SOURCE: Allan S. Gnagy, "The Apeiron: Anaximander's Concept of the Endless Ground of Nature," in The Northwest Missouri State University Studies, 1975, pp. 1-19.

[In the essay that follows, Gnagy presents a comprehensive account of Anaximander's central idea—the Boundless apeiron—and surveys the most influential interpretations of this doctrine.]

Introduction

The problem with which this paper deals is the interpretation of the only extant fragment of the writings of Anaximander, a Greek philosopher whose dates are approximately estimated at 610-546 B.C. The fragment is of considerable interest to scholars of ancient Greek philosophy, because it is agreed to be the earliest verbatim quotation from that tradition, and, because of its brevity, it is open to a wide variety of interpretations. This variety will be evident to the reader, as will also be the fact that this paper attempts to add to the divergent opinions, by an emphasis on the dynamic character of Anaximander's philosophy. Anaximander was one of several cosmologists usually called the Milesian, or Ionian, physicists, or nature-thinkers. Their concern was to understand the overall structure and processes of the natural world by identifying the ground of change, the Greek word for which was "arché," which literally means "beginning," and eventually came to approximate our word, "principle" or "ground." The dynamic emphasis is necessitated, in my view, by the general belief, traceable back to Aristotle, that they conceived the object of their search to be merely material, in the sense of an inert, passive matter—a belief which I do not think is supported by the strictest construction of the evidence.

A note is perhaps in order here, to clarify a possible source of confusion regarding the ancient sources named in the paper: the fragment was originally recorded, and hence preserved for us, by Theophrastus, who was Aristotle's main research assistant (fourth century B.C.); it was Theophrastus' dissertation on the already-ancient Presocratic philosophers upon which Aristotle depended in writing his own lecture-essays on Physics. Theophrastus' work is no longer extant, but portions of it were copied by Simplicius, in the sixth century A.D., as additional documentation for his own commentary on Aristotle's Physics; Simplicius' work was entitled, Of the Opinions of the Physicists, but is often referred to in modern scholarship as his Physics. The numberings used in references to Simplicius' Physics are the page-and-line numberings in the appropriate volume of the Berlin Academy's Commentaria in Aristotelem Graeca. The numberings in references to Aristotle's works are the standard book-chapter-and-line numberings in the accepted Greek text adhered to in Sir David Ross' Collected Works of Aristotle.

References to "Diels-Kranz" are to the photographic reprints (1952 and 1954) of the fifth edition of Die Fragmente der Vorsokratiker, a monumental compilation and critical redaction of all the known quotations from the Presocratic Greek philosophers.

Part I: The Text

The fragment of Anaximander's writing is found in Simplicius' commentary on Aristotle's Physics: the commentary is entitled, Of the Opinions of the Physicists; at 24,13 (Diels-Kranz 12A9), it reads, in my own translation, as follows:

Anaximander … declared the endless (apeiron) to be the ground (arche) and element of things, he being the first one who applied this designation of "ground"; he says that it is neither water nor any other of what are said to be elements, but rather some other indeterminate (apeiron) nature, out of which all the heavens and the worlds in them come to be; out of which elements is the coming-to-be of things, and perishing into them occurs, "according to what should be, for they give compensation and reparation to one another for injustice, each in the proper time," speaking of them thus in more poetic terms. It is evident, then, that this one who had watched the transformation of the four elements into one another did not think it worth while to make any one of these that which underlies, but rather something else besides them.

(I have enclosed in quotation marks what I consider to be the fragment from Anaximander.)

1. The phrase, "ground and element" is not to be understood as a quotation from Anaximander, nor yet a paraphrase. In the context, taken by Simplicius from Theophrastus, the latter is reporting how the Peripatetic concept of arché is related to something Anaximander had said over two hundred years earlier. "Ground and element" appears to be a stock phrase in Peripatetic discourse, especially considering the fact that the Greek word for "element" (stoicheion) was not used philosophically until Empedocles,¹ and in a systematic way only with Plato; but it is only with Aristotle that it received a precise definition, as "that out of which a thing is composed, which is contained in it as a primary constituent, and which cannot be resolved into something different in kind."² As we shall see, Anaximander did not conceive of his "substrate" as a constituent of things. Aristotelean metaphysics regards the arché as a principle which is also a constituent of things, so that the word is yoked with "element", creating a phrase full of Peripatetic import, but which is not likely to be Anaximandrean.

2. According to most commentators, the "things" mentioned in the first sentence of our text are the concrete, compound individuals of the empirical world. However, Kahn raises questions about the phrase, and offers a different interpretation; he thinks the "things" are not the concrete individuals, but the very principles associated with the elements, and which characterize them, i.e., "the hot," "the cold," etc. These principles Kahn understands to "perish" into and arise out of one another, and he terms them "elemental powers." He goes on to say that passages from Diogenes and Anaxagoras support his thesis. Further, he claims that "the things" are the referents of the phrases later on in the text, "out of which," "into them," and which give compensation and reparation to one another.³

Interesting though this thesis may be, it cannot be supported, for several reasons. One is that the first part of the text is not a quotation from Anaximander, but Theophrastus' commentary, in indirect discourse; and an interpretation like Kahn's is not possible in the Peripatetic framework, where "things" are concrete individuals, and clearly not predicative principles such as "hot," "cold," etc. Furthermore, if what Kahn says were true, the rest of the fragment would be nonsense, because Anaximander's point is that genesis is from the "indeterminate nature," and it is not elements, nor the principles which characterize them, which are born and destroyed, but the things of which these are constituents. In this case, the evidence is in favor of the more general interpretation, that the "things" are the concrete individuals of the visible world. The "elemental powers" do not destroy one another, but exchange hegemonies, take turns dominating.

3. Apeiron, to make a bad pun, is the word in this text which has generated "no end" of controversy, and it is the central problem of this paper. Although it cannot be understood fully, apart from a study of the whole text, we shall try to consider the majority of problems arising in the commentaries, and in the second part of the paper, we will concentrate on a full discussion of it. As Kahn has forcefully shown, apeiron is an adjective with a distinctively verbal coloring, having to do with dynamic movement. Kahn gives the sense of it as "what cannot be passed over or traversed from end to end."⁴ While it is obvious that this sense can be applied to whatever is "spatially infinite," it is also applicable to other situations. And although it is true that Homer and others use the term as poetic exaggeration, to describe the immense sea,⁵ we shall see that it has other applications besides the poetic one. But before we come to that discussion, we must look at the oldest interpretation, that apeiron means "spatially infinite."

Spatial infinity is probably the meaning which Aristotle attached to Anaximander's apeiron, certain doubts notwithstanding.⁶ He at least implies this, when he argues that an infinite substance, such as air or water, would leave no room for any other kind of substance.⁷ Kirk argues that this could well have been Anaximander's reason for positing some other substance than, for example, Thaïes' water.⁸ Aristotle, however, explains the belief in an infinite source as a means of guaranteeing the continuation of the process of becoming, and although he argues against this reasoning, he does seem to attribute it to Anaximander.⁹ Interestingly enough, Aristotle's criticism is that a cyclical motion of becoming and perishing does not require an infinite source, because the destruction of one thing is the generation of another; a cycle need not be infinite, in the spatial sense. As we shall later argue, that is in fact the sense in which Anaximander employed the term, apeiron. It is, then, Aristotle's interpretation that led most of the historians of the 19th and early 20th centuries to attribute to the apeiron the character of a spatially infinite material substance.¹⁰

Kirk holds that spatial infinity was probably not exactly Anaximander's meaning, since the concepts of spatial and temporal infinity had not been fully distinguished before the Eleatic analyses of infinity, e.g., those of Melissos and Zeno.¹¹ Kirk is correct, that Anaximander did not mean spatial infinity merely, though for different reasons than those Kirk puts forward. Kirk is also correct, that if Anaximander had meant simply a "huge, inexhaustible mass,"¹² that would be unremarkable, and hence not Anaximander's thesis at all,¹³ even though that is the most common usage of apeiron in Greek literature before and after Anaximander. The concern of the Milesian nature-thinkers is process, becoming, and the idea merely of an infinitely extended substance is static, and does not accord well with a view of dynamic change. All in all, we must conclude that Aristotle was mistaken in classifying Anaximander's apeiron as some infinitely extended substances.

The above view, that the apeiron is a spatially infinite material, has been inferred from considering the word, apeiron, to mean "externally unbounded."¹⁴ Another possibility has been proposed, that the word means "internally unbounded," something like "containing no distinctions within itself." However imprecise this language may be, it seems to have at least two senses: it may mean that the arché is homogeneous and not analysable into parts, i.e., it has no internal divisions, it cannot be broken down into heterogeneous constituent forms; in this case, of course, it approximates the Aristotelean notion of element, the lower limit of analysis. But such an homogeneous substance would be identifiable, as having some determinate form, as distinct from other kinds of substance. The other sense of "internally unbounded" is "that which is not identifiable as any known, empirical substance," that is, "indeterminate." Its form in this case is to have no form of determination. It is evident that Aristotle and other ancient authorities also understood the arché of Anaximander in this sense of indeterminacy, for note the following passages:

(1) The passage further along in the text (p. 5): … neither water nor any other of what are said to be elements, but rather some other indeterminate nature …

(2) Aristotle, Physics 4,203a16: All the physicists make the infinite a property of some other nature belonging to the so-called elements, such as water or air or that which is intermediate between these.

(3) Aristotle, Physics 5,204b22: But yet, neither can the infinite body be one and simple, whether it be, as some say, that which is beside the elements, from which they generate the elements, or whether it be expressed simply. For there are some people who make what is beside the elements the infinite, and not air or water, so that the rest be not destroyed by their infinite substance; for the elements are opposed to each other (for example, air is cold, water moist, and fire hot), and if one of those were infinite the rest would already have been destroyed. But, as it is, they say that the infinite is different from these, and that they come into being from it.

(4) Simplicius, Physics 24,26: Anaximenes son of Eurystratos, of Miletus, a companion of Anaximander, also says that the underlying nature is one and infinite like him, but not indefinite (aoriston) as Anaximander says, but definite, for he identifies it as air …

These passages show that the ancient commentators understood Anaximander's express intention, not to identify his arché with any of the known substances, with their empirical attributes of "hot," "cold," etc. But at the same time, we have seen that those commentators understood the term, apeiron, to mean spatial infinity. It was Anaximander's refusal to identify the apeiron by any familiar, empirical form, along with the spatial interpretation, which led the historians of the past two generations to dismiss the question of the nature of the arché, i.e., its qualitative determinations, as unclear, hence as unimportant.¹⁵

If Anaximander was the first to apply the term, apeiron, to the arché, we are faced with the problem of how he intended it. As we have seen, traditional interpreters see it as meaning "spatially infinite," and its lack of positive characterization is a problem quite apart from its spatial properties. But more modern scholarship, stimulated by Burnet, has tended to construe it as having the primary sense of "indeterminate," "indefinite," in spite of the fact that the word is rarely used this way in Greek literature.¹⁶ To convey the sense of "indeterminate," another word, aoriston, is commonly used. Note Kirk's conclusion regarding this problem:

In any case, the lack of a positive identification was conspicuously implied. Either to apeiron meant "the spatially indefinite," and was implied to be indefinite in kind because it was not formally identified as fire, air, water, or earth; or Anaximander intended it to mean primarily "that which is indefinite in kind," but naturally assumed it to be of unlimited extent and duration—properties which, when expressed, would be expressed in terms of all-inclusiveness and divine immortality.¹⁷

With this analysis of the problem in mind, Kirk opts for the second interpretation, that Anaximander's primary meaning for apeiron was "indefinite in kind." But it must be said that Kirk's interpretation is strained, to say the least, for the Greek word, apeiron, does not mean "indefinite in kind"; it is used for either spatial or temporal infinity, "endlessness," and if we accept the limitation of choice stated above, that is, between just two alternatives, spatial infinity or indefiniteness, we should have to choose, on linguistic grounds alone, the former. Of course it is recognized from the earliest commentaries, that Anaximander's arché was indeterminate, but this meaning cannot be derived from the mere use of the word, apeiron, as it appears at this point in the text. But because Aristotle, and commentators since, have puzzled over the indeterminacy of Anaximanders' arché, we must look briefly at some of the possible reasons for it.

The reason which Aristotle offers for positing an indefinite substance, in Physics 5,204b22, rather than some definite one, is that if it were infinite and determinate, there would be but one substance and no others; there would be no distinctions, no plurality within the unity but only an omnivorous One; such a radical monism would of course be the end of the metaphysical pursuit, i.e., of searching out the unity and relatedness of the diverse facts of experience; it would be the denial of the kosmos, of the universe. Kirk may be correct that this probably was one of Anaximander's reasons for leaving his arché indeterminate. Kirk calls it a possible motive, along with Aristotle's reasoning in Physics 4,203b15, that infinity is necessary to ensure that "becoming shall not fail"; but Kirk notes also that the latter is an argument for spatial infinity, whereas the former is an argument for indeterminacy.¹⁸ Whether or not these were Anaximander's reasons, Theophrastus, further along in our text, uses the term, apeiron, to convey the idea of indeterminacy:

he says that it is neither water nor any other of what are said to be elements, but rather some other indeterminate (apeiron) nature….

This is clearly an unusual use of the word, and requires some investigation. Possibly, it is assumed by Theophrastus that since there are many "elements," it is clear that none of them can be infinite, according to Aristotle's reasoning noted above …; hence it might be argued that the existence of a multiplicity of elements of different but definite forms requires that each be spatially finite. In this way, definiteness and fini tude are inseparably bound together, and if we call some substance "spatially infinite," then we imply that it cannot have a definite form. But surely this is a strange and roundabout way for Theophrastus to speak of indeterminacy, only by "implication." We should rather conclude that he recorded it from Anaximander's writing, without clearly grasping its meaning in context. If he had intended to write "indefinite," surely he would have used aoriston, as indeed he does in Physics 24,26 … It is even remotely possible that Simplicius, in recording Theophrastus' words, mistakenly used apeiron where the latter had aoriston.

The difficulties noted above remain paradoxical and insoluble, so long as we suppose the term, apeiron, to have only two possible meanings, either "spatial infinity" or "indeterminateness." Another interpretation has been proposed, however, by scholars such as Cornford, Kirk, and Kahn, but in a rather tentative and incomplete way, without full emphasis and without a consistent carrying-out of the consequences. What Anaximander may have intended, it is suggested, is neither spatial infinity nor qualitative indeterminacy, but rather the endlessness of the cycle of nature, the coming and going of the seasons, the coming-to-be and perishing of things. We shall return to this notion later, after a more adequate look at the text.

As Cornford¹⁹ and others point out, the "older" historians of philosophy tended to accept Aristotle's contention that the Milesian nature-thinkers were concerned only with "principles of a material kind." As Seligman²⁰ points out, Aristotle was influenced by his own philosophy of four causes, and in his survey of earlier thinkers, he was searching for their concepts of material cause. He found such a concept in Anaximander's arché, among others. The Aristotelean notion of matter involves not merely spatial properties, but logical ones, which fit into the Peripatetic philosophy of becoming—matter is the principle of potentiality, or the "power to become." Hence Aristotle thinks of the apeiron in terms of his own concept of prime matter, pure potentiality. One of his criticisms of it is that it is purely passive, and offers no motive principle, by which the potential can become actual.²¹ However, it must be pointed out here that this criticism does not touch the meaning of Anaximander's arché, since it is premised on the Aristotelean distinction between potentiality and actuality; this division naturally creates problems in any metaphysics, precisely because the two terms are not motive principles. It is evident, then, that the lack of a motive principle in the matter-form dichotomy is Aristotle's difficulty, not Anaximander's, since the latter articulated no such distinction. Aristotle had to look beyond matter and form for a motive principle, and it is clear that whatever is posited as the Mover is itself the arché. It is at least probable that Anaximander did not hold the potentiality-actuality distinction, and fur thermore, as we shall see, his apeiron is more akin to a motive principle than a material one, anyway. Theophrastus speaks of Anaximander's arché as "eternal motion,"²² and Aristotle attributes to it the functions of "surrounding and guiding all."²³ At the very least, this implies that the arché is active in some sense, and if it guides all, then it is also an initiating source of motion. Aristotle attributes this phrase, "surrounding and guiding," to all those who posit an infinite primary matter, without a separate cause of motion, which surely must include Anaximander.²⁴ But we must also recognize that Anaximander probably did not separate the problem of motion to the same degree as Aristotle did; rather, he was concerned to investigate the ground of motion and change itself, without distinguishing motion from that which is in motion. In Anaximander's thought, being and becoming are not so radically distinguished as they are in later Greek thought, that is, after Parmenides.

Another controversy of scholarship involves the interpretation of the clause, "being the first one who applied this designation of 'ground' (arché)." The tradi tional interpretation, held by recent scholars also, is that Anaximander was the first to use the term, arché. But Burnet claimed that the meaning of the clause is that Anaximander was the first to say of the arché that it was apeiron. Jaeger, particularly, spends considerable time discussing this point and concludes that Burnet is in error. It is true that arché, a distinctly technical term in Peripatetic thought, is not thus attested in other Presocratic writings.²⁵ But Simplicius, in another place, states clearly that Anaximander was the first to use arché, i.e., in Physics 150,23. Jaeger also notes that Hippolytus, writing independently of Simplicius, says the same.²⁶ Therefore, the testimony must go back to Theophrastus, who had direct access to Anaximander's writing, and the phrase in question must mean that Anaximander was the first to use arché. Jaeger goes on to raise the question, whether or not Anaximander might have meant the term, arché, in the Aristotelean sense of "principle." He brings forward two quotations from Melissos, who lived roughly between Anaximander and Aristotle, and who did employ the word, arché:

(1) Simplicius, Physics 110,3: Whatever has a beginning (arché) and an end is neither eternal nor infinite, (apeiron)

(2) Simplicius, Physics 29,22: Since, then, it did not come into being, it is now and always was and always will be and has no beginning (arché) nor end, but is infinite, (apeiron)

Jaeger believes that these passages point to an Anaximandrean arché principle, saying that the apeiron is arché, since anything that has a beginning cannot be eternal or infinite. I do not think that Jaeger has established by citation of these passages, that the Milesians, nor that Melissos, used the term arché to mean "principle," in the Aristotelean sense; but there is, in the quotations, a more important aspect to be noted for purposes of this paper: the word, apeiron, is weighted toward a temporal usage, more than a spatial one; at least, this is unquestionably true of the second quotation, if not of the first, and it is the thesis of this paper that Anaximander's use of apeiron is thoroughly temporal and dynamic.

Kirk, on the other hand, maintains that Burnet's interpretation is more relevant to the trend of Simplicius' argument,²⁷ and also observes that Theophrastus used arché in talking about Thales, without noting that the latter did not use the word himself. He concludes that "no technical use of arché was implied by Theophrastus—the use he referred to was of to apeiron."²⁸ But this conclusion is beside the point, since the question is not whether Anaximander used the term in a "technical" sense, but whether he was the first one to use it at all. Also, Theophrastus' failure to mention whether Thales used the term implies nothing at all; the entire passage is taken from Simplicius' treatise on the Aristotelean notion of arché, and in this context it is more natural to note who first used the word, than to say who did not. The fact that Anaximander first used the term, arché, does not, of course, imply that he used it in an Aristotelean sense.

Kahn's grammatical treatment lends support to Burnet's interpretation, though he admits that the evidence is fairly evenly weighted.²⁹ Although Kahn takes note of Simplicius' clear attribution of arché to Anaximander, in Physics 150,23…, he also points out that the same Simplicius, in de Caelo 615,15, says that Anaximander was the first to posit an infinite substratum. Hence, Kahn's conclusion, with which I must agree, is that Anaximander was the first to employ the concept of apeiron, but there is no source to testify that he was the first to use the word. Hence, the evidence on the whole supports the traditional interpretation, that Anaximander was the first to use the term, arché³⁰

The foregoing discussion must decide, against Burnet, Kirk, and Guthrie, that Anaximander was the originator of the term, arché; this does not detract from the originality of Anaximander's concept of apeiron, but rather focuses attention upon the fact that the apeiron is the ground of the elements, and not one more element among them. Then to this aspect of his thought we now turn.

When Theophrastus writes, "he says that it is neither water nor any other of what are said to be elements, but rather some other indeterminate nature," it is seen that Anaximander explicitly refused to identify his arché with any of the usual "elements" of the popular cosmology which figure so prominently in later Presocratic thought. Each of these elements is identifiable by some empirical property, e.g., the "nature" of water is to be wet, and this nature is definite. But the arché of Anaximander is of "some other nature," i.e., it does not have an empirically identifiable property, as do the others, or at least, its nature has not yet been determined. But Anaximander does not go on to try to determine its nature; rather he goes on to say that it is the source of all things, that is, it is ground of becoming—and it is in the context of becoming that we must understand the apeiron.

We now turn our attention to what I believe is the direct quotation from Anaximander's writing, viz.,

… according to what should be, for they give compensation and reparation to one another for injustice, each in the proper time, …

Although there is some disagreement among scholars regarding exactly where the direct quotation begins, there is general agreement, that what Anaximander is referring to is the conflict among the "elements," or what amounts to the same thing, among the qualities which characterize each of the four elements. Some modern writers, for example Kahn, argue that Anaximander does not restrict the elements to the four of the popular Greek cosmology,³¹ but this is not a matter of great importance for the picture presented by Anaximander. The conflict of the elements is most dramatically displayed in the cyclical changes of the seasons through the year, as Cornford, Kirk, and Raven, make clear; what one sees by a casual observation of the seasonal changes is the coming and going of certain dominant qualities, e.g., heat, cold, drought, and moisture, which take turns ruling over one another through the different seasons. It appears that the Milesians sought, among other things, to identify which particular quality dominated in any given event or object; hence, the qualities dominating summer are the hot and the dry, though the cold and the wet are not altogether absent; but the hot and the dry, because of their hubris, must repay the cold and the wet, by in turn being dominated by them—and this is the source of the seasonal cycle. With this in mind, we must reject a misinterpretation found in Seligman, that the elements "destroy" one another; Seligman says that the elements must pass away, or die for their injustices, that injustice is cumulative, and that this leads eventually to a catastrophic end to our world.³² His view is not borne out by the text, which explicitly states that the coming-to-be is of things out of the elements, and the perishing which follows is likewise of the things. It is not the elements which are created and destroyed, but concrete, compound things. Anaximander's point here is that the seasons return again, because the opposites never destroy one another, but they exchange hegemonies, and live again to return to dominance; first one rules, and then another, so that no single one can destroy the others. Imbalance is always compensated for by a counterbalance; the great figure of a balance-scale, constantly swinging, or a pendulum, may serve to illuminate this idea of an oscillating natural cycle. It is the constant movement of weight and counterweight which keeps the universe stable. On the momentary and partial view of things, there appears always to be imbalance, injustice, but "in the long run," sub specie aeternitatis, the universe is lawlike, balanced, and just. According to this view, individual things do not enter into the conflict of justice and injustice; they simply come to be and perish. But Seligman insists on arguing that Anaximander did not hold that the system is stable, and so makes nonsense out of the text. Since the system of nature is cyclical, i.e., each "element" always returns, it is incoherent to suppose that the elements are destroyed, or that injustice is cumulative. It is clear that Anaximander held to no doctrine of a catastrophic end of the world.

The "poetic" terms in which Anaximander couches the above fragment, that is, the use of legalistic and moral terms such as "compensation and reparation," "justice and injustice," lead some commentators to see in the text a belief in a "moral force" governing nature. Seligman, in particular, among the more recent writers, sees a moral law governing all becoming.³³ Others, however, hasten to deny the view of a moral force, calling the use of "justice" and "injustice" a metaphor.³⁴ But we need to go more deeply than the notion of mere "metaphor," in order to appreciate what is being said. "Justice," "injustice," "reparation," are intended to show an order in nature, a system of balance and counterbalance, but they are not meant as an argument for a moral force. We must recall that the dichotomy between nature and the peculiarly human sphere (convention) developed in Greek thought only with the sophists and with Socrates; there is no clear separation of the two realms, so Anaximander's usage is not "metaphorical" in the sense of a transference of reference from one class of entities to another. The Greek concept of justice is fundamentally a notion of balance, of equilibrium, of balancing one claim against another, so as to produce harmony. Justice is conceived thus as an emulation of nature, so that human justice becomes a "metaphor" derived from the equilibrium displayed by nature; the Greeks did not see nature anthropomorphically, but rather saw man physiomorphically. But surely for Anaximander, the distinction is not even this sharp. Human society was understood as an integral part of the great burgeoning, growing, breathing-and-dying hubbub of nature, with all of the latter's essential features, not as something in a class apart from nature.

Part II: What Is Anaximander's Apeiron?

As the foregoing discussion has shown, Anaximander's use of the word, apeiron, cannot be considered merely as meaning "spatially infinite," nor as "indefinite," though indefinite the arché was, independently of the use of apeiron. Anaximander's arché is not a "material" concept, either in the sense of a spatial entity, nor as Aristotelean potentiality. It is not an element, in the sense of all the other elements which constitute things, nor is it a mixture of elements. Neither is it the primeval Chaos, nor an intermediate element standing between every pair of opposites. It is not at all an analytic notion, as are all of the above, i.e., it is not the object of the search for the "parts" or the constituents of compound individuals. All such conceptions are static, and do not accord well with the force of the tiny quotation recorded by Theophrastus. To hold any of the above notions is to ignore the content of the fragment, to gloss over the central role of the verb, "to become," and of the all-important reference to time as the ordering principle. How striking a picture is the giving back and forth to one another, among the elements, of justice and reparation for injustice! And yet the static conceptions of the Anaximandrean arché do ignore this vision of ceaseless activity, of giving back and forth, of coming to rule and being overthrown, exhibited in the fragment. A dynamic, temporal interpretation of apeiron, one of endlessness through time, of an activity, is more consistent with Anaximander's words than a spatial one. But it must be stressed here that this is not the endlessness of a temporal "straight line," stretching back into an infinite past and forward into an infinite future. Such a spatially-conceived time needed to wait for later; the endlessness of Anaximander's apeiron is not the endlessness of a causal or a number series. It is the endlessness of an ever-turning wheel, of the ceaselessly-recurring cycle of birth and death, of creation and destruction, of coming-to-be and perishing. Aristotle himself attests, in Physics 207al, that apeiron was predicated of finger rings, and we have seen in the writings of Melissos … that it was used to signify temporal endlessness, quite as much as spatial. Anaximander's arché, then, is not a basic "stuff" or material out of which things are composed, but the very ground of process, change, and coming-to-be. It is difficult to overemphasize this point, and it has generally been underemphasized by recent scholars who, though they recognize it, are still too much bound by the older views to embrace it with resolve. Perhaps Cornford makes it more forcefully than most others, in his Principium Sapientiae. The apeiron of Anaximander is not so much substance, element, or principle of being, as the ground of becoming, the motive principle of coming-to-be and perishing, and this is the justification for my translation of arché as "ground."

In Part I, it was argued, in support of the traditional view, that Theophrastus attributes the first use of the term, arché, not apeiron, to Anaximander. If we understand the apeiron as the ground of process, of becoming, then it is not surprising that he should adopt a word like arché, with its distinctively temporal connotation, as "beginning." It appears a matter of universal agreement that Anaximander could not have intended the word to have the Peripatetic sense of "principle," and it hardly seems worth while arguing the point. However, granted that arché for Anaximander does not mean "principle" in an Aristotelean sense, it is evident that it means more than merely a temporal beginning. Obviously, if a ring or a turning wheel is "endless," it also is without an absolute beginning; or, to put it more precisely, any arbitrarily-chosen end-point is also a beginning, and vice-versa. On the cyclical interpretation of nature, we cannot identify any event within nature which is its beginning. Hence, Anaximander's refusal to identify the apeiron with any of the "so-called elements." This, then, stands as a clarification of the reason for the indefiniteness of the apeiron.

Now, the arché cannot be the "first member" of a linear series, for it is not any "part" of the series, and this is why it is more than a mere temporal beginning. Anaximander's use of the term, arché, was intended, not to locate a starting point, but rather to call our attention to the essentially temporal nature of his worldview. It is the view of this paper that, although his arché is not an Aristotelean "principle," it is nevertheless a principle, and more than a beginning of a series.

An aspect of Anaximander's worldview which is too often overlooked by modern interpreters is the order exhibited by nature, which suggests a turning wheel, a circle. This order is explicitly named by the phrases, "according to what should be," and "each in the proper time;" it is not merely that nature is cyclical, but that the seasons follow always in the same order, taking turns one by one, and that this order is "as it should be." What calls for explanation, in Anaximander's mind, is not the existence of "things," but the sequential order of events. The give and take of "compensation and reparation for injustice" is not chaotic; injustice participates in the ordered whole on an equal footing with justice. Imbalance requires balance—the pendulum, to keep swinging, must go past balance to imbalance. Beyond justice and injustice there is a rational order. But what is this order? Is it a deity or an impersonal entity? Is it Heraclitus' reified logos? Is it "mind"? None of these possibilities touches on what Anaximander named apeiron, because they are all definite, and he insisted on its indefiniteness. Let us return to our understanding of apeiron as the "endlessness" of a ring, a sphere, a turning wheel. The endlessness is a characteristic of the whole ring, not of any part, in the same sense that infinity is the property of the total number-series, and not of any single number. What is apeiron, endless, is nature in its overarching, synthetic wholeness. Nature as a whole is arché, ground, in the sense that before there can be parts, there must be a whole; before we can talk about a segment of a ring, we must have the whole ring; it is from the whole that any analysis must begin—Anaximander is embracing the doctrine of the priority of the whole to the parts. The apeiron, then, is the ground, in the sense that by virtue of its wholeness and orderliness, there are parts, and they are parts of a process. It is by virtue of an underlying and all-embracing unity that the elements may commit injustices upon one another, and make repayment. Opposites must be opposites on some common ground, or they cannot be opposites, they cannot be in conflict.³⁵ The apeiron, then, is the ground upon which the ceaseless conflict of the elements is permitted to take place; it is at once the possibility of their conflict, and that which unifies them. It is not the sum of all that is in nature, but it is the intelligible order of nature. Anaximander is without a doubt deeply imbedded in the synthetic tradition of philosophy, insofar as that division into "analytic" and "synthetic" has validity, and most of the misinterpretations of his thought are due to approaching him analytically. Understood in this way, as synthetic unity, we can understand why Anaximander attributes "surrounding and guiding all" to his arché.

Notes

¹ Kahn, C. H., Anaximander and the Origins of Greek Cosmology, New York: Columbia University Press, 1958, p. 121.

²Ibid., loc. cit.; quoted from Aristotle, Metaphysics 3,1014,a6f.

³Ibid., pp. 181 ff.

⁴Ibid., p. 232.

⁵Ibid., p. 233.

⁶ Kirk, G. S., and Raven, J. E., The Presocratic Philosophers, Cambridge: Cambridge University Press, 1966, p. 108.

⁷"Ibid., p. 112.

⁸Ibid., p. 114.

⁹Ibid., p. 111.

¹⁰ For examples, note: W. Windelband, History of Ancient Philosophy, and A History of Philosophy, vol. I, New York: Harper Torchbooks, 1958: and also, Zeller's Die Philosophie der Griechen, 7th éd., Leipzig, 1923.

¹¹ Kirk and Raven, op. cit., p. 109; Guthrie, W. K. C, A History of Greek Philosophy, vol. I, Cambridge: Cambridge University Press, 1962, p. 85; also Kahn, op. cit., p. 233.

¹² The wording is Kahn's, he. cit.

¹³ Kirk and Raven, loc. cit.

¹⁴ Guthrie, op. cit., p. 84.

¹⁵ See Windelband, A History of Philosophy, vol. I, New York: Harper, 1958, p. 33.

¹⁶ Kirk and Raven, op. cit., p. 109, and Kahn, op. cit., pp. 232f.

¹⁷ Kirk and Raven, op. cit., pp. 109f.

¹⁸ Kirk and Raven, op. cit., pp. 113f.

¹⁹ Cornford, F. M., Principium Sapientiae, New York: Harper & Row, 1952, p. 159.

²⁰ Seligman, P., The Apeiron of Anaximander, London: University of London Press, 1962, p. 24.

²¹Ibid., p. 29.

²² Simplicius, Physics 1121,5.

²³ Aristotle, Physics 4,203b7.

²⁴ Cf. Kirk and Raven, op. cit., pp. 114f.

²⁵ Jaeger, W., Die Theologie der frühen Griechischen Denker, Stuttgart: W. Kohlhammer Verlag, 1964, pp. 37f.

²⁶Ibid., p. 38.

²⁷ Kirk and Raven, op. cit., p. 108.

²⁸Loc. cit.

²⁹ Kahn, op. cit., p. 30.

³⁰Loc. cit.

³¹ Cf. Cornford, op. cit., p. 168; Kirk and Raven, op. cit., p. 119, and Kahn, op. cit., p. 150, where the latter argues that Anaximander did not restrict the elements to four only.

³² Seligman, op. cit., p. 72.

³³Ibid., p. 111.

³⁴ Kirk and Raven, op. cit., p. 119.

³⁵ Cf. Kirk and Raven, op. cit., pp. 118f.