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A compendium of articles

Anaximander (609/610 BC – c. 547 BC) was the second of the physical philosophers of Ionia, a citizen of Miletus, and a companion or pupil of Thales. Little is known of his life and work. Aelian makes him the leader of the Milesian colony to Amphipolis, and hence some have inferred that he was a prominent citizen. The computations of Apollodorus of Athens have fixed his birth in 611, and his death shortly after 547 B.C. Ancient sources represent him as a successful student of astronomy and geography, and an early proponent of exact science. He has also been said to have introduced such astronomical instruments as the sundial and the gnomon to ancient Greece.

Cosmology and the apeiron

Anaximander's reputation is due mainly to a cosmological work, little of which remains. From the few extant fragments, we learn that he believed the beginning or first principle (arche, a word first found in Anaximander's writings, and which he probably invented) is an endless, unlimited mass (apeiron), subject to neither old age nor decay, which perpetually yields fresh materials from which everything we can perceive is derived. He never defined this principle precisely, and it has generally (e.g. by Aristotle and Augustine) been understood as a sort of primal chaos. It embraced the opposites of hot and cold, wet and dry, and directed the movement of things, by which there grew up all of the host of shapes and differences which are found in the world. Out of the vague and limitless body there sprung a central mass — this earth of ours, cylindrical in shape, poised equidistant from surrounding orbs of fire, which had originally clung to it like the bark round a tree, until their continuity was severed, and they parted into several wheel-shaped and fire-filled bubbles of air. Man himself and the animals had come into being by like transmutations. Mankind was supposed by Anaximander to have sprung from some other species of animals, probably aquatic. For this, even though he had no theory of natural selection, some people consider him to be evolutionary theory's most ancient proponent.

Anaximander offered up the theory of the apeiron in direct response to the earlier theory of Thales, who had claimed that the primary substance was water. Anaximander reasoned that water cannot embrace all of the opposites found in nature — for example, water can only be wet, never dry — and therefore, it can not be the one primary substance. Nor could any of the other candidates, so Anaximander postulated the apeiron as a substance that, although it could not be perceived directly, could explain the opposites he could clearly see around him.

Known Works

On Nature, circa ? (fragment survives): Subject –  Philosophy
Referenced in Simplicus

• Map, circa ? (lost): Subject -- (First?) Map of the Known World
Referenced in  Agathemerus, Geographie informatio

Some of Anaximander's ideas were also preserved in Theophrastus's (lost) history of philosophy, and re-quoted by later authors.

A compendium of articles:

1.Anaximander Orders the Cosmos
2.Anaximander (c. 610 -546 BCE)
3.Anaximander Fragments and Commentary
4.Anaximander: A lecture
5.Greek astronomy
6.The trigonometric functions
7.The history of cartography.

1. Anaximander Orders the Cosmos
By Robert Adler

Anaximander of Miletus, the pupil of Thales, was the first to depict the inhabited Earth on a chart. After him Hecataeus of Miletus, a much travelled man, made it more precise so as to he a thing of wonder.
-the geographer Agathemerus

What the system of Anaximander represents for us is nothing less than the advent, in the West at any rate, of a rational outlook    the natural world.
-Charles H. Kuhn

Anaximander ((c. 610 B.C.-e. 546 B.C.) was an incredibly bold thinker. With great expansiveness of mind he asked, and answered, one of the prototypical questions of early Greek science-how did the world come to be? Realizing that the substances and qualities we perceive inevitably change amid pass away, he postulated the existence of the apeiron, "the boundless." The apeiron was material, but with no beginning or end in time or space. It served as both the source and fate of everything we see. The enormity of that concept forced him to drastically revise the status of the Earth. To Anaximander the Earth, in fact our whole cosmos, is not only finite in size and limited in duration, but is just one of an in-finite number of worlds. What an amazing-and chilling-degree of objectivity to be achieved more than 2,500 years ago.

Who was this remarkably imaginative man? Like his mentor, Thales, we know little about him. Anaximander, son of Praxiades, was born in Miletus. One source tells us he was sixty-four years old around 546 B.C. He is said to have led a political delegation to Sparta, where he presented the Spartans with two of his great innovations-a sundial and his map of the world. He may have founded a new Milesian colony in Apollonia, near the Black Sea. There's a tradition that he was something of a showman, dressing and speaking dramatically. He was the first philosopher to write his ideas down in prose rather than in the poetic tradition of Homer or Hesiod. It's a measure of how long ago he lived, and how many layers of history separate us from him, that only one cryptic sentence survives of all he wrote:

‘That from which all things are born is also the cause of their coming to an end, as is meet, for they pay reparations and atonement unto each other for their mutual injustice in the order of time.’

Anaximander created the first coherent naturalistic system of the world. He believed that a primordial undifferentiated substance, "the Boundless," has always existed and is always in motion. Just as flowing water can spontaneously spawn a whirlpool, the boundless spontaneously generated the rotating germ or seed of the world. Once formed, the qualities of hot and cold, and later of dry and wet, separated out and began to interact. The hottest material moved outward, leaving a cool, wet interior surrounded by a fiery shell. The intense heat caused moisture to evaporate, building up pressure and eventually blasting the shell apart. Its remnants coalesced into rotating rings of fire surrounded by opaque tubes of mist. Eventually the heat evaporated enough water to expose dry land, creating the Earth on which life eventually emerged. Light blazing out through openings in the fiery tubes appears to us as the Sun, the Moon, and the stars. Rhythmic changes in the openings cause the phases of the Moon as well as eclipses of the Sun and Moon.

One of Anaximander's remarkable accomplishments was to pro-pose an evolutionary theory twenty-three centuries before Darwin. Anaximander argued that all land animals, including humans, evolved from fishlike ancestors. He thought that the earliest forms of life arose spontaneously through the interaction of primordial warmth and moisture. Those first creatures, protected by bark-like shells, lived in the seas. As dry land appeared, some were faced with the problem of adapting to new conditions. Again Anaximander shows the remarkable extent to which he was able to free himself from any trace of anthropocentrism. Humans evolved from water creatures just as did all other land animals, with one difference. Because human infants are so helpless at birth, he surmised that they must have been nurtured by some other kind of sea creature before they could survive on land.

Clearly, Anaximander did not create a full-blown theory of evolution capable of explaining the descent of all creatures. That would be left for Darwin to accomplish. Still, Anaximander caught at least a glimpse of evolution. As in Darwin's day and our own, it's an idea that many people found disturbing. Writing 150 years after Anaximander, Plato chose to believe in the transmigration of souls, first taught by Pythagoras. Plato turned the idea into a kind of reverse evolution, arguing that immoral or stupid men were reborn as animals (or as women). It's not difficult to guess whom Plato was skewering when he said, "The fourth kind of animal, whose habitat is water, came from the most utterly mindless men."

Mindless or not, Anaximander understood and utilized one of the basic assumptions of science-that the same processes that take place on Earth must occur throughout the universe. This belief led Newton, twenty-two centuries later, to propose the law of universal gravitation, which explains both the fall of an apple and the orbit of the moon. Anaximander realized that the same sequence of events that spawned the Earth and the bodies around it must occur over and over within the boundless, at many other places and times. So he boldly pro-claimed that there must be an infinite number of worlds that, like our own, are born, exist for a time, and, "paying reparations," cycle back into nothingness.

Anaximander's conceptualization of the boundless allowed him to solve a problem that had bedevilled his mentor, Thales, and would stymie his successor, Anaximenes. In their attempt to give a satisfactory answer to the question of what kept the Earth in place, Thales had it floating on water and Anaximenes saw it cushioned on air, but neither of them explained what held up the supporting substance. Anaximander, with his characteristic incisiveness, divorced himself completely from the earthbound sensory evidence of up and down. He envisioned the Earth at rest within an infinite, symmetrical universe. Why should it fall? It was in equilibrium, "not dominated by anything," and there-fore had no more reason to move in one direction than another. In this, as in many other of his ideas, he was far ahead of his time.

Once he had freed the Earth from its supports and could visualize it floating freely within the cosmos, Anaximander could also surmise that it had another, potentially habitable side. He pictured the Earth as a short, drum-shaped cylinder. The flat surfaces, he thought, are three times larger in diameter than the distance between them. The inhabited world forms one of the flat surfaces. We don't know if he believed that people lived on die opposite surface. However, someone who could envision an infinite number of worlds almost certainly would not have balked at picturing humans on the other side of the Earth.

Anaximander reduced the Earth to an infinitesimal dot in a boundless universe, but he also made it a worthy object of study in its own right. Later geographers identified him as the first to draw a map of the world. Since there are surviving examples of extremely simple world maps from Babylonia from about the same time, he may well have been inspired by examples he had seen or heard described. His map has not survived, but it most likely showed the inhabited surface of the Earth as a circle completely ringed by an ocean. The known landmasses may have been shown surrounding what we now know as the Mediterranean Sea. It probably stretched as far west as the Pillars of Hercules-our Gibraltar-east to Babylonia, north into Europe, and south into Libya. Inspired by Anaximander, mapmaking progressed rapidly. A few decades later another Milesian, Hecataeus, would improve Anaximander's map based in part on his own extensive travels, making it "a thing of wonder." Writing just a century after Anaximander's death, the historian Herodotus found the old circular maps laughable out of date.

Anaximander's interest in mapping was not limited to the Earth. He is also said to have produced a map of the heavens in the form of a sphere. He appears to have divided up the heavenly sphere into bands, some of which crossed the others. This may he why he is said to have discovered the obliquity of the ecliptic. We don't know the details, but if in fact he mapped the heavens as a sphere, it would have been an extremely significant step. The Babylonians and Egyptians, with whom the ancient Greeks had contact, had accumulated centuries of astronomical observations. They had noticed patterns within them, which they used to keep their calendars in order and to make predictions. But they had not come up with a physical model of the heavens. Anaximander may have been the first to wed Eastern astronomy to Greek geometry, in the process creating a powerful unifying system.

The details of Anaximander’s cosmology, like his sketchy map, may now seem laughable. But by envisioning the cosmos as an understandable whole, and by insisting that its origin, development, observable phenomena, and fate can all be explained as the dynamic interaction of basic and universal laws "in the order of time," he set in place the conceptual foundation of science.


2. Anaximander (c. 610 -546 BCE)
Taken from the Internet Encyclopaedia of Philosophy

Anaximander was the author of the first surviving lines of Western philosophy. He speculated and argued about 'the Boundless' as the origin of all that is. He also worked on the fields of what we now call geography and biology. Moreover, Anaximander was the first speculative astronomer. He originated the world-picture of the open universe, which replaced the closed universe of the celestial vault.

Table of Contents
Life and sources
The 'Boundless' as principle
The arguments regarding the Boundless
The Boundless has no origin
The origin must be boundless
The 'long since' argument
The fragment
The origin of the cosmos
Speculative astronomy
The celestial bodies make full circles
The earth floats unsupported in space
Why the earth does not fall
The celestial bodies lie behind one another
The order of the celestial bodies
The celestial bodies as wheels
The distances of the celestial bodies
A representation of Anaximander's universe
Map of the world
Suggestions for Further Reading

Life and sources

The history of written Greek philosophy starts with Anaximander of Miletus in Asia Minor, a fellow-citizen of Thales. He was the first who dared to write a treatise in prose, which has been called traditionally On Nature. This book has been lost, although it probably was available in the library of the Lyceum at the times of Aristotle and his successor Theophrastus. It is said that Apollodorus, in the second century BCE, stumbled upon a copy of it, perhaps in the famous library of Alexandria. Recently, evidence has appeared that it was part of the collection of the library of Taormina in Sicily, where a fragment of a catalogue has been found, on whichAnaximander's name can be read. Only one fragment of the book has come down to us, quoted by Simplicius (after Theophrastus), in the sixth century AD. It is perhaps the most famous and most discussed phrase in the history of philosophy.

We also know very little of Anaximander's life. He is said to have led a mission that founded a colony called Apollonia on the coast of the Black Sea. He also probably introduced the gnomon (a perpendicular sun-dial) into Greece and erected one in Sparta. So he seems to have been a much-traveled man, which is not astonishing, as the Milesians were known to be audacious sailors. It is also reported that he displayed solemn manners and wore pompous garments. Most of the information on Anaximander comes from Aristotle and his pupil Theophrastus, whose book on the history of philosophy was used, excerpted, and quoted by many other authors, the so-called doxographers, before it was lost. Sometimes, in these texts words or expressions appear that can with some certainty be ascribed to Anaximander himself. Relatively many testimonies, approximately one third of them, have to do with astronomical and cosmological questions. Hermann Diels and Walter Kranz have edited the doxography (A) and the existing texts (B) of the Presocratic philosophers in Die Fragmente der Vorsokratiker, Berlin 1951-19526. (A quotation like "DK 12A17" means: "Diels/Kranz, Anaximander, doxographical report no.17".)

The 'Boundless' as principle

According to Aristotle and Theophrastus, the first Greek philosophers were looking for the 'origin' or 'principle' (the Greek word 'archê' has both meanings) of all things. Anaximander is said to have identified it with 'the Boundless' or 'the Unlimited' (Greek: 'apeiron', i.e. 'that which has no boundaries'). Already in ancient times, it is complained that Anaximander did not explain what he meant by 'the Boundless'. More recently, authors have disputed whether the Boundless should be interpreted as spatially or temporarily without limits, or perhaps as that which has no qualifications, or as that which is inexhaustible. Some scholars have even defended the meaning 'that which is not experienced', by relating the Greek word 'apeiron' not to 'peras' ('boundary', 'limit'), but to 'perao' ('to experience', 'to apperceive'). The suggestion, however, is almost irresistible that Greek philosophy, by making the Boundless into the principle of all things, has started on a high level of abstraction. On the other hand, some have pointed out that this use of 'apeiron' is atypical for Greek thought, which was occupied with limit, symmetry and harmony. The Pythagoreans placed the boundless (the 'apeiron') on the list of negative things, and for Aristotle, too, perfection became aligned with limit (Greek: 'peras'), and thus 'apeiron' with imperfection. Therefore, some authors suspect eastern (Iranian) influence on Anaximander's ideas.

The arguments regarding the Boundless

It seems that Anaximander not only put forward the thesis that the Boundless is the principle, but also tried to argue for it. We might say that he was the first who made use of philosophical arguments. Anaximander's arguments have come down to us in the disguise of Aristotelian jargon. Therefore, any reconstruction of the arguments used by the Milesian must remain conjectural. Verbatim reconstruction is of course impossible. Nevertheless, the data, provided they are handled with care, allow us to catch glimpses of what the arguments of Anaximander must have looked like. The important thing is, however, that he did not just utter apodictic statements, but also tried to give arguments. This is what makes him the first philosopher.

The Boundless has no origin

Aristotle reports a curious argument, which probably goes back to Anaximander, in which it is argued that the Boundless has no origin, because it is itself the origin. We would say that it looks more like a string of associations and word-plays than like a formal argument. It runs as follows: "Everything has an origin or is an origin. The Boundless has no origin. For then it would have a limit. Moreover, it is both unborn and immortal, being a kind of origin. For that which has become has also, necessarily, an end, and there is a termination to every process of destruction" (Physics 203b6-10, DK 12A15). The Greeks were familiar with the idea of the immortal Homeric gods. Anaximander added two distinctive features to the concept of divinity: his Boundless is an impersonal something (or 'nature', the Greek word is 'phusis'), and it is not only immortal but also unborn. However, perhaps not Anaximander, but Thales should be credited with this new idea. Diogenes Laërtius ascribes to Thales the aphorism: "What is the divine? That which has no origin and no end" (DK 11A1 (36)). Similar arguments, within different contexts, are used by Melissus (DK 30B2[9]) and Plato (Phaedrus 245d1-6).

The origin must be boundless

Several sources give another argument which is somehow the other way round and answers the question of why the origin should be boundless. In Aristotle's version, it runs like this: "(The belief that there is something Boundless stems from) the idea that only then genesis and decay will never stop, when that from which is taken what has been generated, is boundless" (Physics 203b18-20, DK 12A15, other versions in DK12A14 and 12A17). In this argument, the Boundless seems to be associated with an inexhaustible source. Obviously, it is taken for granted that "genesis and decay will never stop", and the Boundless has to guarantee the ongoing of the process, like an ever-floating fountain.

The 'long since' argument

A third argument is relatively long and somewhat strange. It turns on one key word (in Greek: 'êdê'), which is here translated with 'long since'. It is reproduced by Aristotle: "Some make this (viz. that which is additional to the elements) the Boundless, but not air or water, lest the others should be destroyed by one of them, being boundless; for they are opposite to one another (the air, for instance, is cold, the water wet, and the fire hot). If any of them should be boundless, it would long since have destroyed the others; but now there is, they say, something other from which they are all generated" (Physics 204b25-29, DK 12A16).

This is not only virtually the same argument as used by Plato in his Phaedo (72a12-b5), but even more interesting is that it was used almost 2500 years later by Friedrich Nietzsche in his attempts to prove his thesis of the Eternal Recurrence: "If the world had a goal, it would have been reached. If there were for it some unintended final state, this also must have been reached. If it were at all capable of a pausing and becoming fixed, if it were capable of 'being', if in the whole course of its becoming it possessed even for a moment this capability of 'being', then again all becoming would long since have come to an end." Nietzsche wrote these words in his notebook in 1885, but already in Die Philosophie im tragischen Zeitalter der Griechen (1873), which was not published during his lifetime, he mentioned the argument and credited Anaximander with it.

The fragment

The only existing fragment of Anaximander's book (DK 12B1) is surrounded by all kinds of questions. The ancient Greeks did not use quotation marks, so that we cannot be sure where Simplicius, who has handed down the text to us, is still paraphrasing Anaximander and where he begins to quote him. The text is cast in indirect speech, even the part which most authors agree is a real quotation. One important word of the text ('allêlois', here translated by 'upon one another') is missing in some manuscripts. As regards the interpretation of the fragment, it is heavily disputed whether it means to refer to Anaximander's principle, the Boundless, or not. The Greek original has relative pronouns in the plural (here rendered by 'whence' and 'thence'), which makes it difficult to relate them to the Boundless. However, Simplicius' impression that it is written in rather poetic words has been repeated in several ways by many authors. Therefore, we offer a translation, in which some poetic features of the original, such as chiasmus and alliteration have been imitated:

Whence things have their origin,
Thence also their destruction happens,
As is the order of things;
For they execute the sentence upon one another
- The condemnation for the crime -
In conformity with the ordinance of Time.

In the fourth and fifth line a more fluent translation is given for what is usually rendered rather cryptic by something like "giving justice and reparation to one another for their injustice."
We may distinguish roughly two lines of interpretation, which may be labelled the 'horizontal' and the 'vertical'. The horizontal interpretation holds that in the fragment nothing is said about the relation of the things to the Boundless, whereas the vertical interpretation maintains that the fragment describes the relationship of the things to the Boundless. The upholders of the horizontal interpretation usually do not deny that Anaximander taught that all things are generated from the Boundless, but they simply hold that this is not what is said in the fragment. They argue that the fragment describes the battle between the elements (or of things in general), which accounts for the origin and destruction of things. The most obvious difficulty, however, for this 'horizontal' interpretation is that it implies two cycles of becoming and decay: one from and into the Boundless, and the other caused by the mutual give and take of the elements or things in general. In other words, in the 'horizontal' interpretation the Boundless is superfluous. This is the strongest argument in favour of the 'vertical' interpretation, which holds that the fragment refers to the Boundless, notwithstanding the plural relative pronouns. According to the 'vertical' interpretation, then, the Boundless should be regarded not only as the ever-flowing fountain from which everything ultimately springs, but also as the yawning abyss (as some say, comparable with Hesiod's 'Chaos') into which everything ultimately perishes.

The suggestion has been raised that Anaximander's formula in the first two lines of the fragment should have been the model for Aristotle's definition of the 'principle' (Greek: 'archê') of all things in Metaphysics 983b8. There is some sense in this suggestion. For what could be more natural for Aristotle than to borrow his definition of the notion of 'archê', which he uses to indicate the principle of the first pre-Socratic philosophers, from Anaximander, the one who introduced the notion?
It is certainly important that we possess one text from Anaximander's book. On the other hand, we must recognize that we know hardly anything of its original context, as the rest of the book has been lost. We do not know from which part of his book it is, nor whether it is a text the author himself thought crucial or just a line that caught one reader's attention as an example of Anaximander's poetic writing style. The danger exists that we are tempted to use this stray text - beautiful and mysterious as it is - in order to produce all kinds of profound interpretations that are hard to verify. Perhaps a better way of understanding what Anaximander has to say is to study carefully the doxography, which goes back to people like Aristotle and Theophrastus, who probably have had Anaximander's book before their eyes, and who tried to reformulate what they thought were its central claims.

The origin of the cosmos

The Boundless seems to have played a role in Anaximander's account of the origin of the cosmos. Its eternal movement is said to have caused the origin of the heavens. Elsewhere, it is said that "all the heavens and the worlds within them" have sprung from "some boundless nature". A part of this process is described in rather poetic language, full of images, which seems to be idiosyncratic for Anaximander: "a germ, pregnant with hot and cold, was separated [or: separated itself] off from the eternal, whereupon out of this germ a sphere of fire grew around the vapour that surrounds the earth, like a bark round a tree" (DK 12A10). Subsequently, the sphere of fire is said to have fallen apart into several rings, and this event was the origin of sun, moon, and stars. There are authors who have, quite anachronistically, seen here a kind of foreshadowing of the Kant-Laplace theory of the origin of the solar system. Some sources even mention innumerable worlds (in time and/or in space), which looks like a plausible consequence of the Boundless as principle. But this is presumably a later theory, incorrectly read back into Anaximander.


At first sight, the reports on Anaximander's astronomy look rather bizarre and obscure. Some authors even think that they are so confused that we should give up trying to offer a satisfying and coherent interpretation. The only way of understanding Anaximander's astronomical ideas, however, is to take them seriously and treat them as such, that is, as astronomical ideas. It will appear that many of the features of his universe that look strange at first sight make perfect sense on closer inspection.

Speculative astronomy

The astronomy of neighbouring peoples, such as the Babylonians and the Egyptians, consists mainly of observations of the rising and disappearance of celestial bodies and of their paths across the celestial vault. These observations were made with the naked eye and with the help of some simple instruments as the gnomon. The Babylonians, in particular, were rather advanced observers. Archaeologists have found an abundance of cuneiform texts on astronomical observations. In contrast, there exists only one report of an observation made by Anaximander, which concerns the date on which the Pleiades set in the morning. This is no coincidence, for Anaximander's merits do not lie in the field of observational astronomy, unlike the Babylonians and the Egyptians, but in that of speculative astronomy. We may discern three of his astronomical speculations:

(1) That the celestial bodies make full circles and pass also beneath the earth,
(2) That the earth floats free and unsupported in space, and
(3) That the celestial bodies lie behind one another.

Notwithstanding their rather primitive outlook, these three propositions, which make up the core of Anaximander's astronomy, meant a tremendous jump forward and constitute the origin of our Western concept of the universe.

(1) The celestial bodies make full circles

The idea that the celestial bodies, in their daily course, make full circles and thus pass also beneath the earth - from Anaximander's viewpoint - is so self-evident to us that it is hard to understand how daring its introduction was. That the celestial bodies make full circles is not something he could have observed, but a conclusion he must have drawn. We would say that this is a conclusion that lies to hand. We can see - at the northern hemisphere, like Anaximander - the stars around the Polar star making full circles, and we can also observe that the more southerly stars sometimes disappear behind the horizon. We may argue that the stars of which we see only arcs in reality also describe full circles, just like those near the Polar star. As regards the sun and moon, we can observe that the arcs they describe are sometimes bigger and sometimes smaller, and we are able to predict exactly where they will rise the next day. Therefore, it seems not too bold a conjecture to say that these celestial bodies also describe full circles. Nevertheless, it was a daring conclusion, precisely because it necessarily entailed the concept of the earth hanging free and unsupported in space.

(2) The earth floats unsupported in space

Anaximander boldly asserts that the earth floats free in the centre of the universe, unsupported by water, pillars, or whatever. This idea means a complete revolution in our understanding of the universe. Obviously, the earth hanging free in space is not something Anaximander could have observed. Apparently, he drew this bold conclusion from his assumption that the celestial bodies make full circles. More than 2500 years later astronauts really saw the unsupported earth floating in space and thus provided the ultimate confirmation of Anaximander's conception. The shape of the earth, according to Anaximander, is cylindrical, like a column-drum, its diameter being three times its height. We live on top of it. Some scholars have wondered why Anaximander chose this strange shape. The strangeness disappears, however, when we realize that Anaximander thought that the earth was flat and circular, as suggested by the horizon. For one who thinks, as Anaximander did, that the earth floats unsupported in the centre of the universe, the cylinder-shape lies at hand.

Why the earth does not fall
We may assume that Anaximander somehow had to defend his bold theory of the free-floating, unsupported earth against the obvious question of why the earth does not fall. Aristotle's version of Anaximander's argument runs like this: "But there are some who say that it (viz. the earth) stays where it is because of equality, such as among the ancients Anaximander. For that which is situated in the centre and at equal distances from the extremes, has no inclination whatsoever to move up rather than down or sideways; and since it is impossible to move in opposite directions at the same time, it necessarily stays where it is." (De caelo 295b10ff., DK 12A26) Many authors have pointed to the fact that this is the first known example of an argument that is based on the principle of sufficient reason (the principle that for everything which occurs there is a reason or explanation for why it occurs, and why this way rather than that).

Anaximander's argument returns in a famous text in the Phaedo (108E4 ff.), where Plato, for the first time in history, tries to express the sphericity of the earth. Even more interesting is that the same argument, within a different context, returns with the great protagonist of the principle of sufficient reason, Leibniz. In his second letter to Clarke, he uses an example, which he ascribes to Archimedes but which reminds us strongly of Anaximander: "And therefore Archimedes (...) in his book De aequilibrio, was obliged to make use of a particular case of the great Principle of a sufficient reason. He takes it for granted that if there be a balance in which everything is alike on both sides, and if equal weights are hung on the two ends of that balance, the whole will stay at rest. This is because there is no reason why one side should weigh down, rather than the other".

One may doubt, however, whether the argument is not fallacious. Aristotle already thought the argument to be deceiving. He ridicules it by saying that according to the same kind of argument a hair, which was subject to an even pulling power from opposing sides, would not break, and that a man, being just as hungry as thirsty, placed in between food and drink, must necessarily remain where he is and starve. To him it was the wrong argument for the right proposition. Absolute propositions concerning the non-existence of things are always in danger of becoming falsified on closer investigation. They contain a kind of subjective aspect: 'as far as I know'. Several authors, however, have said that Anaximander's argument is clear and ingenious. Already at first sight this qualification sounds strange, for the argument evidently must be wrong, as the earth is not in the centre of the universe, although it certainly is not supported by anything but gravity. Nevertheless, we have to wait until Newton for a better answer to the question why the earth does not fall.

(3) The celestial bodies lie behind one another

When Anaximander looked at the heaven, he imagined, for the first time in history, space. Anaximander's vision implied depth in the universe, that is, the idea that the celestial bodies lie behind one another. Although it sounds simple, this is a remarkable idea, because it cannot be based on direct observation. We do not see depth in the universe. The more natural and primitive idea is that of the celestial vault, a kind of dome or tent, onto which the celestial bodies are attached, all of them at the same distance, like in a planetarium. One meets this kind of conception in Homer, when he speaks of the brazen or iron heaven, which is apparently conceived of as something solid, being supported by Atlas, or by pillars.

The order of the celestial bodies

Anaximander placed the celestial bodies in the wrong order. He thought that the stars were nearest to the earth, then followed the moon, and the sun farthest away. Some authors have wondered why Anaximander made the stars the nearest celestial bodies, for he should have noticed the occurrence of star-occultations by the moon. This is a typical anachronism, which shows that it not easy to look at the phenomena with Anaximander's eyes. Nowadays, we know that the stars are behind the moon, and thus we speak of star-occultation when we see a star disappear behind the moon. But Anaximander had no reason at all, from his point of view, to speak of a star-occultation when he saw a star disappear when the moon was at the same place. So it is a petitio principii to say that for him occultations of stars were easy to observe. Perhaps he observed stars disappearing and appearing again, but he did not observe - could not see it as - the occultation of the star, for that interpretation did not fit his paradigm. The easiest way to understand his way of looking at it - if he observed the phenomenon at all - is that he must have thought that the brighter light of the moon outshines the much smaller light of the star for a while. Anaximander's order of the celestial bodies is clearly that of increasing brightness. Unfortunately, the sources do not give further information of his considerations at this point.

The celestial bodies as wheels

A peculiar feature of Anaximander's astronomy is that the celestial bodies are said to be like chariot wheels (the Greek words for this image are presumably his own). The rims of these wheels are of opaque vapour, they are hollow, and filled with fire. This fire shines through at openings in the wheels, and this is what we see as the sun, the moon, or the stars. Sometimes, the opening of the sun wheel closes: then we observe an eclipse. The opening of the moon wheel regularly closes and opens again, which accounts for the phases of the moon. This image of the celestial bodies as huge wheels seems strange at first sight, but there is a good reason for it. There is no doxographic evidence of it, but it is quite certain that the question of why the celestial bodies do not fall upon the earth must have been as serious a problem to Anaximander as the question of why the earth does not fall. The explanation of the celestial bodies as wheels, then, provides an answer to both questions. The celestial bodies have no reason whatsoever to move otherwise than in circles around the earth, as each point on them is always as far from the earth as any other. It is because of reasons like this that for ages to come, when Anaximander's concept of the universe had been replaced by a spherical one, the celestial bodies were thought of as somehow attached to crystalline or ethereal sphere-shells, and not as free-floating bodies.

Many authors, following Diels, make the image of the celestial wheels more difficult than is necessary. They say that the light of a celestial bodies shines through the openings of its wheel 'as through the nozzle of a bellows'. This is an incorrect translation of an expression that probably goes back to Anaximander himself. The image of a bellows, somehow connected to a celestial wheel, tends to complicate rather than elucidate the meaning of the text. If we were to understand that every celestial body had such a bellows, the result would be hundreds of nozzles (or pipes), extending from the celestial wheels towards the earth. Anaximander's intention, however, can be better understood not as an image, but as a comparison of the light of the celestial bodies with that of lightning. Lightning, according to Anaximander, is a momentary flash of light against a dark cloud. The light of a celestial body is like a permanent beam of lightning fire that originates from the opaque cloudy substance of the celestial wheel.

The distances of the celestial bodies

The doxography gives us some figures about the dimensions of Anaximander's universe: the sun wheel is 27 or 28 times the earth, and the moon wheel is 19 times the earth. More than a century ago, two great scholars, Paul Tannery and Hermann Diels, solved the problem of Anaximander's numbers. They suggested that the celestial wheels were one unit thick, this unit being the diameter of the earth. The full series, they argued, had to be: 9 and 10 for the stars, 18 and 19 for the moon, and 27 and 28 for the sun. These numbers are best understood as indicating the distances of the celestial bodies to the earth. In others words, they indicate the radii of concentric circles, made by the celestial wheels, with the earth as the centre. See Figure 1, a plane view of Anaximander's universe.

Plane view of Anaximander's Universe

These numbers cannot be based on observation. In order to understand their meaning, we have to look at Hesiod's Theogony 722-725, where it is said that a brazen anvil would take nine days to fall from heaven to earth before it arrives on the tenth day. It is not a bold guess to suppose that Anaximander knew this text. The agreement with his numbers is too close to neglect, for the numbers 9 and 10 are exactly those extrapolated for Anaximander's star wheel. Hesiod can be seen as a forerunner to Anaximander, for he tried to imagine the distance to the heaven. In the Greek counting system Hesiod's numbers should be taken to mean 'a very long time'. Thus, Troy was conquered in the tenth year after having stood the siege for nine years; and Odysseus scoured the seas for nine years before reaching his homeland in the tenth year. We may infer that Anaximander, with his number 9 (1 x 3 x 3) for the star ring, simply was trying to say that the stars are very far away. Now the numbers 18 and 27 can easily be interpreted as 'farther' (2 x 3 x 3, for the moon ring) and 'farthest' (3 x 3 x 3, for the sun ring). And this is exactly what we should expect one to say, who had discovered that the image of the celestial vault was wrong but that the celestial bodies were behind one another, and who wished to share this new knowledge with his fellow citizens in a language they were able to understand.

A representation of Anaximander's universe

Although it is not attested in the doxography, we may assume that Anaximander himself drew a map of the universe, like that in figure 1. The numbers, 9, 10, 18, etc., can easily be understood as instructions for making such a map. Although Diogenes Laërtius reports that he made a 'sphere', the drawing or construction of a three-dimensional model must be considered to have been beyond Anaximander's abilities. On the other hand, it is quite easy to explain the movements of the celestial bodies with the help of a plan view, by making broad gestures, describing circles in the air, and indicating direction, speed, and inclination with your hands, as is said of a quarrel between Anaxagoras and Oenopides (DK 41A2).

Almost nothing of Anaximander's opinions about the stars has been handed down to us. Probably the best way to imagine them is as a conglomerate of several wheels, each of which has one or more holes, through which the inner fire shines, which we see as stars. The most likely sum-total of these star wheels is a sphere. The only movement of these star wheels is a rotation around the earth from east to west, always at the same speed, and always at the same place relative to one another in the heaven. The sun wheel shows the same rotation from east to west as the stars, but there are two differences. The first is that the speed of the rotation of the sun wheel is not the same as that of the stars. We can see this phenomenon by observing how the sun lags behind by approximately one degree per day. The second difference is that the sun wheel as a whole changes its position in the heaven. In summer it moves towards the north along the axis of the heaven and we see a large part of it above the horizon, whereas in winter we only observe a small part of the sun wheel, as it moves towards the south. This movement of the sun wheel accounts for the seasons. The same holds mutatis mutandis for the moon. Today, we use to describe this movement of the sun (and mutatis mutandis of the moon and the planets) as a retrograde movement, from west to east, which is a counter-movement to the daily rotation from east to west. In terms of Anaximander's ancient astronomy it is more appropriate and less anachronistic to describe it as a slower movement of the sun wheel from east to west. The result is that we see different stars in different seasons, until the sun, at the end of a year, reaches its old position between the stars.

Due to the inclination of the axis of the heaven, the celestial bodies do not circle around the earth in the same plane as the earth's - flat - surface, but are tilted. This inclination amounts to about 38.5 degrees when measured at Delphi, the world's navel. The earth being flat, the inclination must be the same all over its surface. This tilting of the heaven's axis must have been one of the biggest riddles of the universe. Why is it tilted at all? Who or what is responsible for this phenomenon? And why is it tilted just the way it is? Unfortunately, the doxography on Anaximander has nothing to tell us about this problem. Later, other Presocratics like Empedocles, Diogenes of Apollonia, and Anaxagoras discuss the tilting of the heavens.

Although there exists a report that says the contrary, it is not likely that Anaximander was acquainted with the obliquity of the ecliptic, which is the yearly path of the sun along the stars. The ecliptic is a concept which belongs to the doctrine of a spherical earth within a spherical universe. A three-dimensional representation of Anaximander's universe is given in Figures 2 and 3.
3d representation of Anaximander's universe

Map of the world

Anaximander is said to have made the first map of the world. Although this map has been lost, we can imagine what it must have looked like, because Herodotus, who has seen such old maps, describes them. Anaximander's map must have been circular, like the top of his drum-shaped earth. The river Ocean surrounded it. The Mediterranean Sea was in the middle of the map, which was divided into two halves by a line that ran through Delphi, the world's navel. The northern half was called 'Europe', the southern half 'Asia'. The habitable world (Greek: 'oikoumenê') consisted of two relatively small strips of land to the north and south of the Mediterranean Sea (containing Spain, Italy, Greece, and Asia Minor on the one side, and Egypt and Libya on the other side), together with the lands to the east of the Mediterranean Sea: Palestine, Assyria, Persia, and Arabia. The lands to the north of this small 'habitable world' were the cold countries where mythical people lived. The lands to the south of it were the hot countries of the black burnt people.

The doxography tells us that according to Anaximander life originated from the moisture that covered the earth before it was dried up by the sun. The first animals were a kind of fish, with a thorny skin (the Greek word is the same that was used for the metaphor 'the bark of a tree' in Anaximander's cosmology). Originally, men were generated from fishes and were fed in the manner of a viviparous shark. The reason for this is said to be that the human child needs long protection in order to survive. Some authors have, rather anachronistically, seen in these scattered statements a proto-evolutionist theory.

It is no use trying to unify the information on Anaximander into one all-compassing and consistent whole. His work will always remain truncated, like the mutilated and decapitated statue that has been found at the market-place of Miletus and that bears his name. Nevertheless, by what we know of him, we may say that he was one of the greatest minds that ever lived. By speculating and arguing about the 'Boundless' he was the first metaphysician. By drawing a map of the world he was the first geographer. But above all, by boldly speculating about the universe he broke with the ancient image of the celestial vault and became the discoverer of the Western world-picture.

Suggestions for Further Reading

Diels, H. and W. Kranz, Die Fragmente der Vorsokratiker. Zürich/Hildesheim 1964
The standard collection of the texts of and the doxography on Anaximander and the other presocratics.

Guthrie, W.K.C. A History of Greek Philosophy I, The Earlier Presocratics and the Pythagoreans. London/New York 1985 (Cambridge 1962)

 Kirk, G.S., J.E. Raven, and M. Schofield, The Presocratic Philosophers, Cambridge 1995 (1957)
The above two works each have a good survey of Anaximander's thoughts in the context of ancient Greek philosophy, with translations of the most important doxography.

Kahn, C.H. Anaximander and the Origins of Greek Cosmology. New York 1960 (Indianapolis/Cambridge 1994)
A classical study on Anaximander's cosmology and his fragment, also with many translations.

Furley, D.J. and R.E. Allen, eds. Studies in Presocratic Philosophy, Vol. I,
The Beginnings of Philosophy. New York/London 1970
Contains many interesting articles on Anaximander by different authors.

Couprie, D.L., R. Hahn, and G. Naddaf, Anaximander in Context. Albany 2003
A volume with three recent studies on Anaximander.

Kahn, C.H. "Anaximander and the Arguments Concerning the Apeiron at Physics 203b4-1". in: Festschrift E. Kapp, Hamburg 1958, pp.19-29.

 Stokes, M.C. "Anaximander's Argument". in: R.A. Shiner & J. King-Farlow, eds.,
New Essays on Plato and the Presocratics. 1976, pp.1-22.  
Two articles on some of Anaximander's arguments.

Dicks, D.R. "Solstices, Equinoxes, and the Presocratics",
The Journal of Hellenic Studies 86. 1966, pp.26-40
 Kahn, C.H. "On Early Greek Astronomy".
The Journal of Hellenic Studies 90. 1970, pp.99-116
Two conflicting articles on Anaximander's astronomy.

Furley, D.J. The Greek Cosmologists, Volume I, Cambridge 1987
Dicks, D.R. Early Greek Astronomy to Aristotle . Ithaca/New York 1970
Two good books on early Greek astronomy.

Bodnár, I.M. "Anaximander's Rings", Classical Quarterly 38. 1988, pp. 49-51

O'Brien, D. "Anaximander's Measurements", The Classical Quarterly 17. 1967, pp.423-432
Two articles on important details of Anaximander's astronomy.

McKirahan, R. "Anaximander's Infinite Worlds", in A. Preus, ed.,
Essays in Ancient Greek Philosophy VI: Before Plato, Albany 2001, pp. 49-65

A recent article on 'innumerable worlds.'

Heidel, W.A. The Frame of the Ancient Greek Maps.
With a Discussion of the Discovery of the Sphericity of the Earth. New York 1937.
An old but still valuable book on Anaximander's map of the world.

Loenen, J.H.M.M. "Was Anaximander an Evolutionist?" Mnemosyme 4. 1954, pp.215-232
A discussion of Anaximander's biology.

West, M.L. Early Greek Philosophy and the Orient. Oxford 1971.
A discussion of possible Iranian influence on Anaximander.

Conche, M. Anaximandre. Fragments et Témoignages. Paris 1991.
The best book in French.

Classen, C.J. Ansätze. Beiträge zum Verständnis der frühgriechischen Philosophie.
Würzburg/Amsterdam 1986
The best book in German.

3. Anaximander Fragments and Commentary
Arthur Fairbanks, ed. and trans. The First Philosophers of Greece
(London: K. Paul, Trench, Trubner, 1898), 8-16.

Fairbanks's Introduction
Fragments of Anaximandros
Passages relating to Anaximandros in Aristotle
Passages relating to Anaximandros in the Doxographists

Fairbanks's Introduction
Anaximandros of Miletos was a companion or pupil of Thales. According to Apollodoros he was born in the second or third year of the forty-second Olympiad (611-610B.C.). Of his life little is known; Zeller infers from the statement of Aelian (V.H. iii. 17) to the effect that he led the Milesian colony into Apollonia, that he was a man of influence in Miletos. He was a student of geography and astronomy; and various inventions, such as the sundial, are attributed to him. His book, which was referred to as the first philosophical treatise in Greece, may not have received the title "GREEK" until after his death. It soon became rare, and Simplicius does not seem to have had access to it.

The Fragments of Anaximandros
1. 'Immortal and indestructible,' 'surrounds all and directs all.'
2. '(To that they return when they are destroyed) of necessity; for he says that they suffer punishment and give satisfaction to one another for injustice.'

Passages relating to Anaximandros in Aristotle
Arist. Phys. i. 4; 187 a 12. For some who hold that the real, the underlying substance, is a unity, either one of the three [elements] or something else that is denser than fire and more rarefied than air, teach that other things are generated by condensation and rarefaction... 20. And others believe that existing opposites are separated from the unity, as Anaximandros says, and those also who say that unity and multiplicity exist, as Empedokles and Anaxagoras; for these separate other things from the mixture.

Phys. iii. 4; 203 b 7. There is no beginning of the infinite, for in that case it would have an end. But it is without beginning and indestructible, as being a sort of first principle; for it is necessary that whatever comes into existence should have an end, and there is a conclusion of all destruction. Wherefore as we say, there is no first principle of this [i.e. the infinite], but it itself [Page 10] seems to be the first principle of all other things and to surround all and to direct all, as they say who think that there are no other causes besides the infinite (such as mind, or friendship), but that it itself is divine ; for it is immortal and indestructible, as Anaximandros and most of the physicists say.

Simpl. Phys. 32 r; 150, 20. There is another method, according to which they do not attribute change to matter itself, nor do they suppose that generation takes place by a transformation of the underlying substance, but by separation; for the opposites existing in the substance which is infinite matter are separated, according to Anaximandros, who was the earliest thinker to call the underlying substance the first principle. And the opposites are heat and cold, dry and moist, and the rest.

Phys. iii. 5 ; 204 b 22. But it is not possible that infinite matter is one and simple ; either, as some say, that it is something different from the elements, from which they are generated, or that it is absolutely one. For there are some who make the infinite of this character, but they do not consider it to be air or water, in order that other things may not be blotted out by the infinite; for these are mutually antagonistic to one another, inasmuch as air is cold, water is moist, and fire hot; if one of these were infinite, the rest would be at once blotted out ; but now they say that the infinite is something different from these things, namely, that from which they come.

Phys. iii. 8; 208 a S. In order that generation may actually occur, it is not necessary to prove that the infinite should actually be matter that sense can perceive; for it is possible that destruction of one thing is generation of another, provided the all is limited.

De Coelo iii. 5 ; 303 b 11. For some say that there is only one underlying substance; and of these some [Page 11] say that it is water, some that it is air, some that it is fire, and some that it is more rarefied than water and denser than air ; and these last say that being infinite it surrounds all the heavens.

Meteor. 2 ; 355 a 21. It is natural that this very thing should be unintelligible to those who say that at first when the earth was moist and the universe including the earth was warmed by the sun, then air was formed and the whole heavens were dried, and this produced the winds and made the heavens revolve.

Metaph. xii. 2 ; 1069 b 18. So not only is it very properly admitted that all things are generated from not-being, but also that they all come from being:- potentially from being, actually from not-being ; and this is the unity of Anaxagoras (for this is better than to say that all things exist together), and it is the mixture of Empedokles and Anaximandros.

Plut. Symp. viii. 730 E. Wherefore they (the Syrians) reverence the fish as of the same origin and the same family as man, holding a more reasonable philosophy than that of Anaximandros; for he declares, not that fishes and men were generated at the same time, but that at first men were generated in the form of fishes, and that growing up as sharks do till they were able to help themselves, they then came forth on the dry ground.

Passages relating to Anaximandros in the Doxographists
(Theophrastos, Dox. 477) Simpl. Phys. 6 r ; 24, 26. Among those who say that the first principle is one and movable and infinite, is Anaximandros of Miletos, son of Praxiades, pupil and successor of Thales. He said that the first principle and element of all things is infinite, and he was the first to apply this word to [Page 12] the first principle; and he says that it is neither water nor any other one of the things called elements, but the infinite is something of a different nature, from which came all the heavens and the worlds in them ; and from what source things arise, to that they return of necessity when they are destroyed ; for he says that they suffer punishment and give satisfaction5 to one another for injustice according to the order of time, putting it in rather poetical language. Evidently when he sees the four elements changing into one another, he does not deem it right to make any one of these the underlying substance, but something else besides them. And he does not think that things come into being by change in the nature of the element, but by the separation of the opposites which the eternal motion causes. On this account Aristotle compares him with Anaxagoras.

Simpl. Phys. 6 v; 27, 23 ; Dox. 478. The translation is given under Anaxagoras, infra.

Alex. in Meteor. 91 r (vol. is 268 Id.), Dox. 494. Some of the physicists say that the sea is what is left of the first moisture;6 for when the region about the earth was moist, the upper part of the moisture was evaporated by the sun, and from it came the winds and the revolutions of the sun and moon, since these made their revolutions by reason of the vapours and exhalations, and revolved in those regions where they found an abundance of them. What is left of this moisture in the hollow places is the sea; so it diminishes in quantity, being evaporated gradually by the sun, and finally it will be completely dried up. Theophrastos says that Anaximandros and Diogenes were of this opinion.

[Page 13] Hipp. Phil. 6; Dox. 559, Anaximandros was a pupil of Thales. He was a Milesian son of Praxiades. He said that the first principle of things is of the nature of the infinite, and from this the heavens and the worlds in them arise. And this (first principle) is eternal and does not grow old, and it surrounds all the worlds. He says of time that in it generation and being and destruction are determined. He said that the first principle and the element of beings is the infinite, a word which he was the earliest to apply to the first principle. Besides this, motion is eternal, and as a result of it the heavens arise. The earth is a heavenly body, controlled by no other power, and keeping its position because it is the same distance from all things; the form of it is curved, cylindrical like a stone column; it has two faces, one of these is the ground beneath our feet, and the other is opposite to it. The stars are a circle of fire, separated from the fire about the world, and surrounded by air. There are certain breathing-holes like the holes of a flute through which we see the stars; so that when the holes are stopped up, there are eclipses. The moon is sometimes full and sometimes in other phases as these holes are stopped up or open. The circle of the sun is twenty-seven times that of the moon, and the sun is higher than the moon, but the circles of the fixed stars are lower. Animals come into being through vapours raised by the sun. Man, however, came into being from another animal, namely the fish, for at first he was like a fish. Winds are due to a separation of the lightest vapours and the motion of the masses of these vapours ; and moisture comes from [Page 14] the vapour raised by the sun from them;and lightning occurs when a wind falls upon clouds and separates them. Anaximandros was born in the third year of the forty-second Olympiad.

Plut. Strom. 2 ; Dox. 579. Anaximandros, the companion of Thales, says that the infinite is the sole cause of all generation and destruction, and from it the heavens were separated, and similarly all the worlds, which are infinite in number. And he declared that destruction and, far earlier, generation have taken place since an indefinite time, since all things are involved in a cycle. He says that the earth is a cylinder in form, and that its depth is one-third of its breadth. And he says that at the beginning of this world something [Diels] productive of heat and cold from the eternal being was separated therefrom, and a sort of sphere of this flame surrounded the air about the earth, as bark surrounds a tree ; then this sphere was broken into parts and defined into distinct circles, and thus arose the sun and the moon and the stars. Farther he says that at the beginning man was generated from all sorts of animals, since all the rest can quickly get food for themselves, but man alone requires careful feeding for a long time; such a being at the beginning could not have preserved his existence. Such is the teaching of Anaximandros.

Herm. L G. P. 10; Dox. 653. His compatriot Anaximandros says that the first principle is older than water and is eternal motion; in this all things come into being, and all things perish.

Aet. Plac. i. 3: Dox. 277. Anaximandros of Miletos, son of Praxiades, says that the first principle of things is the infinite; for from this all things come, and all [Page 15] things perish and return to this.12 Accordingly, an infinite number of worlds have been generated and have perished again and returned to their source. So he calls it infinite, in order that the generation which takes place may not lessen it. But be fails to say what the infinite is, whether it is air or water or earth or some other thing. He fails to show what matter is, and simply calls it the active cause. For the infinite is nothing else but matter ; and matter cannot be energy, unless an active agent is its substance. 7 ; 802. Anaximandros declared that the infinite heavens are gods.

Aet. ii. 1 ; Dox. 327. Anaximandros (et al.): Infinite worlds exist in the infinite in every cycle ;
Dox. 329, and these worlds are equally distant from each other. 4 ; 331.  The world is perishable. 11 ; 340. Anaximandros : The heavens arise from a mixture of heat and cold. 13 ; 342. The stars are wheel-shaped masses of air, full of fire, breathing out flames from pores in different parts. 15 ; 345. Anaximandros et al.: The sun has the highest position of all, the moon is next in order, and beneath it are the fixed stars and the planets. 16 ; 345. The stars are carried on by the circles and the spheres in which each one moves. 20; 348. The circle of the sun is twenty-eight times as large as the earth, like a chariot wheel, having a hollow centre and this full of fire, shining in every part, and sending out fire through a narrow opening like the air from a flute. 21 ; 351. The sun is equal in size to the earth, but the circle from which it sends forth its exhalations, and by which it is borne through the heavens, is twenty-seven times as large as the earth. 24 ; 354. An eclipse takes place when the outlet for the fiery exhalations is closed. 25 355. The circle of the moon is nineteen times as large [Page 16] as the earth, and like the circle of the sun is full of fire and eclipses are due to the revolutions of the wheel ; for it is like a chariot wheel, hollow inside, and the centre of it is full of fire, but there is only one exit for the fire. 28; 358. The moon shines by its own light. 29 ; 359. The moon is eclipsed when the hole in the wheel is stopped.

Aet. iii. 3 ; Dox. 367. Anaximandros said that lightning is due to wind; for when it is surrounded and pressed together by a thick cloud and so driven out by reason of its lightness and rarefaction, then the - breaking makes a noise, while the separation makes a rift of brightness in the darkness of the cloud.

Aet. iv. 3; Dox. 387. Anaximandros et al. The soul is like air in its nature.

Aet. v. 19 ; Dox. 430. Anaximandros said that the first animals were generated in the moisture, and were covered -with a prickly skin; and as they grew older, they became drier, and after the skin broke off from them, they lived for a little while.

Cic. de Nat. Deor. i. 10; Dox. 531. It was the opinion of Anaximandros that gods have a beginning, at long intervals rising and setting, and that they are the innumerable worlds. But who of us can think of god except as immortal?

4.  Anaximander: A lecture

Like Thales, Anaximander was a monist. But he rejected Thales’ supposition that water is the material archê. Instead, he proposed the apeiron (the indefinite, or the infinite). Why did he do this?
There is only one extant fragment (6 = B1). It was recorded by the commentator Simplicius (6th C.), who was preserving an account of Anaximander given by Aristotle’s student Theophrastus; it’s possible that Simplicius may have gotten the quote from yet another commentator, Alexander, in his now lost commentary on Aristotle’s Physics. Here is the fragment:

They pay penalty and retribution to each other for their injustice in accordance with the ordering of time.

Before trying to figure out what this means, let’s look at the context in Simplicius:

Anaximander ... said that the indefinite was the first principle and element of things that are, and he was the first to introduce this name for the first principle [i.e., he was the first to call the first principle indefinite]. He says that the first principle is neither water nor any other of the things called elements, but some other nature which is indefinite ....

Here’s a quite different translation (Barnes, EGP 74-75):

Anaximander ... said that the infinite is principle and element of the things that exist. He was the first to introduce this word “principle”. He says that it is neither water nor any other of the so-called elements but some different infinite nature ....

There are two significant differences between these translations:

The text (which reads, literally: he was the first to use this name of [the] principle) is ambiguous as to which word (archê, ‘principle’ or apeiron, ‘infinite’, ‘indefinite’) Anaximander introduced. This is not so important.

Should we translate apeiron as “infinite” or “indefinite”? This is important, and we will have to make a decision about it.

Continuing from Simplicius:

... out of which come to be all the heavens and the worlds in them. The things that are perish into the things out of which they come to be, according to necessity, for they pay penalty and retribution to each other for their injustice in accordance with the ordering of time, as he says in rather poetical language.

What does the fragment mean?

... they pay penalty and retribution ...

• What are they?
• The opposites. Cf. KRS pp. 119-120.

 ... for their injustice ...

• What’s that?
• Destruction, annihilation

 ... in accordance with the ordering of time.

• What’s that?
• Regularity, predictability

 Simplicius’s words (just before he begins quoting Anaximander) add something important which seems to capture Anaximander’s idea:

... according to necessity...

• What does that mean?
•The process does not just happen, but must be that way.

 Aristotle (Phys. 204b22) helps out here:

... for the elements are opposed to each other (for example, air is cold, water moist, and fire hot), and if one of these 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.
There are two possible lines of thought here (3a vs. 3b):

1. The conflict of opposites: the opposites are at war with one another.

2. Hot, cold, etc. are thought of as things, not qualities.

3a. No one of the opposites could have been infinite, or there would be nothing else.

3b. No one of the opposites could have been the archê, or its opposite would never have come to be.

4. But all the “elements” are either opposites or are essentially connected to an opposite
(e.g., water is cold, fire is hot).

5. Therefore, no element, no familiar stuff can be the original archê.

What, then, does apeiron mean? These have all been considered possibilities:

(1)Spatially infinite.
(2)Qualitatively indefinite.
(3)Temporally infinite (i.e., eternal).

(2) seems most plausible: Anaximander posits the apeiron in response to Thales. His objection to water cannot have been that there was only a finite amount of it. Rather, it was that water is a determinate kind of stuff, essentially cold and wet. If originally there was only water, we are left with no account of how there could be any hot, or dry, or fire. See KRS 109-110.

What’s crucial for Anaximander is that the original element be neutral in quality, independent of all the so-called elements (earth, air, fire, water) and pairs of opposites (hot/cold, wet/dry). Still, he may also have supposed it to be infinite in extent (i.e., without spatial boundaries).
For details on Anaximander’s cosmological theory, see Guthrie, pp. 89-90.

Assessment of Anaximander:

a.A response to a (perceived) logical difficulty in Thales’ theory.

b.Postulation of a theoretical entity to explain observable phenomena.

c. The postulation of something beyond experience was not new (cf. the gods). What was new: what is postulated is not personified or anthropomorphic. It is a kind of matter.

d. Problem: how can the apeiron contain the opposites it gives rise to and still be a simple unity? Cf. Guthrie, p. 87.