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Jürgen Lawrenz

Arche and Apeiron in Early Presocratic Philosophy

Metaphysical speculation began, long before it was so named, among the presocratic Greeks as an enquiry into cosmology and first principles from two utterly disparate perspectives. The first of these, propounded by Herakleitos, noted the incessant flux (panta rhei) which characterises phenomena; the second, advanced by his contemporary Parmenides, taught the doctrine of a single immutable substance. These rivalling perspectives endure to this day: they announce one of the basic themes on which metaphysics since then has strung up an immense set of variations.

Behind both stands the concept of arche, a term introduced into philosophical discourse by Anaximandros, rendered into English via Latin as ‘principle’ and bearing the meaning of the ‘first-begotten or underlying substance’ of all things. Historically this might be called the first brick to leave the kiln in which the metaphysical fire was burning. Moreover, where Thales’ teachings were apparently still subject to aural dispersion, Anaximandros, not content with the word of mouth, becomes the first philosopher among the still relatively small band of logographoi to publish his theories in a formal text. His book at once set out to encompass what was known and to be known and thereby furnished a role model (presumably peri physeos) for a dozen generations to come, carrying echoes down as far as the Romans (De rerum natura). It gave a comprehensive depiction of cosmogony and cosmology, astronomy and geography, meteorology and biology and down to a phylogeny of the human species. For Anaximandros, Barnes writes [19], “Nature embraces every object of experience and every subject of rational enquiry except the productions of human contrivance.”

Meaning of ‘Apeiron’

His own contribution to the more stringently philosophical debate on archaeai was the startling concept of the apeiron, which leaps out of the pages of Greek philosophy like a spiky porcupine, never formally groomed as a legitimate occupant of place in a philosophical agenda dominated from the beginning by principles of rationality and intelligibility. We may supposed it to have emerged from debate on candidates for the ‘Urstoff’ or primeval substance; and it is perhaps permissible to suppose lively exchanges on the virtues and demerits of sundry elements, culminating in a shock of recognition by Anaximandros that none of these substances, being determinate, qualified and hence failed to satisfy empirical as well as theoretical criteria. The apeiron, initially perhaps merely a device to evade commitment to untenable propositions, proved itself in the long run a truly metaphysical conception with ramifications that have resisted erosion by time. Yet our first duty is to note that it proved indigestible to Greek philosophy for the aforesaid reasons, to which insistence on form as the fundamental criterion of being must be added. Indeed it is dubious whether the man himself was altogether aware of the problems raised by his conception; and hence the idea of the apeiron — this notion of a formless, homogeneous, all-pervading, incorruptible and morally neutral substance — stood for all Greek philosophy as a signpost at a corner of its domain, pointing to an incognisant reality into which one may not transgress.

This does not, by any means, tarnish the profound genius of the man who proposed it; and it is only fair to mention that modern cosmology is (paradoxically) cut from the same cloth. However, this must be laid to the account of a changed temper of philosophical inquiry.

As to its meaning, we may begin with ‘unlimited’, which cannot be too far off the mark, because peras, its root, means ‘boundary’. But if it were as simple as that, we would not have a metaphysical problem on our hands. When the concept recurs in the work of Anaxagoras, there is a shift towards something more concretely apprehensible, if only by negation:

“By apeira he (Anaxagoras) probably meant incomprehensible and unknowable to us. This is shown by the words, ‘so that we cannot know the number of the things being separated off (apokrisis), either theoretically or in practice.’ That he believed them to be finite in kind, he makes plain; for he says that Mind knows all things, but if they were literally infinite, they would be altogether unknowable, since knowledge limits and sets bounds to what is known.” (Simplicius, Cael. 608.24; quoted in Guthrie, I, pp. 420-4).

This puts into perspective the feature of Anaximandros’ apeiron that worried the Greeks so much: it lacked every attribute by which ‘being’ might be designated; and worse, it presented itself as a de-anthropomorphised entity, unlike kaoV which in its guise as a god retained at least an affiliation with fusiV, which on the whole was still regarded as a plenum.

The major stumbling block was the “literally infinite” mentioned by Simplicius. To the Greeks such expressions carried suggestions of offence against the logos and it would not be an exaggeration to claim that all of Greek philosophy is one long effort to circumvallate reality by the compass of reason and to disallow as existent or even possible what reason cannot contend with. However, if we place Anaximandros in the roster of creative metaphysical thinkers (indeed as the first of that line), then we cannot stand still with his merely theoretical conceptions: there is another dimension to the apeiron which may suitably be dealt with first inasmuch as it springs from a lineage much more ancient (e.g. Hesiod, Orphism) and still a powerful presence to him.

Ethics and mortality

Only one sentence from Anaximandros’ book actually survives into our era— but what a sentence!
The origin of things is in the illimitable. It is the source of their existence to which in the end they return as ordained by the law of necessity: for they are answerable to and must atone for offending against the just decrees of time.

Unexpectedly we here confront a gnomic utterance that makes no distinction between animate and inanimate Being, placing them both in an ethical context. Its core idea: the unlawful and indeed punishable emancipation of individual existence from non-Being, which necessitates both atonement and a return to that state.

It is necessary to dwell on this for a moment, for apart from any other consideration we might wish to attach to the utterance, it is primarily representative of a type of cognition still new to the world, namely the conceptualisation in rational terms of a notion formerly entrenched in and reserved to mythological (theological) thinking and in virtue of this transplantation turned into an eminently metaphysical concept. Mortality, i.e. the inevitability of death is not itself the key issue, which recurs as a topos in innumerable myths (e.g. Garden of Eden, Gilgamesh) and in many cultures also embraces the (personified) forces of nature. Anaximandros’s ‘guilt’ is not the sin of Adam and Eve, who in defying their creator acquired consciousness of their mortality as both a stain and a spur. His concept embraces a view instead which may be characterised as the protest of the emergent, which in the act of differentiating itself from an impassive and chaotic sameness seeks to define and impose value on its exceptionality. But acquisition of form is the resultant of an act, an effort — as we would say today, an entropy-producing contraction of matter in a focus of energy which, after running its course, must ineluctably dissipate again. It is not clear whether Anaximandros adverts consciousness (however insignificant) to all differentiated matter; but this is scarcely a crucial distinction. For him, as for all Greeks, form implies intelligibility. Thus the concept of ‘atonement’ is wide enough in its applicability to indicate that an animate being and an inanimate substance share in the necessity of ultimate dissolution.

The tragic concept of man

Before proceeding, let me note that the possible composition of this Urstoff of Anaximandros is never an issue (Aristotle will designate it as a ‘potentiality’). The step Anaximandros took beyond Thales led him, as noted, into the ethical and metaphysical dimensions: into questions concerned with eternal justice and with the right to life which all animate creatures assert.

He is herewith at one with the tragic poets in asking: whence this restless activity of creativity and dissolution, this living and dying; what meaning to the interminable drone of death agonies? If life is worth nothing, then why does it happen? For it happens: and it happens under conditions of unlawfulness and consequently guilt; and accordingly the imperative of atonement is stressed. But no more than this can be extracted. Anaximandros does not enlighten us about the possibility of escaping from this eternal cycle.

Pythagoras took one consequence and taught palingenesis. It is unlikely that he was prefigured in this by Anaximandros. The abiding impression conveyed by the latter’s concept is of the tragic constitution of existence, of the impenetrability of eternal justice, against which inanimate matter has no recourse whatever, while man’s sole counter is the concept of value. But such a concept is fundamentally inimical to transmigration and its hidden motive spring in the suggestion of compensation.

In this regard, and especially in its emphasis on atonement and the final irrefragable value of existence against non-existence, it is a philosophical counterpane to the attic stage, of which it has been said with a great deal of insight that its tragedies are metaphysics spun into the veil of poetry.


Anaximandros’s idea arose, as noted, from his doubts about determinate stuff being eligible as arche. I like to think of this as an eminently ‘metaphysical misgiving’, whose issue was an intuition that an arche cannot be matter at all; that indeterminacy (apeira) is surely the condition at the opposite pole from determinacy and that without this contrast, the very condition of being is inexplicable — for as much as genesis presupposes agency, it cannot work on matter already formed. Impossible to know what Anaximandros’ thought process might have been: yet he worked within a tradition which kept before his eyes the notion of a continuum of formed matter throughout the intelligible cosmos, in which Eros functioned as the principle of fecundity. But Eros transforms: it cannot have escaped him, with his predilections. Hence he must seek the formless, the unbounded, the passive, inactive, neutral, atemporal and nonspatial in which determinacy is latent but not explicit — in short, the apeiron.

But to describe this concept in any terms other than negatives would seem to be impossible. Even denomination as a featureless waste is almost asking too much; but whatever else we make of it, the apeiron is not a res extensa; indeed not a res in any sense of the word. It is as close as a Greek philosopher ever came to the edge of that abyss beyond cognition where neither logos nor gnome can reach.

The apeiron, then, is an unvarying and sempitermal One from which the evanescent mutable Many precipitate to run their course and perish. Once in the realm of being, Ananke presides; for there is a natural craving among all created forms for their spot in the sun and fear of the extinguishing of their light; so that without eternal justice tipping the scales impartially, the apeiron would cease to be an arche; and this, we may take it, would have been inconceivable.

The opposition between mere shape and intelligible form espoused by Aristotle is binding on the whole intellectual atmosphere which governed Greek philosophical thinking. However, the principle of causation in its aristotelian form obviously postdates the efforts of Anaximandros, whose somewhat naive hylozoism assumed a single homogeneous entity capable of self-caused apokrisis in analogy with biological generation. The analytical mind of Aristotle later dissected the intellectual problem into its components and arrived at the correct identification of the apeiron as a manifold. But the recognition of this as the minimum requirement to support the notion of self-causation was an idea that arose from the concept of the apeiron and it took several generations for it to become sufficiently acclimatised among thinkers to bear the fruit which is visible in the work of Aristotle.

Under those tenets, the sum of intelligible forms in the universe comprise that harmonic order which is the knowable cosmos, in opposition to chaos as the image of unrealised potential. But intelligibility implies measurability; a thing imbued with intelligible form is seen to possess circumference, weight and all the other attributes that make it accessible to man’s reason. As the example of the pythagorean discovery of irrational numbers shows, nothing was more abhorrent to the Greek intellect than appearances which elude the grasp of the logos; and from this we are forcibly pushed to the conclusion that the incompatibility between ancient and modern thinking revolves in principle around what the ancient thinkers and scientists perceived as the essential meaninglessness of unformed entities.

Looking back from this vantage point at the apeiron of Anaximandros, we must acknowledge that the principal difficulty with it as a concept was precisely this open-endedness, unformedness, unconstrainedness and hence its ontological ambiguity; and yet its illimitability has no point of intellectual contact with ‘eternity’, ‘infinity’ or the ‘boundlessness’ of our modern universe. The Greek vocabulary contained no terms capable of a one-to-one correspondence to the terms by which they are usually translated. Ascribing negativity to the concept is (certainly within hellenic philosophical schemata) simply an admission that something lacking numerical definition, extent, weight, measure, boundary represents formlessness as a principle and can therefore only be regarded as a diffusion of potential. As such, formlessness is admissible as a debating point, though plainly peripheral to the central canons of a philosophy of intelligible forms.

This latter type of cognition is essential to the Greek spirit and rescues the apeiron from complete ostracism. Formed substance means, incontestably, corporeal substance. It means, in the context I have sketched for Anaximandros (and taken up by Anaxagoras), a drive or desire for emancipation which invests spuriously precipitating clusters of substance, differentiating themselves from their formless environment and rising from lethargy into full individuality against the indifference and impassivity of their host. In other words: the Apeiron represents in itself an agenda-setting general conception of change; it was adopted as such by Heraclitus and Parmenides, each of whom found his own way of dealing with it and thereby fixed that agenda as a dichotomous theoretical framework for all time to come (the history of philosophical and scientific effort devoted to it presents itself to us like the swing of a pendulum, but to date no end or final solution is in sight).


Anaximandros also branched out from older ‘wisdom’ in the role he assigned to earth in his cosmology. Thales seems still to have taught that the earth is flat (somewhat like a tambourine) and floats on water — presumably the ‘real’ ocean of which Plato speaks in the Critias. His successor considered this an unsatisfactory theory because it opens itself to infinite regress. Consequently Anaximandros replaced it with a spherical earth hanging motionlessly and unsupported in the midst of space and surrounded by the concentric shells (wheel rims) occupied respectively by sun, moon and the stars. His reply to such critical objections as, what is there to prevent the earth from hurtling aimlessly hither and thither, was: What is to prevent the earth from sitting still? Motion requires a charge (impetus or attraction), while ‘hurtling’ (i.e. falling) implies directionality, but as the earth occupies the exact geometric centre of the heavens, all directions are equal, hence all difference between up and down and sideways becomes inoperative.

This discrimination between hypothesis and conceptualisation reveals the mind of the philosopher. On the lookout for a law, he conceived of this astonishing instance of gravitational symmetry that satisfies completely the ‘euclidian’ model of geometrical cosmology. But the point to be brought out from Anaximandros’s main ideas is that they click naturally into the chain begun by Thales and continue the opening of cognitive terrain for the questing intellect. Such speculations, which strike us powerfully as conveying a notably profound insight into nature are, in a sense, forever: they impregnate the philosophic enterprise with their blazing energy and are apt, as in this instance, to bear fruit in millennia still to come.

Across the ford, into terra nova

With Anaximenes, supposedly his pupil, we regress partially to former positions — a first indication of the resistance offered by the Greek mind to the apeiron. His choice of air as the arche (pneuma) was, however, a fecund source in non-Ionian terrain, where it soon became the principal attribute of life itself and eventually equated with the mode of existence of the immortals, so that his conception finally debouched in Christianity — one of the latter’s ultimate philosophical sources. In antiquity Anaximenes enjoyed the reputation of figurehead of the Milesian School; his philosophy became one of the mainstreams via Pythagoras, who probably studied with him.

Yet it was the latter who then built a bridge back to Anaximandros and devised a ‘method’ with an evolutionary potential not fully realised until over a thousand years later.

To us his central insight is deja-vu; the excitement of discovery unrecapturable. But when, as a result of his researches into the mathematics of acoustical phenomena, he stumbled upon the realisation that numbers and their ratios can express in their perfectly abstract medium certain attributes of matter and its behaviour, irrespective of the specificity of that matter, he unravelled one of the underlying conditions of the mind’s operations, namely its capacity for minting metaphysical truths from the physical constitution of the world (laws of nature) and disclosed the existence of a realm of being purely of the mind.

The other two prominent thinkers in the wake of Anaximandros, Herakleitos and Parmenides, confronted the apeiron more directly in its implications relative to the paradox of change. For change is paradoxical, and an enormous mythographic tradition devoted itself to the elucidation of the why and how of the transformation of matter into other matter, of matter into life and vice versa, and of the mystery of kinematics. That myths are generally satisfied with the explanatory closure of attribution to divine intervention and reason dissatisfied with the implausibility of ‘just-so stories’ may serve as one pointer to the success of philosophy in ancient Greece.

Anaximandros’ apeiron did pose the problem of when, why and how a monodirectional apokrisis may stop. Herakleitos may have arrived at his perspective via the condensation/rarefaction theory advanced by Anaximenes — here was a concept of a transformation continuum which also offered itself as an intelligible percept without sacrificing form. Indeed it explained the metamorphoses of form and incidentally furnished a happy blending of mythological with ‘scientific’ principles. However, Anaximenes’ adoption of air as an arche may have struck Herakleitos as indadequate on account of its passivity. Hence his answer was that fire served as the agency. Fire is creative and combustive, forming and destroying. Be it noted that Herakleitos makes no claim for fire to be an element; instead it must be understood as a process, as possibly the very instance of eternal justice of the famous quote, inasmuch as fire is fuelled by plenty and starved by penury of material. The metaphysical core of his philosophy is therefore the contrast between what can be phenomenally grasped and its true nature as one substance of infinite plasticity.

Completely at variance with this theory is the thought promulgated by Parmenides, who effectively denied apokrisis altogether and registered his protest against the apeiron as an unintelligible entity (insustainable in logic) by invoking reason and logic as arbiters between possibility and being.

The world, he says, either is or is not; there can be no middle way. For logically, if we say “x is”, then we admit its being and find ourselves excluded from any claim that “x is not”. Yet in supposing creation and transformation, we would be compelled to admit of x that it has the capacity “not to be what it is” en route to being something else. But “to be” and “not to be” are mutually exclusive propositions; accordingly the idea change is specious, since it entails passage through a stage of non-being. Parmenides therefore arrived at the conclusion that whatever is, is; and it is forever, without change, unable to decompose or recompose. The world that is must be one immutable entity.

But what of the perception of change which is our daily experience? For Parmenides this is effectively a ‘play of light’ (phainos); an illusory condition with which we humans must contend, for it is not given to us to withdraw the veil (aletheia) from ultimate reality, a prerogative reserved to the gods. But we can conceive of this ultimate reality if we admit his proposition that through our minds we have mediate access to it. Here, despite his maladversion against Pythagoras, a meeting of minds at the fringes of their metaphysical orbits!

These three scions of Anaximandros set (as it were) the agenda for metaphysics. Their philosophies blossomed out in rich apparel among such as Anaxagoras, Empedokles, Demokritos; but to the most cursory reading of Plato’s dialogues, where metaphysics attains its first pinnacle, the legacy of Herakleitos, Pythagoras and Parmenides looms in huge bulk and from there fanned out as the mainstream of Western philosophy. And if there is merit to Whitehead’s quip that in the main we have been adding footnotes to Plato’s philosophy since then, this compliment must be extended to the foursome of this chapter, without whom such an agenda may not ever have come into existence.


Barnes, Jonathan: The Presocratic Philosophers, Routledge, London 1982
Burnet, John: Early Greek Philosophy, Oxford University Press 1920
Collingwood, R. G.: The Idea of Nature, Oxford University Press 1945
Copleston, Frederick: A History of Philosophy, Vol. I. Doubleday, New York 1962
Nestle, Wilhelm: Die Vorsokratiker, Düsseldorf, Diederichs 1956
Guthrie, W.K.C.: A History of Greek Philosophy, Vols. I & II. Cambridge University Press 1965
Sarton, George: A History of Science, Wiley, New York 1964
Schrödinger, Erwin: Nature and the Greeks, Cambridge University Press 1954