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4. The Conceptions of Being.

The fact that things of experience change into one another was

the stimulus to the first philosophical reflections, and wonder l at

this must indeed have arisen early among a people so mobile and

with so varied an experience of Nature as the lonians. To this

fact, which furnished the fundamental motive of its reflection, the

Ionic philosophy gave liveliest expression in Heraclitus, who seems

to have been unwearied 2 in seeking the most pointed formulations

for this universal mutability of all things, and especially for the

sudden changes of opposites into each other. But while myth gave


1 Cf. upon the philosophical value of the Oavudieiv, Arist. Met. I. 2, 982 b 12.
2 Fragm. (Schust.) 41-44, 60, 63, 67.

32 The Greeks : Cosmological Period. [PART I.


to this view the garb of a fabled account of the formation of the

world, science asked for the abiding ground of all these changes,

and fixed this question in the conception of the cosmic matter, or

l{ world-8tuff" ( Weltstoff"), which experiences all these transforma

tions, from which all individual things arise, and into which they

become again transformed (d/>x>?)- In this conception l was tacitly

contained the presupposition of the unity of the world; whether the

Milesians 2 already sought to justify this we do not know. It was a

later eclectic straggler 3 who first attempted to justify this Monism

by the transformation of all things into one another, and by the

inter-connection of all things without exception.
1. That, however, a single cosmic matter, or world-stuff, lies at

the basis of the entire process of nature, appears in ancient tradi

tion as a self-evident presupposition of the Ionic School. The only

question was to determine what this elementary matter was. The

nearest course was then to seek for it in what was given in experi

ence, and so Thales declared it to be water; Anaximenes, air. To

this choice they were probably determined only by the mobility,

changeability, and apparent inner vitality 4 of water and air. It is

evident, too, that the Milesians thought little in this connection of

the chemical peculiarities of water and air, but only of the states

of aggregation 5 concerned. While the solid appears in itself dead,

moved only from without, the liquid and volatile make the impres

sion of independent mobility and vitality f. and the monistic prepos

session of this first philosophising was so great that the Milesians

never once thought of asking for a reason or ground of this cease

less change of the cosmic matter, but instead assumed this as a self-

intelligible fact a matter of course as they did all change or

occurrence ; at most they described its individual forms. The cos

mic matter passed with them for something in itself living : they

thought of it as animated, just as are particular organisms, 6 and for

this reason their doctrine is usually characterised from the stand

point of the later separation in conceptions as Hylozoism.


1 Which Aristotle in the Met. I. 3, 983 b 8, has defined, not without the

admixture of his own categories.


2 The expression dpx 1 ?? which, moreover, bears in itself the memory of the

chronological fancies of the Cosmologists, is said by Simplicius to have been

used first by Anaximander.
3 Diogenes of Apollonia. Cf. Simpl. Phys. (D.) 32 r 151, 30, and Arist. Gen. et

Corr. I. 6, 322 b 13.


* Schol. in Arist. 514 a 33.
5 For vSwp, vyp6v is frequently substituted. With regard to the dijp of Anaxi

menes the accounts are such that the attempt has been made to distinguish his

metaphysical "air" from the empirical : Hitter, I. 217 ; Brandis, I. 144.
6 Plut. Plac. I. 3 (Doxogr. D. 278). Perhaps this is intended in the conjec

ture of Aristotle, Met. I. 3, 983 b 22.


()nAi . 1, 4.] Conceptions of Being : The Milesians. 33


2. If we ask, however, why Anaximenes, whose doctrine, like

that of Thales, seems to have kept within the bounds of experience,

substituted air for water, we learn l that he believed air to have a

characteristic which water lacked, a characteristic, too, which his

predecessor Anaximander had postulated as indispensable for the

conception of primitive matter, viz. that of infinity. As motive for

this postulate of Anaximander there is related the argument that a

finite cosmic matter would exhaust itself in the ceaseless succession

of productions. 2 But Anaximander had also seen that this demand

made by the conception of the apxy could not be satisfied by any

matter or substance which we can perceive, and had on this account

transferred the cosmic matter beyond experience. He maintained

boldly the reality of an original ground of things, possessing all the

properties that are necessary, if we are to derive the changes in the

world of experience from something itself abiding and raised above

change, even though such a ground might not be found in experi

ence. He drew from the conception of the dpx^ the consequence,

that though no object of experience corresponds to this conception,

we must yet, to explain experience, assume such a conception behind

it as real and conditioning it. He therefore called the cosmic mat

ter "the Infinite" (TO obrapov), and ascribed to it all the qualities

postulated in the conception of the apx>j that is, that it had never

begun to be, and was imperishable, inexhaustible, and indestructible.
The conception of matter, thus constructed by Anaximander is,

nevertheless, clear only in the respect that it is to unite within it

spatial infinity and the quality of being without beginning or end

in time, and thus the mark of the all-embracing and all-determin

ing; 3 on the other hand, with reference to its qualitative deter

mination, it cannot be made clear what the philosopher intended.

Later accounts give us to understand that he expressly maintained

that the original matter was qualitatively undetermined or indefinite

(dd/aio-Tos), 4 while the statements of Aristotle 5 speak more for the

assumption of a mixture of all kinds of matter known in experience,

a mixture completely adjusted or equalised, and therefore as a

whole indifferent or neutral. The most probable view here is, that

Anaximander reproduced in the form of an abstract conception the

iSimpl. Phys. (D.) 6 24, 26.


2 Plut. Plac. I. 3 (Doxogr. D. 277) ; Arist. Phys. III. 8, 208 a 8.
3 Arist. Phys. III. 4, 203 b 7.
4 Schol. in Arist. 514 a 33 ; Herbart, Einleitung in die Philosophic (Ges.

W., I. 196).


5 Me.t. XII. 2, 1069 b 18, and especially Phys. I. 4, 187 a 20. Cf. also Simpl.

Phys. (D.) 33 r 154, 14 (according to Theophrastus) . This much-treated contro

versy will be spoken of more in detail below ( 6).

34 The Greeks : Cosmological Period. [PART. X


unclear idea of the mythical chaos which was "one" and yet also

" all." This he did by assuming as the cosmic matter an infinite,

corporeal mass, in which the various empirical substances were so

mixed that no definite quality could be ascribed to it as a whole.

For this reason, however, the separation of the individual qualities

out of this self-moved matter could no longer be regarded as properly

a qualitative change in it. With this view the conception of the

unity of the world as regards quality would be given up, to be sure,

and an essential preparation made for the later development.
3. Still another predicate was given by Anaxirnander to the In

finite, TO Otiov, the divine. As a last remembrance of the religious

home in which scientific reflection arose, it shows for the first time

the inclination of philosophers, constantly recurring in history, to

view as " Deity " the highest conception which theory has led them

to use for explaining the world, and so to give it at the same time

a sanction for the religious consciousness. Anaximander s matter is

the first philosophic conception of God, the first attempt, and one

which remains still entirely within the physical, to strip the idea

of God of all mythical form.


But while the religious need thus maintained itself in the deter

mination of metaphysical conception, the possibility of an influence

of the results of science upon the religious life was brought nearer, the

more these results met and responded to an impulse which hitherto

had been dominant only in an obscure and uncertain manner within

that life. The transformation which the Greek myths had undergone,

as well in the import given them in cosmogonic fancy as in that given

to their ethical interpretation, tended everywhere toward a mono

theistic culmination (Pherecydes, Solon); and to this movement

its final result, a clearly outspoken monism, was now proffered by

science.
This relation was brought to expression by Xenophanes, not a

thinker and investigator, but an imaginative disciple of science,

strong in his convictions, who brought the new teaching from East

to West and gave it a thoroughly religious colouring. His mainte

nance of monotheism, which he expressed as enthusiastic intuition in

the saying, 1 that whithersoever he looked all was constantly flowing

together for him into one Nature (/uW cis <wriv), took on at once,

however, that sharp polemis turn against the popular faith, by which

he is principally characterised in literature. The scorn, which he

poured out with abundant wit over the anthropomorphism of myth

ology, 2 the anger with which he pursued the poets as the portrayers
1 Timon in Sext. Emp. Pyrrh. Hyp. I. 224. 2 Clem. Alex. Strom. V. 601.

CHAP. 1. 4.] Conceptions of Being : Xenophanes. 35


of these divine figures provided with all the weaknesses and vices of

human nature, 1 these rest upon an ideal of God which will have

the Supreme Being regarded as incomparable with man in both

bodily and mental characteristics. When he passes to positive at

tributes, Xenophanes becomes more obscure. On the one hand, the

deity as ev KCU vav is identified with the universe, and to this " World-

God " are then ascribed all the predicates of the Milesian a.pxn

(eternity, existence that has not become what it is, imperishability) ;

on the other hand, qualities are ascribed to the deity, some of which

are spatial, as the spherical form, while others are psychical func

tions. Among these latter the omnipresence of the knowing activity

and of the rational guidance of things is expressly mentioned. In

this respect the World-God of Xenophanes appears only as the

highest among the rest of " gods and men."


While here a predominantly theological turn of philosophy is

already manifested, the exchange of the point of view of metaphysics

and natural science taken by Anaximander, for the religious point

of view of Xenophanes shows itself in two essential deviations.

The conception of the World-God is for the latter an object of

religious reverence, and scarcely a means for understanding Nature.

The Colophonian s sense for knowledge of Nature is slight, his ideas

are in part very childlike, and, as compared with those of the Mile

sians, undeveloped. And so for his views, the characteristic of

infinity, which Milesian science regarded as necessary in the cosmic

matter, could be dispensed with ; on the contrary, it seemed to him

more in accordance with the dignity of the divine Nature, 2 to think

of this as limited within itself, as entirely shut up or complete, con

sequently as regards its spatial aspect, spherical. And while the

Milesians thought of the original ground of things as ever in motion

spontaneously, and as characterised by living variety in its inter

nal structure, Xeuophanes struck out this postulate hitherto in use-

for the explanation of Nature, and declared the World-God to be

immovable and perfectly homogeneous in all its parts. How, indeed,

he thought that the variety of individual things whose reality he

did not doubt, could be reconciled with this view, must remain

uncertain.


4. As was required by the conception of change, the Milesian

conception of the World-substance had united without clear discrim

ination two essential elements : the one that of a substance re

maining like itself, the other that of independent or self-subsistent


1 Sext. Emp. Adv. Math. IX. 193.
2 Ilippol. Ref. I. 14 (Doxogr. I). 565). In other passages, again, it is said

that he would have the deity thought neither limited nor unlimited (?).


36 The Greeks : Cosmological Period. [PART I.


changeability. In the thought of Xenophanes the first element was

isolated ; the same process took place for the second through Hera

clitus, His doctrine presupposes the work of the Milesians, from

the conclusion of which it is separated by a generation, in this way :

their effort to determine or define in conceptions an abiding world-

ground has been recognised as hopeless. There is nothing abiding,

either in the world or in its constitution taken as a whole. Not

only individual things, but also the universe as a whole, are involved

in perpetual, ceaseless revolution: all flows, and nothing abides. We

cannot say of things that they are ; they become only, and pass away

in the ever-changing play of the movement of the universe. That,

then, which abides and deserves the name of deity, is not a thing,

and not substance or matter, but motion, the cosmic process, Becom

ing itself.


To meet a strong demand that seems made by this turn to abstrac

tion, Heraclitus found help in the sensuous perception in which this

motion presented itself to him : that of fire. / The co-operation of

this in the conversion of things of Nature into each other had been

already noticed by the Milesians ; to this may have been added

ancient Oriental mystical ideas, which contact with the Persians

made especially accessible to the lonians of that day.; But when

Heraclitus declared the world to be an ever-living fire, and Fire,

therefore, to be the essence of all things, he understood by this apxn

not a material or substance which survived all its transformations,

but just the transforming process itself in its ever-darting, vibrating

activity (ziingelnde), the soaring up and vanishing which corre

spond to the Becoming and passing away. 1
At the same time, however, this idea takes on a still firmer form,

in that Heraclitus emphasised much more strongly than the Mile

sians the fact that this change is accomplished in accordance with

definite relations, and in a succession that remains always the same. 2

This rhythm of events (which later times have called the uniformity

of Nature under law) is therefore the only permanent ; it is termed

by Heraclitus the destiny (ei/Ma/o/ue vi;), the order (8iip;), the reason

(Ao yo?) of the world. These predicates, in which physical, ethical,


1 The difficulty of ascribing to such a motion without any substrate, to a mere

Becoming, the highest reality and the capacity to produce things, was evidently

very much less for undeveloped thought not yet conscious of its categories than

for later apprehension. The conception of Becoming as fire, hovering between

the symbolic and the real meaning of the term, was supported by the use of

language which treats of functions and relations as also substantives. But

Heraclitus does not disdain to let the dim idea of a World-substance stand in the

background in his metaphors (of the clay kneaded ever anew, of the drink

continually stirred).
2 Further in detail on this point in the following section.

CHAP. 1, 4.] Conceptions of Being : Heraclitus, Parmenides. 37


and logical order in the world appear as still identified, prove only

the undeveloped state of thought which does not yet know how to

separate the different motives. The conception, however, which

Heraclitus has grasped with complete clearness, and carried though

with all the strength of his austere personality, is that of order, a

conception, nevertheless, whose validity was for him as much a

matter of conviction as of knowledge.
5. In evident opposition to this theory of the Ephesian, the con

ception of Being was worked out by Parmenides, the head of the

Eleatic School, and the most important thinker of this period. Yet

it is not easy to reconstruct his formulation of this conception from

the few fragments of his didactic poem, the quite unique character

of which consists in the union of dryest abstraction with grand and

rich imagery. That there is a Being (O-TI yap etvai), is for the Ele

atic a postulate of such cogent evidence that he only states this

position without proving it, and that he explains it only by a nega

tive turn of thought which first discloses to us completely the sense

in which we are to understand his main thought. " Non-being "

(py cfvcu), he adds, or that which "is" not (TO firj eov), cannot be

and cannot be thought. For all thought is in relation to a some

thing that is, which forms its content. 1 This view of the correla

tive nature of Being and consciousness leads so far with Parmenides

that the two, thought and Being, are declared to be fully identical.

No thought to whose content Being does not belong, no Being

that is not thought : thought and Being are the same.


These propositions, which look so abstractly ontological if we con

sider only the words, take on quite another meaning when we con

sider that the fragments of the great Elean leave no doubt as to

what he desired to have regarded as " Being " or that which " is."

This was corporeality, materiality (TO TrAe ov). For him, " being" and

"filling space" are the same. This "Being," this function of filling

space, is precisely the same in the case of all that " is " ; there is,

therefore, only the one, single Being which has no internal distinc

tions. " Non-being," or what is not [has not the attribute of Being],

means, accordingly, incorporeal ity, empty space (TO KCVO V). This

double meaning of the emu (Being) employed by Parmenides, ac

cording to which the word means at one time " the full " and at an

other time " Reality," leads then to the proposition that empty space

cannot be.


Now for the nai ve, sensuous way of looking at things which

lurks even in these principles of Parmenides, the separateness of


1 Fr., ed. Karsten, vv. 94 ff.

38 The Greeks : Gosmological Period. [PART I.


bhings, by virtue of which they present themselves in their plurality

and multiplicity, consists in their separation by empty space ; and,

on the other hand, all that takes place in the corporeal world, i.e.

all motion, consists in the change of place which the " full " experi

ences in the "empty" (or the "Void"). If, therefore, the Void is

not real or actual, then the plurality and motion of individual things

cannot be real.
The number and variety of things presented in co-existence and

succession by experience had given the Milesians occasion to ask

for the common abiding ground of which all these things were

metamorphoses. When, however, the conception of cosmic sub

stance or world-stuff has culminated with Parmenides in the con

ception of Being, there seems so little possibility of uniting these

individual things with it, that reality is denied them, and the one

unitary Being remains also the only being. 1 The conception formed

for the purpose of explanation has so developed internally that to

maintain it involves the denial of that which was to be explained

by it. In this sense the Eleatic doctrine is acosmism : the mani-

foldness of things has sunk in the All-one : the latter alone " is,"

the former are deception and seeming.
According to Parmenides, however, we are to predicate of the

One that it is eternal, has never come into being, is imperishable,

and especially (as Xenophanes had maintained) that it is through

and through one in kind, one with itself, without any distinctions

or differences, i.e. completely homogeneous and absolutely unchange

able. He follows Xenophanes also in regarding the One as limited,

complete, and definitive. Being is then a well-rounded sphere, per

fectly homogeneous within itself, and this only and unitary world-

body is at the same time the world-thought, 2 simple, excluding all

particulars from itself : TO yap TrAe ov eo-ri VOT//WI.


6. All these attempts, in part fantastic, in part regardlessly

abstract, were needed in order to gain the presuppositions for the

development of the first usable conceptions for apprehending Nature.

For important as were the motives of thought that had come to

recognition therein, neither the world-stuff or cosmic matter of the

Milesians, nor the "Fire-Becoming" of Heraclitus, nor the Being of

Parmenides were available for explaining Nature. Now the imper

fection of the first had become clear through the contrast which


1 A great role in these considerations of the Eleatics is obviously played by

the ambiguities in language, by which, on the one hand, the fv means both

numerical unity and also qualitative unity or simplicity, while the verb elvai has

not only the function of the copula, but also the meaning of " Reality."


2 Hence, terms like " materialism " and " idealism " do not apply to this naive

identification of consciousness and its object, the corporeal world.


CHAP. 1, 4.] Conceptions of Being : Empedocles. 39


separated the two latter as by a gulf, and with the recognition of

this, occasion was given for the more independent investigators of

the next period to separate in their conceptions the two motifs

(being and becoming), and by setting them over against one another

to think out new forms of relation, out of which permanently valua

ble categories for the knowledge of Nature resulted.


These mediating attempts have in common, on the one hand, the

recognition of the Eleatic postulate that that which " is " must be

thought throughout not only as eternal, without a beginning and

imperishable, but also as homogeneous, and as regards its qualities

unchangeable ; on the other hand, however, they assent also to the

thought of Heraclitus that an undeniable reality belongs to Becom

ing and change (Geschehen), and so to the manifoldness of things.

Common to them, also, in their adjustment of these two needs of

thought is the attempt to assume a plurality of beings, each of which

should satisfy for itself the postulate of Parmenides ; while, on

the other hand, by changing their spatial relations, they were to

bring about the changeful variety of individual things which expe

rience shows. If the Milesians had spoken of qualitative changes

of the cosmic substance or matter, the Eleatic principle had ex

cluded the possibility of it ; if, nevertheless, change ought to receive

recognition, as with Heraclitus, and be attributed to Being itself,

it must be reduced to a kind of change which leaves untouched

the qualities of the existent. Such a change, however, was think

able only as a change of place, i.e. as motion. The investigators of

Nature in the fifth century maintained, therefore, with the Eleatics,

the (qualitative) unchangeableness of the existent, but against the

Eleatics, its plurality and motion ; 1 with Heraclitus, they insisted

upon the reality of occurrence and change, and against Heraclitus,

upon the Being of permanent and unchangeable substances as under

lying and producing the same. Their common view is this : there

is a plurality of existing beings which, unchangeable in them

selves, make the change and variety of individual things compre

hensible.


7. This principle seems to have been asserted first and in its

most imperfect form by Empedodes, in a form, however, that was

widely influential historically. He put forward as " elements " 2 the

four which are still current in the popular modes of thought, earth,


1 Later (Plato, Theaet. 181 D ; Arist. var. Zoc.), d\Xo/w<m (qualitative change)

and irepHfropd (change of place) are contrasted as species of Klvijffis or /iera/SoXij.

In reality this is done here, though the terms are as yet lacking.


2 Instead of the later expression o-roixeta, we find in Empedocles the more

poetic term " roots of all things,"


40 The Greeks : Cosmological Period. [PART I.


water, air, and fire. 1 Each of these is according to this system,

without beginning and imperishable, homogeneous and unchange

able, but at the same time divisible into parts, and in these parts

capable of change of place. Out of the mixture of the elements

arise individual things, which in turn cease to exist when the mix

ture is separated into the elements ; to the kind of mixture made

are due the various qualities of individual things, which are often

different from the properties of the elements themselves.


"At the same time the note of unchangeableness and a deviation

from the Milesian Hylozoism assert themselves in the system of

Empedocles .to the extent that In- could not assign independent ca

pacity of motion to these material elements which experience only

changing states of motion and mechanical mixings. On this account

he was obliged to seek a ccw.se of motion independent of the four

elements. As such a cause he designated love and hate. The out

come, however, of this first attempt to set over against a dead matter,

deprived by abstraction of all motion of its own, the force which

moves it, as a metaphysically independent something, was very

obscure. Love and hate are, with Empedocles, not mere properties,

functions, or relations of the elements, but rather independent

powers set over against them ; but how we are to think the reality

of these moving forces is not disclosed in any satisfactory way in the

fragments. 2 Only this seems certain, that in fixing the dual nature

of the principle of motion the thought was also operative that two

distinct causes, love and hate, were requisite to account for the

good and the evil in the change of things of our experience, 3 a first

indication that determinations of " worth " or value are beginning

to be introduced into the theory of Nature.


8.! Empedocles thought it possible to derive the special qualities

of individual things from the proper mixture of the four elements :

whether he attempted so to derive them, and if so, how, we do not

indeed know. This difficulty was avoided by Anaxagoras, who,

from the Eleatic principle that nothing that is can arise or pass

away, drew the conclusion that as many elements must be assumed


1 Aside from dependence upon his predecessors, his selection was evidently

due to the inclination to regard the different states of aggregation as the original

essence of things. No importance seems to have attached to the number four,

in this. The dialectical construction which Plato and Aristotle gave for this is

quite remote from the thought of the Agrigentine.
2 If <pi\ia and veZVos are occasionally counted by the later recorders as fifth

and sixth dpx 1 ? of Empedocles, we must not infer from this that he regarded

them as substances. His obscure and almost mythical terminology rests, for

the most part, upon the fact that conceptions standing for functions are substan

tives in language. 3 Arist. Met. I. 4, 984 b 32.
4 He called them a-ir^iara (seeds of things), or also simply xP nf J - aTa (sub

stances).


CHAP. 1, 4.] Conceptions of Being : Anaxagoras. 41


as there are simple substances in the things of experience, meaning

by simple substances those which on repeated division always sep

arate into parts qualitatively the same with their wholes^ Such

elementary substances were later, in accordance with his definition,

called homoiomeriai. At that time, however, when only mechanical

division or change of temperature were known as means of investi

gation, this conception of element (in principle entirely correspond

ing to the conceptions of the chemistry of to-day) applied to the

greater part of the substances given in experience, 1 and on that ac

count Anaxagoras maintained that there were countless elements dif

fering in form, colour, and taste. He held that they were present

throughout the entire universe in a very finely divided state. Their

coming together or compounding (o-uyK/oio-is) constitutes the arising,

their separation (SiaKpions) the passing away, of individual things.

There is, accordingly, something of every substance present in every

thing: it is only for our sensuous apprehension that the individual

thing takes on the properties of that substance or of those sub

stances which may be present in a preponderating degree.


The elements, as the true being, are regarded now by Anaxagoras

also as eternal, without beginning or end, unchangeable, and though

movable in space, yet not in motion of themselves. Here, too, then,

we must ask for a force which is the cause of motion. Since, how

ever, this force must be regarded as existent, a something that is,

Anaxagoras hit upon the expedient of assigning it to a special,

single sort of matter or elementary substance. This force-element

or motive-matter (Bewecjuitgsstojf) is conceived to be the lightest and

most mobile of all elements. In distinction from all the others it is

that one of the homoiomeriai which alone is in motion of itself, and

communicates this its own motion to the rest ; it moves itself and

the rest. To determine the inner nature of this " force-substance,"

however, two lines of thought unite : the property of originating mo

tion is, for the naive mode of looking at things, the surest sign of the

animate; this exceptional kind of matter, then, which is self-moved?

must be animate matter or " soul-stuff" (Seelenstojf), its quality

must be animate or psychical. 2 And, secondly, a power is known

through its effect : if, now, this motive-matter is the cause of the

formation of the world, to bring about which it has separated out

the remaining idle elements, then we must be able to know its

nature from this which it has accomplished. But the universe, in

particular the regular revolution of the stars, makes the impression


1 According to the fragments of Anaxagoras, bones, flesh, and marrow also ;

on the other hand, the metals.


2 [The Greek ^v^t and German Seele include both these meanings.]

42 The G-reeks : Cosmological Period. [PART I.


of beautiful and purposive order (/cotr/uos). Such a mastering of

gigantic masses in a harmonious system, this undisturbed circling

of countless worlds, on which Anaxagoras turned his wondering

contemplation, it seemed to him could be the result only of a mind

arranging the movements according to ends, and ruling them. For

this reason he characterised the force-substance as Reason (vous) or

as " Thought-stuff."
The vovs of Anaxagoras is then a stuff or substance, a corporeal

element, homogeneous, unproduced, and imperishable, diffused in a

finely divided state throughout the universe ; different from the

other substances, however, not only in degree, as being the finest,

lightest, and most mobile, but also in essence, since it alone is self-

moved, and by virtue of its own motion moves the other elements in

the purposive way which we recognise in the order of the world.

This emphasising of the order in the universe is a Heraclitic element

in the teaching of Anaxagoras, and the conclusion drawn from the

ordered movements to a rational cause of them, acting according to

ends, is the first instance of the ideological explanation of nature. 1

With this procedure a conception of worth ( Werthbegriff) namely,

beauty and perfection is made a principle of explanation in the

theoretical field also.


9. The Atomism of Leucippus developed from the Eleatici concep

tion of Being in a direction opposite to that just traced. While

Empedocles maintained that some, and Anaxagoras that all, qualities

were metaphysically primitive, the founder of the school of Abdera

remained in accord with the position of Parmenides, that no "Being"

belongs to any of all the various qualitative determinations exhibited

by experience, and that the sole property of Being is the property of

filling space, corporeality, TO TrXt ov. If now, however, the plurality of

things, and the mutations taking place among them as they come

and go, were to be made intelligible, then instead of the single world-

body, with no internal distinctions which Parmenides had taught, a

plurality of such must be assumed, separated from one another, not

by other Being, but by that which is not Being, Non-being: i.e. by the

incorporeal, by empty space. This entity, then, which is Non-being [i.e.

not Being in the true sense], must have in its turn a kind of Being,

or of metaphysical reality ascribed to it, 2 and Leucippus regarded it


1 As such he was praised by Plato (Phced. 97 B), and overestimated by

Aristotle (Met. I. 3, 984 b). Cf., however, 5. The moderns (Hegel) have

added the further over-estimate of seeking to interpret the *oDs as an immate

rial principle. But the fragments (Simpl. Phys. (D.) 33 T 156, 13) leave no

doubt that this lightest, purest element, which does not mingle with the rest,

but only plays about them and moves them as living force, was also a space

filling matter or stuff. 2 Plut. Ado. Col. 4, 2, 1109.

CHAP. 1, 4.] Conceptions of Being : Leueippus, Zeno. 43


as the unlimited, the aTrtipov, in contrast with the limitation which

Being proper possesses, according to Parmenides. Leueippus, there

fore, shatters in pieces the world-body of Parmenides, and scatters

its parts through infinite space. Each of these parts, however, is,

like the absolute Being of Parmenides, eternal and unchangeable,

without beginning, indestructible, homogeneous, limited, and indi

visible. Hence these portions of Being are called atoms, aro/iot;

and for the reasons which had led Anaximander to his concept

of the aarttpov Leueippus maintained that there were countless

numbers of such atoms, infinitely varied in form. Their size must

be taken as imperceptibly small, since all things in our experience

are divisible. Since, however, they all possess only the one like

quality of filling space, differences between them can be only quan

titative ; differences in size, form, and situation.


Out of such metaphysical considerations grew the concept of the

atom, which has proved so fruitful for the theoretical science of

Nature just because, as was evident already in the system of Leu

eippus, it contains the postulate that all qualitative differences

exhibited by Nature are to be reduced to quantitative. The things

which we perceive, Leueippus taught, are combinations oF~afoirn? ;

they arise when atoms unite, and pass away when they part. The

properties which we perceive in these complexes are only seeming

or appearance ; there exist in truth only the determinations of size,

form, arrangement, and situation of the individual atoms which

constitute Being.
Empty space is, accordingly, the presupposition as well for the

uniting and separating of atoms as for their separateness and shape.

All " becoming," or change, is in its essence motion of atoms in space.

If we ask for the ground of this motion of the atoms, 1 since space

as properly not a true Being cannot be allowed as cause, and

Atomism recognises nothing as actual except space and the atoms,

this ground can be sought only in the atoms themselves; i.e. the

atoms are of themselves in motion, and this, their independent mo

tion, is as truly without beginning and end as is their being. And as

the atomj are indefinitely varied in size and form, and completely

independent of one another, so their original motions are infinite in

variety. They fly confusedly about in infinite space, which knows

no above and below, no within and without, each for itself, until

their accidental meeting leads to the formation of things and worlds.

The separation between the conceptions of matter and moving force
1 Arist. Phys. VIII. 1, 252 a 32, says of the Atomists that they did not ask as

to the origin of motion as a matter of course, for they declared motion itself

to be causeless (cf. Met. I. 4).

44 The Greeks: Cosmological Period. [PART I.


which Empedocles and Anaxagoras, each in his way, had attempted r

was thus in turn abolished by the Atomists. They ascribed to the

particles of matter the capacity, not indeed of qualitative change

(dAAotWis), but of independent motion (KIV-TJO-IS in the narrower sense r

equivalent to Trtpt^opa), and took up again in this sense the principle

of Milesian hylozoism.


10. In opposition to these pluralistic systems, JZenn, the friend

and disciple of Parmenides, sought to defend the Eleatic doctrine by

setting forth the contradictions in which the assumption of a plural

ity of Beings is involved. As regards size, he pointed out, it fol

lows that the totality of Being must be on the one hand infinitely

small, on the other hand infinitely great: infinitely small, because

the combination of any number whatever of parts, each of which is

to be infinitely small, never yields anything more than an infinitely

small sum ; l infinitely great, on the contrary, because the bound

ary which is to separate two parts must itself be an existent some

thing, i.e. spatial magnitude, which again is itself separated from

the two parts by a boundary of which the same holds true, and so

on in infinitum. From the latter argument, which was called that

from dichotomy (the IK Sixo-ro/uas), Zeno reasoned also that as

regards number, what is must be unlimited, while, on the other hand,

this complete Being, not in process of becoming, is to be regarded

also as numerically limited [i.e. as complete]. And just as with the

assumption of the " many," so the position that empty space ~is real

is held to refute itself by a regress ad infinitum : if all that is is in

space, and thus space is itself an existing entity, then it must itself

be in a space, and this last likewise, etc. When the concept of the

infinite, to which the Atomists had given a new turn, became thus

prominent, all the enigmas involved in it for the contrasting points

of view of intellect and sense-perception became prominent also, and

Zeno used them to involve in a reductio ad absurdum the opponents

of the doctrine of the one, self-limited Being.


/ This dialectic, however, cut both ways, as was shown in the Ele

atic School itself, by the fact that a cotemporary of Zeno, Melissus,

who shared his opinions, saw himself forced to declare that the

Being of Parmenides was as unlimited in space as in time. For as

Being can arise neither from other Being nor from Non-being, so

it can be limited neither by existing Being (for then there must be

a second Being), nor by a non-existent (for then this non-existent

must be) : a line of argument more consistent from a purely theo-


1 The argument can be directed only against Atomism, and applies to this

weakly.

CHAP. 1, 4.] Conceptions of Being : Pythagoreans. 45


retical point of view than the position of the master, which had

been influenced by determinations of worth.


11. The Pythagoreans took a mediating position in these ques

tions : for this, as for their other doctrines, they were happily fitted

by their employment with mathematics, and by the manner in which

they prosecuted this study. Its chief direction seems to have been

arithmetical ; even the geometrical knowledge ascribed to them (as

the well-known proposition named after Pythagoras) amounts to a

linear representation of simple relations between numbers (3 2 + 4 2

= 5 2 , etc.). It was not, however, in the general relations of construc

tions in space only that the Pythagoreans found numbers to be the

determining principles ; the same was found to be true also in such

phenomena of the corporeal world as they were chiefly engaged

with. Their theoretical investigations concerning music taught them

that harmony was based upon simple numerical relations of the

length of the strings (octave, third, fourth), and their knowledge

of astronomy, which was far advanced, led them to the view that

the harmony prevailing in the motions in the heavenly bodies had,

like the harmony in music, 1 its ground in an order, in accordance

with which the various spheres of the universe moved about a com

mon centre at intervals fixed by numbers. Suggestions so various

as these mentioned seem to have united to evoke in a man like

Philolaus the thought, that the permanent Being which philosophy

was seeking was to be found in numbers. In contrast with the

changing things of experience mathematical conceptions possess as

regards their content the marks of a validity not subject to time

they are eternal, without beginning, imperishable, unchangeable,

and even immovable ; and while they thus satisfy the Eleatic postu

late for Being, they present, on the other hand, fixed relations,

that rhythmical order which Heraclitus had demanded. Thus, then,

the Pythagoreans found the abiding essense of the world in the

mathematical relations, and in particular in numbers, a solution

of the problem more abstract than the Milesian, more capable of

"being represented to perception or imagination than the Eleatic,

clearer than the Heraclitic, more difficult than those offered by

cotemporary mediating attempts.


The Pythagorean doctrine of numbers, as carried out by them, was

attached partly to the numerous observations they had made on the

arithmetical relations, partly to analogies which they discovered or

sometimes artificially introduced, between numerical and philosophi

cal problems. The definite nature of each individual number and
1 Out of this analogy arose the fantastic idea of the harmony of the spheres.

46 The Greeks: Cosmological Period. L I>AHT J -


the endlessness of the number series must indeed have at first sug

gested that reality belongs as well to the limited as to the unlimited,

and by transferring this thought into the geometrical sphere the

Pythagoreans came to recognise, in addition to the elements as the

limited, a Reality as belonging also to space as the unlimited void.

They thought of the elements, however, as determined by the forms

of the simple solids : fire by the tetrahedron, earth by the cube,

air by the octahedron, water by the icosahedron, and a fifth material,

aether, which they added as the celestial element to the four terres

trial elements assumed by Empedocles, by the dodecahedron. 1 In

these conceptions the prevailing idea was this : corporeality, or the

essential quality of bodies, consists in the mathematical limitation

of the unlimited, in the shaping out of space into forms. Mathemati

cal forms are made the essence of physical reality.


The Pythagoreans further believed that in the antithesis between

the limited and the unlimited they recognised the antithesis found

in numbers between the odd and the even ; 2 and this antithesis was

again identified with that between the perfect and the imperfect,

the good and the bad, 3 in this last case not without the influence of

old ideas connected with the religious faith of the oracles. Their

Weltanschauung becomes thus dualistic: over against the limited,

odd. perfect, and good stands the limitless, even, imperfect, and bad.

As, however, both principles are united in the number one, 4 which

has the value of an even as well as of an odd number, so in the

world as a whole these antitheses are adjusted to form a harmony.

The world is harmony of numbers.


Some of the Pythagoreans, 5 moreover, sought to trace out through

the various realms of experience that fundamental antithesis, in the

assumption of which all the school were agreed, and so a table of ten

pairs ofopposites came into existence: viz. limited and unlimited

odd and even one and many right and left male and female

at rest and in motion straight and curved light and dark


1 While the main line of the Pythagoreans thus followed Empedocles, a later,

Kcphantus, conceived of this limitation of space in the sense of Atomism.
2 The reason presented for this, viz. that even numbers permit of bisection

to infinity (?), is indeed very questionable and artificial (Simpl. Phys. D. 105 r

455, 20).
8 Nor must we here overlook the factor which had already asserted itself with

Xenophanes and Pannenides, viz. that to the Greek the conception of measure

was one that had a high ethical worth ; so that the infinite, which derides all

measure, must to him appear imperfect, while the definite or limited (ireTepao--

tdvov) was necessarily regarded as more valuable.
* Arist. Met. I. 5, 986 a 19.
5 Or men standing in close relations with Pythagoreanism, such as the physi

cian Alcmaeon, a perhaps somewhat older contemporary of Philolaus. Cf.

Arist. Met. I. 5, 980 a 2-2.

CHAP. 1, 5.] Conception* of Cosmic Processes. 47


good and bad square and oblong or with unequal sides. This is

evidently a collection put together without system, to fill out the

sacred number ten, but an attempt at an articulation may at least be

recognised.


In accordance, then, with this or a similar scheme the Pythagoreans

exerted themselves to make an order of things corresponding to the

system of numbers, by assigning the fundamental conceptions in

every department of knowledge to various numbers, and on the other

hand by adjudging to every individual number, but especially to those

from one to ten, determining significance in the various spheres of

reality. The fantastic nature of the symbolic interpretation into

which they fell in doing this must yet not cause us to overlook the

fact that the attempt was therewith made to recognise an abiding order

of things which could be grasped and expressed in conceptions, and to

find the ultimate ground of this order in mathematical relations.
Nor did it escape the notice of the Pythagoreans themselves,

notably of the later members of the school, that numbers could not

be called the principles (a-jx<u) of things in the same way in which

the term is applied to the various " stuffs," or kinds of matter, to the

elements, etc., that things have not arisen out of them, but are

formed according to them; and perhaps they best and most effec

tively express their thoughts when they say that all things are

copies or imitations of numbers. With this conception the world of

mathematical forms was thought as a higher, more original reality,

of which the empirical reality was held to be only a copy : to the

former belonged abiding Being ; the latter was the contrasted world

of Becoming and change.



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