On the ultimately cultural importance of Anaximander's cosmological notion of the apeiron, the unlimited.
The pre-Socratic Greek philosopher Anaximander made famous the term apeiron (ἄπειρον), which means literally “un-limit”. We can of course express this in English in various ways, such as through words like unlimited, limitless, boundless, infinite, indefinite, but the apeiron, though essentially a source of matter, occupies a particular area of philosophical metaphysics insofar as it says something quite profound about culture and science.
It is a commonplace regarding the pre-Socratic philosophers, i.e. the group of thinking gentlemen gathered mainly on the peripheries of the early Greek world, in Ionia and Magna Graecia (today western Turkey and southern Italy, respectively) in the 7th to early 5th century BC, before Socrates, that they were occupied with nature and the heavens more than with human beings. This is true to some extent, but what is sometimes forgotten is that in many instances, especially in the work of such pre-Socratics as Heraclitus and Empedocles, their views on nature have a direct bearing on the lives of human beings themselves. This is also true in the case of Anaximander’s apeiron.
Many pre-Socratics had considered a particular element to be the prime element, above all others in nature (e.g. air according to Anaximenes, water according to Thales, fire according to Heraclitus), but Anaximander discarded their special status and posited the apeiron instead. At its face, the apeiron is that seminal cosmological area from which all else emanates, sometimes described as a sort of primordial chaos. It is thus a type of arche, or “beginning” of things. From it, all the universe and its worlds come into being, and these worlds, like the apeiron itself, are limitless or innumerable. So too it creates all the opposites. As it causes the creation of things, it also causes their destruction, and these events come about in cycles. Anaximander appears to have posited the apeiron rather than any of the standard elements because, since the latter contain some properties but not others (e.g. fire is hot but not cold) and since they can turn into each other (e.g. water can vaporize), none of them can be the all-embracing constituent of the universe. Now, since the four elements are traditionally linked to some divinity or other in Greek mythology, such as earth to Gaia (which literally means earth in Greek), Anaximander, by demoting them in this way, played a crucial role in the general shift from mythology to science that was taking place in the early Greek world of his time. Admittedly, Aristotle, in Book 3 of his Physics, says that Anaximander referred to the apeiron as divine, since it is immortal and indestructible, but this is a divine force of a much more nebulous sort, a higher natural power far removed from the vulgar pantheon of anthropomorphic deities.
In spite of this divine nature of the apeiron, it is not really considered either positive or negative, which is highly significant. It is simply the immutable – but neither benevolent nor malevolent – source of things. As such, it sets the stage for a general post-archaic Greek attitude to the divine that I touched upon in the post Certain Skepticism (of July 3 of last year), which considers the divine to be a higher but disinterested natural law, not a normative force that seeks to reward or punish our behavior. This state of affairs in turn ordains that it is human beings who must seek out the truth, since it has not been given to them on stone tablets or through the mouth of a prophet who claims to be divinely favored. If the world is in some sense apeiron, as Anaximander says, it is the task of human beings to chart it as far as possible.
But how can one chart what is infinite? Well, one can never chart it completely, of course, which means that, although we may become ever more knowledgeable, we will never possess the whole truth. This notion goes hand in hand with the democratic culture that ancient Greek civilization introduced to the world and which became the cornerstone of the West. Typical Greek, in fact, was the idea that the natural laws of the cosmos could in some way be applied to human society also. If complete knowledge cannot be grasped by anyone, the Greeks might reasonably ask, how could anyone claim complete power over any other? Since we are all powerless before the natural law, since we shall all die and be consumed by the apeiron whence we came, we learn a certain humility – we learn to debate with our neighbors rather than to whip them into obedience. When the apeiron teaches us to be aporetic – from another Greek word meaning “without path” – i.e. unsure or inclined to doubt, we may begin to make progress. (Interesting to note is that the adjective apeiros, from the verb peiraomai - try, test, examine - can mean "ignorant", "inexperienced", or "untested".) As autocracy and theocracy arrested development in every empire and nation surrounding the Greeks, the Greeks themselves, by recognizing the existence of the apeiron and the limits to their own understanding, allowed science and the arts to flourish.
This is one of the main reasons why, for most of history, scientific development proceeded quicker in a West that was politically freer than other cultures. This may all seem obvious enough for us today, but in order for most things to be obvious they still had to be discovered by someone, and that someone was usually a Greek fellow about two and a half millennia ago. It is when we forget the sources of our knowledge, and therefore forget the time when that knowledge did not exist, that we grow arrogant in our belief that the benefits of our current state cannot be lost. It is precisely then, of course, that we risk losing them. When we forget the apeiron, we come to believe that we have all the answers, and we then begin to bully others into conforming to our own point of view. Our democracy then begins to decline.