plato and aristotle number || time, number, and eternity in plato and aristotle

Time, Number, and Eternity in Plato and AristotleAuthor(s): W. von LeydenSource: The Philosophical Quarterly, Vol. 14, No. 54, Plato and Aristotle Number (Jan., 1964),pp. 35-52Published by: Wiley for The Philosophical QuarterlyStable URL: http://www.jstor.org/stable/2955440 .

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35

TIME, NUMBER, AND ETERNITY IN PLATO AND ARISTOTLE*

The traditional account of Plato's and Aristotle's views on time and

eternity is in brief that (1) there are two meanings of the word 'eternal' which Plato was the first to use in the sense of a mode of existence un- conditioned by time and therefore allowing no distinction between past, present, and future, while Aristotle employed it to express the notion of

everlasting existence or sempiternity; (2) in keeping with these two uses Plato and Aristotle likewise arrived at two different notions of time in that Plato contrasted it with eternity and thought of it as having a beginning, while for Aristotle the two concepts merged into one, that of everlasting time. A version of this account has recently been put forward again by Professor W. Kneale1 in a paper dealing with the concept of eternity in relation to that of necessary existence. Though I certainly do not wish to

dispute the main gist of his version, I nevertheless doubt, in spite of the

reputation of both medieval and modern expositors, whether their inter-

pretation of this important theme is altogether correct. My misgivings are, first, that Plato's doctrine, if examined in detail, contains considerably less contrast between the concepts of eternity and time than the traditional account makes out, and secondly that there is accordingly also less of a contrast between Plato's and Aristotle's views. I think that the two kinds of contrast were over-estimated by the Christian Fathers and medieval

philosophers in the light of theism and biblical revelation, and that this has led to a certain misrepresentation of the original points of doctrine. While

my purpose here is to attempt to restore these to their genuine dress, an additional reason for taking an interest in these ancient views is that both uses of the word 'eternity' have always been philosophically important, the first in connection with the timeless present we employ when talking of

necessary truths as in mathematical statements, the second in connection with the cosmological problem of the duration of contingent existence, in

particular with the conservation principle in physics.

I. PLATO

In close analogy to his belief that the sensible, temporal world partakes of an intelligible, timeless world, or that it is a likeness of one, Plato defined time as an everlasting likeness (aicbvios EiKCbv), moving by number, of eternity (cicbv) that abides in unity. Now what precisely did he mean by this cele- brated definition ? For though its terms seem concise, their meaning is by no means obvious.

*I am much indebted to Professor A. C. Lloyd who read this paper and made helpful comments.

1" Time and Eternity in Theology ", Arist. Soc. Proc., Vol. LXI, 1960-1, pp. 87 ff.



36 W. VON LEYDEN

(a) Eternity (Aion) : In the early language of the Greeks the word adicv never stood for

eternity. It was used by Homer of human life as a span allotted to each man2 and in a narrower sense may have signified the living force of human life or the source of vitality,3 so that Homer could in fact couple adcbv with wyvX', by which it was later superseded.4 While the poets continued to employ the word in its old significance, sometimes with a slight implication of life-destiny5, the Presocratic philosophers used it as a term for lastingness or long, even infinitely long, duration.6 When the distinction between sempiternity and eternity in the sense of timelessness originated among the Eleatics, none of them expressed the latter notion by the word adicv. Thus Plato is to be credited with the introduction of this term in the sense of timeless eternity, though in further defining the concept he adopts a language similar to Parmenides' description of the One as being now all at once, a

single whole,7 remarking that it is incorrect to conceive of something eternal in terms of everlasting duration or to say of it that it " was " or " will be ", as these terms only apply to things moving in time. For him, as for Par- menides, the word 'is ' makes up the proper designation of the eternal; or, as Simplicius put it,8 Aion is a unit (yovas) in which temporal distinctions are all present together.

Now it is indubitable that the way in which Parmenides and Plato conceived of a timeless present was handed on, in terms of Aion, to Hellen- istic times and to the Christian era.9 And it is also worth noting that Aion, being the mode of existence of a pattern of reality which is intelligible and normative, was ranked by Plato and his medieval followers as superior to time.10 On the other hand, whatever contrast he may have made between the created world and its timeless archetype must have been considerably lessened by his conception of the eternal model of the world as a living being."l He talks as though adicv could be coupled with the term co5ov in a way similar to that in which Aristotle coupled it with 0oi0112 or Homer with yvux. This suggests to me that the old meaning of adcbv to which I have drawn attention still lingered on in the formulation of Plato's as well

211., IV. 478, V. 685, IX. 415; Od., V. 152.

3Hymn. Horn. Mere., 42. 4GI., XIV. 453; Od., IX. 523. Cf. A. C. Pearson, Verbal Scholarship and the Growth

of some abstract Terms, 1922, p. 30; in general C. Lackeit, Aion, Diss. K6nigsberg, 1916. 5Pindar, Pyth. VIII. 97 ; Sophocles, Antig. 528; Aj. 645; Phil. 179, 1348; Trach. 34. 6So probably in Heraclitus, 22 B 50 and 52; Empedocles, 31 B 16, 2. References

are to fragments in Die Fragmente der Vorsokratiker (Diels-Kranz, 6th ed.). 7VOv E-rTV 6poU wTav, EV, CUVEXES, 28 B 8, 5-6. 81n Arist. Categ., p. 356, 8-10 (Kalbfleisch). 9Cf. Plutarch, De E ap. Delph., 20, 393 A 8 f.; Plotinus, Enn., III. 7, 3; St. Augus-

tine, Enarr. in Ps., II. 7, para. 6; CI. 25, para. 10; Conf., IX. 10, para. 24; In Ioann. Ev. Tract., 38, 10; De Civ. Dei, IX, 21; Boethius, De Cons. Phil., V, 6; St. Thomas Aquinas, Summa Theol., I. 10, Art. 1.

10To compare with Euripides, Heracl., 900, where Aion is the child of Chronos. 1Timaeus, 37 D.

12Metaphysics, A. 7, 1072 b 28-30; De Caelo, I. 9, 279 a 21-8.



TIME, NUMBER, AND ETERNITY IN PLATO AND ARISTOTLE 37

as Aristotle's doctrine, and that consequently the novel meaning of the word as timeless present ran alongside the temporal one of lastingness or everlastingness. Hence, if Plato coupled Aion with terms like 'life' or 'living being' in the sense I have indicated, he need not, as Professor Kneale is inclined to think,13 have been running together two incompatible notions. For if to him Aion possibly meant, in part, the whole lifetime of what is identical throughout, he could in this connection meaningfully talk of an eternal living being or life.

However, the rapprochement between time and eternity which I perceive in Plato's doctrine is borne out not so much by the notion of temporality implicit in part of his concept of Aion as by the two key-terms EiKCbV (likeness or image) and Aplie6os (number) in his definition of time. I will proceed, therefore, to an enquiry into the meaning of both these terms.

(b) Time as a Likeness of Eternity Plato introduces the first, EiKC&V, to indicate that the temporal world is

a likeness or image of the eternal. Though he holds that a description of this " likeness " can itself only be " likely " and though indeed the connection between EiKcbv and EiKcbs is obvious,14 it is nevertheless significant that he treats the physical world and time as akin to the timeless model. What, then, is meant by the term 'likeness' and how are we to understand the nature of time if defined as a likeness of eternity ?

For purposes of elucidation it may be appropriate first to consider Democritus' definition of time as a pavTacia resembling day and night.15 Admittedly, this is not a very clear definition; however, it was also ascribed to Epicurus, and since we know what Epicurus could have meant by it we may as well start with his interpretation. Now Epicurus states that time is a peculiar symptom or accident ('iio6v -ri aviiTcoPa),16 and Sextus, quoting this definition in the words "time is a symptom of symptoms ",17

explains that days, nights, motions and such like states are symptoms occurring to things-day being a symptom of air illuminated by the sun, motion a symptom of body, etc.-and that time is a symptom of these states. Presumably, then, since the definition of time as a " day-like and night-like phantasm " was ascribed to Epicurus as well as Democritus, the term yavTacoiia in this definition should correspond to Epicurus' phrase i'i6v Ti

avirrjTTopia. On the other hand, though the former term does not itself occur in the fragments of Democritus, I think it may safely be taken as a synonym

13Loc. cit., pp. 93-4, 99-100, 107.

14J. B. Skemp, The theory of motion in Plato's later Dialogues, 1942, p. 67; G. Vlastos, " The disorderly motion in the Timaeus ", Class. Quart., 33, 1939, p. 73.

15Sextus Empiricus, Adv. Math., X. 181 (Usener, Epicurea, 1887, ad fr. 294, p. 352, 32).

16Letter to Herodotus, 72-3; see fr. 79 (Usener).

17aCiTrrTcoa avpTi-rcoT&TcoV, Adv. Math., X. 219 ff. (fr. 294 Us.).



38 W. VON LEYDEN

of (pwraoTa,18 and this term, as we know from peripatetic terminology pre- served in doxographical reports on Leucippus and Democritus,l9 was generally regarded as consisting of appearances made up of subjective elements. One might thus infer from the two arguments in conjunction that for any one who, like the atomists, defined time as a phantasm resembling day and night, time could not exist in the world of true knowledge or alternatively, as Lucretius put it,20 have any independent nature. Since Democritus held that symptoms or accidents are real only by opinion or that they are relative to a percipient, there is perhaps a sense in which his philosophy in general might be called a "philosophy of perspective ".21 The point is of course debatable and has in fact been disputed, but it may be borne in mind: it is relevant to my discussion of the relation between the terms pavTracia and EiKCbV in Plato's doctrine, to which I now turn.

If Plato calls time an "eikon ", a likeness of eternity, its nature must be for him more real than for Democritus. As he explains in the Sophist (235 D if.), there are two types of imitating or image-making arts, the likeness- making (eiKaTlrKii) and the semblance-making ((pavTaxolKni) art. While one makes a likeness (EiKcbv) of a thing if one copies its true proportions in all three dimensions, one makes a semblance (pavTracla) if, like a painter, one

produces a perspective picture which seems like the original, but in fact is not. Plato compares such perspective illusions with the productions of a

sophist who abandons truth for things that are not,22 and he remarks that the only safeguard against this kind of image lies in a science of measurement and numeration, described in the Protagoras (356 D-E) and of capital importance in the Philebus. Of this science I shall have more to say later.

Now while on Democritus' view time is a phantasm, a semblance, on Plato's view it is a likeness. Since he regards it as a likeness of eternity, the highest-order mode of existence, it must be for him particularly "well- founded " (to use Leibniz's terminology). As an " eikon ", at any rate, it is not so much in contrast with its model as intimately connected with it.23 Nor need it be rectified or controlled, like a phantasm, by an outside science of measurement and numeration. For as an " eikon " it represents its model

truthfully, and besides it implies in its own nature a standard of measure-

18W. Cronert, Kolotes und Menedemus, 1906, p. 104, n. 501, quotes an Epicurean fragment from papyrus Hercul. 1413, in which the terms qavTacia, fiipal, and viuKEs occur in a definition of time. Part of this fragment is quoted by Diels, Vorsokratiker, 68 A 72. S. Luria, Die Infinitesimaltheorie der antiken Atomisten, 1932, pp. 164-5, maintains that pavTaaia and a)p1rTTcopa have a different meaning, overlooking the fact that time for Epicurus is a special kind of symptom. The point is clearly stated by C. Bailey, Epicurus, 1926, p. 241; The Greek Atomists and Epicurus, 1928, pp. 306 and 309.

19Diels, op. cit., 67 A 33; 68 A 135 (vol. II, p. 117, 35-7). 20De rer. nat., I. 459 f. 21E. Frank, Plato und die sogenannten Pythagoreer, 1923, pp. 19-24, 234-5, 341-2. 22Cf. also Republic, X. 598 A-B. For further evidence of Plato's rejection of per-

spective space see E. Pfuhl in Jahrbuch des Kais. Arch. Inst., XXV, 1910, pp. 12 ff. 23This point is brought out by Proclus, In Plat. Tim. Comment., 241 E (III, p. 11,

31 Diehl). For the concept of EiKCoV in Plato generally see R. Robinson, Plato's Earlier Dialectic, 1953 (2nd ed.), pp. 218-22; also D. W. Hamlyn, "Eikasia in Plato's Republic", The Philosophical Quarterly, 1958.




ment or numeration. That this is Plato's view is indicated by his insistence on the connection of time with number and on its importance as a factor

whereby to introduce order in the formation of the world. I think, in fact, we should take the definition of time as "proceeding by number " as

complementary to the statement that it is a likeness of eternity and accord-

ingly examine more closely its numerical nature as viewed by Plato.

(c) Time and Number Plato's definition of time appears to be the first in Greek philosophy in

which there is an explicit mention of number. No doubt, the Presocratics

may have prepared the way for such a coupling of time with number by their insistence on the regular and orderly organization of temporal reality, an insistence which, as has been judiciously observed,24 fostered the evolution of Greek science in general precisely by engendering the consideration of the quantitative aspect of the natural world. The Pythagoreans with their

theory of number must have had a considerable influence in this direction

too, though there is only one, Archytas of Tarentum, of whose definition of time a more detailed account has been transmitted. Even here, the authen-

ticity of his alleged book rTpi T-ro rravtos, which contained definitions of

time, is highly improbable, while another alleged definition of his, according to which time is the " number of a certain movement or the interval proper to the nature of the universe ",25 shows traces of a later origin; none of these definitions is therefore included in Diels' collection of Archytas' genuine fragments.26 Thus Plato, so far as our knowledge goes, was the first to define time in connection with number, and we must seek to find out what is meant

by this definition. References in his works to the numerical character of time are not many,

and there is not sufficient evidence for believing that it is to be explained in connection with his theory of " ideal numbers ".27 But as time is said in the Timaeus to " proceed by number " or to " revolve according to number ", there should be a standard by which it can be measured. This, as Plato explains, is provided by the uniform revolutions of the five planets which divide the temporal flow into EprP Xp6vovo (37 E 3) and such regular periods as days, nights, months, and years. The planets, he says accordingly, determine and safeguard the numbers of time (38 C 6),28 they are requisites for the making of time (38 E 4) or " organs of time " (41 E 5, 42 D 5). He

definitely intimates (39 C 6 f.) that the courses of all planets describe periods 24A. Rey, La jeunesse de la science grecque, 1933, pp. 321 and 329; R. Mondolfo,

Problemi del pensiero antico, 1936, pp. 26-7.

25Simplicius, In Arist. Phys., p. 786, 11 f. (Diels); In Arist. Categ., p. 350, 10 f. (Kalbfleisch).

26From the sometimes literal correspondence of Ps.-Archytas' definitions with those of Aristotle the conclusion should be drawn that the former are derived from the latter rather than conversely. as was the case with P. Duhem, " Le temps selon les philosophes hellenes ", Revue de Philosophie, July 1911, p. 10.

27For references to such a connexion see A. Levi, II concetto del tempo nella filosofia di Platone, 1920, p. 100.

28Cf. the expression tp-rpov &apleoOu -ro Xp6vou in the Laws, XII, 947 B 2.



40 W. VON LEYDEN

of time, not only those of the sun and moon. Men, he complains, do not estimate the numerical duration of all these revolutions relatively to one another and even scarcely know that any one of these makes time since by reference to each orbit different kinds of month and year could be ascertained simultaneously. Perhaps, when speaking of the stars as opycva Xp6vcov (41 E 5), Plato wishes to indicate by the genitive plural the existence of such manifold time-systems.29 His chief point would seem to be that all the intricate dances30 of the stars are wrought on a scheme of reason which throughout the temporal world is set forth by an unfailing order of uniformity, succession, and periodic repetition. Similarly, he believes that, while all the different periods of time, if compared with one another, produce too many involved ratios to be calculated, it is possible to determine the length of one period in which the revolutions of all the heavenly bodies are comprised. This is for him the " perfect year ", completed by a " perfect number of time " (TXAEos &pie6os xpovou, 39 D 3), at the end of which all the heavenly bodies return to their starting-places. He suggests no exact length for this period, but he probably has the " Great Year " in mind of which, it appears, there were various calculations in vogue ever since the fifth century. The recurrent movements of the stars, he significantly concludes, serve the purpose of making the world most like the perfect (TrAEos), intelligible model.

By reflecting on celestial numbers, in Plato's view, men should also contemplate, compute, and correct the directions of their own thoughts. For him there exists a correspondence between astronomical cycles and those in the world of man,31 though it is only the divine element in human understanding that is akin to and can conform to the measures of the heavenly revolutions. The reason is that the cycles of the stars are infinite, always coming full circle, whereas the cycle of men's lives is limited, its beginning and end never combining.32 However, since to everything on earth a certain length of time is assigned, Plato throughout insists on the importance of observing these "apportioned life-spans " or "appointed periods .33 He believes, for instance, that diseases have their fixed times too and therefore should not be interfered with in the hope of shortening them or of prolonging life, though, when interference is indicated, drugs should always be administered at the right moment.34

29A. E. Taylor, A Commentary on Plato's Timaeus, 1928, p. 689, remarks that these passages in the Timaeus state what Aristotle (Physics, IV. 10, 218 b 3) only says would be the case on a hypothesis which he himself does not advocate. Hence Taylor tries (pp. 689, 691) to interpret the Platonic idea of time on the lines of the modern theory of relativity. Cf. also E. A. Milne in a review in Philosophy, 1949, pp. 349-51.

30Proclus, op. cit., 247 A, B (p. 28, 1 and 11, Diehl), suggests deriving from the dancing orbits (Xopdai) of the stars the etymological root of xp6vos = Xop6voos; similarly Simplicius, In Arist. Phys., p. 786, 30 (Diels) ;In Arist. Categ., p. 351, 34 (Kalbfleisch).

31Tim., 42 C, 47 B-D, 81 B, 90 C-D, 91 E, Laws, X. 897 B ff., Rep., VIII. 546 A-C. The last passage contains the phrase ITEpioSos, fv d&pi0p6S TTEpiAaJplvsiE T-XEioS.

32This apparently was an old notion, ascribed to Alcmaeon of Croton by an early Peripatetic; see Diels, Vorsokratiker, 24 B 2.

33Tim., 42 B 3, 89 B 6. 3489 B-C; the importance of the right time (Kairos) for the treatment of illnesses

is stressed in Hippocratean writings (Littre, II, 266-7; IX, 251).




Of course, there is nothing novel in Plato's insistence that at certain times something is to be done which at other times would not fit into the context of prior and subsequent events, or in his intimation that the right opportunity, the Kairos, conforms to what is irpErrov, 86ov and -rTplov35 and, next to God and together with Tyche, rules over the world.36 An awareness of the Kairos as denoting due measure already occurs in Hesiod,37 the Seven

Sages,38 Theognis,39 Pindar,40 and the Tragedians; it was worshipped in

Olympia,41 and Lysippus made a statue of it after Ion of Chios had honoured it with a hymn. None the less, Plato's acknowledgement of the significance of the Kairos in human life merits discussion. There is a connection between his association of time with number and the choice of right moments on the one hand and his idea of a science of measurement and numeration, which assumes so much importance in his later writings, on the other. The theme is particularly relevant to my argument, for, as he explains in the

Republic (VII, 525 B f.), mathematics, i.e. both numeration and measure-

ment, is a means of establishing a state of being in the midst of the world of becoming. I shall therefore mention a few examples of the connection which he perceives between the science of numeration and the nature of time as " proceeding by number ".

One of the four classes into which the science of measurement is said to divide things is that of the infinite, which comprises anything that admits of greatness, intensity, or endless comparison. Another is that of the finite which consists of the equal, the double, and any definite number. The third class represents a mixture of the infinite with the finite and renders these commensurable by the introduction of number. Now in the Philebus (26 B and 30 C) Plato says that among all the beauties of the world the seasons also partake of the infinite and finite and that the mixture of these two

represents a cause which orders the years and the months. Here we have an

express statement about the connection between the science of measurement and astronomical determinations of time described in the Timaeus. However, there also appears to be a connection between that science and temporal determinations in earth-born life. In the Politicus (284 E) the science of measurement is said to fall into two classes. One is concerned with measuring number and spatial magnitudes in regard to relative greatness and smallness; the other with measuring numbers and magnitudes in relation to standards that lie between extremes. Now Plato maintains that, only if the comparison between deficiency and excess in all the arts concerning quantities and qualities is carried out in relation to such standards, do the works and

35Politicus, 284 E. Cf. Diels, Vorsokratiker, 68 B 226, 72 B 1, 88 B 7. A convenient survey of Plato's uses of pETpov and KaipoS is appended to R. G. Bury's edition of the Philebus, 1897, pp. 169 f.

36Laws, IV, 709 B. 37Works and Days, 694. 38Diels, Vorsokratiker, 10 3 5, E 1, C 17, 88 B 7. 39V. 401. 4001. XIII. 48; Pyth. IV. 286. 41Pausanias, V. 14, 9.



42 W. VON LEYDEN

pursuits of life conform to beauty and perfection. In the Philebus (66A), he regards measure, moderation, and TO Kciptov as one of the first possessions bestowed on men by the " eternal nature " and as precisely the standards whereby the science of measurement ascertains the numbers of all that lies between the One and the Many and whereby it obtains control of the sensible world. As I have remarked before, the science of measurement in Plato's view rectifies the inconsistencies of sense-perception (Protagoras, 356 D f.); certainly, its aim is knowledge of what is (&Ei 6v (Republic, VII. 527 B). The Kairos, then, like the other standards of measurement inherent in the lifetime and daily activities of individuals, must imply something of the nature of being and of the eternal.

The various illustrations and arguments I have advanced may explain why, in Plato's opinion, time proceeds according to number and how in this capacity it represents a " moving likeness " of eternity.

(d) The Infinity of Time However, Plato calls time not merely a likeness of eternity but a like-

ness which is itself eternal. I will consider now this term aic&vlos in connection with my original question as to what extent time, on Plato's view, is like its eternal model.

It follows from all that is said explicitly in the Timaeus about the formation of the world that time, involving as it does duration and succession, cannot be eternal in the sense in which its model is regarded as eternal, nor indeed in the sense of everlastingness a parte ante, since Plato's statements imply the creation of time and a beginning of the world in time (28 B, 37 C, 38 B, C, 39 E, 49 A). On the other hand, what Plato repeatedly states is that time and the world are infinite a parte post (27 D 6, 31 B 3, 33 A 2, 38 C 3, 40 B 5). This asymmetrical relation between a generated world and its infinity a parte post is puzzling if compared both with his doctrine in the Phaedrus (245 D) and with Aristotle's statements about the inter- dependence of the terms ySvriT-s-0capros and ayEvriToS-acpappTos.42

True, in some sense the world for Plato is unoriginated because he regards being, space, and becoming as having been in existence, like a timeless substratum, before the birth of the universe (52 D 3). Hence his teaching of a generated world means the putting into operation of a scheme of orderliness in a world of which the raw material, i.e. a state of disorderly motion (30 A, 53 A-B, 69 B), already exists; since time is part of this scheme, it is coeval with its introduction. Now Plato says (37 C 6) that the world was a likeness of the eternal even before the making of time and that time was fashioned only in order that the world should resemble the eternal to an even greater extent. Hence the existence of pre-temporal motion, supposing that this is everlasting a parte ante, can in no way be the explanation for time being an eternal likeness of eternity.43 It is rather the orderly state

42De Caelo, I. 12, 282 a 21 ff. 43This is particularly so, since (assuming the text is correct and ayaxAa means ' like-

ness ') Plato does not really say that the pre-temporal world was " a likeness of the eternal " but only that it was " a likeness of the everlasting gods ", where the point of similarity may just lie in the divinity,

' everlasting ' being a conventional and irrelevant

epithet. (I owe this point to Professor A. C. Lloyd.)




of movement and becoming, of which time is both the expression and the

measure, in virtue of which eternity is most closely represented in the world. A different question arises if the teaching of the Timaeus is taken as

metaphorical on account of its mythical imagery and because it contains discourse about the temporal world which on Plato's own showing44 can only be likely or analogical. This line of interpretation became traditional in the Academy, from the immediate followers of Plato onwards to the Neo- platonists, the only exceptions being Aristotle, Plutarch, and Atticus, who believed in the literal meaning of Plato's doctrine. Owing to an equal amount of evidence on either side the question remains an open one. None the less, I want to suggest very tentatively that Plato's teaching, so far as the creation of time is concerned, may be taken in its literal meaning, though this need not imply that time had a beginning.

Keeping in mind the fact that time for Plato is a likeness of the eternal, one might argue that the creation of time on his view can only mean the creation of temporality as a whole, not just the formation of the opening moment of the time-series.45 No single moment, not even any limited series of moments, can make time similar to the eternal model, unless all these serve as constituents of one comprehensive form or order. Time would be such an order if regarded as the temporal organization of the world as a whole.

There can be no doubt that Plato thought that in this capacity time is

cyclical and that the universe as a whole is a kind of spherical space-time. He speaks of time as revolving (38 A 7) and of the universe as wrEpio5oS (58 A 5), which term, as Cornford has pointed out,46 may cover both " circum- ference " and "revolution ". As against Taylor47 it should be urged that there are in fact several allusions in the Timaeus to time as inseparable from circular motion and the continual cycles of birth, growth, decay, and death, though admittedly on Plato's view this cyclical order does not imply a point-to-point repetition of any series of events : the recurrence or identity in kind of the units of periodic repetition, such as day, summer, or year, can very well go together with numerically different events.

The idea of a cyclical temporal order can be found in Empedocles48 and also in a fragment of the comic playwright Hermippos, who thought of time in terms of the repetitions of the annual circle.49 Cornford has pointed out50 that there is an allusion in this fragment to the derivation of Eviaur6s from EV EcvTC) which is also found in Plato's Cratylus.51 Now these notions of a

44Timaeus, 29 B-C. 45For a similar distinction see G. Vlastos, loc. cit., p. 76, n. 2. 46Plato's Cosmology, 1937, p. 243.

470p. cit., p. 190. 48Diels, Vorsokratiker, 31 B 17, 29; also fr. 26, 1. 49Fr. 4 (Kock). 500p. Cit., p. 104. 51410 C-D. Cornford also refers to Ps.-Hippocr. Tnpi ipt opaScov, ch. XVI and Plu-

tarch, Def. Orac., 12, 416 A; one might add Skythinos, Diels, Vorsokratiker, 22 C 3, 2, and Critias, ibid., 88 B 18. Cf. also K. Reinhardt, " Heraclitea ", Hermes 77, 1942, pp. 229-30.



44 W. VON LEYDEN

temporal cycle encompassing the world's duration bear some resemblance to the nature of time as a form by which, according to Plato's account, order is impressed on the world. We have to think of this form as embracing all the periods of the planets, and inasmuch as it combines end and beginning for an infinite number of times it can be called unlimited and everlasting. Such an interpretation was offered by Proclus,52 and it appears to be a clue to the understanding of the partly literal, partly metaphorical sense of Plato's teaching. For as a cyclic form time may be created without having a beginning and without the puzzling implication of a pre-existing " chaos ". That is to say, if the creation of time does not mean the com- mencement of the temporal series but the impression of a cyclic form which has no beginning, there can be nothing "before" this form, because a " before " can only exist if there is a first moment. According to a report by Proclus,53 Atticus and his followers supposed that before the birth of the universe there was a time but not an orderly time. This is unreasonable not only because the idea of an unordered time would, in Plato's eyes, be self-contradictory, but because the term ' before ' has no meaning in relation to time as a cyclic form. If Plato speaks of an original state of things in terms of 'before' (52 D 4, 53 A 7), we should understand this term meta-

phorically and perhaps describe the " pre-temporal" mode of existence by saying that it falls outside time but is contiguous to it like anything lying round a circle.

On such lines the interpretations of Xenocrates, Grantor, Chalcidius, and other Platonists were advanced. They thereby arrived at the notion of everlastingness a parte ante, in conformity with Plato's ideas of an ungenerate life of human souls.54 Whether or not these are correct interpretations of Plato's views in the Timaeus, it appears to me very probable that time for him is a likeness of eternity not only because, proceeding by number, it secures an ordered and regular world, but also because he thought that its nature is cyclical.55

II. ARISTOTLE

Whereas in my foregoing discussion I have tried to argue that there is less of a separation between the eternal and the temporal in Plato's doctrine than is commonly assumed, my subsequent argument is to the effect that, on Aristotle's view, if carefully examined, there exists a distinction between time, even infinite time, on the one hand, and something which contains all time and as such is not in time but is eternal on the other. Both sets of

argument, together with my attempts to show that Aristotle developed his

theory of time largely on lines indicated by Plato, should lessen considerably the contrast that tradition has taught us to perceive between the two thinkers in regard to their views on this subject.

52Op. cit., 229 E (II. 289, 20 f., Diehl); 247 C (III. 29, 3); 248 A (III. 30, 30 f.). 530p. cit., 250 B (III. 37, 11 f.). 54Meno 86 A; Phaedr. 245 D. 55Cf. here also R. Mondolfo, L'Infinito nel pensiero dei Greci, 1934, p. 69.




(a) Eternity A close resemblance exists between the concluding words of Plato's

Timaeus and a sentence in the first book of Aristotle's De Caelo (I. 9, 279 a 10). Both for Plato and for Aristotle the heaven is one, unique, and complete. Yet while Plato emphasizes that it has come to be,56 Aristotle merely asserts that the heaven " is " one, unique, and complete. The difference in wording is an instance of self-assertion on the part of Aristotle, and it is well to remind ourselves that, as Werner Jaeger has suggested,57 the passages immediately following the sentence in De Caelo are most probably derived from the dialogue TEpl pXAoaopias which contained early signs of Aristotle's polemic against Plato's cosmology. What then is Aristotle's own theory of the heaven, and is it in fact polemical throughout ?

Outside the heaven, he maintains, there is no body, place or void, and hence no movement or time: whatever it is that is beyond the outermost sphere, its nature is unalterable and timeless. In further defining such transcendent existence (TrdKE) Aristotle introduces the term adciv, which, however, he does not seem to use here in the Platonic sense of timelessness, since he speaks of the things beyond as continuing TOV crraVTa oaiova. Aion

signifies for him the relative lastingness of a single being, according to the original meaning of the word to which I have referred. An insect as well as a man, a nation or a whole epoch have their Aion58; similarly the entire world, whose Aion is everlastingness for him, since, as shown in the last three chapters of Book I of the De Caelo, its duration is infinite. Now the fact that the timelessness of transcendent existence as well as the world's infinite duration are defined by Aristotle in terms of Aion makes it difficult to interpret the exact meaning of this term in the context where it is first introduced. An ambiguity there certainly is, for Simplicius59 remarks that Alexander of Aphrodisias was uncertain whether the characteristics ascribed to the things beyond referred to the prime mover or to the first heaven, i.e. the outermost sphere of the fixed stars.

I think the ambiguity is due to certain of Aristotle's definitions which are intended to distinguish spatial transcendence from things inside the heaven but which fail to distinguish it from the heaven as a whole. For one thing, in maintaining that spatial transcendence lacks properties of place, he shows that it must differ from particular things inside the world, but not from the first heaven itself, since this is not encompassed by anything, and in the absence of an encompassing body its place, in the eyes of Aristotle,60 cannot be determined. Secondly, in maintaining that transcendence lacks the properties of time, he asserts not that it is timeless but that it endures unalterably through all time, though in this capacity it can differ only from

56Cf. also Tim., 31 B 3. 57Aristoteles, 1923, pp. 317 ff. (Eng. Tr., 1934, pp. 302 ff.). 58279 a 23-5; cf. U. von Wilamowitz-Moellendorff, Euripides Heracles, 1933, on

line 669. 59In Arist. de Caelo, p. 287, 19 f. (Heiberg). 60Physics, IV. 5, 212 b 14.



46 W. VON LEYDEN

all that comes-to-be and passes away, but not from the first heaven and the world as a whole, which are everlasting too. The distinctive features, therefore, whereby Aristotle wishes to describe the nature of T-raK equally apply to the outermost sphere: in fact, the same attributes which he applies to T-rKE in one place (279 a 19-21) he applies to the first heaven in another (270 b 1-2). This ambiguity explains the uncertainties felt by early commentators. Nevertheless, two important aspects of Aristotle's doctrine can be stated fairly clearly.

The first is that in his view the word aidov stands for something different from infinite time or everlastingness. For he insists on defining it as an encompassing term (-r6 -rrpiXov TrAos), even when applied to the infinity of the world's duration. Thus Aion is a container and infinite time the contained. In the second place, he attaches to Aion a divine significance, for from it, he says, the life of all other things is derived. The expression he uses to denote this derivation (efpTrnrTai 279 a 29) is similar to that used in a passage of the Metaphysics, where the heaven and nature are said to " depend " (-pTrrTal) on a sublime principle which is immaterial and which initiates motion.61 Aristotle there refers to the prime mover and it is also he to whom Aion is assigned as the best and most eternal form of life (1072 b 29). In the passage of the De Caelo a prime mover is not explicitly men- tioned, but in the equivocal language of the concluding passage of Ch. 9 (279 a 33 f.) some such thing may be indicated, especially by the term KIVE(-al 62

In the De Generatione et Corruptione, Bk. II, chapters 10 and 11, Aristotle continues this argument in a way which considerably approximates his views to Plato's. In explaining the relation between the revolution of the first heaven and the processes of coming-to-be and passing away, he makes the point (336 a 24 f.) that the former cannot be the immediate cause of the latter, since its motion is a single motion, of the same nature, and always producing the same effect, so that it cannot be regarded as the cause of two processes which are contrary to one another. In order to explain these processes he refers to the annual movement of the sun along the Zodiac (i.e. along the inclined circle of the ecliptic), which implies two types of movement. On account of the inclination the sun alternately approaches and retreats, generating when it approaches, destroying when it retreats. He then remarks (336 b 10) that the times and the lives of every living being63 have a number (&piOo6s) by which they are distinguished, and that there is an order (TraiS) controlling all things and a period by which every time and life is measured (iETpETTra).

6lMetaphysics, A. 7, 1072 b 14. 62279 b 1. Simplicius (op. cit., p. 291, 25 f.) says he read KIVTE (" fortasse recte ", as

D. J. Allan points out in his Oxford edition of De Caelo, 1936) in another MS and under- stands this term as pertaining to the motionless realm outside the heaven. Yet KIVET could also be predicated of the first heaven (cf. W. D. Ross, Aristotle's Physics, 1936, p. 97).

63ot Xpovol Koi ot Pioi iK&o-rcOV, an expression tantamount to the poetically used aiobv as finite duration. Cf. the phrase oi Xpovoi ElpappEvoi in Meteor., I. 14, 352 a 29.




The point, I think, which Aristotle wishes to stress is that all periods and processes in nature depend on the eternity of the revolution of the first heaven and imitate its circular motion by being themselves cyclical, though what recurs is not always the same individual but only the same species (338 b 6 ff.). Their continuity likewise resembles64 the continuity of the heavenly revolution with the difference that the latter is a continuity of being, while the former is a continuity of alternations. After all, processes in nature are too far removed from their source to be able to be continuously, and at times they exist only potentially, so that they are not absolutely free from not-being. On the other hand, their perfection, coherence, and continuity consist in the everlastingness of their alternations : in this lies their closest approximation to eternal being (336 b 31 f.).

Characteristically, the etymology of the word aicov, for Aristotle, is that Aion " is always ,65 while that of Aither, the fifth element, of which the first heaven is composed and whose nature it is to move in a circle, is for him that the Aither "runs always ".66 The distinction is significant. Aion as a Telos, as an encompassing form, stands for the complete actualization of the process of circular revolution and recurrent periods.67 Motion and time, no matter whether finite or infinite, are incomplete processes68 : they are incomplete and imperfect not only if conceived in terms of a straight line (this is demonstrated in Aristotelian fashion in the De Caelo, Bk. I, and elsewhere), but even if conceived as cyclical, for in this case they have no end. It is only on account of the total form of their duration-and this is what the term Aion stands for-that the infinite cycle of revolutions attains perfection and unity.

In sum, Plato and Aristotle agree that all finite durations depend on the heavenly revolutions and themselves constitute a series which is in a sense cyclical. True, in Plato's doctrine time is rooted in an original act of creation; none the less, in representing a cyclic order impressed on the world as a whole, it can copy in this capacity a timeless present, called by him Aion. What Aristotle calls Aion is, on his view, likewise imitated by the periodic repetitions in the temporal world, while itself encompassing it as its Telos and actualization. As such Aion is not the same as infinite time or sempiternity. Moreover, he grants Aion a divine nature, and it may in fact apply as a mode of existence to what lies outside the first heaven. If it is so applied, it must practically come to mean the same as timelessness.

641ieTrITai, 337 a 4.

65De Caelo, I. 9, 279 a 27; for the same derivation see Chrysippus (Stoic. Vet. Fr., II. 163, p. 47, 28-30, Arnim) and Plotinus, Enn., III. 7, 4 (I., p. 314, 28, Volkmann).

66De Caelo, I. 3, 270 b 23; the derivation is suggested by Plato in Cratylus, 410 B.

67I am in general agreement here with J. F. Callahan's Four Views of Time in Ancient Philosophy, 1948, p. 87, and also B. Stenzel-Mugdan, Philosophische Motive im Weltbild des Aristoteles, 1924, p. 12.

68Physics, III, chs. 1 and 2; VIII. 5, 257 b 8; III. 6, 206 a 21 f.



48 W. VON LEYDEN

(b) Time as the Number of Motion I will complete my account of Aristotle's doctrine by drawing attention

to that part of it in which, not unlike Plato, he defines time in terms of number and in close connection with motion.

In Book IV, Ch. 10 of the Physics, he rejects three views which, he says, are derived from tradition. The first is the identification of time with the movement of the universe. This he confutes on the ground that even a partial revolution is time. I mention the view only because it was taken by Eudemus, Theophrastus, and Alexander as that set forth in Plato's Timaeus,69 so that Aristotle's criticism would involve a critique of Plato- to my mind an unjustified interpretation. The attribution in question, as was pointed out by Proclus70 and Simplicius,71 rests on a misunderstanding of Timaeus 39 B-D and other passages, in which Plato defines time not as the motion of the heavenly bodies but as its measure. It is indeed difficult to find in the Timaeus any such definition as the one which Aristotle criti- cizes, though similar ones can be found among Plato's followers in the Academy.72

The second view, the identification of time with the sphere of the universe, Aristotle dismisses as being too naive to need refutation. According to Simplicius,73 this was thought to be a reference to the Pythagoreans, but such a reference is doubtful since the attribution of any such definition to Pythagoras himself or to Archytas is late.74 It has also been maintained75 that Aristotle does not at this point criticize any Pythagorean definition, but merely a traditional symbolic name for the heaven.

With the refutation of these two traditional views Aristotle discards any identification of time with cosmic motion. It remains for him to discuss whether time is some other kind of motion, or alternatively a property of motion. However, in his view, to identify time with motion is to ignore the difference between the former as in some sense omnipresent and the latter as happening only in the thing moving or at the place where a thing moves. Besides, movements are always faster or slower, but not so time. Finally, if time were identical with motion, a state of rest would have to be outside time-an impossible implication.

And yet, it is obvious that time, though it is not the same as motion or change,76 is closely related to it. In order to show that this is so Aristotle explains that failure, such as may occur during sleep, to notice a change of consciousness or the interval between a later and an earlier "now" prevents

69Simplicius, In Arist. Phys., p. 700, 17-19 (Diels). 70In Plat. Tim., 270 B (III. 90, 15-17, Diehl): 71In Arist. Phys., p. 703, 21 f.; p. 704, 11 f.; p. 717, 21 f. (Diels). 72E.g. Xenocrates, Dox. Graec., 318 b 13-14, Diels (fr. 40, Heinze); Hestiaios, Dox.

Graec., 318 b 15-16. 73In Arist. Phys., p. 700, 19-22 (Diels). 74Cf. Aetius, Placita, I. 21,1 (Diels, Vorsokratiker, 58 B 33); Simplicius, In Arist.

Phys., p. 786, 11 f. (Diels). 75H. Cherniss, Aristotle's Criticism of Presocratic Philosophy, 1935, p. 216. 76These two terms are used interchangeably in the first four books of the Physics.




the perception of a time-lapse. The argument is significant in that the sufficient as well as necessary condition of any time-lapse is found to lie in the distinction of two "nows" and of a "before" and "after " in motion. In this connection Aristotle explains that before and after are in respect of their " substratum "77 the same as movement, i.e. as an earlier or later phase they are themselves a movement; but as being earlier or later, i.e. in " essence "78 and in the way in which they are defined and numbered, they are not a movement. In his view, it is precisely in the latter sense that they are essential for the recognition of time, which he accordingly defines as the " number of motion in respect of before and after " (219 b 2). Thus for him time is neither motion nor a quantity of motion, as Speusippus understood it,79 but that in respect of which motion can be counted.

Aristotle's next point is that what assesses the numerical value of before and after in motion is the "now ", of which he also distinguishes two

meanings. In respect of its " substratum ", i.e. by being an earlier or later cross-section of time, the now is always the same. But for a moment to be earlier or later, i.e. to be counted at different cross-sections, means that it is different in its essence and relations. In fact the numerical evaluation of before and after can be effected only if a moment is in one sense identical and in another always changing, if it is both a sort of unit80 and the repetition of a unit in a series of different relations. Similarly, if Aristotle speaks of a mutual dependence of time and the now (219 b 33 - 220 a 4), this should be regarded as applying on the one hand to time as a continuum and to the

unifying capacity of the now, on the other to time as a number and to the dividing capacity of the now. This twofold nature can be defined by saying81 that motion inasmuch as it is continuous and potentially numerable represents time in concreto, while if actually numbered it represents it in abstracto.

It is partly by virtue of the dividing or abstract nature of the now (which, incidentally, Plato anticipated in his discussion of that "para- doxical somewhat ", the Eiaipvr;s or " instantaneous "82) that Aristotle defines time as the number of motion. In this capacity, he endows time with a characteristic which seems foreign to its conception as a continuum. According to Simplicius,83 Straton thought it difficult to define time, which

776 WOTE 6v, 219 a 20; for this expression see A. Torstrik in Rhein. Mus., 12, 1857, p. 161 f.; Ross, op. cit., pp. 63 and 598.

78Instead of -r6 Evat, the ancient commentators put -rTCj Ayc (Simplicius, In Arist. Phys., p. 712, 26, Diels; Themistius, In Arist. Phys., p. 146, 14, Schenkl) or T-r 6ptiapo (Philoponus, In Arist. Phys., p. 720, 28, Vitelli) and St. Thomas put ratio (Comment. Phys. Arist., Opera Omnia, II, 1884, p. 205).

79Plutarch, Quaest. Plat., VIII. 4, 1007 B (fr. 53, Lang). 8001ov lov&s &piOpoO, 220 a 4. 81Cf. G. Wunderle, Die Lehre des Aristoteles von der Zeit, Diss. Miinchen, 1908, p. 36. 82Parmenides, 156 D - 157 A. For Plato the tEaipvrlS is a mentally fixed point and

does not constitute time in concreto. He regards it as being outside time and representing a limit between two parts of time, but also their connecting link. Like Aristotle's vrv (cf. Physics, vi. 3, 234 a 24 ff.) it is a logical cross-section of a process of change, in which it is impossible for a thing to be moving or stationary.

83In Arist. Phys., p. 789, 2 f. (Diels).



50 W. VON LEYDEN

is a continuum, in terms of number which is discrete, and consequently criticized Aristotle's arithmetical definition. As appears from a passage in the De Anima (I. 3, 407 a 6-10), Aristotle was himself aware of the fact that thoughts, being like integers, do not correspond to the organization of undivided continua such as time or motion. The reason why he nevertheless defined time as a number was that, if the before and after in movement are counted by successive nows, sections of a continuum are counted, of which time is the number counted, not that by which it is counted.

Recalling the way in which Antiphon the Sophist defined time, namely as a form of understanding and a measure,84 one might say that Aristotle

developed this definition without drawing the conclusion that time, by being mind-dependent and a number, is not objectively real. By his twofold treatment of it in respect of its substratum and its definition, he comes to grant it a form of existence which is independent of consciousness and which is not a number, but a concrete numerable in motion. On the other hand, that the now " measures " time, as is stated in all but one of the MSS. of the Physics (219 b 12), can scarcely be taken as a genuine view of Aris- totle.85 What he maintains is that the passage of time can be marked by discriminating different moments within it and that the recognition of such a plurality of moments implies a numerical account of change. The term 'measure ', however, is introduced by Aristotle when he speaks of the mutual determination of time and motion (220 b 15 - 221 a 9). He argues that, while nows and numbers, being discrete, cannot measure either motion or time, units that are parts of either motion or time can, and he concludes that time could in this respect be called the measure of motion, a definition not liable to Straton's criticism.

The discussion of the measurement of motion by time and vice versa leads, at the end of Book IV of the Physics, to a discussion of the standard of such a measurement. This part of Aristotle's doctrine marks the connection between his account of the physical nature of time and his cosmological views. According to him, the standard of measurement is derived from a movement that is uniform and continuous and this can only be movement in a circle, as exhibited in the rotation of the heavenly sphere. However, the way in which such a standard can primarily be established involves difficulties, for the ideas of uniform motion and uniform time presuppose each other. Nevertheless, a standard is indispensable, particularly in order to secure the unity of time and time-reckoning. That this is Aristotle's concern is shown by his refusal to believe in the existence of several worlds -on which assumption there should be, as Plato intimated, several different

time-systems simultaneously (218 b 3-5). In defence of his denial that there can be several simultaneous times Aristotle points out that simultaneous movements, though they may differ as movements, have the same

84v6rnpa i PETrpov, Diels, Vorsokratiker, 87 B 9.

86Cf. A. Torstrik, " 'ber die Abhandlung des Aristoteles von der Zeit ", Philologus 26, 1867, p. 467; Ross, op. cit., p. 599.




number, just as the number of seven dogs and seven horses is the same, though the units counted are different. Such a comparison of time with an abstract number raises difficulties, particularly if, according to Aristotle's original definition, time is to be a concrete numerable. Medieval commentators noticed the incoherence and regarded the idea of a unitary time- system as an open question.86

Although the uniformity of circular motion furnishes a standard of unitary time-reckoning, time itself for Aristotle is not to be thought of as moving in a circle. It is plausible, he says, to identify it with the motion of the celestial sphere, because processes in time appear to be cyclical. Properly speaking, however, it is not time or the periods in time which are circular, but their primary measure.

All this sober, rational analysis of time and number enables Aristotle to dissociate himself from certain other unscientific reflections circulating in antiquity. Time, for instance, was said to be a force of oblivion and hence to conceal and to destroy, and alternatively to be a constructive power, revealing and generating. The Eclogae of Stobaeus (I. 8) are a mine of information on this topic. True, the view that time is actively engaged in the vicissitudes of life and death was not taken by Aristotle as too naive to be discussed in two passages of his Physics.87 At first sight it even seems as if he supports the view of time as a destructive power and denies only that it causes things to rise or prosper. Naturally, his final view on the matter is different. Plato had already taught the immanence of the cause of change in things which change,88 and for Aristotle too, if we look at the beginning of Books II and III of his Physics, it is obvious that things by nature have within themselves a principle of change or movement. Thus, in the two almost identical passages where he says that time by its nature is the cause of destruction rather than of coming-to-be (221 b 1, 222 b 19), the insertion of 'rather' in both sentences must, as was acutely observed by Simplicius,89 serve a purpose. Aristotle presumably reasoned as follows. If time had any influence on the processes of change at all, it would, since it is the number of change and change removes what is,90 determine those leading to destruction rather than those that have to do with generation. But since, as results from the enquiry in the Physics, time is to be defined as the number of change, it cannot have any influence on change whatsoever, not even on that which leads to destruction. Coming-to-be as well as passing away takes place "incidentally " in time.91

86Cf. A. Mansion, " La theorie aristotelienne du temps chez les peripateticiens medievaux ", Revue neoscolastique de Philosophie 36, 1934, p. 277 and passim.

87IV. 12, 221 a 30 - 221 b 7; 13, 222 b 16-27. 88Laws, 904 C. 89InArist. Phys., pp. 740, 26; 755, 21 (Diels). 90Cf. Metaph., A, 9, 1074 b 27. 91For a 17th century revival of the controversy over whether or not time itself

is a cause see my " Antiquity and Authority ", Journal of the History of Ideas, XIX, 1958, pp. 486-7.



52 W. VON LEYDEN

CONCLUSION

I think it can be safely concluded from all these points of doctrine that, not unlike Plato, Aristotle wished to distinguish between eternity and time and that by ' eternity' he meant what as such is not in time, either because it always exists92 or because, like Aion, it embraces all time. In fact, it would be misleading to form the impression that, rather than believing, like Plato, in eternity on the one hand and in time on the other, Aristotle only believed in an infinite time or the sempiternity of the heavens. It seems to me more adequate to sum up his position by saying (a) that, since he believed that the everlastingness of time is merely potential or always in the making,93 eternity is for him precisely the total and perfect form (TeXos) of the durational extent of the first heaven and hence a unifying principle which sets a limit (rrEpaS) to everything it embraces; and (b) that time, for

him, being something purely quantitative,94 is intimately bound up with the " now " as the unit of time-reckoning, which in this capacity is likewise, though in a different sense, a unifying principle and a limit.

The relevant concept running through both his and Plato's discussions, linking one to the other and also, within each, the concept of temporality to that of eternity, is that of number. By ' number ', of course, both meant 'rational number ', i.e. 'integer ' and ' fractional number ', not 'real number' which includes irrationals. As a consequence, there are difficulties for instance in Aristotle's views of the " now " and of continuity, which would not arise in connection with modern arithmetical theory. While one might likewise prefer the phrase 'rotation of the earth' for 'rotation of the heavenly sphere', it is doubtful whether this translation into modern idiom would make any difference in principle. What one would certainly wish to reject as part of an obsolete metaphysics is the view of circular motion as the primary kind of motion, though this does not mean that we do not still hold the rotation of the earth to be our chief practical measure of time. On the other hand, surprisingly or no, once we translate Plato's or Aris- totle's discussion into modern terminology, it comes in part very near certain statements of modern kinematic relativity. To say this, however, is not to deny that eternity, in both Plato's and Aristotle's eyes, is the ultimate standard or form on which time, the all-inclusive system of orderliness in nature, is modelled.

W. VON LEYDEN

University of Durham.

92Physics, IV. 12, 221 b 4-5. 93Physics, IV. 13, 206 a 22-3, 207 b 14-15. 94Cf. the passage in Plutarch's Quaestiones Platonicae, VIII. 4 (1007 A-B) containing

comments on two kinds of definitions of time, one concerning its qualitative and another its quantitative characteristics.



plato and aristotle number || time, number, and eternity in plato and aristotle

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