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:

  1. 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.

  2. 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:

  1. A response to a (perceived) logical difficulty in Thales’ theory.
  2. Postulation of a theoretical entity to explain observable phenomena.
  3. 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.
  4. Problem: how can the apeiron contain the opposites it gives rise to and still be a simple unity? Cf. Guthrie, p. 87.

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Copyright © 2002, S. Marc Cohen