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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).
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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. hen Philosophie, I. Berlin, 1884.
As the fact of change — that is, the cosmic processes — furnished the most immediate occasion for reflection upon the abiding Being, to. on the other hand, the various conceptions of Being had i» their ultimate aim only to make the processes of Nature intel-
This task was indeed occasionally forgotten, or set aside, :a the development of the conceptions of Being, as by the Eleatics ; bat immediately afterward the further progress of thought proved to be determined all the more by the renewed attention given to
formed
hfible.
I have translated this word variously by "change," "occur- ■aer. " *' event," "taking place," "coming to pais," "becoming," etc. The at vhU-h i* ordinarily used for the Greek ylyroiuu leems hardly broad enough. TV Ortnan means any natural process or event. ]
1 [GeaektAen.
48 The Greek* : Co*mologieal Period. [Part L
Becoming and change, and by the need of so thinking Being thai Becoming and change could not only be reconciled with but also be made intelligible by it. Hand in hand, then, with ideas of Beingi go those of Becoming, the two in constant relation to one another.
To the Ionians the living activity of the world was something so much a matter of course that they never thought of asking for
cause of it Naive Hylozoism could have in view only the explana tion of particular occurrence or cosmic process. Explanation, however, consists in reducing what striking — not a matter of course or intelligible in itself — to such simpler forms of occur rence as seem to need no explanation, inasmuch as they are most familiar to our perception. That things change their form, their qualities, their working upon one another, seemed to the Mile sians to require explanation. They contented themselves in this with conceiving these changes as condensation or rarefaction of the cosmic matter. This latter process did not seem to them to need farther explanation, though Anaximenes at least did add, that these changes in the state of aggregation were connected with changes in temperature — condensation with cooling, rarefaction with growing
warm. This contrast gave rise to the arrangement of the states of aggregation in a series corresponding to the degree of rarefaction or condensation of the primitive matter viz. fire, air, water, earth
(or stone).
The Milesians used these ideas not only to explain individual
phenomena of Nature, particularly the meteorological processes so important for a sea-faring people, but also to explain the develop ment of the present state of the world out of the prime matter. Thus Thales conceived water as in part rarefying to form air and fire, and in part condensing to form earth and stone; Anaximenes, starting from air, taught an analogous process of world-formation. As result of these views was assumed that the earth — resting on water, according to the first, on air, according to the second — occupied the centre of the sphere of air revolving about it, and this sphere of air was yet again surrounded by sphere of fire, which either broke through or shone through in the stars.
In setting forth this process of world-origination, which was per haps still regarded by Thales and Anaximander as process occur ring once for all, the Milesians attached themselves closely to the cosmogonic poetry. * Not until later does the consideration seem to
Hence intelligible that there were also physicists (not known to us by name) who would regard the world-stuff as an intermediate stage between ail and water, or between air and fire.
Henco, nUn, the designation of the world-stuff as ipx'h (beginning).
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C*a». 1, $ 5. ] Cosmic Processes : Anaximander, Heraclitus. 49
have gained prevalence, that if to change of form a change back to the original form corresponds, and at the same time, matter
to be regarded as not only eternal but eternally living,
to assume a ceaseless process of world-formation and world-destruc tion, countless number of successive worlds. 1
Although these essential constituents characterise also the physical theories of Anaximander, he was led beyond them by his aetaphysical conception of the iwapov. The infinite, self-moved natter which was intended by this obscure conception was indeed, u whole, to have no definite properties. It was held, however, to contain qualitative opposites within itself, and in its process of evolu tion to exclude them from itself, so that they became Anaximander remained then a Hylozoist in so far as he regarded nutter as self-moved; he had seen, however, that the differences most be put into they were to come forth out of on occasion of its self-motion. If, then, as regards his doctrine of Being, he ap proached the later theory of plurality of primitive substances, and abandoned the doctrine that the primitive matter was changeable in quality, he was yet entirely at one with the other Milesians as
regards his conception of the causelessness of the cosmic process, and thought that by the union of the two opposites, the warm and the cold, which he conceived as the first to come out from the ivupov, he could explain water. This done, he could proceed with his cosmog ony along the oceanic path taken by Thales.
Bat besides these physical and metaphysical determinations, the only fragment preserved from him, giving his own words, repre- tents the perishing of things as an expiation for injustice, and so presents the first dim attempt to present the world-process as
itktml necessity, and to conceive of the shadows of transitoriness, vhich rest even on the bright picture of Hellenic life, as retribution lot sin. However doubtful the particular interpretation of this ctterance, there yet without doubt voiced in the need of giving v> physical necessity the worth of an ethical order. Here Anaxi- aander appears as predecessor of Heraclitus.
The order of events which Heraclitus thought he could estab lish as the only constant amid the mutation of things, had two **a*nttal marks, the harmony of opposites and the circuit completed
Tfcft* doctrine was supported, probably by Anaximander, certainly by ttaxnaenea. It repeated in Heraclitus and Empedocles.
Tbe decisive passages (or this very controverted question (Ritter, Sevdel, Wter, are Artst. Phy*. 187 20, and Simpl. Phyt. (D. ) 33' 154, 14 (after TWophrastus) also tbe continuation of the passage in the following note.
SonpL Fifs. fT>. ) 6* 24, 18. Cf. Th. Ziegler, Arch. Qetch. d. Philot. , HI
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50 The Greeks : Cosmological Period. [Part I.
matter in its successive changes in the universe. The observation that everything in the world is in process of constant change was exaggerated by Heraclitus to the claim that everything is con tinually changing into its opposite. The " other " was for him eo ipso the opposed. The "flux of things " became transformed in his poetic rhetoric into a ceaseless strife of opposites, and this strife (iroAt/ios) he declared to be the father of things. All that seems to be for a shorter or longer time is the product of opposed motions and forces which in their operation maintain themselves in equilib rium.
The universe is thus at every moment a unity divided in itself and again re-united, a strife which finds its reconciliation, a want that finds its satisfaction. The essence of the world is the invisible harmony in which all differences and oppositions are solved. The world is Becoming, and Becoming is unity of oppo
sites.
These antitheses, according to the view of Heraclitus, present
themselves particularly in the two processes taking place in con trary directions, through which, on the one hand, fire becomes changed into all things, and, on the other hand, all things change back into fire. The same stages are passed through in both processes: on the "way downward" fire passes over, by condensation, into water and earth, on the "way upward" earth and water, by rare faction, pass over into fire ; and these two ways are alike. Change and counter-change run on side by side, and the semblance of a per manent thing makes its appearance where for a time there is as much counter-change upon the one way as there is change upon the other. The fantastic forms in which Heraclitus put these views envelop the essential thought of a sequence of changes taking place in conformity to law, and of a continual compensation of these
changes. The world is produced from the fire in ever-repeated rhythm and at fixed intervals of time, and then again flashes up in fire, to arise from it anew, a Phoenix. 1
In this ceaseless transformation of all things nothing individual persists, but only the order, in which the exchange between the contrary movements is effected, — the law of change, which consti tutes the meaning and worth of the whole. If in the struggle be tween opposites it seems as though something new were constantly arising, this new is at the same time always a perishing product. The Becoming of Heraclitus produces no Being, as the Being of Parmenides produces no Becoming.
1 In details his physical, and especially his astronomical, ideas are weak. Metaphysical inquiry is more important with him than explanatory investiga tion. He shares this with his opponent, Parmenides.
Chat. 1, f 5. ] Cosmic Processes : Parmenides, Empedocles. 51
4. In fact, the doctrine of Being held by the Eleatics excluded with plurality and change, events or cosmic processes, also. Ac cording to their metaphysics an event or occurrence is incomprehen sible, it is impossible. This metaphysics tolerates no physics. Parmenides denies to time, as to space, independent reality (iVAo
rm^u rov iovrof) : for him there is only timeless Being with no dis tinctions. Although Parmenides added to the first part of his didac- tic poem, which presents the doctrine of Being, a second part which treats physical problems, this is yet done with the protest in advance that he is here presenting not truth, but the " opinions of mortals. " At the basis of all these ordinary opinions lies the false presupposi tion, previously rejected, that in addition to Being there is still •Bother, Non-being. All becoming, all plurality and motion, rest on tie interaction of these, opposites, which are then further designated as light and darkness, warmth and cold A Weltanschauung is then portrayed in poetic imagery, in which fire shapes the dark empty space into corporeal structures, a mode of representation which in part reminds us of Heraclitus, and in part accords with the astro nomical teaching of the Pythagoreans. The all-ruling Fire-power lia^wr), as inexorable necessity (Sun/), with the help of love (ip<*t) {ones together what is akin, working from the centre of the world outward. Appropriation of the doctrines of others and polemic
against them appear in motley mixture, agreeably V) the purpose of the whole. Over this tissue thus interwoven hovers a poetic breath of plastic formative power, but original research and clear concep tions are lacking.
5. Ideas more definite, and more usable for explaining the par ticular, are found among the successors, who transformed the Eleatic conception of Being into the conceptions of element, homoiomeriae, and atom, expressly for this purpose. They all declare that by occurrence or coming to be nothing else is to be understood than the notion of unchangeable corporeal particles. Empedocles and Anax- apemu seem still to have sought to connect with this the denial of *=pty space, — a principle which they received from Parmenides. They ascribed to their substances universal divisibility, and re garded parts as capable of displacement in such a way that as these puts mixed and reciprocally interpenetrated, all space should be always filled out The motion in the world consists, then, in this
■TV hypothetical exposition of how the world would have to be thought addition to Being, Non-being, plurality, and becoming were also regarded as >w bad, on the one hand, polemic purpose; and on the other, met the
**ai A bi* disciple*, who probably demanded of the master an explanation of us awn of the empirical world.
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52 The Greeks : Cosmological Period. [Pabt I
displacement of the parts of matter, each of which is always crowd ing and displacing the other. Things at a distance from one another cannot act upon one another, except as parts of the one flow out and penetrate into the other. This action is the more possible in pro portion as the effluxes of the one body resemble in their spatial form the pores of the other. So at least Empedocles taught, and the assumption of an infinite divisibility of substances is attested in the case of Anaxagoras also. Another picture of occurrence more akin to the present way of thinking is that presented by Leucippus. The atoms which impinge upon each other in empty space act upon each other by pressure and impact, group themselves together, and so form greater or smaller things or masses which are not separated and destroyed until some impact or pressure of other masses comes from without. All occurrence and coming, to be consists in this process in which atom-complexes are successively formed and shattered.
The fundamental form of world-motion in all three systems, how ever, is that of the vortex, of circular rotation (Sivy). According to Empedocles it is brought about by the forces of love and hate acting among the elements ; according to Anaxagoras it is begun by the Reason-stuff acting according to ends, and then continues with mechanical consistency ; according to Leucippus it is the result always occurring from the collision of several atoms. The principle of mechanism was with Empedocles still enveloped in myth, with Anaxagoras it first made a half-successful attempt to break through the covering, and was completely carried through only by Leucippus. What hindered the first two from reaching this position was the introduction of considerations of worth into their explanatory theory. The one was for tracing the good and the evil back to cor responding powers of mind, which were, to be sure, not ascribed to any being, but mythically hypostatised ; the other believed that he could explain the order of the whole only from the assumption that purposive, rationally considered impulse had originated the motions. Yet both came so near the position of Leucippus as to demand a teleological explanation for the beginning only of the vortex-motion; the farther course of the motions, and thus every individual occur rence, they explained, as did Leucippus, purely mechanically, by the pushing and crowding of the particles of matter after these are once in motion in the manner determined. They proceeded so con sistently in this that they did not exclude from this mechanical explanation even the origination and functions of organisms, among which, moreover, plants are regarded as being as truly animate as are animals. Anaxagoras is reproached for this by Plato and Aristotle-,
C«at. 1. J 5. ] Cosmic Processes : Anaragoras, Leuctppus. 53
and an expression of Empedocles has been handed down,' according to which he taught that the animals had arisen here and there, with out any rule, in odd and grotesque forms, and that in the course of tune only those fitted for life maintained themselves. The principle of the survival of the fittest, which plays so great a part in the biology of to-day, i. e. in Darwinism, is here already clearly formu lated.
On the ground of these ideas, an interesting contrast discloses itself in the case of the three investigators, as regards their atti- tade toward cosmogonic theories. For Empedocles and for Leu-
•ippus, namely, the process of world-formation and world-dissolu tion is a perpetual one ; for Anaxagoras, on the contrary, it is one chat takes place once for all. Between the first two there is again the difference that Empedocles, like Heraclitus, teaches that the world arises and perishes in periodic alternation ; while Atomism, on the contrary, holds that a countless number of worlds come into being and pass away. According to the principles of Empedocles, so be more explicit, there are four different states of the elements ; their complete intermixture, in which love alone rules, and hate is exploded, he calls " when hate penetrates, this
o-tftaipos (sphere) ;
aomogeneous world-sphere becomes separated into the individual
things, until the elements are completely parted from one another ; tod out of this separate condition love brings them again together, until full union is again attained. Neither in the case of complete mixture, nor in that of complete separation, are there individual things ; in both cases the Eleatic acosmism makes its appearance.
A world of individual things in motion exists only where love and bate struggle with one another in mingling and separating the •leroents.
It is otherwise with Leucippus. Some of the atoms that dart shoot irregularly in the universe strike together here and there.
Frvm the various impulses to motion which the individual particles bnntf with them, where such aggregations occur, there results, «rrording to mathematical necessity (ivaynri), a whirling movement of the whole, which draws into itself neighbouring atoms and atom- -»*aplexes, and sometimes even whole " worlds," and so gradually
• Ari«t. P%yt. II. 8, 198 b 29. Moreover, wc find an expression already ■onfcoied to Anaximander, which teaches a transformation of organisms by alteration to changed conditions of life : Plut. Plae. V. 10, 1 {Dot. D. 430, 15). I■* ataa. aim, the oldest thinkers claimed no other origin than that of growth 3C. of the animal world : so Empedocles in Plut. Strom, fr. 2. {Dox. D. 679, IT).
'• £<id>ntly not without suggestion from the Kleatic world-sphere, which thix ■bassse. folly adjusted mingling of all elements, taught by Empedocles, miwli
54 The Greeks : Cosmological Period. [Part L
extends. Meanwhile such a system in process of revolution is differentiating itself, since, by the rotation, the finer, more movable atoms are driven to the periphery, the more inert and massy are gathered in the centre ; and so like finds its way to like, not by inclination or love, but through their like conformity to the law of pressure and impact. So there arise at various times and in differ ent places in the boundless universe, various worlds, each of which continues in motion within itself, according to mechanical law, until it perhaps is shattered in pieces by collision with another world, or is drawn into the revolution of a greater. So, the Atomists main tained, the sun and moon were at one time worlds by themselves, which subsequently fell into the greater vortex of which our earth is the centre. How near in principle this whole conception is to the natural science of to-day is obvious.
The teleological point of view taken by Anaxagoras excludes, on the contrary, a plurality of worlds in time as well as a plurality of worlds in space. The ordering mind, which introduces the pur posive motion of the elements, forms just this one world only, which is the most perfect. 1 Anaxagoras, therefore, quite in the manner of the cosmogonic poetry, describes how the beginning of the world was preceded by a chaotic primitive condition, in which the ele ments were intermingled without order and without motion. Then came the vovs, the " Eeason-stuff " (Vernunftsloff), and set it into ordered motion. This vortex-motion began at one point, the pole of the celestial vault, and extended gradually throughout the entire mass of matter, separating and dividing the elements, so that they now perform their mighty revolution in a uniformly harmonious manner. The teleological motive of the doctrine of Anaxagoras is due essentially to his admiration of the order in the stellar world, which, after it has performed the rotations started by the voCs, moves on without disturbance always in the same track. There is no ground for assuming that this teleological
attention to the adaptation to ends in living beings, or even to the connected system of Nature as beneficent to man ; its gaze was fixed on the beauty of the starry heavens ; and what is related of the views of Anaxagoras on terrestrial things, on organisms, and on man, keeps quite within the setting of the mechanical mode of
explanation in vogue among his contemporaries. What he said, too. with regard to the presence of life on other heavenly bodies, might just as well have come from the Atomists.
1 This motive, fully carried out, is found in Plato, Tim. 81, with unmistak able reference to the opposition between Anaxagoras and the Atomists.
cosmology directed
Caar. 1, $ 5. ] Connie Proce»»e» : Zeno, the Pythagoreans. 55
Accordingly, although Anazagoras conceived of the vo\h as also the principle of animation, and thought of the particles of this substance as mingled in prater or leaser number with organic bodies, yet the central point in this con- arpcion is that of the authorship of the astronomical world-order. The other ••if, the moment or factor of the cause of animate life, is much more energeti cally emphasised in the transformation which a younger eclectic natural penkwopher, Diogenes of Apollonia, undertook to effect in the conception of Aaaxagoras by connecting it with the hylozoistic principle of Anaximenes. He designated air as &px1 [first principle, primitive element], fitted it out, kcwever, with the characteristics of the rout, — omniscience and force acting sKording to ends, — named this " rational air" also rvtuiia [spirit], and found this formative principle in man and other organisms as well as in the universe. A rich physiological knowledge enabled him to carry through in detail this •-i>ju£ht as applied to the structure and functions of the human body. With
t-ta teleology became the dominant mode of apprehending also the organic mid.
His fragments have been collected by Schorn (Bonn, 1820) and Panzerbieter Lops. 1830). Cf. K. Steinhart in Ersch und GrUber's Encyclopadie.
6. All these doctrines, however, presuppose the conception of motion as one that is intelligible of itself and in need of no further explanation. They thought they had explained qualitative change •hen they had pointed out as its true essence motion, whether between the parts of a continuously connected matter, or in empty
The opposition, therefore, which the Eleatic School brought tu bear upon all these doctrines was directed first of all against this conception of motion, and Zeno showed that this could by no means be taken so simply, but was rather full of contradictions which inca pacitated it for serving as principle of explanation.
Among Zeno's famous proofs of the impossibility of motion,1 the weakest is that which proceeds from the relativity of the amount of station, by showing that the movement of a wagon is variously esti mated if it is observed either from wagons also in motion but in different directions and at varying rates of speed, or again from two
vagons one of which is moving and one standing still. The three other proofs, on the contrary, which made use of the analysis into hscrete parts, infinitely many and infinitely small, of the space passed through by motion, and the time occupied by were ftronger. and for a long time were not overcome. The first proof was with reference to the impossibility of passing through a fixed space. This was regarded as proved by the infinite divisibility of
:he line, since the infinite number of points which must be attained before reaching the goal permitted no beginning of motion. The nae thought appears, somewhat varied, in the second argument, »Lxh seeks to prove the impossibility of passing through a space vA*A has movable boundaries. The argument (known as that of
int Pkfs VL 239 b. 9. Cf Ed. Wellmann, Ztnon't Beweise gegen die a*mr*mg umd ikrt Widerlegungen (Frankfurt a. O. 1870).
space.
.
»
0,
it,
56 The Greeks : Cosmological Period. [Part L
Achilles and the tortoise) is, that since the pursuer in every inter val or subdivision of time must first reach the point from which the pursued simultaneously starts, it follows that the latter will always be in advance, though by an interval which becomes constantly smaller and approaches a minimum. The third argument has refer ence to the infinitely small extent of tlie motion performed in a. 7iy instant. According to this argument, called "the resting arrow," the moved body is in every instant in some one point of its track ; its movement in this instant is then equal to zero; but from ever so many zeros no real magnitude arises.
Together with the above-mentioned difficulties (<bropuu) with regard to space and plurality, these argumentations of Zeno set forth an extremely skilfully projected system of refuting the mechanical theories, especially Atomism, — a refutation which was intended to serve at the same time as indirect proof of the correct ness of the Eleatic conception of Being.
7. The number-theory of the Pythagoreans, too, was determined by Eleatic conceptions in so far as its procedure was, in the main, to demonstrate mathematical forms to be the fundamental relations of reality. When, however, they termed the actual world of reality an imitation of the mathematical forms, they thereby ascribed a sort of reality, even though of a derivative and secondary character, to individual things, and to what takes place among them. They were also the less inclined to withdraw from answering cosmological and physical questions as they were able to bring to philosophy the brilliant results of their astronomical investigation. They had come to a knowledge of the spherical form of the earth and of the heav enly bodies ; they were aware also that the change of day and night depends upon a movement of the earth itself. At first, indeed, they thought of this movement as a circuit performed about a central fire to which the earth presented always the same side, a side unknown to us. 1 On the other hand, they assumed that about this same cen tral fire there moved in concentric circles, outside the earth's track, successively the moon, the sun, the planets, and finally the heaven containing the fixed stars. They brought into this system, however, in a way, the metaphysical dualism which they had maintained be tween the perfect and the imperfect, inasmuch as they regarded the
1 Already in Plato's time the hypothesis of the central fire was given up by the younger Pythagoreans, Ecphantus, Hicetus of Syracuse (and with it that of the "counter-earth," which had hitherto been assumed as placed between the central fire and the earth, invented merely to fill out the number ten), and instead the earth was located in the centre of the universe and provided with a rotation on its axis. With this latter assumption that of a resting position of the heaven of the fixed stars was connected.
Chap. 1, § 6. ] Conceptions of Cognition. 57
heaven of the stars, on account of the sublime uniformity of its motions, as the realm of perfection ; the world " beneath the moon," on the contrary, on account of the unrest of its changing formations and motions, they regarded as that of imperfection.
This way of looking at things runs parallel to that of Anaxagoias, and leads, though in another way, to the interweaving and complica tion of theory with considerations of worth [ethical or aesthetic
It teas in connection with astronomical insight that the thought of an order of Nature in conformity to law dawned as clear knowledge upon the Grecian mind. Anaxagoras reasons from this to an ordering principle. Pythagoreanism finds in the heavens the divine rest of unchangeableness {Sichgleichbleibens) which it misses upon the earth. Here we have a meeting of the ancient religious ideas and the very different result yielded thus far by the scientific work of the Greeks. This latter, seeking a Permanent in the muta tion of occurrence, found such a permanence only in the great, simple relations, in the revolution of the stars, which abides ever the same. In the terrestrial world, with its whole change of manifold, con stantly intersecting motions, this uniformity remained still hidden from Greek science : she regarded this terrestrial world rather as a domain of the imperfect, the lower, which wants the sure order of that other world. In a certain sense this may be looked upon as the ultimate result of the first period, a result which had a determin ing influence for after time.
What the attitude of the Pythagoreans was to the question concerning a peri odic change of origination and annihilation of the world is uncertain. A plurality of co-existing worlds is excluded in their system. In their theory of world-for mation and in their particular physical doctrines they concede so prominent a place to fire that they come very near to Heraclitus. Aristotle even places one of the contemporaries of Philolaus, Hippasus of Metapontura, in immediate con nection with Heraclitus (Met. I. 3).
Their assumption of ether as a fifth element out of which the spherical shells of the heavens were formed, in addition to the four elements of Empedocles, is doubtless connected with the separation which they made between heaven and earth. It is not less difficult to decide whether they derived the elements from a common ground, and if so, how : according to many passages it would seem as if they had spoken of a progressive "attraction," i. e. in this case (cf. above, p. M), mathematical shaping out or forming of empty space by the Iv (one), the original number, which is exalted above limitation and the unlimited. Yet it max, too, that in regard to these questions various views were held within the •ebool side by side.
§ 6. The Conception! of Cognition.
values].
It Schneidewin, Uebtr dieKeime erkenntnitstheorttischer und ethiseher Phi- lotopkrme bei den vortokratischen Denkern, Pbilos. Monatshefte, II. (1860), pp. 157. 345, 429.
B. Mfinz, Die Keime der Brkenntnitstheorit in der vorsophittischen Periods in griechiteMn Philotophie. Vienna, 1880.
. 58 The Greeks : Cosmological Period. [Part L
The question, what things really are, or what is the intrinsic nature of things, which is already contained in the Milesian con ception of the apxn, presupposes that the current, original and naive mode of thinking of the world has been shaken, although this pre supposition has not come to clear recognition in consciousness. The question proves that reflective thought is no longer satisfied with the ideas which it finds current, and that it seeks truth behind or above them. Those ideas are given, however, through sense-per ception and through the involuntary elaboration of this in thought, —an elaboration that has been transmitted from generation to generation, until it has became consolidated and fixed and embodied in language, and so forms a part of the thinker's data. When the individual with his reflection transcends these ideas so given — and it is in this that philosophical activity ultimately consists — he does it on the ground of logical needs which assert themselves as he re flects on the given. His philosophising, then, even though he takes no account of this fact, grows out of discrepancies between his expe rience and his thought — out of the inadequacy exhibited by what is presented to his perception or imagination, when set over against the demands and presuppositions of his understanding. However unconscious of this its inner ground naive philosophising may be at the outset, attention cannot fail to be turned in time to the diver sity in the sources of the conflicting ideas within.
1. The first observations, therefore, which the Grecian philosophers made on human knowledge concern this contrast between experience and reflection. The farther the explanatory theories of science became separated from the way of looking at things which belongs to daily life, the clearer it became to their authors that those theories sprang from another source than that of the customary opinions. To be sure they have not as yet much to say on this point. They set opinion (Sofa) over against truth, and this often means only that their own doctrines are true and the opinions of others false. So much only is certain to them, that they owe their own views to reflection, while the mass of mankind — concerning whose intellectual activity it is just the older philosophers, Heraclitus, Parmenides, Empedocles, who express themselves in an extremely depreciatory manner — persist in the illusion of the senses. Only through thinking (<f>p<wtiv, vohv, Aoyos), then, is the truth found ; the senses, if alone, give fraud and a lie. l So strong has reflection become in itself that it not only proceeds to con sequences which to the common thinking have become absolutely
» Heracl. Frag. (Schust. ) 11, 123 ; Parmen. Frag.