No More Learning

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 "world-stuff" ( Weltstoff), which experiences all these transforma tions, from which all individual things arise, and into which they become again transformed (apxi)- 1° tn^s conception1 was tacitly contained the presupposition of the unity of the world; whether the Milesians * already sought to justify this we do not know. It was a later eclectic straggler * 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 * 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 ' 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 ; 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 /{escribed its individual forms. The cos
mic matter passed with—f! hem for something in itself living : they thought of it as animated, just as are particular organisms,* 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, 083 b 8, has defined, not without the admixture of his own categories.
* The expression ipx'hy 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.
8 Diogenes of Apollonia. Cf. Simpl. Pkyt. (D. ) 32r 151, 30, and Arist. Uen «f Corr. I. 6, 322 b 13.
♦ Schol. in Arist. 614 a 33.
6 For tSup, irypir is frequently substituted. With regard to the i-fip 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.
• Pint. Plac. 1. 3 (Doxogr. D. 278). Perhaps this is intended in the conjee tore of Aristotle, Met. I. 3, 983 b 22.
Case. 1, 4j 4. ] Conceptions of Being : The Milesians. 38
2. If we ask, however, why Anaximenes, whose doctrine, like :aat of Thales, seems to have kept withia the bounds of experience, rabstituted air for water, we learn ' that he believed air to have a characteristic which water lacked, — a characteristic, too, which his predecessor Anaximander had postulated as indispensable for the
of primitive matter, viz. that of infinity. As motive for 'Jus postulate of Anaximander there is related the argument that a inite cosmic matter would exhaust itself in the ceaseless succession U productions. * But Anaximander had also seen that this demand aide by the conception of the &pxq could not be satisfied by any Salter or substance which we can perceive, and had on this account transferred the cosmic matter beyond experience. He maintained tetdly 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 -iiange, — even though such a ground might not be found in experi- -are. /He drew from the conception of the apxy the consequence, •-bat though no object of experience corresponds to this conception, ve miut yet, to explain experience, assume such a conception behind it as real and conditioning it. He therefore called the cosmic mat ter "tke Infinite" (to awupov), and ascribed to it all the qualities postulated in the conception of the Apxn ■ that is, that it had never tiegnn to be, and was imperishable, inexhaustible, and indestructible.
The conception of matter, thus constructed by Anaximander is, 2«Tertheless, clear only in the respect that it is to unite within it fpacal infinity and the quality of being without beginning or end va time, and thus the mark of the all-embracing and all-determin- ;ar;* 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 tiat the original matter was qualitatively undetermined or indefinite
tun m),* while the statements of Aristotle* speak more for the Mscmption of a mixture of all kinds of matter known in experience, — a mixture completely adjusted or equalised, and therefore as a *Me indifferent or neutral. The most probable view here is, that Aaaximander reproduced in the form of an abstract conception the
conception
1 Sk*pL Pkf*. (DA «» 24, 26.
' nm. PUtc. I. 3 (Dozogr. D. 277) ; ArUt. Phy>. III. 8, 208 a 8.
•ArtaL P%p. III. 4, 203 b 7.
• Scant. In Arist. 614 a 33 ; Herbart, Einleitung in die Philosophie (Gei.
r . l 1M).
' Jfcf. XIX 2, 1000 b 18, and especially Pkyi. I. 4, 187 a 20. CI. also Simpl.
Van fl». ) 3P 164, 14 (according to Theophrastus) . This much-treated contro- ■■V win be spoken of more In detail below (§ 6).
84 The Q-rer. ks : Gosmological Period. [Part. ! •
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 Anaximander to the In finite, — to Qtiov, 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,' that whithersoever he looked all was constantly flowing together for him into one Nature (/xiav <« <f>wriv), took on at once, however, that sharp polemic 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,* the anger with which he pursued the poets as the portrayers » Tunon in Sext. Emp. Pyrrh. Hyp. I. 224. * Clem. Alex. Strom. V. 601 .
Omr. 1. $ 4. ] Conception* of Being : Xenophanet. 85
:' these divine figures provided with all the weaknesses and vices of auun nature,1 — these rest upon an ideal of God which will have Cite Supreme Being regarded as incomparable with man in both
•«Iily and mental characteristics. When he passes to positive at- '. r. butes, Xenophanes becomes more obscure. On the one hand, the iatj as tr tax Tag/is identified with the universe, and to this " World- GW are then ascribed all the predicates of the Milesian dpxv
(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 tins respect the World-God of Xenophanes appears only as the i-^hest among the rest of " gods and men. "
While here a predominantly theological turn of philosophy is Lready 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 r»lizious reverence, and scarcely a means for understanding Nature. Thf Colophonian's sense for knowledge of Nature is slight, his ideas »T* in part very childlike, and, as compared with those of the Mile- ■aas, undeveloped. And so for his views, the characteristic of
infinity, which Milesian science regarded as necessary in the cosmic asatter, could be dispensed with ; on the contrary, it seemed to him man in accordance with the dignity of the divine Nature,' to think of this as limited within itself, as entirely shut up or complete, con-
as regards its spatial aspect, spherical. And while the Milesians thought of the original ground of things as ever in motion 'P*«taneously, and as characterised by living variety in its inter- sal structure, Xenophanes struck out this postulate hitherto in use for the explanation of Nature, and declared the World-God to be rmmcmblc and perfectly homogeneous in all its parts. How, indeed, he thought that the variety of individual things whose reality he 6d not doubt, could be reconciled with this view, must remain ■arm iin.
4 As was required by the conception of change, the Milesian '*»r»ption of the World-substance had united without clear discrim- -sa:>on two essential elements : the one that of a substance re-
■ii--ir. g like itself, the other that of independent or self-subsistent
; H:ppo( B'f. 1. 14 (Doxogr. T>. ofio). In other passages, again, it is said A» bt woold bare the deity thought neither limited nor unlimited (? >.
«*q:*»ntly
1 Men. Kmp. Ait. Math. IX. 193.
S6 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 Ionians 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 ipxv 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. ' 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 (ilfia. pfi. ivri), the order (8£ktj), the reason
(Aoyos) 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 Are, 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. inBut Heraclitus does not disdain to let the dim idea of a World -substance stand the background in his metaphors (of the clay kneaded ever anew, of the drink continually stirred).
1 Further in detail on this point in the following section.
C«af. 1, { 4. ] Conceptions of Being : Heraclitus, Parmenides. 37
ud logical order in the world appear as still identified, prove only the undeveloped state of thought which does not yet know how to
the different motives. The conception, however, which Heraelitos has grasped with complete clearness, and carried though vita all the strength of his austere personality, is that of order, a
separate
nevertheless, whose validity was for him as much a aatter of conviction as of knowledge.
5. In evident opposition to this theory of the Ephesian, the con- option of Being was worked out by Parmenides, the head of the Qeatic 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 (fori yap tlvai), is for the Ele- itic a postulate of such cogent evidence that he only states this position without proving and that he explains only by nega tive turn of thought which first discloses to us completely the sense m which we are to understand his main thought. "Non-being"
<j$i umu), he adds, or that which " " not (to fiij i6t>), cannot be •ad cannot be thought. For all thought in relation to 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 not thought thought and Being are the same.
These propositions, which look so abstractly ontological we con sider only the words, take on quite another meaning when we con- uder that the fragments of the great Elean leave no doubt as to vhat he desired to have regarded as " Being " or that which " is. " This was corporeality, materiality (to wXiw). For him, " being" and - tilling space " are the same. This " Being," this function of filling
•pace, is precisely the same in the case of all that " " there is, thatefore, only the one, single Being which has no internal distinc- boat. " Non-being," or what is not [has not the attribute of Being], wu. 1. accordingly, incorporeality, empty space (to kcvoV). This table meaning of the cW (Being) employed by Parmenides, ac- «*ding to which the word means at one time " the full " and at an other time " Reality," leads then to the proposition that empty space
«uoi be.
Nov for the naive, sensuous way of looking at things which
«rk» even in these principles of Parmenides, the separateness of Fr. , ed. Kanten, vv. W fl.
conception,
1
is ;
if
is
:
is is
aa
it,
it
38 The Greeks : Cotmological Period. [Past L
things, 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 corr- ception of Being, there seems so little possibility of uniting these individual things with that reality 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 involves the denial of that which was to be explained by it. In this sense the Eleatic doctrine 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 eternal, has never come into being, imperishable, and especially (as Xenophanes had maintained) that 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 then well-rounded sphere, per fectly homogeneous within itself, and this only and unitary world- body at the same time the world-thought,3 simple, excluding all particulars from itself to yap irAcov iarl vmjpa.
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 Natura 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
A great role in these considerations of the Eleatios is obviously played by the ambiguities in language, by which, on the one hand, the Iv means both numerical unity and also qualitative unity or simplicity, while the verb cImu has not only the function of the copula, but also the meaning of " Reality.
"
Hence, terms like " materialism " and " idealism " do not apply to this naive identification of consciousness and its object, the corporeal world.
11
6.
is
:
is a
is is
is it
:
is
it is
it
:
it,
Caar. 1, f 4. ] Conceptions of Being : Empedoclet. 39
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 inchangeable ; on the other hand, however, they assent also to the thought of Heraclitus that an undeniable reality belongs to Becom ing and change (Oeschehen), 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
»hould satisfy for itself the postulate of Parmenides; while, on the other hand, by changing their spatial relations, they were to :ring 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 ; nevertheless, change ought to receive recognition, as with Heraclitus, and be attributed to Being itself,
most be reduced to kind of change which leaves untouched lie qualities of the existent. Such 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 with Heraclitus, they insisted spon the reality of occurrence and change, and against Heraclitus, apon the Being of permanent and unchangeable substances as under lying and producing the same. Their common view this there
a plurality of existing beings which, unchangeable in them- ■errea, make the change and variety of individual things compre hensible.
This principle seems to have been asserted first and in its Boat imperfect form by Empedocles, — in form, however, that was widely influential historically. He put forward as "elements"* the looj which are still current in the popular modes of thought, — earth,
(Plato, Thtatl. 181 Arist. var. loc. ), iXXoiwfftt (qualitative change) ay4 (change of place) are contrasted an species of kIkijo-u or /irra^oXi).
separated
U rr»itiT tlit* done here, though the terms are as yet lacking.
Instead of the later expression troix'ta, we find in Empedocles the more
tnKtr term " root* of nil things," j><(iiiia. ra. .
>
7
in
;D
a
if,
a
is
it
is :
;
'
a
40 The Greeks : Cosmological Period. [Part L
water, air, and fire. ' 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 he 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 cause 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 as 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 not disclosed in any satisfactory way in the fragments. " 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,* — a first indication that determinations of " worth " or value are beginning to be introduced into the theory of Nature.
Empedocles thought 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 so, how, we do not indeed know. This difficulty was avoided by Anaxagoras, who, from the Eleatic principle that nothing that can arise or pass away, drew the conclusion that as many elements must be assumed*
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 quite remote from the thought of the Agrigentine.
If <pi\ia and ttiKoi are occasionally counted by the later recorders as fifth and sixth apxt 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. Arist. Met. 984 32.
He called them exipiiara (seeds of things), or also simply xpi>/uira (sab- stances
*21 ).
8.
»
I. 4,
if
b
i« :
is
it
is
;
it, a
Ciap. 1, j 4. ] Conception* of Being : Anaxagoras. 41
as there are simple substances in the things of experience, meaning br simple substances those which on repeated division always sep- irate into parts qualitatively the same with their wholes. Such ->mentary substances were later, in accordance with his definition, xlW komoiomeriai. At that time, however, when only mechanical hnsion or change of temperature were known as means of investi- . irion, this conception of element (in principle entirely correspond- aig to the conceptions of the chemistry of to-day) applied to the neater 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 cooiing together or compounding (o-iryKpuri? ) constitutes the arising, '■heir separation (Stoxptoit) 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 'Jung takes on the properties of that substance or of those sub- sances which may be present in a preponderating degree.
The elements, as the true being, are regarded now by Anaxagoras ibo as eternal, without beginning or end, unchangeable, and though aorable 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-
jrer, this force must be regarded as existent, a something that Anaxagoras hit upon the expedient of assigning to special,
«ingle sort of matter or elementary substance. This force-element » motive-matter (Beicegungsstoff) conceived to be the lightest and ■vost mobile of all elements. In distinction from all the others
chat one of the komoiomeriai which alone in motion of itself, and wounnnicates this its own motion to the rest moves itself and the rest. To determine the inner nature of this " force-substance," aowerer, two lines of thought unite the property of originating mo- be* is. for the naive mode of looking at things, the surest sign of the ntmate this exceptional kind of matter, then, which self-moved, aast be animate matter or "soul-stuff" (Seelenstoff), its quality mast be animate or psychical. * And, secondly, power known through its effect now, this motive-matter the cause of the formation of the world, to bring about which has separated out •j« remaining idle elements, then we must be able to know its satar* from this which has accomplished. But the universe, in
. articular the regular revolution of the stars, makes the impression
AflBonUog to the fragments of Anaxagoras, bones, flesh, and marrow also • Ac other hand, the metals.
[The Creak fv%i aad German Seele include both these meanings. ]
11
;
it
is is,
if, it
it
is a
; it
:
is is
it a
;
:
is
is
42 The Greeks : Cosmological Period. [Part L
of beautiful and purposive order (koo>io? ). 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 (kovs) or as " Thought-stuff. "
The covs 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 aHeraclitic 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 teleological 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 Eleatic 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 jtAcov. 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 (Phmd. 97 B), and overestimated by Aristotle (Met. I. 3, 984 b). Cf. , however, § 6. The moderns (Hegel) have added the further over-estimate of seeking to interpret the mvs as an immate rial principle. But the fragments (Simpl. Phys. (D. ) 33' 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. a Plut. Adv. Col. 4, 2, 1109.
(. '■at. l; f 4. ] Conception* of Being : Leucippus, Zeno. 43
as the unlimited, the imipov, in contrast with the limitation which Bring proper possesses, according to Parmenides. Leucippus, there fore, shatters in pieces the world-body of Parmenides, and scatters iu parts through infinite space. Each of these parts, however,
like the absolute Being of Parmenides, eternal and unchangeable, without beginning, indestructible, homogeneous, limited, and indi-
nsible. Hence these portions of Being are called atoms,
aad for the reasons which had led Anaximander to his
of the iriipov Leucippus 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 dirigible. Since, however, they all possess only the one like quality of filling space, differences between them can be only quan- titatiTe differences in size, form, and situation.
Out of such metaphysical considerations grew the concept of the Uom, which has proved so fruitful for the theoretical science of Nature just because, as was evident already in the system of Leu- dppus, it contains the postulate that all qualitative differences exhibited by Nature are to be reduced to quantitative. The things which we perceive, Leucippus taught, are combinations of atoms iktj 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 'oastitute Being.
Empty space is, accordingly, the presupposition as well for the •miting and separating of atoms as for their separateness and shape. AH *• becoming," or change, in its essence motion of atoms in space. If we ask for the ground of this motion of the atoms,1 since space ai properly not true Being cannot be allowed as cause, and Atomism recognises nothing as actual except space and the atoms, ibis ground can be sought only in the atoms themselves; i. e. the
are of themselves in motion, and this, their independent mo- as truly without beginning and end as their being. And as
the atomj are indefinitely varied in size and form, and completely taoeprodent of one another, so their original motions are infinite in variety. They fly confusedly about in infinite space, which knows ao shore 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
Srs*. Pkf. VIII. —262 32, says of the AtomUts that they did not aak as to tbt orifia of motion as a matter ol course, for they declared motion itself -: V t»a«rir«« (cf. Met 4).
aTopot; concept
I.
1, a
>
,
is i
;
is
a
is
;
;
is,
44 The Greeks: Cosmological Period. [Part I.
which Empedocles and Anaxagoras, each in his way, had attempted, was thus in turn abolished by the Atomists. They ascribed to the particles of matter the capacity, not indeed of qualitative change (aAAotWts), but of independent motion (nLvqcns in the narrower sense, equivalent to wtpi<l>opa), and took up again in this sense the principle of Milesian hylozoism.
10. In opposition to these pluralistic systems, Zeno, 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 ; 1 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 ck 8i^oTo/i. tos), 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, Melisstis, 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.
Cwat. 1, f 4. ] Conception* 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* + 4'
= 5*, 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- non centre at intervals fixed by numbers. Suggestions so various m these mentioned seem to have united to evoke in a man like Plul'AauM the thought, that the permanent Being which philosophy
fa 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 "f the problem more abstract than the Milesian, more capable of
to perception or imagination than the Eleatic, clearer than the Heraclitic, more difficult than those offered by
'^temporary mediating attempts.
The Pythagorean doctrine of numbers, as carried out by them, was
ittaebed partly to the numerous observations they had made on the arithmetical relations, partly to analogies which they discovered or ibmetimes artificially introduced, between numerical and philosophi cal problems. The definite nature of each individual number and
being represented
1 Out of this analogy arose the fantastic idea of the harmony of the spheres.
46 The Greeks : Cosmological Period. [Part I.
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, tether, 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,* 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 of opposites 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, Ecphantus, conceived of this limitation of space in the sense of Atomism.
* The reason presented for this, viz. that even numbers permit of bisection to infinity (? ), is indeed very questionable and artificial (Simpl. Fhys. D. 105'
465, 20).
* Nor must we here overlook the factor which had already asserted itself with
Xenophanes and Parmenides, 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 {rtrtpac- nimv) was necessarily regarded as more valuable.
« Arist. Met. I. 5, 986 a 19.
6 Or men standing in close relations with Pythagoreanism, such as the physi cian Alcmseon, a perhaps somewhat older contemporary of Philolaui. Cf Arist. Met. I. 6, 986 a 22.
Caar. 1. § 5. ] Conceptions 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 acred 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.
Xor did it escape the notice of the Pythagoreans themselves, notably of the later members of the school, that numbers could not he called the principles (dpx<") °f 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
according to them; and perhaps they best and most effec tively express their thoughts when they say that all things are mfiesor imitations of numbers. With this conception the world of ra&thematical 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.
5 5. Conceptions of Cosmic Processes. 1
E. Hardy, Der Btgriff der Phytis in griechisr.