Dancy, R. M._thales, Anaximander, And Infinity_1989_Apeiron, 22, 3, Pp. 149-190

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Thaies, Anaximander, and Infinity

R .M . Dancy

l Introduction

Let m e begin by retracting my title. I shall translate άπειρον 'unlimit-

ed' rather than 'infinite': 'unlimited' more transparently disassembles

into components corresponding to those of the Greek word. 'Bound-

less' would do as well. Something tha t is άπειρ ο ν has no πείρατα , no

bounds or limits.1

To Hegelians, this is 'bad', 'spurious', 'wrong' or'merely negative' infinity.2

But it is good enough for me, and, I sug-gest, for the Milesians as well.

The doxographical tradition stemming from Aristotle and The-

ophrastus tells us that these people discussed a question about the ori-gin of the universe as we know it. The tradition uses the term αρχήin this connection: the αρχή is the beginning, the origin or source fromwhich the universe came.

1 I simplify the morphology: see Snell [1955-] 1012-14 s.w. άπείριτος, απείρωνand LSJ s.w. άπειρος (Β), πείραρ, πέρας . Α little more is said below(pp. 163-4) by way of justification fo r this translation, in particular as to thesense of πείρατα.

2 See Science of Logic Bk. i, sec. 1, IIC, (b) and Observation 1' (Hegel [1832/45] iii142-8 and 158-63; translation in Hegel [1892b] i 151-6 and 164-8), lesser Logic §94 (Hegel [1832/45] vi 184-6, translation in Hegel [1929] 174-6), Stace [1923] §§197-8. Hegel appears to be trying to work this discussion into his discussion ofAnaximander in the Lectures on the History of Philosophy, Part I, Section 1,Chapter i, A 2 (Hegel [1832/45] xiii 205, translation in Hegel [1892a] 186-7), butI am unable to sort out the references of his pronouns well enough to makesense of the passage.

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150 R. M. Dancy

There is more to the notion of an α ρ χ ή in Aristotle than is capturedin the word 'beginning': he also characterizes the Milesian α ρ χή assomething that survives in the products that emerge from it; he as-

similates the Milesian α ρ χ ή to his own matter. I shall not here be con-cerned w ith this assimilation or its correctness, but it forces us to usea more neutral translation for α ρχ ή than 'beginning', at least in dis-cussing Aristotle. 'Principle' is the word standardly employed, and Ishall often follow the standard. But for now, let us stick to 'beginning'.3

3 There is, in fact, more even in the earlier uses of ' αρχή ' than is captured bythe word 'beginning': there is a political metaphor. The α ρχή governs things.See Terpander f r . 698 Page (from Clement of Alexandria):

Zeus, beginning of all things, leader of all things,Zeus, I send to you this beginning of hymns(Ζεΰ πάντων ά ρ χ ά , πάντων ά γ ή τ ω ρ ,Ζ ε ΰ σοι πέμπω ταύταν ύμνων άρχάν ) .

along with the use of the root verb άρχειν in the sense 'to rule' in Odyssey 6.12(the only un amb iguous occurrence in this sense in early epic: Snell [1955-]

1383.54-7, 1378.76-7):and Alcinoos then ruled [sc. in the city of the Phaeacians, 1. 3](Αλκίνοος δε τ ό τ ' ά ρ χ ε ... )

The verb is frequently used in the sense 'to lead', 'to command ' in militarycontexts; sometimes this is virtually indistinguishable from th e sense 'to rule'(Snell [1955-] 1381.53ff.), as in Iliad ii 494:

Leitus and Peneleus commanded th e Boeotians(Βοιωτών μεν Πηνέλεως και Λήιτος ήρχο ν) .

And the noun ά ρ χ ο ς is used to mean 'commander' or 'ruler', (S nell [1955-]1373.37ff., 1376.60ff.) as in Iliad i 144, where Agamemnon says of the ship thatis to re turn Chryseis to her father:

... let there be one counsel-bearing man as commander(... ε ϊ ς δε τις ά ρχ ος άνήρ βουληφόρος Εστω) ,

or Odyssey viii 390-1, where Alcinoos says:

For twelve pre-eminent kings in the communi tyact as rulers (άρχοι), and I myself am a thirteenth.

Indeed, there is in inscription from Miletus itself, dated to the sixth centuryBC, that uses ά ρ χ ο ς in this sense (LSJ s.v.: SIC 3d).

Stokes [1971] 30-1 poins out that tha t Anaximander 's αρχή has this func-tion, but, to judge from Stokes [1976] 5-6, he does not think it has anything todo with the sense of the word ' αρχή' . In fact, it would help in the under-standing of Aristotle, Physics Γ 4, 203b7-8, which is w hat Stokes is discussingin both places. But on the present occasion I wan t mostly to steer clear of thatpassage and its surroundings (203b3-15): see Kahn [1958], Stokes [1976].






Thaies, Anaximander, and Infinity 151

The tradition clearly tells us that Thaies said that the αρχή , the be-ginning, was water, and Anaximenes said that it was air. The tradi-tion is hazier about Anaximander. It tells us clearly enough that

Anaximander said that the αρχή was άπειρον: that the beginning wasunlimited. The haze has to do with the status of this assertion. It doesnot sound on a par with the other two. Suppose one man tells us thatwhat is in the bathtub is water, another tells us that it is gin, and a

third tells us that it is more than enough to go around: the third m anis answering a different question about what is in the bathtub fromthe question the others are answering. That is the way Anaximandersounds: Thales and Anaximenes are telling us what the αρχή is, and

Anaximander is telling us how much there is of it.Modern scholarship has a way around this: the term άπειρον, un-

limited, is construed to mean 'indeterminate', ' indefinite ' . Then thetraditional story takes a linear shape: Thales said the αρχή was water,Anaximander said it was άπειρον , that is, had no definite character,and Anaximenes said it was air.

I think this is a mistake. Rather, I think the tradition is telling usthe following. Thales said that the beginning was water; Anaximenes

said it was air. Anaximander denied that it had any definite character.He also said it was unlimited. But in saying that it was unlimited, hedid not mean that it had no definite character: he meant rather thatthere was no end of it.

This may sound like a trivial difference. But recognition of this differ-ence goes with something else: if we see why Anaximander might havethought the αρχή unlimited, we can see why he might have been led

to the further conclusion that it had no definite character. It was nota conclusion merely given him by the word άπειρον.My main concern in this paper is to explain this point. There are

many other questions that must be dealt with. Not the least of themis the question whether, even if this is what the tradition is telling us,there is any reason to accept the tradition. Along the way, I shall betrying to explain why I think there is no reason not to accept it.

2 Thales

According to the tradition, Thales said that the αρχή was water. Thetradition has been doubted. I think these doubts are ill-founded. I shallexplain this, and then ask: how much water did Thales think therewas? The answer will be: anyway, not an unlimited quantity.






152 R. M. Dancy

2.1 Water

Aristotle ascribes the watery αρχή to Thaies only once, in Metaph A

3, 983b20-3:

4

Thales ... says [the αρχή] is water (which is why he as-serted that the earth is on w ater ) . . . .'He (b22-7, text in n. 4) then offerssome conjectures5 as to w hy Thales might have thought that the αρχήwas water.

In de Caelo B 13,6 where he is concerned with the question why itis that the earth stays where it is, Aristotle says only (294a28-30): Others

4 For future reference, here is a fuller version of the passage (983bl8-27):Yet, as to the number and the form of this sort of principle, they do

not all say the same thing,[b20] but Thales, the originator of this sort of philosophy, says it is

water (which is why he asserted that the earth is on water),[b22] perhaps taking this conception from seeing that th e nutriment of

all things is wet, and that the hot itself comes-to-be out of this and livesby this (for that out of which they come-to-be is the principle of allthings)

[b25] - taking this conception because of this and because of the factthat the seeds of all things have the moist nature and that water is [the]principle for wet [ things].18 το

μέντοι πλήθος και το είδος της τοιαύτης αρχ ή ς ου το αυτό20 πάντες λέγουσιν, αλλά Θαλής μεν ό της τοιαύτης αρχηγός

φιλιοσοφίας ύδωρ φησϊν είναι (διό και την γήν εφ' ύδατοςάπεφήνατο είναι), λαβών ίσως την ύπόληψιν ταύτην εκ του πάντωνό ρ ά ν την τροφήν ό γ ρ ά ν ούσαν και αυτό το θερμόν εκ τούτου

γιγνόμενον και τούτα) ζών (το δ' εξ ου γίγνεται, τοϋτ' εστίν25 αρχή πάντων) — δια τε δη τούτο την ύπόληψιν λαβών ταύτηνκαΐ 6ιά το πάντων τα σπέρματα την φύσιν ΰ γ ρ ά ν Εχειν,το δ' ύδωρ αρχήν της φύσεως είναι τοις ύγποΐς.

5 Notice in particular Ισως ('perhaps') in b22, and the Aristotelian sound of thereasons given in b25-7.

6 Again for future reference, here is 294al9-24, a28-bl. The difficulty to whichAristotle refers in the opening sentence is that the earth stays suspended in

mid-air, despite its plain natural tendency downward.So the difficulty has come-to-be a philosophical commonplace; but as

for th e solutions to it, one might wonder whether they do not seem moreabsurd than the difficulty.

[a21/22] For some, for these reasons, say the [part] of the earth belowis unlimited, saying it is rooted in [the] unlimited, as did Xenophanes ofColophon, so that they would not have the trouble of investigating the






Thaies, Anaximander, and In nity 153

[say the earth rests] on water. For this [is] the earliest account we havereceived, which they say Thales the Milesian gave ... .' And there isan allusion to this view of Thales' in Seneca (Quaest not iii 14),7 which

just might be independent of Aristotle: it adds the curious detail thatThales explained earthquakes as rockings of the boat.8 But plainly nogreat weight can be placed on Seneca's testimony.

[a28] Others [say the earth rests] on water. For this [is] the earliest acc oun t we

have received, w hich they say ThaJes the Milesian gave, that it rests where it isthrough being afloat, like a stick or some other such th ing (for none of these thingsis of a nature to rest on air, but on water),

[a32/33] as if the same account were not true of the earth and of the water thatsupports the earth; for neither is water of a nature to rest in space: it is on something.294a

ώστε το μεν άπορεΐ ν εΐκότως έγένετο φιλο-20 σόφημα παοιν: το δε περί τά ς τούτου λύσεις, μη μάλλον

άτ οπ ους είναι δοκεϊν της α π ο ρ ί α ς , θαυμάσειεν αν τις . ο ΐ μεν

γ αρ δια ταύτα άπ ε ι ρ ο ν το κ ά τ ω της γης είναί φασιν, έ π 'άπειρ ο ν αυτήν έρριζώσθαι λέγοντες, ώσπερ Ξενοφάνης δ Κο-λοφώνιος, Ινα μη π ρ ά γ μ α τ ' Εχωσι ζητούντες την αΐτία ν

ο ΐ δ' εφ' ύδατος κεΐσθαι: τούτον γαρ άρχαιό-τατον παρειλήφαμεν τον λόγον, δν φασιν είπεϊν Θαλήν

30 τον Μιλήσιον, ως δια το πλωτήν είναι μένουσαν ώσπερξύλον ή τι τοιούτον Ετερ ο ν ( και γαρ τούτων έπ' α έ ρ ο ς μεν ού-θέν πέφυκε μένειν, αλλ' εφ' ύδατος), ώσπερ ου τον αυτόν

λόγον δντα περί της γης και του ύδατος του όχοϋντος την γήνουδέ γ α ρ το ύ δ ω ρ πέφυκε μένειν μετέωρον, αλλ' επί τινός εστίν.

294b

In 294a22-3, έπ' άπειρ ο ν αυτήν έρριζώσθαι λέγοντες is bracketed by Allan[1936], with some reason.

7 = DK 11A15 (i 78.6-8) = Kirk & Raven [1957] 92 t90 = Kirk, Raven, &Schofield [1983] 93 n. 2:

Thales' opinion is absurd. For he says that the circle of the world is heldup by water and rides it in the manner of a ship, and is tossed about byits motion on the occasions it is said to 'quake'.

Thaletis inepta sententia est. ait enim teirarum orbem aqua sustineri etvehi more navigii mobilitateque eius fluctuare tune cum dicitur tremere.

8 See also Aetius iii 15.1 and 9.






154 R. M. Dancy

Suppose we accept the ascription to Thales of the idea th at the ea rthrests on w ate r. This leads to the following skeptical train of thought .

9

Aristotle knew of a s ta tement to the effect that Thales said that the

earth rested on water. He did not have this from some w ork of Thales(there probably was none anyway) , but at second hand (notice ' theysay' in de Caelo 294a29

10). If we read the account in the Metaphysics in

the l ight of this, we shall be drawn to the claim about the α ρ χ ή , al-

ready embedded in speculation on Aristotle's part. It m i g h t be that a l lAristotle had was the information about the earth resting on w a t e r .He also knew of two other people from Miletus, Anaximander andAnaximenes, who had answers to the question 'What is the αρχή?' ;

he further knew that Anaximenes thought the earth rested on air.1 1

He might have thought to him self: Well, they're all from Miletus; theymust have talked about these things, like we do here in Athens; sow h a t did Thales think the α ρ χ ή w as? Since A naximenes had the earthresting on air, which was his α ρ χή , Thales must have thought it w aswater, which is why he says that the earth rests on water .

Then the ascription of a watery α ρ χ ή to Thales is a fabrication of

Aristotle's.

But this is too much skepticism: it assumes a historical naivete onAristotle's part that, as the immediate sequel demonstrates, he lacks.In 983b27-984a8 he deals with those

12'who think even the very an-

cient [men], ... the first to theologize' (983b28-9), e.g., Homer, sub-scribed to the watery α ρ χ ή , on the ground that 'they made Oceanusand T ethys the p arents of coming-to-be, and [ma de] the oath of the

9 Due in substance to Cherniss [1951] 320-3 (rpr. Furley & Allen [1970/75] i 3-5,

Cherniss [1977] 63-6); I have embellished it some.

10 Text in n. 6.

11 He names Anax imenes among others as subscribing to this view at de Caelo B

13. 294bl3ff.

12 Ross [1924] i 130 ad 27 supposes the reference is to Plato, Cratylus 402b,

Theaetetus 152e, 160d, 180c. B ut there Plato is tracing the genealogy of the Her-aclitean flux-theory, not the water-cosmogony, and he does not ment i on

Thales - which, curiously, makes Cherniss all the m ore suspicious: see Cher-niss [1951] 321-2 (rpr. Furley & Allen [1970/75] i 4, Cherniss [1977] 64-5). There

is, further, no reason to take Plato seriously. See Snell [1944] (rpr. 1976), in

Snell [1966] 121-3 = Classen [1976] 481-3; Snell thinks the reference is to Hip-

pias, and that Plato himself made use of Hippias (Snell [1966] 125 = Classen

[1976] 486).







gods sworn on water' (b30-l).13 He is properly skeptical about this at-tempt to push the water-cosmogony back to far antiquity (983b33-4a2)14;l^ut', he says, Thaies, at any ra te , is said to have asserted this about

th e first cause.'

15

So he knows of people who ascribe the water-theory to Homer, anddoes not trust them, a nd knows of others16 who ascribe it to Thales.He is prepared to place more trust in these latter. He is hardly manufac-tur ing history.

Thales, at any rate, is said to have asserted that the αρχή was water.

2.2 How much water?

Toward the beginning of the Physics, Aristotle lays out options for prin-ciples (A 2,184bl5-22): there might be one or more, and if one, it mightbe either static or in motion, etc. Simplicius, commenting on this pas-sage, tries to sort out who picked which option. He is relying for hisinformation on Theophrastus,17 although what form his informationf rom Theophrastus comes in is an open question. Under the headingOne principle, in motion', Simplicius adds another pair of options:some made their one moving principle limited and others made it un-limited.

Simplicius ranks Thales among those who 'say it is limited' (Phys

23.22). He adds a reason for the selection of water as the αρχή thatis not in Aristotle: the dead dry out (23.25); so there is some slight rea-son to think he is not relying purely on Aristotle here, and therefore

13 Allusions to the Iliad. For Oceanus and Tethys, see xiv 200-1, 246 (both are tobe found in Kirk, Raven , & Schofield [1983] 13-14 tt8-9). For the gods' swear-ing by the river Styx, see ii 755, xiv 271, xv 37-8.

14 'Whether, then, this view about nature is in fact primitive and ancient mayperhaps be unclear ... ( ε ΐ μεν ούν αρχαία τις αοτη και παλαιά τετύχηκεν ούσαπερί της φύσεως ή δόξα ... .'

15 984a2-3 Θαλής μέντοι λέγεται οοτως άποφήνασθαι περί της πρώτης αίτιας: theimportance of this, omitted from D K and other source-books, was pointed outby Snell [1944] (rpr. 1976), in Snell [1966] 121 = Classen [1976] 481.

16 According to Snell [1944] (rpr. 1976), in Snell [1966] 120-5 = Classen [1976]480-6, Hippias is at least one of the sources.

17 Whom he names often in these pages: cf . Physics 20.19, 21.10, 23.31.






156 R. M. Dancy

for thinking his material comes f rom Theophrastus. Possibly also, then,

when Simplicius fills in details o f Aristotle's argument fo r Thales' con-

clusion that water is the beginning,18

he is also relying on Theophrastus

and no t simply winging it.B ut we can hardly put much trust in these additional details, fo reven if they do go back to Theophrastus, Theophrastus is pretty clear-

ly using the same source that Aristotle used.19

The premisses, then,

m ay well be coming f r om that . B ut when Aristotle cited those premiss-

es, he saw reason to be cautious: perhaps (Metaph 983b23) Thales based

his conclusion about water on these premisses. The caution is gone

f r o m Simplicius' report; we should restore it.

Still, we may be a little less skeptical about the limitedness of thewatery αρχή, fo r that gets indirect confirmation f r om Aristotle. When

Aristot le cites Thales' view that th e earth rests o n water in the de Cae-

lo, he is contrasting it with the view o f Xenophanes to the effect that

the earth goes on downward unendingly (see 294a21-4); this, in Aristo-

tle's opinion, simply avoids the question. He objects to Thales' account

that the water on which the earth is allegedly resting itself needs some-

thing on which to rest. That charge would have misfired if Thales had

said the water went on downward without limit. So, at the very least,

Aristot le did not know o f anything Thales said to the effect that th ewater was unlimited.

There are some difficulties here: I have relegated their discussion

to an appendix. (See pp.183-6 below.) In the final analysis, we may

assume with clear consciences (although hardly with certainty) that

Thales did not make his αρχή unlimited.

Aristotle, Theophrastus, and the tradition make Anaximander'sαρχή unlimited. Let us turn to Anaximander.

18 In 23.26-7 he fills in enough that we we could actually const ruct the a r g u m e n t

f o rma l l y : things are nourished by wh at they come f r o m ; al l things are

nourished by water; so all things come f rom water. This, o f course, he could

easily have done on his own.

19 McDiarmid [1953] 91 says: Ά comparison of the account of Thales' principle

quoted by Simplicius f r om Theophrastus with that given by Aristotle in theMetaphysics leaves little doubt o f Theophrastus' dependence o n Aristotle. ' This

is plainly no t true; McDiarmid does no t attend to the additional premiss sup-

plied in the account o f Simplicius, beyond noting that it is there (91), an dthen presenting a conjecture as to how it might have been written by The-

ophrastus (135).







3 Anaximander

Aristotle does not mention Anaximander in his review of previous

philosophers in Metaphysics A: he is writing an essay on causality, nota history of philosophy. What he says in the Physics makes it plain that

he supposed Anaximander's αρχή to be unlimited, but the clearest

statement that it is comes from Simplicius: again, we suppose, com-

ing from Theophrastus.

3.1 Anaximander's unlimited αρχή

Simplicius tells us about Anaximander, shortly after telling us about

Thales. He had, as we saw, expanded Aristotle's pigeon-holes for αρχή-

positions by adding the option limited or unlimited', and had assigned

to Thales the option 'limited' (23.21ff.); the option 'unlimited' goes to

Anaximander. According to Simplicius, he

said the principle and element of the things that are [is]the unlimit-

ed, [being] first to have introduced this name of the principle. He saysthat it is neither water nor any other of the so-called elements but

some other unlimited nature (24.14-17).20

20 Simplicius, Phys 24.13-23 (= DK 12A9, i 83.3-10, with 12B1, i 89.11-15 = Kirk

& Raven [1957] 105-6 H03A = Kirk , Raven, & Schofield [1983] 106-7 t lOlA

gives lines 13-21; I have fol lowed the p unc tuat ion in D K and Kirk , Raven, &Schofield [1983] rather than that in Diels' text of Simplicius (Diels [1882/1895]),but have not included ei ther the quotation m arks of DK or those of Kirk,

Raven, & Schofield [1983]):

[24.13] But of those who say it is one, in motion, and unlimited,Anaximander , son of Praxiades, a Milesian w ho became successor and

s tudent of Thales, said the principle and element of the things that are[is] the unlimited, [15/16] [being] first to have introduced this name of the

principle.

[16] He says that it is neither water nor any other of the so-called ele-ments but some other un l im i ted na ture , from which all the heavens and

th e cosmoses in them come-to-be;[18] and t ha t the [ things] from which there is coming-to-be for the

[ things] tha t are, into those there comes-to-be destruction as well, in ac-

cordance wi th what must be;[19/20] for they give just ice and retr ibution to each other for their in-

justice in accordance with th e order of t ime,






158 R. M. Dancy

Simplicius' account raises a number of problems. Those that are herepertinent can be sorted out under three main ones.

(1) As it stands, this text says tha t Anaximander was the first to

characterize the αρχή as unlimited. But this has been doubted.In m y view, these doubts are unfounded. But it will be worthwhileto discuss them, for it is central to my picture of what Anaximanderis doing that he did, where Thales did not, characterize the αρχή asunlimited.

(2 ) Given that Anaximander characterized the αρχή as unlimited,we must consider what he meant by that, and why he so character-ized it. My answers here can be put under three sub-headings:

(2a) By characterizing it as 'unlimited' he meant that it had no spa-tial limits.

(2b) He also thought that the αρχή had no temporal limits. But thiswas no part of what the label 'άπειρον ' meant.

(2c) Nor w as it any part of what that label meant that the αρχή wasqualitatively indeterminate or undifferentiated. The idea that it wasunlimited was meant to fill in shortcomings in Thales' view.

[20/21] speaking of them thus m very poetical words[21] And it is clear that he, having seen the changing of the four ele-

ments into each other, did not think it right to make any one of themsubject, but something else apart from them,

p. 24

Των δε §ν και κινούμενον καιάπειρον λεγόντων Αναξίμανδρος μεν

Πραξιάδου Μιλήσιος Θαλοΰ γενόμενος διάδιχος και μαθητής αρχήν τε και15 στοιχεΐον εϊρηκε των οντων το άπειρον, πρώτος τούτο τοϋνομα κομίσας

της αρχής, λ έ γ ε ι δ' αυτήν μήτε Οδωρ μήτε άλλο τιτων καλουμένων είναιστοιχείων, αλλ' έ τ έ ρ α ν τ ι ν ά φύσιν άπειρον, εξ η ς απαντάς γίνεοθαι τουςουρανούς και τους εν αϋτοΐς κόσμους· εξ ων δε ή γ έ ν ε σ ί ς ε σ τ ί τοις ούσι,και την φθ οράν ε ι ς ταύτα γίνεσθαι κατά το χρεών διδόναι γ αρ αυτά δίκην

20 και τίσιν άλλήλοις τη ς αδικίας κατά την του χρόν ου τάξιν, ποιητικωτέροιςούτως όνόμασιν αυτά λέγων: δήλον δε δ τ ι την ε ι ς άλληλα μεταβολήν των

τεττάρων στοιχείων ούτος θεασάμενος ουκ ήξίωσεν ί ν τι τούτων ύποκείμενονποιήσαι, αλλά τι άλλο παρά ταύτα.

The clause at lines 19/20, beginning 'for they give justice', is still in indirectdiscourse: it is still a part of what Simplicius or Theophrastus is reporting

Anaximander as having said, but it cannot be direct quotation.Line 19, 'they give justice': διδόναι δίκην is a Greek idiom for 'to pay the

penalty'.







B ut then, (3) if the previous answers are insufficient, as I think theyare, to determine the nature of Anaximander's αρχή, w hat kind of thingwas it?

And here I shall be saying that the unl imi ted αρχή was,because itwas unlimited, indeterminate or intermediate between any two definitecharacterizations, and so could give rise to opposites.

These conclusions are pu t starkly here, for clarity, and not becausethey are going to be established with any sort of certainty. It will beenough if they are plausible.

3.1.1 Anaximander's terminology. There is another report of Anax-

imander's views that seems also to be derived from Theophrastus21

in Hippolytus (Refutation o f all Heresies i 6.1-522); it sounds like a some-

21 The parallels are brou gh t ou t nicely in Kirk & Raven [1957] 105-6 U 03 = Kirk,Raven, & Schofield [1983] 106-7 t lOl , where the two texts (and ano ther frompseudo-Plutarch tha t does not have any th ing corresponding to the crux here),are arranged in parallel co lumns .

22 Refutatto i 6.1-2 ( = D K 12A11, i 83.41-84.6; differently arranged, = Kirk &Raven [1957] 105-6 1103B = Kirk , Raven , & S chofie ld [1983] 106-7 t lOlB (wi thline 7 emended: see next footnote). I have followed the text in DK ra the r t h antha t in DG 559 ( there are minor divergences).

(1 ) Again, A naxim ander became a pupi l of Thales. Anaximander, sonof Praxiades, a Milesian: he said that the principle of beings is some na-ture of the unlimited, out of which the heavens and the cosmos in themcome-to-be.

[4] And [he said that this is eternal and unaging, which also encom-passes all the cosmoses. And he speaks of t ime as if the coming-to-beand destruc t ion of being were determinate.

[6] (2) He said that the principle and element of the beings is the un-limited, being the first to have called [it] by the name of the principle.

[7/8] And in addition to this [he said] t hat m ot ion is eternal, in whichit t u r n s ou t tha t the heavens come-to-be.

(1 ) Θαλοΰ τοίνυν Αναξίμανδρος γίνεται α κρ οα τής . Αναξίμαν-δρος Π ρ α ξ ι ά δ ο υ Μιλήσιος· ούτος α ρ χ ή ν έφη των δντων φύσιν τινάτου απείρ ου , εξ ης γίνεσθαι τους ουρανούς και τον εν αύτοϊς κοσ-

μον. ταύτη ν δ' άίδιον είναι και άγήρ ω , ή'ν καϊ πάντα ς περιέχειν5 τους κόσμους, λέγει δε χρόνον ως ώρισ μέ νης τ ης γ ε ν έ σ ε ω ς και τηςουσίας και της φθ ορ άς . (2) ούτος μεν α ρ χ ή ν και στοιχεΐον εϊρηκετων όντων το άπειρο ν , πρώτος τοονομα κ α λ έ σ α ς της αρχής, προς δετ ούτω κίνησιν άίδιον είναι, εν ή συμβαίνει γίνεσθαι τουςουρανούς.

The adjective 'unaging', άγήρω, in line 4 is printed as a f ragment in DK13B2, i 89.16-17.






160 R. M. Dancy

what mangled paraphrase from the same source Simplicius used. Thereis a difference in the lines as to what Anaximander first called what;the text of Hippolytus reads:

He said that the principle and element of the beings is the unlimited,being the first to have called [it] by the name of the principle.

In the face of the fuller paraphrase in Simplicius, this looks like partof the mangling.23

But this is not the only way of diagnosing the situation. If therewere reason to prefer Hippolytus' accountas it stands, it would be re-motely possible to return to Simplicius and retranslate the crucial clause

as Toeing first to have introduced this name "principle"' to bring it inline with Hippolytus. This reading has had its defenders,24 althoughall agree that this is not the straightforward sense of the text. Thenshould we prefer Hippolytus' unemended account?

In Phys 150.22-4 Simplicius reports that25

Anaximander says that the contrarieties that are present in thesub-ject, which is an unlimitedbody, are separated out,he being the first

tohave named the subject 'principle' (ένούσας γαρ τά ς έναντιότηταςεν τω ύποκειμένω, ά π ε ί ρ ω δντι σώματι, έκκρίνεσθαι φησιν

Αναξίμανδρος, πρώτος αυτός αρχήν όνομάσας το ύποκείμενον).

23 Hippolytus or his copyist miswrote what originally read 'first to have in -troduced this name [sc. unlimited'] of the principle' (πρώτ ος τούτο τοΰνομακομίσας της αρχής, as in Simplicius) as 'first to have called it by the name ofthe principle' (πρώτος τοονομα καλέσας της αρχής: 'ΚΟΜΙΣΑΣ' is replaced by'ΚΑΛΕΣΑΣ' and 'ΤΟΥΤΟ' drops out of TOYTOTOYNOMA' [the comm onscribal error known as 'haplography']).

So Burnet [1930] (4th ed.) 54-5 n. 2, followed by Stokes [1971] 275 n. 24,Kirk, Raven, & Schofield [1983] loc. cit.; but Kirk reconstructs the text of Hip-polytus as πρώτος [τοΰτο] τοονομα καλέσας της αρχής, and translates it asToeing the first to use this name of the material principle', which seems to medifficult (rather, perhaps, Iseing th e first to call this [sc., th e unlimited] by thename "principle"'?).

24 Kahn [1960] 29-31; the Simplicius passage is so translated in B arn es [1987]74-5. It had not been so translated in Barnes [1979] = Barnes [1982] 29. Thebest account of the translation question seems to me that of Stokes [1971] 275n. 25.

25 150.23-4 are not in DK, but are cited in DG, apparatus ad 476.4 and in Kirk &Raven [1957] 107 = K irk, Raven, & Schofield [1983] 108. On this text, seeStokes [1971] 274 n. 23.







The claim in the last clause may go back to Theophrastus.26

There is, of course, no incompatibility between the straightforwardreadings of both our passages from Simplicius:27 Anaximander might

have been innovative both in his employment of άπειρον and in hisemployment of α ρ χ ή . But scholars have used the latter claim as evi-dence for a forced interpretation of the former.281 incline, rather, towarda reinterpretation of the latter, which I do not think is forced at all.

Simplicius believes that both Anaximander and Anaximenesthought the αρχή was an unlimited body (we shall consider this in moredetail below). He also believes, at least when he is being careful, thatThales thought the αρχή was limited. So he believes that Anaximander

was the first to have named the unlimited body as the αρχή .Burnet29 long ago suggested a paraphrase along these lines,30 think-

ing that this made it fit into the context better. This has been rejectedon grounds of grammar and sense, but, I think, mistakenly.31 The senseof the clause is, as all agree: Anaximander was the first to name thesubject, which is an unlimited body, 'αρχή'. But this does not tell uswhat was innovative about giving the unlimited body that name. Theinnovation need not be in the use of the term 'αρχή'; it could, instead,

lie in the application of it to something unlimited: Anaximander wasthe first to give that name to the unlimited body.32

In any case, there is no convincing ground here for re-translatingSimplicius' account in 24.15-16 to make it square with Hippolytus'.

26 Stokes [1971] 275 n. 24 thinks this needs showing. But certainly Simplicius ha sTheophrastus in mind in this passage: he is controverting Theophrastus in149.32ff.

27 As Stokes [1971] 28 notes.

28 Kahn [1960] 31

29 Bumet [1930] (4th ed.) 55 (n. 2 from p. 54)

30 Burnet has 'material cause' where I have 'αρχή' . This is the version supported

by Kirk [1955], reprinted in Furley & Allen [1970/75] i 324-7.31 See Jaeger [1947] 201 n. 28, followed by Stokes [1971] 274 n. 23. Their claim is

that Όνομάζειν' means "give the name of" (Stokes). I do not deny that, nordo I think Bumet meant to.

32 So McDiarmid [1953], rpr in Furley & Allen [1970/75] i 189 n., but I do not(nor does McDiarmid) think McDiarmid's emendation of αυτός to ούτως is es-sential.






162 R. M. Dancy

A n y w a y , in de Caelo 615.15-1633 Simplic ius says that Anaximan-der was the first to posit the subject that undergoes changes as un-l imited. 34

So we are entitled to read Phys 24.15-16 either way. Plainly weshould read it the way all agree the Greek is best read: Anaximanderw as the first to use 'unl imited ' of the principle. This, an yw ay , is w ha tthe context suggests:35 the dif ference, in Simplicius' account, betweenA n a x i m a n d e r and Thales is precisely th a t Thales did not, and A na x-imander did, posit an unlimited α ρ χ ή . So w h a t w e would haveexpected him to think, even before we look at the text, is that

33 615.13-18 (615.15-18 are printed in DK 12A17)

. . . bu t Anaximander , a fellow-citizen and associate of Thales', [positedas the s ingle elem ent] something f iner th an wa te r but denser than air , be-cause it was necessary for the subject to be well -adap ted for changing tovarious [things].

[15/16] But he was the first to posit [it] as unl imi ted , so th a t he wouldbe able to use it for comings-to-be un st int in gly ; and he posited unl imitedcosmoses, and each of the cosmoses out of an unlimited element of thissort, as it seems.

Αναξίμανδρος δε Θαλοϋ πολίτης και εταίροςαόριστο ν τ ι ύδατ ος μεν λεπτότερο ν αέρος δε πυκ νότερ ο ν , δ ι ό τ ι τ ο ύπ ο κεί -

15 μενον ε υ φ υ έ ς έ χ ρ ή ν είναι προς τη ν εφ' έ κ ά τ ε ρ α μ ετάβασι ν . άπειρο ν δεπρώτ ος ύπεθετο, ίνα έ χ η χρήοθαι προς τά ς γε νέοεις άφθόνως: καικόσ μ ους δε απείρους ο ύτ ος και ί κ α σ τ ο ν τ ω ν κόσμων ε ξ απείρου τ ουτοιούτου στοιχείου ύπεθετο, ω ς δ οκεϊ .

34 Kahn's attempt to dismiss this as throwing 'no fur ther light' on the 'verbalquestion', since 'i t refers to his doctr ine, not to his terminology' (K a hn [1960]31) is lame. Does Kahn suppose tha t A na xim an der used some term other thanά π ε ι ρ ο ν to characterize the αρχή as unl imi ted? No one has any al ternat iveterms to offer. But if he used that one, then he was the first to use it of theαρχή, and we are back where we started.

35 Pace Ka hn [1960] 31, who does not consider the course of Simplicius' com-

mentary here. H e considers it s subsequent course, at least to the extent ofsuggesting t ha t th e f emi n i ne 'αυτήν' in 24.16 'makes clear that it is the wordαρχή, not άπειρο ν , which is uppermost in Simplicius' mind' . I do not supposehe believes this is compelling: of course Simplicius is discussing ά ρ χ α ί in thispassage, and that he is now characterizing Anaximander 's αρχή is no indica-tion wh at was 'uppermost in his mind' in the clause in which he talks aboutAnaximander ' s αρχή being ά π ε ι ρ ο ν , nor, even if it were, would that tell uswhich way to read that clause.







Anaximander was the first to make the αρχή unlimited. It is hardlysurprising th at that is wh a t he says. It is surprising that so m any havewanted to make him say something else.

3.1.2. The spatially unlimited. Regardless of whether he was the first todo it , Anaximander characterized the αρχή as άπ ειρ ον . W hat did hemean by tha t? Here w e come on m ore controversy. But one thing hemust have meant , I think, is that it was spatially unlimited.

I am adopting 'unlimited' as a standard translation for άπειρος.Other translations are possible, and for certain contexts perhaps moreappropriate: in epic, for example, it might perhaps be better to trans-

late phrases such as έπ' άπείρονα γαΐαν ( I l i a d xxiv 342 et passim inHomer) and έπ' άπείρονα πόντον ( I l i a d i 350 etc.) as On the impassibleearth' and On the untraversable sea',

36 or On the unsurveyable earth'

and On the indiscernible sea'.37 In fact, I do not feel the objections to

the translation 'unlimited' or Ixnindless' even in these contexts are verystrong.

38 But, in any case, in the contexts that are of interest here, theword means 'unlimited'.

39

Xenophanes says:40

36 Its use in epic, according to Kahn [1960] 232,

suggests that it is not the noun πέρας [limit'] which is negated by the a-

privative, but the verbal root *per- represented in πείρω, περάω, andπεραίνω, as well as in a number of Indo-European adverbs and preposi-tions, all referring in some way to the direction 'forward, in front' (Greekπρο, Latin pe r , prae, etc.)· The verbal forms indicate a movement in thisdirection, and the group περά ω, πέραν , περαίνω, πεϊραρ envisages thepoint at which the forward motion comes to an end ... The true sense ofαπειρος is therefore 'what cannot be passed over or traversed from end toend'.

Riedel [1987] 16 goes even farther, bu t much of what he has to say I am una-ble to understand. See also Classen [1962] 161ff.

37 Cf. Snell [1955-] 1013.39-40.

38 The analysis of πεϊραρ in Bergren [1975] does no t seem to bear Kahn out (shedoes not cite Kahn, and, unfortunately, has nothing to say about απειρον).

39 As K ahn [1960] 233 agrees.

40 DK 21B28 (i 135.16-17) = Kirk & Raven [1957] 175 t!83 = Kirk, Raven, &Schofield [1983] 175 t!80 (also printed as Kirk & Raven [1957] 11 t3 = KRS 1013).






164 R. M. Dancy

O f earth this l imit upwards is seen at our feettouching aga ins t air, but dow nw a rd it reaches to the unl imi ted.(γαίης μεν τόδε πείρας άνω π α ρ ά ποσσίν ό ρ α τ α ιή έ ρ ι

π ρ ο σ π λ ά ζ ο ν , το κ ά τ ω δ' ες δ πε ιρ ο ν ίκνεΐται.)It is plain from this text that Xenophanes is hearing the word ά π ε ι ρ ο ςas it occurs in the second line as in opposition to πείρας , ' limit', in thefirst line: hence the translation 'unlimited'. Yo u can see an upper l im itto the earth, at your feet; there is no lower one.41

There is an advantage to the translation 'unlimited' as opposed tothe translation ' infinite'. ' Infinity' is a loaded word, and it is often saidthat Anaximander could not have understood the notion of infinity.42

W e should be suspicious here: those who say this do not always showthe firm est grasp of this notion themselves.43 But we can avoid the wo r-ry altogether if we s imply read 'unlimited' as 'without limit'. WhenXenophanes says the earth's extension downward is unlimited, he justmeans it doesn't stop. This idea may boggle the mind, but not becauseit requires any sophisticated mathematical tools.

So I shall stick w ith the idea that whe n A naxim ander calls his α ρχ ή

'unlimited' he means at least that it has no spatial boundaries.One of the reasons for thinking this is right is that it puts us in aposition to make educated guesses as to why Anaximander might havesupposed it to be true.

41 The effort in Comford [1952] 147 n. l to explain this away has been approvedby Kirk (Kirk & Raven [1957] 175-6, Kirk, Raven, & Schofield [1983] 175) andGuthrie [1962] ( vo l. i) 378-9, 381 n. 1, 394. I should prefer the line taken byReinhardt [1916] 116-17. Certainly Guthrie is guilty of exaggerat ion at leastwhen he says (381): 'The balance of the evidence is strongly in favour of afinite universe ... .'

42 E.g. , Cornford [1936] 226, Cornford [1926] 542, Cornford [1952] 175-6, Kirk &Raven [1957] 109-10 = Kirk, Raven, & Schofield [1983] 109-10, Guthr ie [1962](vol. i) 85.

43 Thus Cornford [1952] 176 says:

So long as 'the Unlim ited' is an unl imi ted something (e.g., air) it is notconceived as strictly infinite. It becomes so when it becomes either (1) themathematica l infinite, an abstraction, or (2) em pty space, the physical in-finite, which is 'nothing', as in A t o m i sm .

But there is, in fact, no contradiction in the idea of a 'strictly' infinite quantityof air. For something to be 'strictly' infinite, as far as I can see, is just for thereto be no end to it.







First, the argument Aristotle mentions (de Caelo B 13, 294a32-bl)44

against Thaies' view that the earth rests on wate r is, after all, not onethat requires a lot of background knowledge: if the earth rests on water,

what does the water rest on? Xenophanes avoids the wh ole problemby saying that the earth rests on nothing: it just keeps going down.But if one were disposed to take Thales' suggestion that th e earth restson w ater seriously, one m ig h t easily be led to the thought that, if theearth rests on anything , and that (whatever it rests on) also rests onsomething, ... , well, sooner or later th e idea we find in Xenophanesis going to have to be righ t: som ething or oth er jus t goes on w ith ou tstopping.

W e do not need to suppose that Anaxirnander knew of Xenophanes'couplet. If Xenophanes was in fact avoiding th e question 'What doesth e earth rest on?' by supposing that it just goes on down forever, thenat least someone in the same period as A nax ima nde r was th ink ingabout unlimitedness in connection with this question. Anaximanderwas thinking about the question, and he thought about unlimitedness;as we sha ll see, he has some interesting things to say about the earth

and its suspension. So this is a reasonable train of thought for himto have gone through.45

And its result is that the αρχή is, literally, without spatial limitsor bounds. By 'literally', I mean: there are no curious quirks about

circles and spheres tha t can by some stretch of someone's imagina-tion be called 'unlimited', and it is not a question of the άρχή'3 justbeing too big to think about. If the earth rests on it, then it has, atbest, one limit or bound, and goes on down without stopping; if the

earth is actually embedded in it , it may have no outer bound or limitat all.

W e may be able to supply Anaximander with a second argumentfor the same conclusion, based on another claim the tradition ascribesto him: tha t the course of coming-to-be is eternal. Let us consider thisclaim more closely.

44 Text in n. 6 above.

45 I am not aware of anyone else who supposes it might have been Anax-imander 's train of t hough t . And it is t rue that no ancient source ascribes thispattern of argument to Anaximander .But then, no anc ien t source directlyascribes to him any train of t hough t at all.






166 R. M. Dancy

3.1.3 The unlimited and eternity. It is sometimes said tha t another thingAnaximander meant by calling his αρχή 'unlimited' is th at it had notemporal boundaries.46

There is no question Anaximander th ou gh t the αρχή was temporallyunending: Aristotle says (Phys Γ 4, 203bl3-14)47 tha t Anaximandercalled his unlimited αρχή 'deathless and imperishable' (άθάνατο ν ...και άνώλεθρον) and Hippolytus (i 6.1, n. 22 above), we hope echoingTheophrastus, says Anaximander called it 'eternal and unaging' (άίδιον... και άγήρω) . It may be tha t some of these words are Anaximander ' sown.48

But we cannot conclude from this th at eternity is packed into Anax-

imander's use of 'άπειρον'. There is no attested case of the term'άπειρον ' meaning 'temporally unlimited' in our period,49 and w h a t

46 E.g., by Cornford [1952] 173.

47 More fully, 203blO-15 reads:

but this [principle, sc. the unlimited] is t h ough t to be [a principle] of the

others and to surround all and to steer all,as those say who do notmake, beside the unlimited, other causes such as mind or love; and this[is thought] to be divine; for [it is] deathless and imperishable, as Anax-imander says along with most of those who give an account of nature.10 αλλ' αύτη των

άλλων είναι δοκεϊ και περιέχειν άπαντα και πάντα κυβερ-νάν, ως φασιν δσοι μη ποιοΰσι παρά το άπειρ ο ν αλλάςαι-τίας, οίον νουν ή φιλίαν καϊ τοϋτ' είναι το θείον άθάνατο νγαρ και άνώλεθρον, ώσπερ φησϊν Αναξίμανδρος και οί πλεϊ-

15 στοι των φυσιολόγων.The words άθάνατον ... κα ι άνώλεθρον in lines 13-14 are printed as DK

13B3, i 89.18-19.

48 άθάνατο ν ... και άνώλεθρον appears as a fragment in DK (13B3, i 89.18-19).Perhaps one or the other word does actually come from Anaximander (seeKirk & Raven [1957] 116-17 = Kirk, Raven, & Schofield [1983] 117, K a hn[1960] 43).

The word άγήρω is archaic, and may well go back to Anax imander ;on the

other hand, it is usedfive

t imes in Plato (seeB rand wo od [1976]s.v.).

PerhapsPlato is intentionally echoing Anaximander, but perhaps not,and the laterreports are ta inted by reminiscences of Plato. I suppose th is is unlikely, but Icannot quite share th e confidence of K a hn [1960] 43 that 'at least th e Homericάγήρως must be his [i.e., Anaximander's]'. See also Kirk & Raven [1957]116-17 = Kirk, Raven, & Schofield [1983] 117.

49 Classen [1962] 163 says the first occurrence of άπειρον meaning ' temporallyunlimited' is in Melissus, DK 30B2 (i 269.1= Simplicius, Phys 29.23 and







Aristotle and Hippolytus-Theophrastus show by what they say is t ha tthey, in order to convey the idea of temporal unboundedness, had touse words other than 'άπειρον' to do it. If any of those words go back

to Anaximander , then he, too, had to convey the temporal unbound-edness of his αρχή by using such words: he could not count on'άπειρο ν =' by itself to do the job. Of course, he could have said, andfor all we k now did say, something like: 'M y α ρ χ ή is not jus t spatially,but temporally unlimited, and hereafter when I use the unadorned term"unlimited" I want you to understand that I mean that as well. ' Buthe need not have said that: he might jus t have made it clear that hethought the α ρ χ ή imperishable, unaging, eternal, or whatever , and

let it go at tha t .

109.20-1). Stokes (1976) 7 f f . and 12ff. makes use of this f ragment to impor t atemporal sense fo r 'άπειρο ν' in to Anaxim ander , via Aristotle, Phys Γ 4 .203b3-15. Asmis [1981] 291 follows him in this, an d goes farther: she th inksthe temporal sense is fundamenta l , and arrives at the conclusion that Anax-

imander's άπειρον is simply 'the un en din g succession of generation and des-truction' (283; it is not clear to me how an unending succession can be said to'steer itself, as Asmis is forced to say: see 295-6).

It is not, in fact, at all clear tha t Melissus is employing άπειρο ν in a tem-poral sense in fr . 2: he there argues from the premiss that what there is hasalways been and will always be to the conclusion that it is άπειρον; so taking'άπειρον ' to mean ' temporally unlimited' does make the argument valid. Butthe conclusion he apparently wishes to take away w ith him is not that w h a tthere is is temporally unbounded, but that i t is unbounded in magnitude: seef r . 3 (D K ι 269.9-10 = Simplicius, Phys 109.31-2). And he appears in fr. 4 (i269.13-14 = Simplicius, Phys 110.3-4) to be saying that what has a beginningor an end is neither eternal nor unlimited (άίδιον ούτε άπειρον). So Guthr ie[1965] (vol. ii) 109 (Guthrie also thinks that Aristotle is criticizing Melissus pre-cisely fo r making a transition from temporal to spatial unlimitedness, but thisis a bit dubious).

Άπειρον occurs in Aristotle, de Gen An B 6, 742b21, 22, 23 covering tem-poral unlimitedness, without any apparent spatial connotation; possibly thisreflects a usage in Democri tus (so Asmis [1981] 292-3). But this is a long wayfrom Anaximander: I suspect th e bridge is in fact in Melissus. And, anyway,

we should have been unable to unders tand th e passage if Aristotle had notexplicitly spoken of w h a t is always being άπειρον : the word άπειρον by itselfcannot carry the weight .

There might, curiously, be some indirect support for the existence or eventhe primacy of the alleged temporal sense of άπειρο ν in Anaximander if Bur-kert is r ight in seeing some connection between th e ά πειρ ο ν and the IranianTjeginningless [o r endless] light[s]': see Burkert [1953] 112ff.; but Burkert him-self (116) is inclined to suppose the spatial sense is more fundam enta l






168 R. M. Dancy

Still, he might have arrived at the conclusion that it was eternal bymeans of a consideration quite similar to the one with which we haveprovided him in connection with the conclusion that it is spatially un-

limited. Hesiod has the Muses telling him how things were 'from thebeginning' (εξ αρχής, Theog 115); what they say (or he says) is 'at thevery first Chasm came-to-be' (116). The question certainly suggests it-self: what was going on before that? And this question is particularlypertinent since the whole poem is supposed to be about the gods that'always are' (21, etc.). The move Xenophanes tried out for the earth,applied by Anaximander to the α ρχ ή , whatever it is, suggests itself.

Perhaps that move suggested itself to one other sixth-century figure.

Pherecydes of Syros50

wrote a book, in prose,51

and Diogenes Laertiusprofesses to know it. Diogenes says (i 119):52

There is preserved of the Syran the book he wrote of which the be-ginning is: Zas and Chronos always were, and Chthonie; andChthonie came-to-be named Earth when Zas granted her the earthas a prerogative. Σώζεται δε του Συρίου το τε βιβλίον δ συνέγραψεν,ου ήαρχή· Ζ ά ςμεν καιΧρόνος ήσαν αεί και Χθονίη· Χθονΐη δε όνομαέγένετο Γ η επειδή αυτή Ζ ά ς γήν γέ ρ ας διδοϊ.

Presumably the same idea occurred to Anaximander.If we keep the distinction between 'spatially unlimited' and 'eter-

nal' firmly in mind, we can see how Anaximander might have con-nected them. In particular, we can make the claim that the αρχή iseternal a premiss for an argument leading to the conclusion that it isspatially unlimited.53

50 There were a couple of other Pherecydes apart from the one from Syros whoconcerns us . This one was active in the sixth century BC, but the ancientauthor i t ies disagree as to just when in the sixth century: the 580s or the 540s.See Kirk & R aven [1957] 48-9 = Kirk, Raven, & Schofield [1983] 50, West[1971] 1-4.

51 According to the Suda s.v. 'Pherecydes': DK 7A2, i 44.18-19 Kirk & Raven[1957] 49 t45 = Kirk, Raven, & Schofield [1983] 51 t44), it was the first prose

book. If it was, and if Anaximander wrote a book, Pherecydes' must havecome first.

52 54.20-22 Long; DK 7A1 (i 44.7) < t 7B1 (i 47.3-5) = Kirk & Raven [1957] 54-5 t50= Kirk, Raven, & Schofield [1983] 56 t49

53 This argument is common coin in the literature. But I am unable to see howsense can be made of it under the supposition tha t 'Απειρ ο ν ' means at one andthe same time 'spatially unlimited' and 'eternal'.







The material fo r this is supplied by Aristotle; he gives as an argu-ment in f avo r o f supposing that there is something unlimited the claimthat it is only in that way that there will be no end of coming-to-be

(Phys Γ 4 , 203bl8-20).

54

According to Simplicius (de Caelo 615.15-16)

55

Anaximander made his αρχή unlimited 'so that he would be able touse it fo r comings-to-be unstintingly', and he is echoed in this by Ae-tius i 3.3:Anaximander 'says, at any rate, that it is unlimited, so thatthe coming-to-be may not stop existing at all.'56

If, then, we accept the premiss that unending coming-to-be requiresan unlimited supplier, and we have already arrived at the conclusionthat the course o f coming-to-be is eternal, we have the further con-

clusion that the αρχή that is the source of coming-to-be is unlimitedin size.This is no less speculative than the first of our two arguments on

behalf of the unlimitedness o f Anaximander's αρχή; it may even bemore so. The premiss that without an unlimited source coming-to-becannot keep going is one we should not accept, as Aristotle points out(in Phys Γ 8, 208a8-ll): the destruction of one thing could hook on tothe beginning of another, and in that way the world-order could keep

juggling with a finite stock forever. A nd furthermore, that seems to

54 The third reason Aristotle gives that persuades people of the existence of theunlimited is Tjecause only in this way can coming-to-be and destruction notgive out, if what that which comes-to-be derives f rom is unlimited ( έ τ ι τωούτως δν μόνως μη ύπολείπειν γένεσιν και φθοράν, ε ι άπειρον είη δθεν

αφαιρείται το γιγνόμενον).'55 Text in n. 33 above.

56 This argument may actually occur in a f ragment of Anaximenes, DK 13B3 (i96.5-7):

Air is near the bodiless; and because we come-to-be by virtue of an effluxof this, [it is a] necessity that it be unlimited and rich, because of the factthat it never leaves off.5 εγγύς εστίν ό αήρ του ασωμάτου· και δτι κατ' έκροια ν

τούτου γινόμεθα, ανάγκη αυτόν καΐ άπειρον είναι κα ιπλούσιον δια το μηδέποτε έκλείπειν.

Diels headed this text ( f rom Olympiodorus) 'Gef lschtes'; certainly ασώματοςcanno t be f rom Anaximenes. The substance of the fragment is defended byWest [1971] 100 n. 3 (followed by Barnes [1979] i 315 n. 27 = Barnes [1982] 597n. 27). But West thinks (with Diels) that th e last clause may be derived ulti-mately f rom Aristotle.






170 R. M. Oancy

be the w ay A n ax i man d e r himself thought coming-to-be worked.57 Soit looks as though , if Anaximander did make use of this argument,he contradicted himself, in the sense that his developed position im-

plicitly rejects one of his premisses. He would not be the last man inthe history of philosophy to do this.

3.1.4 Unlimitedness is not the same as inde niteness. There is a long-s tanding dogma58 to the effect tha t something else that is mean t whenAnaximander says his αρ χ ή is ά π ειρ ο ν is that it is quali tatively in -definite, indeterminate or at least undifferentiated. This was an ingeni-ous suggestion when Teichm ller first made it in the nineteenthcentury: he supposed59 that w hen Anaxim ander proclaimed the αρ χ ήto be 'unlimited', among the 'limits' of which he supposed it free werethose established by the qua litatively determ inate elements. There isno very good argument for this, and there is no instance offered ofthe use of the word in which it mu s t or even might mean 'indeter-

minate' or 'undifferentiated'.60 But Teichmuller's suggestion was takenup by others: Comford in particular is responsible for its modem vogue.

Cornford notes61

some occurrences of άπειρον in which it is appliedto a ring.62 He concludes from this:63

57 Both of these points are made by Kirk: Kirk & Rav en [1957] 113-14 = Kirk,Raven,. & Schofield [1983] 114-15, but he does not draw the conclusion I do Iam not clear wha t he thinks the s i tuat ion is .

58 Adhered to by a great number of authors; see, for a sampling, Kirk & Raven[1957] 109 = Kirk, Raven, & Schofield [1983] 110, K a h n [1960] 233, Guthr ie[1962] (vol i) 85f., Ba rne s [1979] 29, Wes t [1971] 79, Furley [1987] 28-9. Aclearly stated dissent, with which I am so far in perfect agreement : Go t tschalk[1965] 51-2.

59 Teichmuller [1874] 57

60 There is an association betwee n th e notions of unlimitedness and inde termina-

cy beginning at least with Plato's Philebus and the infamous 'unwrit ten doc-trines'. It still does not make 'unlimited' (δπειρον ) mean ' indefinite ' ( αόριστο ν ) ,and especially not ' indefinite in character'.

61 Cornford [1936] 226-7, Cornford [1952] 176

62 E.g., Aristophanes f r . 250; Aristotle, Phys Γ 6. 207a2.

63 Cornford [1952] 178.







As applied, then, to th e circle and sphere, "unlimited" means the ab-sence of internal boun daries and distinctions, such as appear whenthe circle of the year is marked off into seasons, each with its prevail-

in g power, or when th e sphere of the world is divided into theprovinces of the four elemental masses. The world was formed [onCornford's interpretation of An axim ander] by the "separating out"of the opposite p ow ers, w hich thu s became distinct and limited oneanother . Before this happened, and at all times in the circumambientstuff, the opposites, we are told, are present, but not distinct or limit-ed. "Unlimited" can thus mean "indistinct", having no boundarywhere "the Hot" ends and "the Cold" begins."

This is a priori lexicography. The word άπειρον did not mean 'un-differentiated' or 'indeterminate', and this line of thought should notconvince us that Anaximander tried to make it mean that. It did noteven mean that to the authors of the doxographical tradition.

There is one text that is decisive against the idea. In his report onAnaximander's 'successor', Anaximenes, Simplicius tells us (Phys

24.26-9 = DK 13A5, i 91.13-15)65 that Anaximenes

... to o says the nature that is subject is one and unlimited, just asthat one [i.e., A naximander] does, but not indefinite, as that one [said],but definite, saying it is air; and it is differen tiated along the linesof the beings by rareness and denseness.

p. 2426 μίαν

μεν και αυτός την ύποκειμένην φύσιν και άπειρον φησιν ώσπερ εκείνος,ουκ αόριστον δε ώσπερ εκείνος, αλλά ώρισμένην, αέρα λέγων αυτήν

διαφέρειν δε μανότητι και πυκνότητι κατά τας ουσίας.According to this, Anaximenes also calls his αρχή 'άπειρον', 'just asAnaximander did', but he thinks the αρχή is air.66 So, if we put any

64 See also Comford [1926] 542: "The term 'unlimited' ... probably does not im-ply, in the strict sense, spatial infinity; it is doubtful whether such a concep-tion had been grasped at this date. It means primarily the absence of internallimits and distinctions, such as divide the elemental masses in the orderedworld. '

65 Again, presumably, relying on Theophrastus .

66 If DK 13B3 stems from Anaximenes (see n. 56 above), we may have a quota-tion from him in which he refers to his αή ρ as άπειρος (i 96.6). It is worthnoting that Diels' grounds fo r doubting the authenticity of this fragment donot include the characterization of αήρ as άπειρον.






172 R. M. Dancy

stock in this report, άπειρον could not h ave mean t 'indeterminate' tothe Milesians.67

Simplicius (or Theophrastus) does characterize Anaximander 's un-

limited αρ χ ή as 'indeterminate' in the above passage; the word usedis ' αόριστος ' (24.2S).68 This is an Aristotelian term;69 we shall have to

consider fu rthe r w hat A naxim and er might have actually said. Bu t wemust be clear about what is in question here: the question is notwhether the tradition characterizes Anaximander's α ρ χ ή as indeter-minate, but whether, when Anaximander called his αρχή άπειρον, 'un-

limited', he meant to be saying that i t was indeterminate. Evidencethat Anaximander thought the αρχή indeterminate is not evidence that

he meant 'indeterminate' by άπειρον .The difference this mak es is simply th at if we allow An axim ander

to have arrived first at the conclusion that the α ρχή w as unlimited, w ecan see how he might have got from there to the fur ther conclusionthat it was indeterminate.

So let us assume that he arrived at the conclusion that the αρχήwas άπειρον, unlimited, by something like the route sketched out

above, and see w h a t happens.

3.1.5 Inde terminateness , ( a ) : apart from the e l emen t s . So far, our conjec-tural reconstruction of Anaximander's thinking goes something likethis. He is mulling over a scheme he heard about from Thales witha watery αρχή. H e thinks to himself: the water can't be either finitein extent or finite in time, since either would simply push the problemback (or down) one stage. So it must be unlimited and eternal.

67 This simple but decisive consideration was urged a gain st Teichm ller by B ur -net [1930] (4th ed.) 58 n. 1.

68 Comparison of the passage above with Phys 154.19-23 (= DK 12A9, i 83.23-6),where Simplicius is expressly qu oting Theophrastus, makes it pretty certainthat th e characterization of Anaximander 's αρχή as αόρ ιστος goes back to

Theophrastus.

69 Heidel [1912] 214-15 supposes that the tradition here imports 'Aristotelian andStoic ύλη,' 'a mere potential substrate which becomes actualized only in deter-minat ion/ and then says of the idea that Anaximander's αρχή is indefinite thatit is 'so palpably the fiction of a brain not schooled to trace the history ofideas, that we may dismiss it without fur ther comment.' This is throwing outthe baby with the bath water.







The question now is: What is it that is unlimited in size and eter-nal? Simplicius (Theophrastus) tells us (Phys 24.16-18) that Anax-imander 'says it is neither water nor any other of what are called

elements but some other unlimited nature, from which all the heavensand the world-orders in them com e-to-be.' And a little later in the samepassage (24.22-3) we are told that An axima nder 'did not think it rightto make any one o f them [sc. the elemen ts] subject, but so m ething elseapart from them.'

In Phys Γ 5, 204b22-9,70 Aristotle provides us with an argum ent rele-vant here; Simplicius (ad loc., Phys 479.30-80.4)71 ascribes this argument

70 (= DK 12A16 = KR 112 t!07 = KR S 113 H05):

B ut then, it's also not possible for the unlimited body to be simple,either, as some say, the [body] apart from the elements, from which theygenerate these [i.e., th e elements], or simply.

[b24/25] For there are some who make this [i .e. , something apart fromth e elements] the unl imi ted, and not air or water , so tha t th e others [e.g.,air or water] won't be destroyed by their unlim ited;

[26/27] fo r they have contrariety toward each other: air, fo r example, iscold, water moist , firehot;

[28/29] if one of these were unlimited, the others would by now havebeen destroyed; but as it is they say that out of which these [arise] isdifferent.204b22 άλλα μην ουδέ 6v και απλούν είναι

σώμα άπειρ ο ν ενδέχεται, ούτε ως λέγουσί τίνες το παρά

τα στοιχεία, εξ ου ταΰτα γεννώσιν, ούθ' απλώς, ε ί σ ΐ ν γαρ τ ι -25 νες οι τοΰτο ποι οϋσι το άπειρο ν , αλλ' ουκ αέρα ή ύ δ ω ρ , δπωςμη τάλλα φθείρεται ύπο του απείρ ου αυτών 6χουσι γαρπρος άλληλα έναντίωσιν , οίον ό μεν αήρ ψυχρός , το δ'ύδωρ ύγρόν , το δε πυρ θερμόν ων ει ηνΕνάπειρο ν , έ φθαρτ οαν ήδη τάλλα· νυν δ' δτερον είναι φασιν εξ ου ταύτα.

71 The text reads:

30 Having shown that no natural body composed of m a ny can

be unlimited, he next shows that neither can a body that is oneand simple be unlimited. For if it is to be a simple [one], it iseither one of the four elements or something else apart fromthese, as A na xim an der's circle speak of what is apart from theelements, from which they generate th e elements. And that none of

480 the elements can be the unlimited is clear even from the basis onwhich An axim and er, intendin g the element to be u nlim ited, positedit not as air or fire or any of the four elements: because these






174 R. M. Dancy

to Anaximander.72 The position Aristotle and Simplicius are discuss-ing is one which starts from the claim that that from which things aregenerated, the α ρχή , is unlimited. It goes from there to the conclusion

that the unlimited body from which the contraries arise has to be in-determinate with respect to those contraries; it is, hence, something'apart from the elements'. The argument is as fol lows:73

are related to each other contrarily, and if any of them wereunlimited, it s contraries would be destroyed by it.

p. 47930 Δεί ξ ας δτι ουδέν σώμα φυσικόν σύνθετον εκ πολλών δ ύ ν α τ α ι είναι

άπειρ ο ν , δείκνυσιν ε φ ε ξ ή ς , δ τ ι ουδέ Εν και απλούν σώμα ά π ε ι ρ ο ν είναιδυνατόν, ε! γαρ είη τι απλού νήν §ν των τε ττ άρω ν στ ο ιχείω ν εστί ν ή άλλοτ ι π αρά τ α ύ τ α , ως λέγουσιν οι περί Άναξίμανδρον το παρά τ α στοιχεία,εξ ου τ α στοιχεία γεννώσι. και δτιο υ δέ ν των στ ο ιχεί ων εί ναι δύ ναται το

480 άπειρ ο ν , δήλον μεν και εξ ων Αναξίμανδρος ά π ε ι ρ ο ν είναι το στ ο ιχεϊο νβουλόμενος ουκ αέρα ή πυρ ή τ ι των τετ τά ρω ν στ οιχείω ν έθετ ο αυτό διατο τ α ύ τ α έχειν προς άλληλα ένα ντίως , και είπερ ην τι τούτων άπειρ ο ν ,φθαρήναι αν υπ' α υ τ ο ύ τ α εναντία.

72 Simplicius is the first of a long line of commentators on the preceding passagew ho tell us that it is Anaxim ander that is in question: see, more recently, Ross[1936] 549 nn. ad 23-4, 24-9; Wagner [1967] 513 (where it is pointed out thatthe argument need not be confined to Anaximander); Hussey [1983] 80. Thepassage is commonly used in the reconstruction of Anaximander's views: Bur-net [1930] (4th ed.) 53-5; Kirk & Raven [1957] 113 = Kirk, Raven, & Schofield[1983] 113-14; Barnes [1979] 30; contra, see Cherniss [1935] 28:

.. . an infinite body apart from and presumably prior to the so-called ele-

ments is supposed to have been set up by Anaximander. But the reasonhere given for the hypothesis of such a distinct body presupposes theAristotelian theory of the interaction of contraries as the explana t ionofthe genesis of the elements, and this is enough to show that the explana-tion is not historically accurate.

(Followed by McDiarmid [1953] 99 = Furley & Allen [1970/75] i 196.) But , ofcourse, it is quite easy to see an argument behind this passage that need notbe stated in terms of Aristotle's own theory of the elements and the contraries.Chemiss [1935] 376 refers to the argument of this passage as 'the peculiarly

Aristotelian argument of the necessary equilibrium of co ntrary forces'; not onlyis the word 'peculiarly' here question-begging, this 'peculiarly Aristotelian' ar-gument 'is itself an Aristotelian adaptation of the old physical and medicaldoctrine of ισονομία των δυνάμεων' (Vlastos [1947], in Furley & Allen [1970/75]i 74 n. 97: the phrase comes from Alcmaeon, DK 24B4, i 215.12: see below on'Equilibrium').

73 Compare the formulat ion in Barnes [1979] 30-1.Perhaps it is worth saying thatI do not think this is a sound argument: as it stands, it is not even valid.







(1 ) The arche is unlimited.

(2 ) There are opposites of various sorts in the universe as we knowit.

(3) If the arche had some definite nature nv

that would be op-posed to some other definite nature n2.

(4 ) B ut then, being unlimited, it would never allow anythingofnature n2 to exist at all.

. ' . (5) The arche cannot have a definite nature; it must be somethingapart from the elements.

I f this, or something like it, is Anaximander 's argument, the sensein which his αρχή is indeterminate is clear: given any pair of contraries,th e unlimited α ρ χή cannot be characterized as either. It is, then, in-determinate between every pair of contraries. If we could suppose thatAnaximander considered every possible characterization of the α ρ χ ήto rule out some opposing characterization, we should have to con-clude that the α ρ χή was uncharacterizable. This, I imagine, is push-

ing the evidence to o hard. It is more likely that Anaximander wouldhave thought of some leading contrary pairs, and concluded that theαρχή was intermediate or indeterminate between each of those.

Which contraries might have occurred to him?74 There are threemain possiblities.

(1) The most straightforward one would come of placing simple trustin our sources. Pseudo-Plutarch, in Strom 2, speaks of 'what is produc-

tive out of the eternal of hot and cold' being 'separated off 'duringth e coming-to-be of this cosmos.' If we put this together with Aristo-tle's statement (Phys A 4,183a20-l) ascribing to Anaximander a 'separat-

ing out' of the contraries, we would have as Anaximandrean contrariesat least hot and cold. And Ae'tius speaks of the heavens being com-posed of a mixture of hot and cold (ii 11.5). Simplicius has a slightlymore complicated picture: he says (Phys 150.24-5) th e 'contrarieties arehot-cold, dry-wet, and the others.'

75Perhaps, then, there were a few

more contraries.

74 See here Lloyd [1964], in Furley & Allen [1970/75] i 259-70.

75 ένα ντιότητες δε ε ί σ ι θερμόν ψυχρον ύ γ ρ ό ν και τα αλλά. This is the continua-tion of the text cited on p.160 above, printed in DK 12A9 (i 13-14).






176 R. M. Dancy

Suppose this line is correct. Then, if the opposites named 'the hot'

and 'the cold', along with perhaps some others, are the f i rs t things

somehow 'separated off f rom the unlimited α ρ χ ή , they are a li t tle

strange. The hot is not here something or other, like the lava of anerupting volcano, or like fire, that is hot, but jus t something named 'the

hot'.76 It is not that what it is is fire or lava, on top of which it is hot;

what i t is, is hot. And we shall certainly encounter such things by thetime we get to Anaxagoras.

B ut the pairs 'hot-cold' and 'wet-dry' are Aristotelian favorites, and

this is unfortunate: it is altogether possible that the Aristotelian tradi-

tion is foisting these contraries off on Anaximander. If that is so, there

are two alternatives.(2 ) The one that involves the smaller departure from the doxographi-

cal tradition is that of supposing that all the tradition does is give prima-

cy of place to its favorite contraries. Anaximander might not have been

restricted to the contraries hot-cold and wet-dry: Simplicius refers to

'the others', and perhaps the leading role given to these two pairs is

an artefact of Aris to tel ianism. W e f ind Alcmaeon operating with awider-ranging list of contraries: wet-dry, cold-hot, and bitter-sweet arementioned (DK12B4). Elsewhere bright-dark (λαμπρόν, ζοφερόνAnax-

agoras, DK 59B4, 34.20-35.1; λευκόν, δνοφόεν Empedocles 31B21.3

& .5) are added to the list.

This is coming close to the initial, suspect, suggestion above: that

Anaximander intended the argument to show the ά π ε ι ρ ο ν indeter-

minate with respect to any pair of contraries you like. B ut perhaps itdoes not go as far , and is for that reason slightly more plausible as

an interpretation of Anaximander. Perhaps we can suppose that Anax-imander listed what contraries he could think of - we do not know

which these were, but any or all of the above are candidates — andargued that the ά πειρ ο ν was indeterminate with respect to them.

Even if this interpretation is more plausible, it is not compelling.

B ut neither is the preceding interpretation compelling.

(3) Another alternative possibility connects with some ancient tes-

timony. Anaximander, our sources tell us, had a curious theory about

the heavenly bodies: the sun, moon, and so on are really hollow wheel-r i ms made of αή ρ , 'air', but filled with fire, and their appearances aredue to the wheel-rims' having holes through which f lame can be seen

76 See Cornford [1952] 162, followed by Guthrie [1962] (vol. i) 79.







(see Hippolytus, Ref i 6.4-5; Pseudo-Plutarch, Strom 2; Aetius ii 13.7,ii 20.1, and ii 25.1). The primacy of fire and air in these accounts,together with the thought that 'air' here might not be atmospheric air

but th e 'air' of Homeric epic, which is a dar k mist, suggest that Anax-imander might have named fire and 'air' as the contraries that weresomehow derived from the indeterminate, unlimited α ρ χ ή . The latertradition then would have replaced these with the hot and the cold,the dry and the wet.7 7

W e are not in a position to make a solid choice between these threealternatives, or even to allot probabilities. I prefer the second. But hereno position will be taken.

3.1.6 Indeterminateness, (b): the ' intermediate' posit ion. At Phys Γ 4,203a 16-18, Aristotle says:

those concerned with nature all posit some other nature from amongthe so-called elements for the unlimited, e.g., water or air or the in-termediate between these (οι δε περί φύσεως πάντες ύποτιθέασινέτέραν τινά φύσιν τω άπ εί ρω των λεγομένων στοιχείων, οίον ύδωρ

ή αέρα ή το μεταξύ τούτων.)W ho picked the intermediate between water and air? Another passagein which Aristotle mentions this intermediate position is de Caelo Γ 5,303blO-13:

Some posited only one [element], and this some [said was] water,some air, some fire, some [something] finer than water but denserthan air, which they say surrounds all the heavens, being unlimited

(δνιοι γαρ §ν μόνον ύποτίθενται, και τούτο οι μεν ύ δ ω ρ , οι δ' αέρα ,οί δε πυρ, οί δ' ύδατος μεν λεπτότερον αέρος δε πυκνότερον, δπεριέχειν φασΐ πάντας τους ουρανούς άπειρο ν δν).

This sounds like Anaximander; when Aristotle mentions Anaximanderin 203bl4,78 it is in the course of describing a position according to whichthe unlimited 'surrounds all and steers all' (203bll-12), and the un-

77 This is the account favored by H lscher [1953], in Gadamer [1968] 109, Furley& Allen [1970/75] i 292-3, followed by Lloyd [1964], in Furley & Allen [1970/75]262-5. It is rejected by Guthrie [1962] (vol. i) 79 n. 1, but on grounds thatseem to me essentially question-begging.







178 R. M. Dancy

l imited heavens are another feature, although a highly controversialone, of A naxim ande r 's cosm ology. And Sim plicius says outright, incomment ing on the passage from the de Caelo, tha t Anaximander is

the in te rmedia te -man (in de Caelo 615.13-14).

79

There is one passage that stands in the way of identifying Ana x-imander as the author of the intermediate-theory: Phys A 4, 187al2-23.

There Aristotle mentions an intermediate-theory (something denserthan fire but finer than air, 187al3-15), and apparently contrasts it withthe theory of An axim ande r (183a20-l). Simplicius, in his comment onthis passage (in de Caelo 149.3ff.), identif ies the intermediate-theory of

this passage with the other interme diate-theory, and notes tha t Alex-

ander ascribes the theory to Anaximander (149.11). He goes on to men-tion Porphyry's objection to this ascription, based on the apparentcontrast between the intermediate-theorist and Anaximander, and thentries to explain the passage in his own way. What he says is not con-vincing; indeed, he seems quite confused. At any rate, he does not

at this point count Anaximander as an intermediate-theorist.B ut in other passages that refer to the intermediate-theory Aristo-

tle is ascribing the theory to Anaximander.80

And, further, it seems

to me quite likely that Aristotle w as correct in this ascription.81


80 The passages are the following (Ross [1936] 482 ad 187al4 gives these refer-

ences and some to commentators who identify Anaxim ander as the autho r of

this theory, but he denies it can be Anaximander , on the basis of 187a20-l):1. An intermed iate between fire an d air:

Phys A 4, 187al4-15: denser than fire, rarer than air.

de Gen et Corr B l, 328b34-35: air, fire, or something between these.

B 5, 332a20-2: there isn't an yt hi ng besides the elem ents, e .g., a m ean be-tween air and water (denser than air but rarer than water) or air and fire

(denser than fire but rarer th an air). (332a25 pretty clearly ties th is to Anax-

imander: see Kirk [1955] in Furley & Allen [1970/75] 329-30.)

Metaph A 7, 988a30-l: denser than fire, rarer than air.

2. An in termediate be tween wate r and air:Phys Γ 4, 203al8: water, air, or something between these .

Γ 5, 205a27-8: water, air, or the mean between these.d e Caelo Γ 5, 303bll-12: rarer than water but denser than air.

De Gen et Corr B l, 332a20-22: above

Metaph A 8, 989al4,-15: denser than air, rarer than water.

3. An interm ediate between fire and water:

Phys A 6, 189b2-3: water, fire, or something between these.







The argument we are ascribing to Anaximander has him decidingfo r an indefinite αρχ ή on the ground, previously arrived at, that it isunlimited: if it had one of a pair o f opposed characters, its unlimited-

ness would no t allow th e existence o f the other character o f that pair .So it is, in an obvious sense, intermediate. What it is intermediate be-tween depends o n which pair o r pairs o f opposed characters are takenas fundamental. W e have been unable to choose here.

The Aristotelian evidence is similarly indecisive. If Anaximanderregarded fire and air/mist as fundamental, that would account in somemeasure fo r Aristotle's vacillation between the pairs fire-air and fire-water: αήρ , air/m ist, is in some way ambiguous between air and water.

B ut it would remain a puzzle how the pair air-water appeared on thelist o f Aristotle's candidates. If Anaximander had a larger list o f oppo-sites between which his αρχή had to remain neutral, that might ac-count for the fuller list o f Aristotle's candidates.

Aristotle describes the intermediate, not just as a mean betweentwo of his elements, but specifically as denser (πυκνότερον 187al4,

303bl2, 988a30, 989al4; παχύτερον 332a22) than one element and finer

(λεπτότερον 187al4-15, 303bl2, 332a22, 988a30-l, 989al5) than another;he never says it is hotter, colder, drier, or wetter than anything. But,for Aristotle, th e characters o f being dense o r fine are derivative f romthe more fundamental characters o f hot, cold, wet and dry (de Gen etCon B2, esp. 329b32ff.). This suggests that he may be describing the

position, not in his own terms, but in someone else's terms.

The pair dense-fine does not play any role in the doxographical tra-dition we have associated with Anaximander; it figures much more

4. Something besides th e elements:de Gen et Con B l, 329a8-10 (connected with 328b34-5 above, and tied to

Anaximander by 329al2-13: see Kirk [1955] in Furley & Allen [1970/75] 330).Phys Γ 5, 204b22-9 (connected with Anaximander by b22-3: Kirk [1955],

Furley & Allen [1970/75] 330; and by Simplicius: see p . O O O above).

81 On the first count, I am in agreement with many others; not so on the se-

cond. See Kirk & Raven [1957] 111 = Kirk, Raven, & Schofield [1983] 112: ' ...a careful study of all Aristotle's references indicates that Anaximander was,after all, in his mind - although Anaximander in fact held no such theory.'

The 'careful study o f all Aristotle's references' to which Kirk here alludes isprovided by him in Kirk [1955], in Furley & Allen [1970/75] i 327-34. The claimtha t 'Anaximander in fact held no such theory' is based on the prior decisionthat Anaximander 's αρχή was 'an originative material qualified only asάπειρον ' (ibid. 329).






180 R. M. Dancy

in the t radi t ion associated with An aximen es. If the characterization of

the interm ediate-position in terms of denseness and fin en ess does notoriginate with Aristotle, tw o altern ative s suggest the mse lves.

(1) Perhaps Aristotle knew it as an alternative characterization ofAnaximenes ' position. But he seems not to hesitate about this: Anaxi-

menes' α ρ χ ή w as air .(2 ) Perhaps he knew it as a characterization of Anaximander ' s po-

sition. Suppose it goes back to the horse's mouth: suppose tha t it isAnaximander 's own. Then it is not, as with Anaximenes , a questionof describing the mechanism by which other things were generatedout of the α ρ χ ή , but of describing the α ρ χ ή itself. And then what it

might do is suggest to Anaximenes a way of making the descriptionof the α ρ χ ή more concrete to use condensation and rarefaction as amechanism.

3.2 The earth and equilibrium

W e can finish by tying up one loose end.Thales thought the earth rested on water, and tha t was closely relat -

ed to his claim that the α ρ χ ή was water .The train of thought we have been attributing to Anaximander goes

like this. He reflects on the water-hypothesis and arrives at the con-clusion that if the earth rests on something, either whatever it is goes

on down forever, or it in turn rests on something else, and either that

goes on down forever, or ... : and so on; whatever, finally, goes on

down forever is the α ρ χ ή . So the αρ χή is unlimited in extent . So itcannot have any of the definite characters that emerge from it.Then w ha t, in An aximan der, supports the e arth? He can no longer

just say 'water', and stop with th at. It looks as if he drew a map ofthe e arth with the earth surrounded by a body of wate r.82 Perhaps,then, he accepted the idea that the earth floats on water; perhaps he

82 See Kahn [1960] 82-4. The evidence is highly indirect: see the passage from

Agathemems printed as DK 12A6, i 82.27-30, with th e cont inuat ion of thatpassage in 68B15, ii 145.12-21, and Herodotus iv 36.

The position of Riedel [1987] 11-12 is very different, but it is unclear wh a t

supports this position.Heidel [1937] says surprisingly little about th e encircling ocean, but see pp.

11-12.







did not, but supposed that the earth is surrounded by water which

is in turn supported by earth underneath it. In either case, the reflec-tions with which we have supplied him force him to continue asking:

'And what supports that?' When he asks the question 'What supportsthe earth?', he is asking what supports the whole works, including the

surrounding water and anything else that requires support. What he

has to get to is something that no longer requires support, because

it goes on without end.

So this is the unlimited, whatever it is. And since it is unlimited,

it must be indeterminate. But because it is indeterminate, it cannot play

the role of earth in Xenophanes or water in Thales: it is not the kind

of thing that something can rest on, or float on. It is neutral with respectto the characters that determine earth and water. Then how can it pro-

vide the needed support? Anaximander's answer is: it doesn't. It is

precisely its neutrality that does the trick, not by providing support,

but by failing to provide any reason for the earth, surrounding water

and all, to go anywhere. The most important tex t here is Aristotle,de

Caelo B 13, 295blO-16:83

... but there are some who say i t remains through uniformity,M

as does, among the ancients, Anaximander; for it is appropriate fortha t which is seated in the middle and related uniformly tothe extremes to move no more up than down or to the sides; and it

b!5 is impossible for it to make motion in opposite directions at thesame time; so that of necessity it remains.

85

83 DK 12A26, i 88.1-5; KR 134 t!25 = KR S 133 H23. See also Hippolytus, Ref i6.3.

84 295bll δια την ομοιότητα: Burnet [1930] (4th ed.) 66 n. l, Stocks (Oxfordt ranslation of the de Caelo) ad loc. wi th note, and Guthr ie [1939] 23 5 w . 234 n.a, all would translate 'through it s indifference', a sense of όμοιότης una t t es t edelsewhere; the same is true of the translation 'because of its equilibrium' inKirk & R av e n [1957] 134 = Kirk, Raven, & Schofield [1983] 134. In Phaedo108e-9a Socrates makes the reason for the earth's staying where it is ' the

uniformity of the heaven itself wi th itself in every direct ion and the equilibri-um of the earth itself (την ομοιότητα του ουρανού αυτού έαυτώ πάντη και τηςγης αυτής τη Ισορροπία ν , 109a2-4; cf. Burnet's notes on 109a2, a3, in Burnet[1911] 128-9). I suspect the phrase in Aristot le should not be taken as referringto the earth's όμοιότης, but to όμοιότης in general, so tha t the sense is thesame as in the Phaedo.

85 Simplicius (de Caelo 532.13-14) confuses the picture some by adding air toequilibrium to hold the earth up, but at 295blO-ll Aristot le refers back to the-






182 R. M. Dancy

10 ε ί σ ϊ

δε τίνες οϊ δια την ομοιότητα φασιν αυτήν μένειν , ώσπερτων α ρ χ α ί ω ν Αναξίμανδρος· μάλλον μεν γαρ ούθέν άνω ή

κ ά τ ω ηε ι ς

τ α πλάγια φέρεσθαι π ρ ο σ ή κ ε ι το επ ί του μ έσουίδρυμένον και ομοίως προς τ α έσ χ α τ α έχον άμα δ'ά δ ύ -1 5 νατον ε ι ς το εναντίον ποιεϊσθαι την κίνησιν ώστ' εξ α ν ά γ κ η ς

μένειν .

This is, as Aristotle himself remarks, an ingenious idea (τοϋτο δελέγεται κομψώς, de Caelo B 13 , 296bl6).86 The idea is that somethingin a balanced state, an equilibrium, will stay that w ay unless some-thing upsets th e balance. It is tempting to say: this is where, in thehistory of philosophy, the Principle of Sufficient Reason first emerges.87

I think we may yield to this temptation, with two provisos. First,that august Principle is, for all anybody knows, false. A nd second,Anaximander did not in fact formulate the Principle or any thing quitelike it: it is a very hasty generalization based on what he appears tohave said about the earth's stability.

But there are mitigating factors. First, th e possible falsity of the prin-

ciple does not make it any less interesting. And, second, there is atleast one other reflection of the idea of equilibrium in what little wehave of Anaximander: the famous fragment. Simplicius (Physics

24.16-21) says that, according to Anaximander , th e αρχή

... is neither w ate r nor any other of the so-called elemen ts but someother unlimited nature, from which all the heavens and the world-orders in them come-to-be; and t hat the [things] from which there

is coming-to-be for the [things] tha t are, into those the re comes-to-bedestruction as well, in accordance with what must be; for they give

ones previously discussed, including th e theory, which he had ascribed toAnaximenes, Anaxagoras, and Dem ocritus, that air supports th e earth(294bl3-23), and then, in our passage, goes on to the theory he ascribes to

Anaximander (see also West [1971] 87 n. 1).86 B ut, according to Heidel [1921] 287, Aristotle 'attributed to the Milesian an ex-

planation utterly alien to his t hought . ' This is because Heidel has decided thatAristotle is talking here in t e rms of spheres (see Heidel [1921] 287 n. 104); butAristotle does not in fact m entio n spheres, an d the ex plan ation does not re-quire them (see, most recently, Bodn r [1988] 50-1).

87 The term is used by Barnes [1979] 24, followed by Bodn r [1988] 50 n. 14.







justice and re tr ibution to each other for their injustice in accordancewi th the orde r of t ime, speaking of them thu s in very poetical w ords

The m a n y difficult ies surrounding this text are not of present con-cern. Somewhere in here, somebody is quo t i ng Anax i mander . And

the quota t ion has to do wi t h a cosmic retr ibut ion, a restoring of

balance.88 So the generalizat ion of the idea of equi l ibr ium from A n a x -

imander 's v iew of the earth is per haps not so hasty after all: w hethe ror not it was actual ly form ulated as a principle, we may here be touch-ing on a pervas ive fea ture o f the way Anaximander thought aboutt h i ngs .

4 Appendix: Thales' limited α ρ χ ή

There are some texts that seem to ascribe to Thales an unlimited α ρχή.I th ink none of them should be taken seriously.

In Phys Γ 4, Aristotle discusses the unlimited ('infinite'); in expla in-

ing its relevance to 'the knowledge of nature' (ή περί φύσεως επιστήμη,202b30), he says (203al-4):

All w ho seem to have d ealt w ith this sort of philosophy in a way w o r -thy of account have mad e an account of the unl imited, and all positit as a principle for the beings . . . .

203a πάντες γαρ oi δοκοΰντες άξι ο -λόγως ήφθαι της τοιαύτης φιλ οσ οφίας πεποίη νται λόγον

περί του απείρου , και πάντες ως α ρ χ ή ν τίνα τιθέασι τωνόντων . . . .

And a little later he says (203al6-18):89

Whereas90 those concerned wi th nature all posit some other na tu refrom a m o n g the so-called e lem en ts for the unlimited, e.g. , water orair or the in te rmedia te be tw een these .

88 An idea explored years ago: Vlastos [1947] (in Furley & Allen [1970/75] 56-91).

89 Text as in Ross [1936].

90 203al6 οι δε answers to 203a4 οι μεν: see b e l o w .






184 R. M. Dancy

203a16 οί δε π ε ρ ί φύσεως π ά ν τ ε ς [ ά ε ϊ ]

ύ π ο τ ι θ έ α σ ι ν έ τ έ ρ α ν τινά φύσιν τ ω ά π ε ί ρ ω τ ων λεγομένων

στοιχείων , οίον ύ δ ω ρ ή α έ ρ α ή το μεταχϋ τούτων.If w e take him at his word, either he is including Thales as havingmade th e water unlimited, or is excluding Thales as not worthy of ac-count.91 But perhaps Aristotle is just being careless about his gener-alizations.

I should think the truth lies somewhere between the latter two al-ternatives. Aristotle does not know, and does not profess to know,

a great deal about Thales; he is likely to consider him at the borderof those whose views have to be taken into account. The point he ismaking here is focused on the notion of the unlimited, not on the no-tion of an α ρ χ ή In the intervening passage (203a4-16), he discusses aview he ascribes to Plato and the Pythagoreans, that the unlimited issomething on its own (καθ' αυτό, a4): not something else, like air,water, or whatever that happens to be unlimited, but something iden-tifiable simply as 'the unlimited'. In 203al6 he turns to the contrasting

view, which he ascribes to 'those concerned with nature', or at anyrate to all those whose views require attention, that there is some other

nature to which being unlimited is accidental: air, water, whatever.Given his reticence elsewhere about Thales, it seems unduly pedanticto insist that he must be thinking explicitly of Thales in thisconnection.92

There is, indeed, another respect in which Aristotle's generaliza-tion here is misleading. He is here telling us that 'those concerned with

nature all' make one or another of water, air, or whatever unlimited.This should lead us to think that Heraclitus, with his fire, is included;Aristotle reinforces this by mentioning him later on in the discussion

91 McDiarmid [1953] adds, as another passage in which 'Aristotle attributes an in-finite principle to all the physical monists' (91), de Caelo Γ 5, 303blO-13 (quotedbelow in connection with Anaximander). This is a mistake. The clause 'whichthey sa y surrounds all the heavens, being unlimited' (b!2-13) need qualifyonly th e immediately preceding clause, 'some say it is something finer thanwater but denser than air' (bll-12).

92 McDiarmid [1953] 90 says: 'Aristotle's generalization that all the physicistsmade their principle infinite is undoubtedly ... meant to include Thales .. . .'The word 'undoubtedly' is not apt.







of the unlimited (5, 205a3-4)93. And yet we f ind him saying in 5,205a25-694 that 'none of those who give an account of nature made fireor earth the one and unlimited' (ούθείς το ε'ν και άπειρον πυρ έποίησεν

ουδέ γην των φυσιολόγων).

95

It is best, then, to treat the generaliza-tion of 203al-4, 16-18, as casual and ill thought out.Simplicius, commenting on Aristotle's generalization, shows a simi-

lar lack o f care; he says (Phys 458.23-6):"

O f these [natural philosophers] those who posit some o ne e lementused to say this was unlimited in magnitude, as Thales [said] water[was], Anaximenes air, and Anaximander th e intermediate ...

τούτων δε οιμεν §ν τι στοιχεΐον ύποτίθεντες τοϋτο άπειρο ν έλεγον τω μεγέθει, ώσπερ

25 Θαλής μεν ϋ δ ω ρ , Άναξιμένης δε και Διογένης αέρα, Αναξίμανδρος δε τομεταξύ ....

As far as Thales, Anaximenes, and Diogenes are concerned, Simpliciusis simply filling in the blanks using Metaph A 3 (983b20, 984a2-7); whathe says is no more independent testimony than is what Ross sayswhen, in a note on the same passage, he writes:97 The reference is

to Thales (ΰδωρ) and to Anaximenes and Diogenes of Apollonia (αέρα). 'But what of Simplicius' classification of Thales and the unfortunate

Hippo among those who limited the αρχή (Phys 23.22-3)? There he wasnot merely following Aristotle's text and filling it in using another stand-by text . So perhaps what he says should be given some independentweight.

There is another possibility. Just after Simplicius comments on

Thales' allegedly limited αρχή, he tells us that the fire of Hippasus and

93 But he does no t there imply that Heracli tus thought his fire unlimited, or thathe t ho ugh t i t l imited .

94 205a25-8are generally t ho ugh t to be misplaced where they s tand in the text:se e Ross [1936] 552 ad he.. The lines have, unfor tunately, entirely vanished

from Barnes' re-edition of the Oxford translation (Barnes [1984] i 349-50).95 He adds: Txit either water or air or the mean between these' (αλλ' ή ύδωρ ή

αέρα ή το μέσον αυτών, 205b26-7), and Ross [1936] 552 ad 27 comments: 'ήϋ δ ω ρ probably refers to T hales, though he does no t seem to have character-ized water as infinite . ' But, again, this is asking to o muc h of the text.

96 458.23-25 = D K 11A13, i 77.21-22

97 Ross [1936] 545 ad 18






186 R. M. Dancy

Heraclitus was also lim ite d (23.34-24.1). W e have a certain amo un t offragmentary material from Heraclitus, but nothing that points in thisdirection. It seems quite plausible tha t here Simplicius is simply going

on the claim he finds Aristotle m aking a little later in the very text heis commenting on, to the effect tha t none of the natural philosophersmade the unlimited one fire (Γ 5, 305a25-6).98 Perhaps, then, Simpliciusis basing his view about Thales ' αρ χ ή on some such inference frommaterial w e already have.

There are tw o texts tha t might have su pplied him w i th the a m m u -nition he needs.

The first is the text in the de Caelo in w hich Aristotle implicitly con-

trasts Xenophanes' unlimitedly descending earth with Thales' waterthat supports the earth (B 13, 294a28ff.). Perhaps, the suggestion is ,Simplicius drew the same inference from this text tha t we did above.It could still be, and I think it is, the correct inference to draw fromthat text. But it wou ld have no independent value. In fact, this all seemsto me rath er unlikely: the inference required is rath er more subtle tha nthat required in the case of Heraclitus' fire.

The other text Simplicius might have used as a basis for his claim

that Thales' α ρ χ ή was limited is the one from Theophrastus in whichit w as claimed that Anaximander was the first to call the α ρ χ ή 'un-

limited'. That w ould entail that Thales had not called it that. But if thiswas Simplicius' basis for claiming a limited α ρ χ ή for Thales, it is in-dependent evidence: a source other tha n Aristotle, claiming that Thaleshad not called his α ρ χ ή 'unlimited'.

Simplicius classified Thales' α ρ χ ή as limited. We need not be tootrusting:we need not suppose tha t either Theophrastus or Simplicius

had at his disposal a text anted ating Aristotle that ascribed to Thalesa limited α ρ χ ή . Bu t, pre tty clearly, neither they nor Aristotle had any-thing that ascribed to him an unlimited αρχή either.

So we may suppose tha t Thales did not say his α ρ χ ή was unlimit-ed. If w e suppose that , w e shall be giving An axima nder room to makea point. And that itself favors our supposition.

Depar tment of Philosophy

Florida State UniversityTallahassee, FL 32306-1054

U.S.A.

98 So also McDiarmid [1953] 90.







Bibliography

Allan [1936]: D.J. Allan, ed., Aristotelis de Caelo. Oxford: Clarendon Press, 1936;

corrected edition, 1955.Asmis [1981]: Asmis, Elizabeth, 'What is Anaximander's ApeironT, ]oumal of

the History of Philosophy 19 (1981) 279-97.

Barnes [1979] & [1982]: Jonathan Barnes, The Presocratic Philosophers, 2 vols.London, Henley, & Boston: Routledge& Kegan Paul, 1979. Reprint, 1vol.,

London & New York: Routledge & Kegan Paul, 1982.

Barnes [1984]: Jonathan Barnes, ed., The Complete Works of Aristotle: The Re-

vised Oxford Translation, 2 vols. Princeton, New Jersey: Princeton Universi-

ty Press, 1984.

Barnes [1987]: Jonathan Barnes, Early Greek Philosophy. Harmondsworth, Mid-

dlesex: Penguin Books, 1987.

Bergren [1975]: Bergren, Ann L.T., The Etymology and Usage ο / Π Ε Ι Ρ Α Ρ in Early

Greek Poetry. [American Classical Studies 2] The American Philological As-sociation (Interbook Inc., N.Y.) , 1975.

Bodnar [1988]: Istv n M . Bodn r, 'Anaximander's Rings', Classical Quarterly

38 (1988) 49-51.

Brandwood [1976]: Leonard Brandwood, A Word Index to Plato. [Compendia 8.]

Leeds: W.S. Maney & Son Ltd., 1976.

Burkert [1963]: Burkert, Walter, 'Iranisches bei Anaximandros', Rheinisches

Museum 106 (1963) 97-134.

Burnet [1911]: John Burnet, Plato's Phaedo. Oxford: Clarendon Press, 1911.

Bumet [1930]: John Bumet, Early Greek Philosophy, 4th edition. London: Mac-

millan, 1930.

Carteron [1926/31]: Henri Carteron, Aristote: Physique, 2 vols. Paris: Societe

d'Edition 'Les Belles Lettres' (Bude), 1926, 1931; 3rd ed. 1961.

Cherniss [1935]: Harold Cherniss, Aristotle's Criticism of Presocratic Philosophy.

Baltimore, Md.: The Johns Hopkins Press, 1935; reprinted, N.Y.: Octagon

Books, Inc., 1964.

Cherniss [1951]: Harold Cherniss, The Characteristics and Effects of Presocratic

Philosophy', Journal of the History o f Ideas 12 (1951) 319-45; reprinted, Furley

& Allen [1970/75] ii 1-28, Cherniss [1977] 62-88.

Cherniss [1977]: Harold Cherniss, Selected Papers, ed. L. Taran. Leiden: E.J.Brill, 1977.

Classen [1962]: Classen, C. Joachim, 'Anaximander', Hermes 90 (1962) 159-72.

Classen [1976]: Carl Joachim Classen, ed., Sophistik. Darmstadt: Wissenschaft-

liche Buchgesellschaft, 1976.






188 R. M. Dancy

Cornford [1926]: F.M. Comford, 'Mystery Religions and Pre-Socratic Greek

Philosophy', in J.B.Bury, S.A. Cook, & F.E. Adcock, eds., The Cambridge

Ancient History, vol. 4, The Persian Empi re and the West (Cambridge Univer-

sity Press, 1926; reprinted, with corrections, 1960), 522-78.

Cornford [1936]: P.M. Cornford, 'The Invention of Space', Essays in Honor of

Gilbert Murray (London: Allen & Unwin , 1936) 215-35.

Comford [1952]: P.M. Cornford, Pnncipium Sapientiae: A Study of the Origins

o f Greek Philosophical Thought, ed. by W.K.C. Guthrie. Cambridge Univer-

sity Press, 1952.

Diels [1882/1895]: H. Diels, Simplici i in Aristotelis Physicorum commentaria, 2 vols.

[Commentaria in Aristotelem graeca 9-10.] Berlin: G. Reimer, 1882 & 1895.

DG: H. Diels, Doxographi graeci. Berlin: Walter de Gruyter, 1965 (reprint of

the original edition of 1879).

DK: Hermann Diels, D ie Fragmente der Vorsokratiker, 3 vols. 9th ed., ed. Walther

Kranz. Berlin: Weidmannsche Verlagsbuchhandlung, 1952.

Furley [1987]: Furley, D.J., The Greek Cosmologists, vol. i: The Formation of the

Atomic Theory and Its Earliest Critics. Cambridge University Press, 1987.

Furley & Allen [1970/1975]: D.J. Furley & R.E. Allen, eds., Studies in Presocrat-

i c Philosophy, 2 vols. London: Routledge & Kegan Paul; Atlantic Highlands:Humanities Press, 1970 & 1975.

Gadamer [1968]: Hans-Georg Gadamer, ed., Um d ie B e g r i f f s w e l t der Vorsokratiker.

Darmstadt: Wissenschaftliche Buchgesellschaft, 1968.

Gottschalk [1965]: H.B. Gottschalk, 'Anaximander's Apeiron', Phronesis 10

[1965] 37-53.

Guthrie [1939]: W.K.C. Guthrie, Aristotle:On the Heavens. London: William

Heinemann; Cambridge: Harvard University Press [Loeb], 1939.

Guthrie [1962]: W.K.C. Guthrie, A History of Greek Philosophy, vol. i: The Earli -

er Presocratics and the Pythagoreans. Cambridge University Press, 1962.

Hegel [1832/45]: Hegel, G.W.F. , Werke, ed. P. Marheineke et a l. Berlin: Dun-

cker & Humblot, 1832-1845.

Hegel [1892a]: Hegel, G.W.F. , Lectures on the History o f Philosophy, translated

by E.S. Haldane & F.H. Simson, vol. i. London: Kegan Paul, Trench, Trüb-

ner & Co., Ltd., 1892. Reprint: New York: The Humanities Press, 1974.Hegel [1892b]: Hegel, G.W.F. , The Logic of Hegel, translated from The Ency-

clopedia of the Philosophical Sciences by William Wallace. London: Oxford

University Press, 1892.

Hegel [1929]: Hegel, G.W.F., Science of Logic, translated by W.H. Johnston &

L.G. Struthers, 2 vols. London: George Allen & Unwin Ltd.; N.Y.: Mac-

millan Co., 1929.







Heidel [1912]: W.A. Heidel, On Anaximander', Classical Philology 7 (1912)

212-34. Reprinted, with original pagination, in Heidel [1980].

Heidel [1921]: W.A. Heidel, 'Anaximander's Book, th e Earliest Known Ge-

ographical Treatise', Proceedings o f th e American Academy o f Arts and Sciences56 no. 7 (1921) 239-88. Reprinted, with original pagination, in Heidel [1980].

Heidel [1937]: W.A. Heidel, The Frame o f th e Ancient Greek Maps , with a Discus-

sion of th e Sphericity of th e Earth. [American Geographical Society, Research Ser-

ies 20.] Baltimore: The Lord Baltimore Press, 1937.

Heidel [1980]: W.A. Heidel, Selected Papers , ed. L. Taran. New York & Lon-

don: Garland Publishing, Inc., 1980.

H lscher [1953]: Uvo H lscher, 'Anaximander und die Anf nge derPhilosophie', Hermes 81 (1953) 257-77, 385-418; reprinted, Gadamer [1968]

95-176; abridged and translated as 'Anaximander and the Beginnings of

Greek Philosophy', Furley & Allen [1970/75] i 281-322.

Hussey, Edward, Aristotle's Physics Books I I I and IV. Oxford: Clarendon Press,

1983.

Jaeger [1957]: Werner W . Jaeger, Aristotelis Metaphysica. Oxford: Clarendon

Press, 1957.

Jaeger [1947]: Werner W. Jaeger, The Theology of th e Early Greek Phi losophers .

Oxford: Clarendon Press, 1947.

Kahn [1958]: Charles H. Kahn, 'Anaximander and the Arguments Concern-

ing the απειρον at Physics 203b4-15', Festschrift Erns t Kapp (Hamburg: M.

von Schr der, 1958), 19-29.

Kahn [I960]: Anaximander and the Origins of Greek Cosmology. N.Y.: Columbia

University Press, 1960.

Kirk [1955]: G.S. Kirk, 'Some Problems in Anaximander', Classical Quarterly5 (1955) 21-38; reprinted in Furley & Allen [1970/75] i 323-349.

Kirk & Raven [1957]: G.S. Kirk & J.E. Raven, The Presocratic Philosophers: A

Critical History with a Selection of Texts. Cambridge University Press, 1957;

corrected reprint, 1963.

Kirk, Raven, & Schofield [1983]: G.S. Kirk, J.E. Raven, & M. Schofield, T he

Presocratic Philosophers: A Critical History with a Selection of Texts, 2nd edi-

tion. Cambridge University Press, 1983.Lloyd [1964]: G.E.R. Lloyd, 'Hot and Cold, Dry and Wet in Early Greek

Thought', Journal o f Hellenic Studies 84 (1964) 92-106; reprinted in Furley &

Allen [1970/75] i 255-280.

McDiarmid [1953]: J.B.McDiarmid, Theophrastus on the Presocratic Causes',

Harvard Studies in Classical Philology 61 (1953) 85-156; abridged & reprinted,

Furley & Allen [1970/75] i 178-238.






190 R. M. Dancy

Page: D . L . Page, ed., Poetae melici graeci. Oxford: Clarendon Press, 1962.

Re i nh a r d t [1916]: Karl Reinhard t , Parmemdes und die Geschichte der griechischen

Philosophie. Frankfurt am Main: Vittorio Klostermann, 1916; 2nd ed., 1959.

Riedel [1987]: R iedel, Manfred, "ΑΡΧΗ und ΆΠΕΙΡΟΝ': ber das G r u n d -wort des Anaximander ' , Archiv f r Geschichte der Philosophie 69 (1987) 1-17.

Ross [1924]: W . D . Ross, Aristotle's Metaphysics, 2 vols. Oxford: ClarendonPress, 1924.

Ross [1936]: W . D . Ross, Aristotle's Phy sics. O xf or d: C lar en do n Press, 1936.

Snell [1944]: Bruno Snell, 'Die Nachrichten ber die Lehre des Thaies und dieAnf nge der griechischen Philosophie- und Literaturgeschichte', Philolo-

gu s 96 (1944) 170-182. R ep rin ted , w ith add ition s, in Sne ll [1966] 119-28; thelatter repr inted, wi th fur ther addi t ions , in Classen [1976] 478-90.

Snell [1955-]: Bruno Snell, ed., L·xikon des fr hgnechischen Epos . G ttingen: Van-denhoeck & Ruprecht , 1955-.

Snell [1966]: Bruno Snell, Gesammel te Schriften. G t t ingen: Vandenhoeck &Ruprecht , 1966.

Stace, W .T., The Philosophy o f Hegel : A Systematic Exposition. N . Y . : Dover Pub-lications, 1955.

Stokes [1971]: Michael C. Stokes, One and Many in Presocratic Philosophy.

Washington, D C: Center for Hellenic Studies; Cambridge, M A : HarvardUniversity Press, 1971.

Stokes [1976]: Michael C. Stokes, 'Anaximander's Argument', R . A . Shiner &J. King-Farlow, eds., New Essays on Plato and the Pre-Socratics [Canadian Journal

o f Philosophy, Supp. Vol. 2] (Guelph, Ont.: Can adian Association fo r Pub-lishing in Philosophy, 1976) 1-22.

Teichm ller [1874]: Gustav Teichm ller, Studien zu r Geschichte der B e g n f f e . Berlin:Weidmannsche Buchhandlung, 1874.

Vlastos [1947]: Gregory Vlastos, 'Equality and J ustice in Early Greek Cosmol-ogies', Classical Philology 42 (1947) 156-78; rep rin ted , w it h changes, in Furley& Allen [1970/75] i 56-91.

Wagner, Hans, Anstoteles: Physikvorlesung. D armstadt: W issenschaftliche Buch-gesellschaft, 1967; rpr. 1983.

W e st [1971]: M .L. W est , Early Greek Philosophy and the Orient . Oxford: Claren-don Press, 1971.

Wicksteed & Cornford [1929/34]: Philip H. Wicksteed & Francis M . Cornford,Aristotle: The Physics. London: William Heinemann; Cambridge, Mass.:Harvard University Press [Loeb], i 1929 (revised ed. 1957); ii 1934.

Documents

Dancy, R. M._thales, Anaximander, And Infinity_1989_Apeiron, 22, 3, Pp. 149-190