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1. Introduction
Anaximander was a younger contemporary of Thales, who also sought for the first material principle; he was a disciple and successor of Thales and philosophized in dialogue with him. Anaximander was not mentioned until the time of Aristotle, who classifies him as belonging the "physical" school of thought of Thales. Unlike Thales, Anaximander wrote a philosophical work, entitled On Nature; unfortunately, neither this work nor any of his others has survived. Information about his philosophy come from summaries of it by other writers, especially Aristotle and Theophrastus. Anaximander was said to have drawn the first map of the inhabited world on a tablet, which was a marvel in his day (Agathemerus I, 1)
Anaximander shares Thales' assumption that all things emerged from one original "stuff" and ultimately were that "stuff"; to use Aristotle's terminology, he holds that there is a first (material) principle (archê) of all things. Unlike Thales, however, Anaximander asserts that the first principle is not water, but what he calls the apeiron, translated as the Indeterminate or Limitless. Simplicius, drawing upon Theophrastus' work, gives the following account of Anaximander's view:
Anaximander named the archê and element of existing things the apeiron, being the first to introduce this name for the archê. He says that it is neither water nor any other of the so-called elements, but a different substance that is limitless or indeterminate, from which there come into being all the heavens and the worlds within them. Things perish into those things out of which they have their being, according to necessity; for they make just recompense to one another for their injustice, according to the ordinance [or assessment] of time—so he puts it in somewhat poetical terms (Phys. 24. 13)
For Anaximander, the archê, or first principle, is not any of the elements—earth, water, air or fire—but that which is before all the elements (and everything else), from which the elements emerge and which they all ultimately are (see also Aristotle, Physics 187a 12). Because his archê is no existing thing, Anaximander names it the apeiron, by which he means that the archê is indeterminate and has no characteristics: it is before and beyond all distinctions made with respect to being. As such it cannot be limited by anything, in the sense of being conditioned or caused to be what it is by something else, since it is before all things and encompasses all things. In the passage cited above, Simplicius says that Anaximander was the first to name the archê the apeiron. (See Hippolytus, Refut. 1.5.)
According to Simplicius (and previous interpreters), Anaximander reasons that the first principle (archê) cannot be one of the elements derivative of it, such as water would be: "It is clear that when he observed how the four elements change into one another, he did not think it reasonable to conceive as one of these as underlying the rest, but posited something else" (Phys. 24. 13). If all four elements change into one another, then the first principle cannot be one of these elements but must be prior to all of them; in other words, there must be an source of the four elements that itself has no source, for only that which is not any of the elements could give rise to them. It seems that Anaximander put this forth as a necessary or logical truth: implicitly he is appealing to the impossibility of infinite regress in explanation. Probably alluding to Anaximander, Aristotle explains, "There are some people who make this [a body distinct from the four elements] the infinite, and not air or water, in order that the other elements may not be annihilated by the element which is infinite. They have contrariety with each other—air is cold, water moist, fire hot; if one were infinite, the others by now would have ceased to be. As it is, they say, the infinite is different from them and is their source" (Physics. 204b). By "infinity" in this passage, Aristotle means temporal infinity. If any of the elements were temporally infinite, and so the archê, there would no longer be a balance between opposite elements, such as hot fire and cold earth, because the one infinite element would never be transformed into its opposite, but would remain eternally what it is. Instead, this infinite element would in the long run destroy all the other elements without itself ever being destroyed.
In probable dependence upon Theophrastus' work, Simplicius explains that in Anaximander's philosophy, the opposites emerge from the elements by being separated from it. He writes, "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 Anaximander" (Phys. 32 r; 150, 20). Likewise, Aristotle says of Anaximander's view: "The opposites are in the one and and are separated out" (Physics. 187a 20). The idea of "separation" implies that the opposites were already present in the apeiron but not evident as such, because they were so thoroughly comingled with everything else. In other words, everything already exists in the apeiron but not as detectable. This means that the apeiron is not something different from the opposites that are separated from it but is precisely these opposites not yet separated out but mingled together.
Anaximander may also have reasoned that there must be an infinite source of all things, in order that, as Aristotle says, "Becoming might not fail" (Physics. 203b 18; 208a 8). The apeiron is the undifferentiated source of all things and, as such, is quantitatively infinite, because only as inexhaustible could it be possible for becoming to continue indefinitely. In other words, the apeiron is infinitely immense, having no limits on its volume. (Aristotle refutes this idea, however, by pointing out that there is no need of an infinite body to ensure perpetual becoming because "the passing away of one thing may be the coming to be of another" [Physics 208a 8-9].)
Dependent upon Theophrastus, Simplicius says that Anaximander holds, "Things perish into those things out of which they have their being, according to necessity; for they make just recompense to one another for their injustice, according to the ordinance [or assessment] of time—so he puts it in somewhat poetical terms" (Phys. 24. 13). He means that from the apeiron, opposing pairs emerge (e.g., the wet/dry and the hot/cold) and contend with one another, until one of the pair is annihilated, becoming the other. For example, day will be transformed into night or winter into summer. This is what Anaximander means when he says that things do injustices to one another. (He is personifying the elements of nature, which is why Simplicius says that Anaximander's language is poetic.) But when one thing overcomes its opposite, the way is prepared for its own assimilation by its resurgent opposite. Of necessity, the opposites are kept in balance, since the origin of these forces is the apeiron, the source of all things, which includes all opposites: the one by definition is unified and harmonious. So when day is transformed into night, in time it will be transformed into day, and so the cycle continues forever. This balance of opposing pairs is a reflection of the ultimate harmony that governs the universe.
Anaximander identifies the apeiron as infinite and therefore as god. Aristotle explains:
We cannot say that the apeiron has no effect, and the only effectiveness which we can ascribe to it is that of a principle. Everything is either a source or derived from a source. But there cannot be a source of the apeiron, for that would be a limit of it. Further, as it is a beginning, it is both uncreatable and indestructible. For there must be a point at which what has come to be reaches completion, and also a termination of all passing away. That is why, as we say, there is no principle of this, but it is this which is held to be the principle of other things, and to encompass all and to steer all, as those assert who do not recognize, alongside the infinite, other causes, such as Mind or Friendship. Further they identify it with the Divine, for it is 'deathless and imperishable' as Anaximander says, with the majority of the physicists. (Physics 203b)
Everything is either as source or derived from a source. The apeiron is not derived from a source, because, if it were, it would no longer be the apeiron, for it would be limited or conditioned to be what it is by its source. If it were derived from a source, the apeiron would be caused to be by something else. It would therefore be something as distinct from other things and not the source of all things. As the unlimited, the apeiron not only does not come into being but also does not perish, for, if it did, it would be limited or conditioned by that which can destroy it. To use Aristotle's terminology, the apeiron is the (first) principle (archê) of all things, which owes its existence to no other principle. Likewise, Hippolytus says that Anaximander's apeiron as the archê "is eternal and undecaying, and comprising all the worlds" (Refut. 1.5). Another way of describing the apeiron is to say that it is infinite. Aetius reports, "Anaximander...says that the first principle of things is the infinite; for from this all things come, and all things perish and return to this" (Aet. 1. 3). To be finite is to be limited or conditioned by another thing. To be infinite is not to be limited by anything, but to limit or condition all other things. As infinite or unilimited, the apeiron is not anything, which is why it is called the apeiron, the Indeterminate. The apeiron, as infinite, is the source of all that is created and destroyed, but is none of those things; if it were, it could not be the source of those things. Consistent with Greek assumptions, since it is "uncreatable and indestructible," the apeiron must be god, for it is a assumed that whatever is immortal is divine. Since it is god, the apeiron is no insentient volume of matter, but is aware and has will, so that, as Aristotle says, it "steers all," by which he means it gives direction to the unfolding of all things, which it itself is. It does so while encompassing all (periechein), which seems to mean that the apeiron surrounds the world and contains it.
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