Pythagoreans passed from abstract logical determinations to forms which

indicate the concrete use of numbers. In what pertains to space or

music, determinations of objects formed by the Pythagoreans through

numbers, still bear a somewhat closer relation to the thing, but when

they enter the region of the concrete in nature and in mind, numbers

become purely formal and empty.

a. To show how the Pythagoreans constructed out of numbers the

system of the world, Sextus instances (adv. Math. X. 277-283), space

relations, and undoubtedly we have in them to do with such ideal

principles, for numbers are, in fact, perfect determinations of

abstract space. That is to say, if we begin with the point, the first

negation of vacuity, “the point corresponds to unity; it is indivisible

and the principle of lines, as the unity is that of numbers. While

the point exists as the monad or One, the line expresses the duad or

Two, for both become comprehensible through transition; the line is

the pure relationship of two points and is without breadth. Surface

results from the threefold; but the solid figure or body belongs to

the fourfold, and in it there are three dimensions present. Others say

that body consists of one point” (_i.e._ its essence is one point),

“for the flowing point makes the line, the flowing line, however, makes

surface, and this surface makes body. They distinguish themselves from

the first mentioned, in that the former make numbers primarily proceed

from the monad and the undetermined duad, and then points and lines,

plane surfaces and solid figures, from numbers, while they construct

all from one point.” To the first, distinction is opposition or form

set forth as duality; the others have form as activity. “Thus what is

corporeal is formed under the directing influence of numbers, but from

them also proceed the definite bodies, water, air, fire, and the whole

universe generally, which they declare to be harmonious. This harmony

is one which again consists of numeral relations only, which constitute

the various concords of the absolute harmony.”

We must here remark that the progression from the point to actual space

also has the signification of occupation of space, for “according to

their fundamental tenets and teaching,” says Aristotle (Metaph. I. 8),

“they speak of sensuously perceptible bodies in nowise differently

from those which are mathematical.” Since lines and surfaces are only

abstract moments in space, external construction likewise proceeds from

here very well. On the other hand, the transition from the occupation

of space generally to what is determined, to water, earth, &c., is

quite another thing and is more difficult; or rather the Pythagoreans

have not taken this step, for the universe itself has, with them,

the speculative, simple form, which is found in the fact of being

represented as a system of number-relations. But with all this, the

physical is not yet determined.

b. Another application or exhibition of the essential nature of the

determination of numbers is to be found in the relations of music,

and it is more especially in their case that number constitutes

the determining factor. The differences here show themselves as

various relations of numbers, and this mode of determining what is

musical is the only one. The relation borne by tones to one another

is founded on quantitative differences whereby harmonies may be

formed, in distinction to others by which discords are constituted.

The Pythagoreans, according to Porphyry (De vita Pyth. 30), treated

music as something soul-instructing and scholastic [Psychagogisches

und Pädagogisches]. Pythagoras was the first to discern that musical

relations, these audible differences, are mathematically determinable,

that what we hear as consonance and dissonance is a mathematical

arrangement. The subjective, and, in the case of hearing, simple

feeling which, however, exists inherently in relation, Pythagoras has

justified to the understanding, and he attained his object by means

of fixed determinations. For to him the discovery of the fundamental

tones of harmony are ascribed, and these rest on the most simple

number-relations. Iamblichus (De vita Pyth. XXVI. 115) says that

Pythagoras, in passing by the workshop of a smith, observed the strokes

that gave forth a particular chord; he then took into consideration

the weight of the hammer giving forth a certain harmony, and from that

determined mathematically the tone as related thereto.[44] And finally

he applied the same, and experimented in strings, by which means there

were three different relations presented to him—Diapason, Diapente,

and Diatessaron. It is known that the tone of a string, or, in the wind

instrument, of its equivalent, the column of air in a reed, depends on

three conditions; on its length, on its thickness, and on the amount

of tension. Now if we have two strings of equal thickness and length,

a difference in tension brings about a difference in sound. If we want

to know what tone any string has, we have only to consider its tension,

and this may be measured by the weight depending from the string,

by means of which it is extended. Pythagoras here found that if one

string were weighted with twelve pounds, and another with six (_λόγος

διπλάσιος_, 1 : 2) it would produce the musical chord of the octave

(_διὰ πασῶν_); the proportion of 8 : 12, or of 2 : 3 (_λόγος ἡμιόλιος_)

would give the chord of the fifth (_διὰ πέντε_); the proportion of 9

: 12, or 3 : 4 (_λόγος ἐπίτριτος_), the fourth (_διὰ τεσσάρων_).[45]

A different number of vibrations in like times determines the height

and depth of the tone, and this number is likewise proportionate to

the weight, if thickness and length are equal. In the first case, the

more distended string makes as many vibrations again as the other;

in the second case, it makes three vibrations for the other’s two,

and so it goes on. Here number is the real factor which determines

the difference, for tone, as the vibration of a body, is only a

quantitatively determined quiver or movement, that is, a determination

made through space and time. For there can be no determination for the

difference excepting that of number or the amount of vibrations in one

time; and hence a determination made through numbers is nowhere more

in place than here. There certainly are also qualitative differences,

such as those existing between the tones of metals and catgut strings,

and between the human voice and wind instruments; but the peculiar

musical relation borne by the tone of one instrument to another, in

which harmony is to be found, is a relationship of numbers.

From this point the Pythagoreans enter into further applications of

the theory of music, in which we cannot follow them. The _à priori_

law of progression, and the necessity of movement in number-relations,

is a matter which is entirely dark; minds confused may wander about at

will, for everywhere ideas are hinted at, and superficial harmonies

present themselves and disappear again. But in all that treats of the

further construction of the universe as a numerical system, we have

the whole extent of the confusion and turbidity of thought belonging

to the later Pythagoreans. We cannot say how much pains they took

to express philosophic thought in a system of numbers, and also to

understand the expressions given utterance to by others, and to put in

them all the meaning possible. When they determined the physical and

the moral universe by means of numbers, everything came into indefinite

and insipid relationships in which the Notion disappeared. In this

matter, however, so far as the older Pythagoreans are concerned, we

are acquainted with the main principles only. Plato exemplifies to us

the conception of the universe as a system of numbers, but Cicero and

the ancients always call these numbers the Platonic, and it does not

appear that they were ascribed to the Pythagoreans. It was thus later

on that this came to be said; even in Cicero’s time they had become

proverbially dark, and there is but little after all that is really old.

c. The Pythagoreans further constructed the heavenly bodies of the

visible universe by means of numbers, and here we see at once the

barrenness and abstraction present in the determination of numbers.

Aristotle says (Met. I. 5), “Because they defined numbers to be

the principles of all nature, they brought under numbers and their

relationships all determinations and all sections, both of the heavens

and of all nature; and where anything did not altogether conform, they

sought to supply the deficiency in order to bring about a harmony.

For instance, as the Ten or dekad appeared to them to be the perfect

number, or that which embraces the whole essence of numbers, they

said that the spheres moving in the heavens must be ten; but as only

nine of these are visible, they made out a tenth, the Antichthone

(_ἀντίχθονα_).” These nine are, first the milky way, or the fixed

stars, and after that the seven stars which were then all held to be

planets: Saturn, Jupiter, Mars, Venus, Mercury, the Sun, Moon, and in

the last and ninth place, the Earth. The tenth is thus the Antichthone,

and in regard to this it must remain uncertain whether the Pythagoreans

considered it to be the side of the Earth which is turned away, or as

quite another body.

Aristotle says, in reference to the specially physical character of

these spheres (De cœlo II. 13 and 9), “Fire was by the Pythagoreans

placed in the middle, but the Earth was made a star that moved around

this central body in a circle.” This circle is, then, a sphere, which,

as the most perfect of figures, corresponds to the dekad. We here

find a certain similarity to our ideas of the solar system, but the

Pythagoreans did not believe the fire to be the sun. “They thus,” says

Aristotle, “rely, not on sensuous appearance, but on reasons,” just as

we form conclusions in accordance with reasons as opposed to sensuous

appearances; and indeed this comes to us still as the first example of

things being in themselves different from what they appear. “This fire,

that which is in the centre, they called Jupiter’s place of watch.

Now these ten spheres make, like all that is in motion, a tone; but

each makes a different one, according to the difference in its size

and velocity. This is determined by means of the different distances,

which bear an harmonious relationship to one another, in accordance

with musical intervals; by this means an harmonious sound arises in the

moving spheres”—a universal chorus.

We must acknowledge the grandeur of this idea of determining everything

in the system of the heavenly spheres through number-relations which

have a necessary connection amongst themselves, and have to be

conceived of as thus necessarily related; it is a system of relations

which must also form the basis and essence of what can be heard, or

music. We have, comprehended here in thought, a system of the universe;

the solar system is alone rational to us, for the other stars are

devoid of interest. To say that there is music in the spheres, and

that these movements are tones, may seem just as comprehensible to us

as to say that the sun is still and the earth moves, although both are

opposed to the dictates of sense. For, seeing that we do not see the

movement, it may be that we do not hear the notes. And there is little

difficulty in imagining a universal silence in these vast spheres,

since we do not hear the chorus, but it is more difficult to give a

reason for not hearing this music. The Pythagoreans say, according to

the last quoted passage of Aristotle, that we do not hear it because

we live in it, like the smith who gets accustomed to the blows of

his hammer. Since it belongs to our substance and is identical with

ourselves, nothing else, such as silence, by which we might know

the other, comes into relationship with us, for we are conceived of

as entirely within the movement. But the movement does not become a

tone, in the first place, because pure space and time, the elements in

movement, can only raise themselves into a proper voice, unstimulated

from without, in an animate body, and movement first reaches this

definite, characteristic individuality in the animal proper; and, in

the next place, because the heavenly bodies are not related to one

another as bodies whose sound requires for its production, contact,

friction, or shock, in response to which, and as the negation of its

particularity its own momentary individuality resounds in elasticity;

for heavenly bodies are independent of one another, and have only a

general, non-individual, free motion.

We may thus set aside sound; the music of the spheres is indeed a

wonderful conception, but it is devoid of any real interest for us.

If we retain the conception that motion, as measure, is a necessarily

connected system of numbers, as the only rational part of the theory,

we must maintain that nothing further has transpired to the present

day. In a certain way, indeed, we have made an advance upon Pythagoras.

We have learned from Kepler about laws, about eccentricity, and the

relation of distances to the times of revolution, but no amount of

mathematics has as yet been able to give us the laws of progression

in the harmony through which the distances are determined. We know

empirical numbers well enough, but everything has the semblance of

accident and not of necessity. We are acquainted with an approximate

rule of distances, and thus have correctly foretold the existence

of planets where Ceres, Vesta, Pallas, &c., were afterwards

discovered—that is, between Mars and Jupiter. But astronomy has not as

yet found in it a consistent sequence in which there is rationality;

on the other hand, it even looks with disdain on the appearance of

regularity presented by this sequence, which is, however, on its own

account, a most important matter, and one which should not be forgotten.

d. The Pythagoreans also applied their principle to the Soul, and

thus determined what is spiritual as number. Aristotle (De anim. I.

2) goes on to tell that they thought that solar corpuscles are soul,

others, that it is what moves them; they adopted this idea because

the corpuscles are ever moving, even in perfect stillness, and hence

they must have motion of their own. This does not signify much, but

it is evident from it that the determination of self-movement was

sought for in the soul. The Pythagoreans made a further application

of number-conceptions to the soul after another form, which Aristotle

describes in the same place as follows:—“Thought is the one, knowledge

or science is the two, for it comes alone out of the one. The number

of the plane is popular idea, opinion; the number of the corporeal

is sensuous feeling. Everything is judged of either by thought, or

science, or opinion, or feeling.” In these ideas, which we must,

however, ascribe to later Pythagoreans, we may undoubtedly find some

adequacy, for while thought is pure universality, knowledge deals with

something “other,” since it gives itself a determination and a content;

but feeling is the most developed in its determinateness. “Now because

the soul moves itself, it is the self-moving number,” yet we never find

it said that it is connected with the monad.

This is a simple relationship to number-determinations. Aristotle

instances (De anim. I. 3) one more intricate from Timæus: “The soul

moves itself, and hence also the body because it is bound up with body;

it consists of elements and is divided according to harmonic numbers,

and hence it has feeling and an immediately indwelling (_σύμφυτον_)

harmony. In order that the whole may have an harmonious movement,

Timæus has bent the straight line of harmony (_εὐθυωρίαν_) into a

circle, and again divided off from the whole circle two circles,

which are doubly connected; and the one of these circles is again

divided into seven circles, so that the movements of the soul may

resemble those of the heavens.” The more definite significance of these

ideas Aristotle unfortunately has not given; they contain a profound

knowledge of the harmony of the whole, but yet they are forms which

themselves remain dark, because they are clumsy and unsuitable. There

is always a forcible turning and twisting, a struggle with the material

part of the representation, as there is in mythical and distorted

forms: nothing has the pliability of thought but thought itself. It

is remarkable that the Pythagoreans have grasped the soul as a system

which is a counterpart of the system of the heavens. In Plato’s Timæus

this same idea is more definitely brought forward. Plato also gives

further number-relations, but not their significance as well; even to

the present day no one has been able to make any particular sense out

of them. An arrangement of numbers such as this is easy, but to give to

it a real significance is difficult, and, when done, it always must be

arbitrary.

There is still something worthy of attention in what is said by the

Pythagoreans in reference to the soul, and this is their doctrine

of the transmigration of souls. Cicero (Tusc. Quæst. I. 16) says:

“Pherecydes, the teacher of Pythagoras, first said that the souls

of men were immortal.” The doctrine of the transmigration of souls

extends even to India, and, without doubt, Pythagoras took it from

the Egyptians; indeed Herodotus (II. 123) expressly says so. After he

speaks of the mythical ideas of the Egyptians as to the lower world,

he continues: “The Egyptians were the first to say that the soul of

man is immortal, and that, when the body disappears, it goes into

another living being; and when it has gone through all the animals of

land and sea, and likewise birds, it again takes the body of a man,

the period being completed in 3000 years.” Diogenes Laertius says in

this connection (VIII. 14) that the soul, according to Pythagoras, goes

through a circle. “These ideas,” proceeds Herodotus, “are also found

amongst the Greeks; there are some who, earlier or later, have made

use of this particular doctrine, and have spoken of it as if it were

their own; I know their names very well, but I will not mention them.”

He undoubtedly meant Pythagoras and his followers. In the sequel,

much that is given utterance to is fictitious: “Pythagoras himself

is said to have stated that his former personality was known to him.

Hermes granted him a knowledge of his circumstances before his birth.

He lived as the son of Hermes, Æthalides, and then in the Trojan

war as Euphorbus, the son of Panthous, who killed Patroclus, and was

killed by Menelaus; in the third place he was Hermotimus; fourthly,

Pyrrhus, a fisherman of Delos; in all he lived 207 years. Euphorbus’

shield was offered up to Apollo by Menelaus, and Pythagoras went to the

temple and, from the mouldering shield, showed the existence of signs,

hitherto not known of, by which it was recognized.”[46] We shall not

treat further of these very various and foolish stories.

As in the case of the brotherhood copied from the Egyptian priesthood,

so must we here set aside this oriental and un-Greek idea of the

transmigration of souls. Both were too far removed from the Greek

spirit to have had a place and a development there. With the Greeks,

the consciousness of a higher, freer individuality has become too

strong to allow any permanence to the idea of metempsychosis, according

to which, man, this independent and self-sufficing Being, takes the

form of a beast. They have, indeed, the conception of men as becoming

springs of water, trees, animals, &c., but the idea of degradation

which comes as a consequence of sin, lies at its root. Aristotle (De

anim. I. 3) shortly and in his own manner deals with and annihilates

this idea of the Pythagoreans. “They do not say for what reason soul

dwells in body, nor how the latter is related to it. For owing to

their unity of nature when one acts the other suffers: one moves and

the other is moved, but none of this happens in what is mutually

contingent. According to the Pythagorean myths any soul takes to any

body, which is much like making architects take to flutes. For crafts

must necessarily have tools and soul body; but each tool must have

its proper form and kind.” It is implied in the transmigration of

souls that the organization of the body is something accidental to

the human soul; this refutation by Aristotle is complete. The eternal

idea of metempsychosis had philosophic interest only as the inner

Notion permeating all these forms, the oriental unity which appears in

everything; we have not got this signification here, or at best we have

but a glimmering of it. If we say that the particular soul is, as a

definite thing, to wander about throughout all, we find firstly, that

the soul is not a thing such as Leibnitz’ Monad, which, like a bubble

in the cup of coffee, is possibly a sentient, thinking soul; in the

second place an empty identity of the soul-thing such as this has no

interest in relation to immortality.

3. _Practical Philosophy_. As regards the practical philosophy of

Pythagoras, which is closely connected with what has gone before, there

is but little that is philosophic known to us. Aristotle (Magn. Moral.

I. 1) says of him that “he first sought to speak of virtue, but not in

the right way, for, because he deduced the virtues from numbers, he

could not form of them any proper theory.” The Pythagoreans adopted ten

virtues as well as ten heavenly spheres. Justice, amongst others, is

described as the number which is like itself in like manner (_ἴσακις

ἴσος_); it is an even number, which remains even when multiplied with

itself. Justice is pre-eminently what remains like itself; but this

is an altogether abstract determination, which applies to much that

is, and which does not exhaust the concrete, thus remaining quite

indeterminate.

Under the name of the “Golden words,” we have a collection of

hexameters which are a succession of moral reflections, but which are

rightly ascribed to later Pythagoreans. They are old, well-known, moral

maxims, which are expressed in a simple and dignified way, but which

do not contain anything remarkable. They begin with the direction “to

honour the immortal gods as they are by law established,” and further,

“Honour the oath and then the illustrious heroes;” elsewhere they go

on to direct “honour to be paid to parents and to relatives,” &c.[47]

Such matter does not deserve to be regarded as philosophy, although it

is of importance in the process of development.

The transition from the form of outward morals to morality as existent,

is more important. As in Thales’ time, law-givers and administrators

of states were preeminent in possessing a physical philosophy, so we

see that with Pythagoras practical philosophy is advocated as the means

of constituting a moral life. There we have the speculative Idea,

the absolute essence, in its reality, and in a definite, sensuous

existence; and similarly the moral life is submerged in actuality

as the universal spirit of a people, and as their laws and rule. In

Pythagoras, on the contrary, we have the reality of absolute essence

raised, in speculation, out of sensuous reality, and expressed, though

still imperfectly, as the essence of thought. Morality is likewise

partly raised out of actuality as ordinarily known; it is certainly a

moral disposition of all actuality, but as a brotherhood, and not as

the life of a people. The Pythagorean League is an arbitrary existence

and not a part of the constitution recognized by public sanction; and

in his person Pythagoras isolated himself as teacher, as he also did

his followers. The universal consciousness, the spirit of a people, is

the substance of which the accident is the individual consciousness;

the speculative is thus the fact that pure, universal law is absolute,

individual consciousness, so that this last, because it draws therefrom

its growth and nourishment, becomes universal self-consciousness. These

two sides do not, however, come to us in the form of the opposition;

it is first of all in morality that there is properly this Notion of

the absolute individuality of consciousness which does everything on

its own account. But we see that it was really present to the mind

of Pythagoras that the substance of morality is the universal, from

an example in Diogenes Laertius (VIII. 16). “A Pythagorean answered

to the question of a father who inquired as to the best education he

could give his son, that it should be that which would make him the

citizen of a well-regulated State.” This answer is great and true; to

the great principle of living in the spirit of one’s people, all other

circumstances are subordinate. Nowadays men try to keep education free

from the spirit of the times, but they cannot withdraw themselves

from this supreme power, the State, for even if they try to separate

themselves, they unconsciously remain beneath this universal. The

speculative meaning of the practical philosophy of Pythagoras thus is,

that in this signification, the individual consciousness shall obtain

a moral reality in the brotherhood. But as number is a middle thing

between the sensuous and Notion, the Pythagorean brotherhood is a

middle between universal, actual morality and maintaining that in true

morality the individual, as an individual, is responsible for his own

behaviour; this morality ceases to be universal spirit. If we wish to

see practical philosophy reappear, we shall find it; but, on the whole,

we shall not see it become really speculative until very recent times.

We may satisfy ourselves with this as giving us an idea of the

Pythagorean system. I will, however, shortly give the principal

points of the criticism which Aristotle (Met. I. 8) makes upon the

Pythagorean number-form. He says justly, in the first place: “If only

the limited and the unlimited, the even and odd are made fundamental

ideas, the Pythagoreans do not explain how movement arises, and how,

without movement and change there can be coming into being and passing

away, or the conditions and activities of heavenly objects.” This

defect is significant; arithmetical numbers are dry forms and barren

principles in which life and movement are deficient. Aristotle says

secondly, “From number no other corporeal determinations, such as

weight and lightness, are conceivable;” or number thus cannot pass

into what is concrete. “They say that there is no number outside of

those in the heavenly spheres.” For instance, a heavenly sphere and

a virtue, or a natural manifestation in the earth, are determined as

one and the same number. Each of the first numbers may be exhibited

in each thing or quality; but in so far as number is made to express

a further determination, this quite abstract, quantitative difference

becomes altogether formal; it is as if the plant were five because it

has five stamens. This is just as superficial as are determination

through elements or through particular portions of the globe; it is a

method as formal as that by which men now try to apply the categories

of electricity, magnetism, galvanism, compression and expansion, of

manly and of womanly, to everything. It is a purely empty system of

determination where reality should be dealt with.

To Pythagoras and his disciples there are, moreover, many scientific

conclusions and discoveries ascribed, which, however, do not concern us

at all. Thus, according to Diogenes Laertius (VIII. 14, 27), he is said

to have known that the morning and evening star is the same, and that

the moon derives her light from the sun. We have already mentioned what

he says of music. But what is best known is the Pythagorean Theorem;

it really is the main proposition in geometry, and cannot be regarded

like any other theorem. According to Diogenes, (VIII. 12), Pythagoras,

on discovering the theorem, sacrificed a hecatomb, so important did he

think it; and it may indeed seem remarkable that his joy should have

gone so far as to ordain a great feast to which rich men and all the

people were invited. It was worth the trouble; it was a rejoicing, a

feast of spiritual cognition—at the cost of the oxen.

Other ideas which are brought forward by the Pythagoreans casually and

without any connection, have no philosophic interest, and need only

be mentioned. Aristotle, for instance, says (Phys. IV. 6) that “the

Pythagoreans believed in an empty space which the heavens inspire, and

an empty space which separates natural things and brings about the

distinction between continuous and discrete; it first exists in numbers

and makes them to be different.” Diogenes Laertius (VIII. 26-28) says

much more, all of which is dull; this is like the later writers,

who, generally speaking, take up what is external and devoid of any

intellectual meaning. “The air which encircles the earth is immovable”

(_ἄσειστον_, at least through itself) “and diseased, and all that is

in it is mortal; but what is highest is in continual movement, pure

and healthy, and in it everything is immortal—divine. Sun, moon and

the other stars are gods, for in them warmth has predominance and is

the cause of life. Man is related to the gods because he participates

in warmth, and hence God cares for us. A ray penetrates from the sun

through the thick and cold ether and gives life to everything; they

call air, cold ether, the sea and moisture, thick ether. The soul is a

detached portion of ether.”

C. THE ELEATIC SCHOOL.

The Pythagorean philosophy has not yet got the speculative form of

expression for the Notion. Numbers are not pure Notion, but Notion in

the form of ordinary idea or sensuous perception, and hence a mixture

of both. This expression of absolute essence in what is a pure Notion

or something thought, and the movement of the Notion or of Thought,

is that which we find must come next, and this we discover in the

Eleatic school. In it we see thought becoming free for itself; and in

that which the Eleatics express as absolute essence, we see Thought

grasp itself in purity, and the movement of Thought in Notions. In

the physical philosophy we saw movement represented as an objective

movement, as an origination and passing away. The Pythagoreans

similarly did not reflect upon these Notions, and also treated their

essence, Number, as fleeting. But since alteration is now grasped in

its highest abstraction as Nothing, this objective movement changes

into a subjective one, comes over to the side of consciousness, and

existence becomes the unmoved. We here find the beginning of dialectic,

_i.e._ simply the pure movement of thought in Notions; likewise we

see the opposition of thought to outward appearance or sensuous

Being, or of that which is implicit to the being-for-another of this

implicitness, and in the objective existence we see the contradiction

which it has in itself, or dialectic proper. When we reflect in

anticipation on how the course of pure thought must be formed, we

find (_α_) that pure thought (pure Being, the One) manifests itself

immediately in its rigid isolation and self-identity, and everything

else as null; (_β_) that the hitherto timid thought—which after it

is strengthened, ascribes value to the “other” and constitutes itself

therefrom—shows that it then grasps the other in its simplicity and

even in so doing shows its nullity; (_γ_) finally, Thought manifests

the other in the manifold nature of its determinations. We shall see

this in the development and culture of the Eleatics in history. These

Eleatic propositions still have interest for Philosophy, and are

moments which must necessarily there appear.

Xenophanes, Parmenides, Melissus and Zeno are to be reckoned as

belonging to this school. Xenophanes may be regarded as the founder

of it; Parmenides is supposed to have been his pupil, and Melissus,

and especially Zeno, are called the pupils of Parmenides. In fact,

they are to be taken together as forming the Eleatic school; later on

it lost the name, being then called Sophistic, and its locality was

transferred to Greece proper. What Xenophanes began, Parmenides and

Melissus developed further, and similarly Zeno perfected what these

two taught. Aristotle (Metaph. I. 5) characterizes the first three

thus: “Parmenides seems to comprehend the one as Notion (_κατὰ τὸν

λόγον_), Melissus as matter (_κατὰ τὴν ὕλην_); hence the former says

that it is limited (_πεπερασμένον_) and the latter that it is unlimited

(_ἄπειρον_). But Xenophanes, who was the first of them to express the

theory of the One, made the matter no plainer (_διεσαφήνισεν_), nor did

he deal with either of these aspects (_φύσεως_), but looking into the

heavens”—as we say, into the blue—“said, God is the One. Xenophanes

and Melissus are on the whole less civilized (_μικρὸν ἀγροικότεροι_);

Parmenides, however, is more acute (_μᾶλλον βλέπων_).” There is less to

say of Xenophanes and Melissus, and what has come to us from the latter

in particular—in fragments and derived from the sayings of others—is

still in a state of ferment, and in his case there is least knowledge

obtainable. On the whole, philosophic utterances and Notions are still

poor, and it was in Zeno that Philosophy first attained to a purer

expression of itself.

1. XENOPHANES.

The period at which he lived is clear enough, and as this suffices,

it is a matter of indifference that the year of his birth and of his

death is unknown. According to Diogenes Laertius (IX. 18), he was

contemporary with Anaximander and Pythagoras. Of his circumstances

further than this, it is only known that he, for reasons which are

unknown, escaped from his native town, Colophon, in Asia Minor, to

Magna Græcia, and resided for the most part at Zancle, (now Messina)

and Catana (still called Catania) in Sicily. I find it nowhere said

by the ancients that he lived at Elea, although all recent writers on

the history of Philosophy repeat it, one after the other. Tennemann,

in particular, says (Vol. I. pp. 151 and 414), that about the 61st

Olympiad (536 B.C.), he repaired from Colophon to Elea. Diogenes

Laertius (IX. 20), however, only says that he flourished about the 60th

Olympiad and that he made two thousand verses on the colonization of

Elea, from which it might be easily concluded that he was also born

at Elea. Strabo says this in the beginning of his sixth book—when

describing Elea—of Parmenides and Zeno only, and these he called

Pythagoreans; hence, according to Cicero (Acad. Quæst. IV. 42) the

Eleatic school took its name from these two. Xenophanes was nearly a

hundred years old, and lived to see the Median wars: it is said that he

became so poor that he had not the means of having his children buried,

and was obliged to do so with his own hands. Some say that he had no

teacher; others name Archelaus, which is a chronological error.

He wrote a book “On Nature,” the general subject and title of

Philosophy at that time; some verses have been preserved to us which so

far show no powers of reasoning. Professor Brandis of Bonn collected

them together, with the fragments of Parmenides and Melissus, under

the title “Commentationum Eleaticarum, P. 1,” Altonæ, 1813. The older

philosophers wrote in verse, for prose comes much later on; on account

of the awkward and confused mode of expression in Xenophanes’ poems,

Cicero calls them (Acad. Quæst. IV. 23): _minus boni versus_.

As to his philosophy, Xenophanes in the first place maintained absolute

existence to be the one, and likewise called this God. “The all is

One and God is implanted in all things; He is unchangeable, without

beginning, middle or end.”[48] In some verses by Xenophanes found in

Clemens of Alexandria (Strom. V. 14, p. 714, ed. Potter), it is said:

“One God is greatest amongst gods and men.

Neither like unto mortals in spirit or in form;”

and in Sextus Empiricus (adv. Math. IX. 144):

“He sees everywhere, thinks everywhere, and hears everywhere,”

to which words Diogenes Laertius (IX, 19) adds: “Thought and reason

are everything and eternal.” By this Xenophanes denied the truth of the

conceptions of origination and of passing away, of change, movement,

&c., seeing that they merely belong to sensuous perception. “He found,”

says Tennemann (Vol. I. p. 156) “all origination to be inconceivable:”

the One as the immediate product of pure thought, is, in its immediacy,

Being.

For us the determination of Being is already known and trivial, but

if we know about Being, the One, we place this, as a particular

determination, in a line with all the rest. Here, on the contrary, it

signifies that all else has no reality and is only a semblance. We

must forget our own ideas; we know of God as Spirit. But, because the

Greeks only had before them the sensuous world, these gods of their

imagination, and found in them no satisfaction, they rejected all

as being untrue, and thus came to pure thought. This is a wonderful

advance, and thought thus becomes for the first time free for itself in

the Eleatic school. Being, the One of the Eleatic school, is just this

immersion in the abyss of the abstract identity of the understanding.

Just as this comes first, so it also comes last, as that to which the

understanding comes back, and this is proved in recent times when God

is grasped only as the highest Being. If we say of God that this the

highest Being is outside of and over us, we can know nothing more of

it but that it is, and thus it is the undetermined; for if we knew of

determinations, this would be to possess knowledge. The truth then

simply is that God is the One, not in the sense that there is one God

(this is another determination), but only that He is identical with

Himself; in this there is no other determination, any more than in the

utterance of the Eleatic school. Modern thought has, indeed, passed

through a longer path, not only through what is sensuous, but also

through philosophic ideas and predicates of God, to this all negating

abstraction; but the content, the result arrived at is the same.

With this the dialectic reasoning of the Eleatics is closely connected

in respect that they have also proved that nothing can originate or

pass away. This deduction is to be found in Aristotle’s work, De

Xenophane, Zenone et Gorgia, c. 3. “It is impossible, he says,[49] that

if anything is, it arises (and he even applies this to the Godhead);

for it must arise either from the like or from the unlike. But both are

equally impossible: for it is no more probable that the like should be

engendered from the like, than that it should engender it, for the like

must have determinations identical with one another.” In acknowledging

similarity, the distinction between begetting and begotten falls away.

“Just as little can unlike arise from unlike, for if from the weaker

the stronger takes its rise; or from the smaller, the greater; or from

the worse, the better: or if, conversely, the worse proceeds from the

better, non-being would result from Being: this is impossible, and thus

God is eternal.” The same thing has been expressed as Pantheism or

Spinozaism, which rests on the proposition _ex nihilo fit nihil_. The

unity of God is further proved by Xenophanes: “If God is the mightiest,

He must be One; for were He two or more, He would not have dominion

over the others, but, not having dominion over the others, He could not

be God. Thus were there several, they would be relatively more powerful

or weaker, and thus they would not be gods, for God’s nature is to have

nothing mightier than He. Were they equal, God would no longer possess

the quality of being the mightiest, for the like is neither worse nor

better than the like”—or it does not differ therefrom. “Hence if

God is, and is such as this, He is only one; He could not, were there

several, do what He willed. Since He is one, He is everywhere alike.

He hears, sees and has also the other senses everywhere, for were this

not the case, the parts of God would be one more powerful than the

other, which is impossible. Since God is everywhere alike, He has a

spherical form, for He is not here thus and elsewhere different, but is

everywhere the same. Since He is eternal and one and spherical in form,

He is neither unlimited nor limited. To be unlimited is non-being;

for that has neither middle, beginning, end, nor part; and what is

unlimited corresponds to this description. But whatever non-being is,

Being is not. Mutual limitation would take place if there were several,

but since there is only One, it is not limited. The one does not move

itself, nor is it unmoved; to be unmoved is non-being, for to it none

other comes, nor does it go into another; but to be moved must mean to

be several, for one must move into another. Thus the One neither rests

nor is it moved, for it is neither non-being nor is it many. In all

this God is thus indicated; He is eternal and One, like Himself and

spherical, neither unlimited nor limited, neither at rest nor moved.”

From this result, that nothing can arise from the like or from the

unlike, Aristotle (De Xenophane, Zenone et Gorgia c. 4) draws this

conclusion: “that either there is nothing excepting God, or all else is

eternal.”

We here see a dialectic which may be called metaphysical reasoning, in

which the principle of identity is fundamental. “The nothing is like

nothing and does not pass into Being or conversely; thus nothing can

originate from like.” This, the oldest mode of argument, holds its

place even to the present day, as, for example, in the so-called proof

of the unity of God. This proceeding consists of making presuppositions

such as the power of God, and from them drawing conclusions and denying

the existence of predicates; that is the usual course in our mode of

reasoning. In respect of determinations, it must be remarked that

they, as being negative, are all kept apart from the positive and

merely real being. We reach this abstraction by a more ordinary way,

and do not require a dialectic such as that of the Eleatic school: we

say God is unchangeable, change concerns finite things alone (which

we represent as an empirical proposition); on the one hand we thus

have finite things and change, and on the other, unchangeableness in

this abstract absolute unity with itself. It is the same separation,

only that we also allow the finite to be Being, which the Eleatics

deny. Or else we too proceed from finite things to kinds and genera,

leaving the negative out bit by bit; and the highest order of all is

God, who, as the highest Being, is affirmative only, but devoid of any

determination. Or we pass from what is finite to the infinite, for we

say that the finite as limited must have its basis in the infinite.

In all these different forms which are quite familiar to us, there is

the same difficult question which exists in reference to the Eleatic

thought. Whence comes determination and how is it to be grasped—how

is it in the one, leaving the finite aside, and also how does the

infinite pass out into the finite? The Eleatics in their reflections

were distinguished from this our ordinary reflecting thought, in that

they went speculatively to work (the speculative element being that

change does not exist at all) and that they thus showed that, as Being

was presupposed, change in itself is contradictory and inconceivable.

For from the one, from Being, the determination of the negative, of

the manifold, is withdrawn. Thus while we, in our conception, allow

the actuality of the finite world, the Eleatics are more consistent,

in that they proceeded to say that only the One exists and that the

negative does not exist at all;—a consequence which, if it necessarily

arouses in us surprise, still none the less remains a great abstraction.

Sceptics saw in this the point of view of the uncertainty of all

things, and Sextus several times[50] quotes verses such as these:—

“No man at any time knew clearly and truly; nor will he ever know

What of the gods I say, as also of the universe.

For what he thinks to speak most perfectly

He knows that not at all; his own opinions cleave to all.”

Sextus, generalizing, explains this in the first passage thus: “Let us

imagine that in a house in which are many valuables, there were those

who sought for gold by night; in such a case everyone would think that

he had found the gold, but would not know certainly whether he actually

had found it. Thus philosophers come into this world as into a great

house to seek the truth, but were they to reach it, they could not tell

whether they really had attained to it.” The indefinite expressions

of Xenophanes might also merely mean that none knows that which he

(Xenophanes) here makes known. In the second passage Sextus puts it

thus: “Xenophanes does not make all knowledge void, but only the

scientific and infallible; opinionative knowledge is, however, left. He

expresses this in saying that opinion cleaves to all. So that with him

the criterion is made to be opinion, i.e. the apparent, and not that

which is firm and sure; Parmenides, on the contrary, condemns opinion.”

But from his doctrine of the One, there follows the annihilation of

ordinary ideas, which is what he did in the foregoing dialectic; it

is evident, however, that nobody could know the truth which he hereby

utters. If a thought such as this passed through one’s head, one could

not tell that it was true, and in such a case it would only be an

opinion.

We here find in Xenophanes a double consciousness; a pure consciousness

and consciousness of Being, and a consciousness of opinion. The former

was to him the consciousness of the divine, and it is the pure

dialectic, which is negatively related to all that is determined and

which annuls it. The manner in which he expresses himself towards the

sensuous world and finite thought-determinations is seen most clearly

in his allusions to the Greek mythological conceptions of the gods. He

says, amongst other things, according to Brandis (Comment. Eleat. P. I.

p. 68):—

“Did beasts and lions only have hands,

Works of art thereby to bring forth, as do men,

They would, in creating divine forms, give to them

What in image and size belongs to themselves.”

He also animadverts on the ideas of the gods held by Homer and Hesiod

in verses which Sextus (adv. Math. IX. 193) has preserved to us:—

“Hesiod and Homer have attached to the gods

All that which brings shame and censure to men;

Stealing, adultery, and mutual deceit.”

As, on the one hand, he defined absolute Being to be simple, making

that which is, however, break through and be immediately present in

it, on the other hand he philosophizes on appearances; in reference to

this certain fragments only are transmitted to us, and such physical

opinions as these can have no great interest. They are meant to have no

speculative significance any more than are those of our own physicists.

When he says in this connection

“Out of the earth comes all, and returns to it again,

We all have come from earth and water alike,

Thus all that grows and takes its rise is only earth and water,”[51]

this does not signify existence, physical principles, as did the water

of Thales. For Aristotle expressly says, that no one regarded the earth

as the absolute principle.

2. PARMINIDES.

Parmenides is a striking figure in the Eleatic school, and he arrives

at more definite conceptions than does Xenophanes. He was, according

to Diogenes (IX. 21), born at Elea of a rich and honourable race. Of

his life, however, little is known; Aristotle only says (Met. I. 5)

from tradition that he was a scholar of Xenophanes. Sextus Empiricus

(adv. Math. VII. 111) calls him a friend (_γνώριμος_) of Xenophanes.

Diogenes Laertius further states: “He heard Anaximander and Xenophanes

also, but did not follow the latter” (which seems only to refer to

his place of abode), “but he lived with Aminias and Diochartes the

Pythagorean, attached himself to the latter, and by the former, and

not by Xenophanes, was prevailed upon to lead a quiet life.” That the

period in which his life falls comes between Xenophanes and Zeno—so

that he is contemporaneous with them, though younger than the former

and older than the latter—is ascertained. According to Diogenes (IX.

23) he flourished about the 69th Olympiad (504-501 B.C.). What is

most important is his journey to Athens with Zeno, where Plato makes

them talk with Socrates. This may be accepted generally, but what is

strictly historical in it cannot be ascertained. In the Thætetus Plato

makes Socrates reply to the invitation to examine the Eleatic system:

“For Melissus and the others who assert the All to be One at rest,

I have a certain respect; I have even more for Parmenides. For, to

speak in Homeric language, he seems to me both venerable and strong.

I knew him when he was an old man and I was still quite young, and I

heard wonderful things from him.”[52] And in the Platonic Dialogue

Parmenides (p. 127. Steph. p. 4. Bekk.) where, as is well known, the

conversation is carried on by Parmenides and Socrates, the historic

circumstances of this interview are related in detail. “Parmenides was

very old, had hair which was quite grey, was beautiful in countenance,

about sixty-five years old, and Zeno almost forty.” Tennemann (Vol. I.

p. 415) places the journey in the 80th Olympiad (460-457 B.C.). Thus

Socrates, since he was born in Olympiad 77, 4 (469 B.C.), would seem to

have been still too young to have carried on a dialogue such as Plato

describes, and the principal matter of this dialogue, which is written

in the spirit of the Eleatic school, belongs to Plato himself. Besides,

we know from Parmenides’ life, that he stood in high respect with his

fellow-citizens at Elea, whose prosperity must be chiefly ascribed to

the laws which Parmenides gave them.[53] We also find in the _πίναξ_ of

Cebes (towards the beginning) “a Parmenidian life” used synonymously

with a moral life.

It must be remarked that here, where the Eleatic school is definitely

treated of, Plato does not speak of Xenophanes at all, but only of

Melissus and Parmenides. The fact that Plato, in one of his dialogues,

likewise accords the chief part to Parmenides, and puts in his mouth

the most lofty dialectic that ever was given, does not concern us here.

If with Xenophanes, by the proposition that out of nothing nothing

comes, origination and what depends upon or can be traced back to it is

denied, the opposition between Being and non-being makes its appearance

still more clearly with Parmenides, though still unconsciously. Sextus

Empiricus and Simplicius have preserved to us the most important

fragments from the poems of Parmenides; for Parmenides also propounded

his philosophy as a poem. The first long fragment in Sextus (adv. Math.

VII. 111) is an allegorical preface to his poem on Nature. This preface

is majestic; it is written after the manner of the times, and in it all

there is an energetic, impetuous soul which strives with Being to grasp

and to express it. We can show Parmenides’ philosophy best in his own

words. The introduction runs thus:—

“Horses that bore me, impelled by their courage,

Brought me to the much-famed streets of the goddess

Who leads the wise man to every kind of knowledge.

Maidens point out the way.

The axle sings hot as the daughters of Helios quickly approach,

Leaving the dwelling of night, pressing on to the light,

With mighty hands raising the sheltering veil.”

The maidens are, according to Sextus (adv. Math. VII. 112, 113), the

senses, and Helios’ daughters are more especially the eyes:—

“These are the gates of the pathways of night and of day.

Now the heavenly maidens approach the great doors,

Whose lock double-turned the punishing Dice protects.

To this one soft words were by the maidens addressed

Subtly persuading her the barriers of oak from the gates,

Now to withdraw. Yet these,

Directly the yawning breadth of the doors was revealed,

Drove the horses and waggon, on through the gate.

The goddess received me in friendship, seized with her one hand my

right,

And turning towards me, she said:

‘Oh, thou, who with guides all immortal and horses,

Camest here in my palace,—be welcome, young man.

For no evil fate has led thee into this path,

(Indeed it lies far from the ways of a man)

But Themis and Dice. Now shalt thou all things explore,

The heart never-flinching of the truth that persuades,

The transient opinions which are not to be trusted.

But from such paths keep the inquiring soul far away.

On this way let not the much followed custom

Cause thee to take the rash eye as thy guide,

Or the confused sounding ear and the tongue. Ponder considerately

With thy reason alone, the doctrine much and often examined,

Which I will proclaim. For there lacks but desire on your way.’”

The goddess develops everything from the double knowledge (_α_)

of thought, of the truth, and (_β_) of opinion; these make up the

two parts of the poem. In another fragment taken from Simplicius’

Commentary on Aristotle’s Physics (p. 25; 19 a) and from Proclus

on the Timæus (p. 29 b), we have the principal part of what is here

related preserved to us. “Understand,” says the goddess, “which are the

two roads of knowledge. The one which is only Being, and which is not

non-being, is the path of conviction, the truth is in it. The other

that is not Being, and which is necessarily non-being, is, I must tell

you, a path quite devoid of reason, for thou canst neither know, or

attain to, or express, non-being.” The nothing, in fact, turns into

something, since it is thought or is said: we say something, think

something, if we wish to think and say the nothing. “It is necessary

that saying and thinking should be Being; for Being is, but nothing is

not at all.” There the matter is stated in brief; and in this nothing,

falls negation generally, or in more concrete form, limitation, the

finite, restriction: _determinatio est negatio_ is Spinoza’s great

saying. Parmenides says, whatever form the negation may take, it

does not exist at all. To consider the nothing as the true is “the

way of error in which the ignorant and double-minded mortals wander.

Perplexity of mind sways the erring sense. Those who believe Being

and non-being to be the same, and then again not the same, are like

deaf and blind men surprised, like hordes confusedly driven.” The

error is to confuse them and to ascribe the same value to each, or to

distinguish them as if non-being were the limited generally. “Whichever

way is taken, it leads back to the point from which it started.” It is

a constantly self-contradictory and disintegrating movement. To human

ideas, now this is held to be reality and now its opposite, and then

again a mixture of both.

Simplicius quotes further, in writing on Aristotle’s Physics (p.

17 a; 31, 19): “But the truth is only the ‘is’; this is neither

begotten of anything else, nor transient, entire, alone in its class

(_μουνογενές_), unmoved and without end; it neither was, nor will be,

but is at once the all. For what birth wouldst thou seek for it? How

and whence should it be augmented? That it should be from that which

is not, I shall allow thee neither to say nor to think, for neither

can it be said or thought that the ‘is’ is not. What necessity had

either later or earlier made it begin from the nothing? Thus must it

throughout only be or not be; nor will any force of conviction ever

make something else arise out of that which is not. Thus origination

has disappeared, and decease is incredible. Being is not separable,

for it is entirely like itself; it is nowhere more, else would it not

hold together, nor is it less, for everything is full of Being. The all

is one coherent whole, for Being flows into unison with Being: it is

unchangeable and rests securely in itself; the force of necessity holds

it within the bounds of limitation. It cannot hence be said that it is

imperfect; for it is without defect, while non-existence is wanting in

all.” This Being is not the undetermined (_ἄπειρον_) for it is kept

within the limits of necessity; we similarly find in Aristotle that

limitation is ascribed to Parmenides. The sense in which the expression

“limit” is to be taken is uncertain. According to Parmenides, however,

this absolute limitation is as _Δίκη_, absolute necessity clearly

determined in itself; and it is an important fact that he went beyond

the uncultured conception of the infinite. “Thought, and that on

account of which thought is, are the same. For not without that which

is, in which it expresses itself (_ἐν ᾦ πεφατισμένον ἐστίν_), wilt thou

find Thought, seeing that it is nothing and will be nothing outside of

that which is.” That is the main point. Thought produces itself, and

what is produced is a Thought. Thought is thus identical with Being,

for there is nothing beside Being, this great affirmation. Plotinus,

in quoting (V. Ennead. I. 8) this last fragment says: “Parmenides

adopted this point of view, inasmuch as he did not place Being in

sensuous things; identifying Being with Thought, he maintained it to be

unchangeable.” The Sophists concluded from this: “All is truth; there

is no error, for error is the non-existent, that which is not to be

thought.”

Since in this an advance into the region of the ideal is observable,

Parmenides began Philosophy proper. A man now constitutes himself free

from all ideas and opinions, denies their truth, and says necessity

alone, Being, is the truth. This beginning is certainly still dim and

indefinite, and we cannot say much of what it involves; but to take

up this position certainly is to develop Philosophy proper, which has

not hitherto existed. The dialectic that the transient has no truth,

is implied in it, for if these determinations are taken as they are

usually understood, contradictions ensue. In Simplicius (in Arist.

Phys. p. 27 b.; 31 b.) we have further metaphorical images from

Parmenides. “Since the utmost limit of Being is perfect, it resembles

on every side the form of a well rounded sphere, which from its centre

extends in all directions equally, for it can be neither larger or

smaller in one part or another. There is no non-being which prevents it

from attaining to the like”—from coming into unity with itself—“and

there is no Being where it was devoid of Being, here more and there

less. Because the all is without defect, it is in all places in the

same way like itself in its determinations.” Plotinus in the passage

quoted says: “He compares Being with the spherical form, because it

comprehends all in itself, and Thought is not outside of this, but is

contained in it.” And Simplicius says: “We must not wonder at him,

for on account of the poetic form, he adopts a mythological fiction

(_πλάσματος_).” It immediately strikes us that the sphere is limited,

and furthermore in space, and hence another must be above it; but

then the Notion of the sphere is the similarity of withholding the

different, notwithstanding that even the undifferentiated must be

expressed; hence this image is inconsistent.

Parmenides adds to this doctrine of the truth, the doctrine of human

opinions, the illusive system of the world. Simplicius, writing on

Aristotle’s Physics (p. 7 b; 39 a), tells us that he says: “Men have

two forms of opinion, one of which should not be, and in it they

are mistaken; they set them in opposition to one another in form

and symbol. The one, the ethereal fire of the flame, is quite fine,

identical with itself throughout, but not identical with the other,

for that is also for itself; on the other hand there is what belongs

to night, or thick and ponderous existence.” By the former, warmth,

softness, lightness is expressed, and by the latter, cold. “But since

everything is called light and night, and their qualities are suited

both to the one kind of things and the other, everything alike is

filled with light and dark night; both are alike since nothing exists

without both.” Aristotle (Met. I. 3 and 5), and the other historians,

likewise unanimously attribute to Parmenides the fact that he sets

forth two principles for the system of manifest things, warmth and

cold, through the union of which everything is. Light, fire, is the

active and animate; night, cold, is called the passive.

Parmenides also speaks like a Pythagorean—he was called _ἀνὲρ

Πυθαγορεῖος_ by Strabo—in the following, and likewise mythological

conception: “There are circlets wound round one another, one of which

is of the rare element and the other of the dense, between which others

are to be found, composed of light and darkness mingled. Those which

are less are of impure fire, but those over them of night, through

which proceed the forces of the flames. That which holds this all

together, however, is something fixed, like a wall, under which there

is a fiery wreath, and the most central of the rare spheres again is

fiery. The most central of those mixed is the goddess that reigns over

all, the Divider (_κληροῦχος_), Dice and Necessity. For she is the

principle of all earthly produce and intermingling, which impels the

male to mix with the female, and conversely; she took Love to help

her, creating him first amongst the gods. The air is an exhalation

(_ἀναπνοή_) of the earth; the sun and the milky way, the breath of

fire; and the moon is air and fire mingled, &c.”[54]

It still remains to us to explain the manner in which Parmenides

regarded sensation and thought, which may undoubtedly at first sight

seem to be materialistic. Theophrastus,[55] for example, remarks in

this regard: “Parmenides said nothing more than that there are two

elements. Knowledge is determined according to the preponderance of

the one or of the other; for, according as warmth or cold predominate,

thought varies; it becomes better and purer through warmth, and yet it

requires also a certain balance.”

“For as in each man there still is in his dispersive limbs an

intermingling,

So is the understanding of man; for that

Which is thought by men, is the nature of the limbs,

Both in one and all; for thought is indeed the most.”[56]

He thus takes sensation and thought to be the same, and makes

remembrance and oblivion to arise from these through mingling them,

but whether in the intermingling they take an equal place, whether

this is thought or not, and what condition this is, he leaves quite

undetermined. But that he ascribes sensation to the opposites in and

for themselves is clear, because he says: “The dead do not feel

light or warmth or hear voices, because the fire is out of them;

they feel cold, stillness and the opposite, however, and, speaking

generally, each existence has a certain knowledge.” In fact, this view

of Parmenides is really the opposite of materialism, for materialism

consists in putting together the soul from parts, or independent forces

(the wooden horse of the senses).

3. MELISSUS.

There is little to tell about the life of Melissus. Diogenes Laertius

(IX. 24) calls him a disciple of Parmenides, but the discipleship is

uncertain; it is also said of him that he associated with Heraclitus.

He was born in Samos, like Pythagoras, and was besides a distinguished

statesman amongst his people. It is said by Plutarch (in Pericle, 26)

that, as admiral of the Samians, he gained in battle a victory over the

Athenians. He flourished about the 84th Olympiad (444 B.C.).

In regard to his philosophy, too, there is little to say. Aristotle,

where he mentions him, places him always with Parmenides, as resembling

him in mode of thought. Simplicius, writing on Aristotle’s Physics

(p. 7 sqq.), has preserved several fragments of his prose writings on

Nature, which show the same kind of thoughts and arguments as we find

in Parmenides, but, in part, somewhat more developed. It was a question

whether the reasoning in which it is shown that change does not exist,

or contradicts itself, which, by Aristotle in his incomplete, and, in

some parts, most corrupt work on Xenophanes, Zeno, and Gorgias (c. 2.),

was ascribed to Xenophanes, did not really belong to Melissus.[57]