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In all likelihood, Anaximander was the student of Thales. He was born around 610 BCE., also in Miletus. Like his teacher, his main interests were in natural philosophy, geometry, and astronomy. Also like his teacher, he was apparently a very busy figure; reports tell us that he was the first man to construct a map of the known world, the first to build a sundial, and the first to build a celestial globe with a chart of the stars.
Anaximander was a material monist, but the physis he posits is much more conceptually sophisticated than that of Thales. The evidence we have for him provides a slightly more thorough picture of his thought. Among the many impressive bits and pieces, we can find the first use of the famous principle of sufficient reason and what appears to be the first statement of evolutionary theory.
In Thales' system water was supposed to be the source out of which everything arose. In Anaximander's system the Unbounded (or apeiron) is both the source out of which everything derives and also the unifier within nature. That is to say, in Anaximander's worldview, everything in the universe is in fact just a variation on the Unbounded.
As a physis, the Unbounded has many theoretical advantages over water. As Anaximander no doubt reasoned, the water theory leads to a real problem for the existence of fire. If everything derived from water (and especially if everything still is water in some sense), fire could not possibly survive. In order to allow for the existence of all of the opposites, Anaximander decided to make his physis indefinite, having no particular qualities of its own. Because the Unbounded is entirely neutral between opposites, it does not pose a threat to any of them.
This is clearly a major conceptual step forward. Anaximander has separated his explanatory entity from the entities that need explaining—always a good first step in any explanatory enterprise. He has posited, in fact, the first theoretical entity—an entity that we cannot observe, but that whose existence we infer because of its explanatory role.
In addition to being indefinite, the Unbounded is also limitless or infinite, both temporally and spatially. The Unbounded must be limitless because it must be inexhaustible in order to give rise to everything else in the universe. It must have unlimited potentialities.
In Thales' system we saw hints that water was divine; here we get an explicit statement identifying the Unbounded with divinity. The Unbounded, we are told, is divine because it is deathless and indestructible. This can be read in two ways. Either being divine simply consists in being deathless and indestructible, in which case the Unbounded is divine by default, or else being deathless and destructible are simply two symptoms of divinity, and being divine actually consists in something else. What else it could mean to be divine is unclear. Perhaps the Unbounded is divine in the sense of being the ultimate motive force. Certainly motion is an important property of the Unbounded.
In Thales' thought, we saw the emergence of the first Presocratic preoccupation: the physis problem. With Anaximander we see the emergence of the other two: the plurality problem and the maintenance problem. The plurality problem asks how the single physis could have given rise to the multitude of objects that populate our cosmos. The maintenance problem asks how the cosmos manages to remain relatively stable and predictable.
In answer to the question of plurality, Anaximander posits the following picture: The Unbounded moves with eternal motion (because it is alive, remember the important principle from Thales identifying life with motive force). As the Unbounded moves, something separates off from it. From this something, in turn, hot and cold separate off. Hot becomes fire, which then forms the sun and other heavenly bodies. Cold becomes dark mist which then forms earth and air, both of which originally moist but are dried off by fire.
(Though hot and cold get the generation of the cosmos going, they are not the only opposites with importance in Anaximander's system. Wet and dry are also invoked a lot too. Opposites are, without a doubt, the most important forces in the system.)
When reading about these opposites, such as hot and cold, it is natural to wonder whether they are meant to be qualities or substances. Unfortunately, this distinction is post-Socratic, and so the truth is probably nothing so concrete as either of these extremes. It is best, therefore, to simply think of hot and cold (and moist and dry, and all the other opposites) as forces, or agents of physical change. These forces are present in varying degrees at different places in the cosmos at all times.
The next obvious question to ask, of course, is how the opposites are related to the Unbounded. We know that they somehow come out of it, but does that mean that they were originally in it? There are several possibilities, two of which are ventured by Aristotle. The first possibility is that the Unbounded really is a mixture of all opposites, and the second is that the opposites are simply modifications of the Unbounded. If the first reading is correct, then the fact that the Unbounded possesses no qualities of its own seems threatened. In fact, the first reading makes it seem as if there is not a single physis, but rather an infinite number (i.e. every possible opposite), a reading that some have adopted. The second reading is troubling for another reason: if the opposites are not within the Unbounded originally, it is entirely unclear how they ever arise from it. This seems to be the problem that Anaximander's student Anaximenes seized upon.
Anaximander does at one point describe a vortex motion (dine), in which heavier pieces of the Unbounded settle and lighter pieces fly upwards, but this mechanism is meant explain the separation of the cosmos into heavier and lighter components, as well as the rotation of heavenly bodies. It is never connected to the separation of opposites from the Unbounded, nor is it at all clear how it would help to clarify that matter. We are left without any significant clues, therefore, to help us answer the question of how the opposites are related to, and arise from, the Unbounded.
The opposites are not only crucial to Anaximander's answer to the plurality problem, they are also crucial to his maintenance hypothesis. The lawful state of the world, he believes, is one of equilibrium or balance between opposites. Nature itself, through the governance of the Unbounded, maintains this equilibrium through a mechanism he analogizes to human law courts.
The picture is apparently supposed to go like this: The opposites are continually struggling against each other for dominance. In what sense they are struggling is not clear. Most likely, they are transforming into one another, and thereby destroying one another. The Unbounded steps in and restores the proper balance between them, making them "pay penalty and retribution." The cycles of night and day, and of the four seasons, are perfect examples of the forced equilibrium, and probably the examples Anaxagoras himself had in mind.
The Unbounded, then, is the natural manifestation of physical law, imposing a lawfulness upon continually struggling opposites, and thereby maintaining an equilibrium within the cosmos.
The inherent equilibrium in the cosmos is also responsible for supporting the earth. Unlike his teacher Thales', who believed that the earth was supported by water, and his student Anaximenes, who believed that earth floated on a cushion of air, Anaxagoras was the first to maintain that the earth needs no material support. The earth, he claims, is at rest because it is perfectly balanced within the cosmos. The whole cosmos is symmetrical, with the earth right in the middle. There is no reason, therefore, for it to move in any direction, including down.
In proposing this line of reasoning, Anaximander is the first to make use of an important philosophical principle, most closely associated with the great eighteenth century philosopher G.W. Leibniz: the principle of sufficient reason. The principle of sufficient reason states that there is no effect without a cause, or rather, that nothing happens unless there is a reason for it to happen. Because the earth is equidistant from every part of the cosmos, Anaximander argues, there could be no reason for it to move in one direction rather than another. Therefore, it does not move at all.
Anaximander paints an interesting picture of this perfectly symmetrical cosmos: heavenly bodies are in fact wheels of fire, surrounding the earth. We see only small glimpses of these fiery wheels because we are cut off from them by an opaque air. Within this opaque air, though, are small vents, which afford us a view of small pieces of the fiery wheels. An eclipse occurs, on this view, whenever a vent becomes clogged, blocking our view of the sun wheel.
Perhaps the most startling aspect of Anaximander's thought is his proto-evolutionary theory. Anaximander seems to have anticipated Darwin by over two millennia. He observes that human beings have a long childhood during which time they are heavily dependent on others for their survival. Given this long dependence period, he wonders how the first human beings could have survived, since there would have been no one around to care for them. He reasons that human beings must have evolved from a fishlike creature, since fish have no period of dependence. Modern evolutionary theory agrees with Anaximander; in all likelihood the first animals were fishlike creatures.