Anaximander: 'The Principle of All Things Is the Boundless (To Apeiron)' — The First Philosopher to Surpass His Master

Conclusion First (Key Takeaways)

• The First "Constructive Criticism" in the History of Philosophy: Anaximander inherited his master Thales's question (What is the fundamental principle of all things?) while logically rejecting his answer (water). Sharing the question while renewing the answer — this is the prototype of the "philosophical tradition."
• The Birth of Abstract Thought: To apeiron is not a concrete substance; it is a principle that cannot be grasped by the senses. The idea that what is real is not limited to what the five senses can touch leads to all subsequent metaphysics, mathematics, and theoretical physics.
• The "Decentering" of the Cosmos: His cosmology — that the earth floats unsupported at the center of the universe — dispensed with "supporting turtles" and "supporting pillars." It was the first presentation of a self-sufficient cosmic model that requires no mythological supports for its explanation.

Life and Historical Context

Anaximander was born around 610 BCE in Miletus, a port city in the Ionian region. He was approximately fourteen years younger than his master Thales and is traditionally regarded as Thales's "student or successor" (Diogenes Laërtius, Lives II.1–2). However, the precise meaning of "student" — whether it denotes an institutional teacher–pupil relationship or the intellectual influence of an older fellow citizen — is difficult to determine for this period.

Miletus at the time was one of the most prosperous trading cities in the eastern Mediterranean. It is said to have possessed between 75 and 90 colonies (Pliny, Natural History 5.112; Seneca, Letters 88.44 counts 75), and diverse knowledge and skills flowed in through commerce with Egypt, Babylonia, and Lydia. The precision of Babylonian astronomical records was particularly notable; cuneiform tablets reveal an empirical grasp of the cycles of solar and lunar eclipses (the Saros cycle). Moreover, the Babylonian creation epic Enūma Eliš contains the motif of a world formed through opposition from a primordial chaos (Tiamat), and structural similarities with Anaximander's "separation of opposites from to apeiron" are frequently noted (West, The East Face of Helicon, Oxford UP, 1997, pp. 85–91).

Yet there is a decisive difference. In Babylonian mythology, creation is narrated as an act of the gods. Anaximander eliminated such mythological agents and explained things through natural principles alone. This demythologization was the decisive intellectual innovation of the Milesian school.

Anaximander's activities were remarkably diverse. He is credited with introducing the gnomon (sundial pointer) to Greece (Diogenes Laërtius, Lives II.1; Herodotus, Histories II.109 states that the gnomon itself was transmitted from Babylonia to Greece, suggesting that Anaximander may have served as the intermediary) and used it to measure the times of the solstices and equinoxes. He also produced what is, as far as we know, the first world map (Agathemerus, Geography 1.1), and is further reported to have led a Milesian colonization expedition to Apollonia (Aelian, Various Histories III.17). He was at once a speculative philosopher and a practical engineer and statesman.

He is also said to have written the first philosophical treatise in Greek prose — On Nature (Peri Physeōs / Περὶ φύσεως) — (Themistius, Orations 26, 317c–d; though the precise attribution is debated). Before him, the Greek intellectual tradition was composed in verse (epic form), as exemplified by Hesiod's Theogony. The very choice of discussing natural principles in prose signals a conscious break from mythological storytelling in verse. Whereas Thales left no writings (or they were lost), Anaximander was the first philosopher to commit his thought to writing. Yet only a single fragment survives; everything else is transmitted indirectly through later authors' testimonies (testimonia).

Mini Timeline

• c. 610 BCE: Born in Miletus, Ionia
• 580s BCE: Studies natural philosophy under (or under the influence of) his master Thales
• c. 570 BCE: Introduces the gnomon (sundial) to Greece; observes the solstices and equinoxes
• c. 560 BCE: Produces the first world map; writes On Nature
• c. 547/546 BCE: Dies in Miletus (around the same time as Thales)

What Did Anaximander Ask?

The problem Anaximander confronted was his master Thales's own legacy. Thales had claimed that "the fundamental principle (archē) of all things is water." But Anaximander found a fundamental flaw in this answer.

The logic of his critique, reconstructed by scholars on the basis of Aristotle's report (Physics 204b22–29), runs roughly as follows. Water is opposed to fire. The wet is opposed to the dry. If water is the fundamental principle of all things, how can fire — the opposite of water — arise from water? If one member of a pair of opposites is the fundamental principle, it should annihilate the other. Therefore, the fundamental principle must be something that is not "opposed" to any specific element — that is, something possessing no specific quality. How explicitly Anaximander himself articulated this reasoning is unknown, but as a logical consequence of the concept of to apeiron, many scholars regard this reconstruction as plausible.

This reasoning is not a mere substitution of one answer for another. Having accepted Thales's question — "What is the fundamental principle of all things?" — he made explicit the logical conditions that any answer must satisfy. "The fundamental principle must not possess any specific quality" — the discovery of this constraint was Anaximander's philosophical innovation.

This can be called the first "immanent critique" in the history of philosophy — sharing the opponent's premises while exposing the contradictions of their conclusions. Popper hailed this as the beginning of the "rational tradition" (Popper, Conjectures and Refutations, 1963, Ch. 5). Neither accepting the master's answer uncritically nor rejecting it wholesale, but preserving the framework of the question while improving the answer — this attitude is the fundamental reason that science and philosophy can "progress."

Core Theories

1. To Apeiron — The Boundless

The archē that Anaximander proposed was "to apeiron (τὸ ἄπειρον)" — "the Boundless" or "the Unlimited." The word is the negation of "peras" (limit) and can encompass both the meaning of spatial infinity and the meaning of qualitative indeterminacy (i.e., not limited to any specific quality). Aristotle discusses it mainly in the former sense (Physics, Book III, chs. 4–8), while Theophrastus's testimony (via Simplicius) emphasizes the latter. Most modern scholars believe that Anaximander's own intention centered on qualitative indeterminacy (Kirk & Raven, 1983, pp. 110–117).

To apeiron is neither water, nor fire, nor air. It gives rise to all things while itself remaining fixed to no specific quality. The innovativeness of this idea lies in positing as the fundamental principle something that cannot be grasped by the senses. Thales's "water" could be seen with the eyes and touched with the hands. But to apeiron cannot be apprehended by the five senses. Here lies the origin of the tradition of making "theoretical entities" — things beyond empirical objects — the subject of thought: what would later come to be called "metaphysics."

The concept of the "field" in modern physics — something invisible in itself, yet the source of all matter and force — might be described as a distant descendant of to apeiron. In quantum field theory, elementary particles are understood as "excited states" of a field. The field itself is not any particular particle, yet all particles arise from it. The structural similarity with Anaximander's intuition of 2,600 years ago is striking.

2. The Separation and Return of Opposites — Cosmogony

How do all things arise from to apeiron? Anaximander's answer is the "separation of opposites." From within to apeiron, pairs of opposing qualities — first hot and cold, dry and wet — separate out. From this separation, the concrete elements (fire, air, water, earth) arise, and the world is formed (pseudo-Plutarch, Stromateis ch. 2; Simplicius, Commentary on the Physics 24.13–25).

However, the separated opposites eventually return to to apeiron. This cycle of generation and destruction is condensed in the only surviving fragment (DK 12 B1):

"Whence things have their origin, thence also their destruction happens, as is meet; for they give justice and make reparation to one another for their injustice, in accordance with the arrangement of time." — Simplicius, Commentary on the Physics 24.18–21 (DK 12 B1). Transmitted via Theophrastus.

This fragment is one of the oldest surviving prose texts in Western philosophy. However, it raises a famous interpretive problem. Are the legal and ethical terms — "injustice" (adikia), "justice," "reparation" — Anaximander's own words, or metaphors inserted by Theophrastus when he summarized the text?

Kirk (1955) attributes the legal vocabulary to Theophrastus, arguing that Anaximander's own expression is limited to the phrase "in accordance with what must be" (κατὰ τὸ χρεών). Kahn (1960), on the other hand, argues that the legal vocabulary is Anaximander's original wording, reflecting his understanding of cosmic order through the analogy of legal justice.

Whichever position one takes, the core of the fragment is clear. When one opposite — say, summer's heat — "transgresses" against the other — winter's cold — equilibrium is eventually restored. The cosmos is governed by order, like a court of law.

This thought is structurally similar to "dynamic equilibrium" in ecology and "equilibrium theory" in economics. What is crucial is that Anaximander's cosmos tends not toward unidirectional collapse but toward cyclical restoration. Modern thermodynamics predicts an irreversible "heat death" through increasing entropy. By contrast, Anaximander's cosmos restores equilibrium through "reparation" each time a deviation occurs. It is closer, in fact, to homeostasis in ecology — systems that detect deviation and automatically correct back to the original state. Anaximander's cosmos was a self-regulating system, set in motion by the tension of opposites and maintained in order by the return to equilibrium. This schema of "opposition and equilibrium" flows through Heraclitus's theory of "strife," Empedocles's "Love and Strife," and on to Hegel's dialectics.

3. The Decentering of the Cosmos — The Earth Is Supported by Nothing

The most astonishing claim in Anaximander's cosmology is that the earth floats unsupported at the center of the universe (Aristotle, On the Heavens 295b10–16). Thales had held that "the earth floats on water," but this invites an infinite regress: "What supports the water?" Anaximander cut this regress short. The earth does not fall because it is equidistant from all directions, and therefore has no reason to move.

This argument is a primitive form of the "Principle of Sufficient Reason" — if there is no sufficient reason to move, it does not move. Anaximander applied to cosmology this principle that Leibniz would not formulate until the 17th century — 2,200 years in advance.

In his cosmic model, the earth is cylindrical (with a height one-third of its diameter), surrounded by concentric rings of fire. The celestial bodies are light leaking from openings in these fire rings (Aëtius, Placita II.20–25). The ring of the sun, the outermost, was 27 times the size of the earth; the ring of the moon was 18 times its size. These are multiples of 9 (9×1 = the ring of the stars, 9×2 = the ring of the moon, 9×3 = the ring of the sun), suggesting a model in which the cosmos is structured according to precise mathematical ratios of 3:6:9 (or 1:2:3). Predating the Pythagorean school, this is considered one of the earliest examples of the attitude of "describing the structure of the cosmos with numbers."

Even more debated is the question of whether Anaximander claimed the existence of "innumerable worlds." Testimonies from Augustine and Aëtius suggest that from to apeiron, infinitely many worlds can be generated (Aëtius, Placita I.3.3). If this tradition is correct, our universe is merely one of innumerable worlds born from to apeiron — a striking structural parallel with the modern "multiverse hypothesis." However, some scholars, such as Cornford (1934, CQ 28), interpret "innumerable worlds" not as simultaneously coexisting but as temporally successive (one world perishes before another arises), while others, such as Kirk (1955), question the reliability of this tradition itself.

4. The Origin of Life — A Proto-Theory of Evolution

Anaximander also speculated on the origin of living beings. According to him, the first creatures were born in the moist environment of the sea, covered in spiny shells. When they later moved onto dry land, their shells broke open and they adapted to a different mode of life (Aëtius, Placita V.19.1).

Even more remarkably, he claimed that humans grew inside fish-like creatures and emerged when they had become capable of fending for themselves (pseudo-Plutarch, Stromateis ch. 2; Hippolytus, Refutation of All Heresies I.6.6). His reasoning was that human infants require a much longer period to become self-sufficient compared to other animals, so they could not have survived had they appeared in their present form from the start.

To call this a "precursor" of Darwinian evolution would be an overstatement. There is no mechanism of natural selection, no concept of variation and heredity. However, the idea that living things did not exist in their present form from the beginning but changed from different forms, and the attitude of grounding this claim in rational observation (the vulnerability of human infants), clearly distinguishes it from mythological creationism. Anaximander was one of the first thinkers to conceive of the origin of life as a natural process rather than a divine act.

Key Works Guide

Anaximander's writings have been lost; only a single fragment (DK 12 B1) survives. The following is a guide to the literature for reconstructing his thought.

• Introductory: Diogenes Laërtius, Lives of the Eminent Philosophers, II.1–2 — The most concise biographical source summarizing Anaximander's life and achievements.
• Introductory: Patricia Curd & Daniel W. Graham, eds., The Oxford Handbook of Presocratic Philosophy, Oxford UP, 2008 — An accessible overview of the Milesian school, clearly laying out the relationship with Thales and the meaning of to apeiron.
• Intermediate: Aristotle, Physics, Book III, chs. 4–8 — Aristotle's systematic analysis of to apeiron (the infinite), with direct references to Anaximander. Note that the interpretation is shaped by Aristotle's own theoretical framework.
• Advanced: G. S. Kirk, J. E. Raven, M. Schofield, The Presocratic Philosophers, 2nd ed., Cambridge UP, 1983, Ch. 4 — A critical examination of all fragments and testimonies relating to Anaximander. Provides the most detailed discussion of the interpretive problems surrounding to apeiron.
• Advanced: C. H. Kahn, Anaximander and the Origins of Greek Cosmology, Columbia UP, 1960 (repr. Hackett, 1994) — The classic monograph on Anaximander, offering a detailed reconstruction of his cosmology.

Major Criticisms and Debates

1. Anaximenes's Critique (Contemporary Successor): Anaximenes, the third generation of the Milesian school, apparently considered Anaximander's to apeiron "too indeterminate and lacking in explanatory power." He reverted the archē to a concrete substance — air (aēr) — and explained all change through its condensation and rarefaction (Theophrastus, via Simplicius). In other words, the criticism was that "the Boundless" cannot explain the mechanism of change. This is a legitimate point, revealing that Anaximander's theory lacked a "concrete process of change."

2. Aristotle's Critique (Later): Aristotle argued that "the infinite cannot serve as a principle" (Physics 204a–206b). According to him, the infinite is "incomplete" (in a state of potentiality), whereas a principle must be "complete." Furthermore, admitting the infinite as something that actually exists leads to logical contradictions. However, whether Aristotle interpreted Anaximander's "apeiron" as spatial infinity or qualitative indeterminacy varies depending on the reading of the text.

3. Modern Interpretive Debates: The precise meaning of to apeiron has been the subject of intense debate among scholars since the 20th century. The main positions are: (a) a spatially and quantitatively infinite substance (Cornford, CQ 28, 1934); (b) qualitatively indeterminate (Kirk, "Some Problems in Anaximander," CQ 5, 1955); and (c) an eclectic view combining both spatial and qualitative indeterminacy (Kahn, 1960). More recently, the position has been advanced that to apeiron is not even an "archē" but should be understood as a "field" or "environment" that encompasses all things (Graham, 2006). Decisive evidence is lacking, testifying to the difficulty of recovering Anaximander's true intentions from a single fragment and later testimonies.

Influence and Legacy

Antecedent Thought: Thales's natural philosophy (the very framework of the archē inquiry), Babylonian astronomy (the gnomon; the technical foundation of astronomical observation), Near Eastern cosmogonies (the motif of cosmic generation from primordial chaos).

Direct Successors: Anaximenes concretized the archē as "air," but by introducing the mechanism of condensation and rarefaction, he responded to the problem of "the process of change" that Anaximander had left unresolved. Heraclitus's thought on the "unity of opposites" can be viewed as a variation on Anaximander's "separation and return of opposites."

Distant Successors: Plato's "receptacle" (chōra / χώρα; Timaeus 49a–52d) — which itself has no form but receives all forms — may be regarded as a philosophically refined version of to apeiron. The concept also influenced Aristotle's "matter" (hylē). In the modern period, structural similarities can be discerned with Kant's "thing-in-itself" (Ding an sich) — the unknowable substrate remaining after the forms of cognition have been stripped away — and Spinoza's "substance" (substantia).

Reach into Science: The cosmology of an earth floating unsupported is a distant precursor to the Copernican revolution. The attitude of describing the structure of the cosmos through mathematical ratios, via the Pythagorean school, leads to Kepler's laws of planetary motion. Anaximander's speculations on the origin of life represent one of the most ancient headwaters of the intellectual current that flows through 18th-century natural history (Buffon, Lamarck) to Darwin's theory of evolution.

Connection to the Present

Anaximander's legacy lives on in the present across three dimensions.

First, the attitude of "thinking the invisible." The fundamental concepts of modern physics — fields, energy, dark matter, quantum states — are none of them directly perceptible by the senses. The mode of thought that acknowledges realities accessible only through theoretical reasoning begins with Anaximander's to apeiron. The infinity and continua that underpin mathematics, the "market" posited by economics — these, too, cannot be touched by the five senses. Invisible yet fundamental to all things — this conceptual structure remains at the heart of science and philosophy 2,600 years on.

Second, "critical inheritance" as a way of advancing knowledge. Respecting one's master while logically surpassing their answer — this attitude is structurally identical to the "literature review" in academic papers and "constructive debate" in organizations. Neither wholesale rejection nor uncritical acceptance of the previous generation's work, but improvement — this is the DNA that Anaximander encoded in philosophy.

Third, the worldview of "opposition and equilibrium." In Anaximander's cosmos, opposites commit "injustice" against each other and then "make reparation," thereby maintaining order. This idea of dynamic equilibrium underlies many of the fundamental structures of modern society: homeostasis in ecosystems, the separation of powers in democracy, and the supply–demand equilibrium of market economies. "One-sided domination is injustice, and will eventually be corrected" — this is at once a law of the cosmos and a principle of political philosophy.

Questions for the Reader

• In your own work or studies, have you ever accepted a "master's answer" while "improving the answer within the preserved framework of the question"? What kind of intellectual courage did that require?
• How do the "invisible realities" of modern science (dark matter, quantum fields, mathematical structures) resemble to apeiron, and where do they differ fundamentally?
• If you were to apply Anaximander's model of "equilibrium of opposites" to modern society, in which domain do you think "injustice" has accumulated the most, and where might "reparation" eventually arrive?

References

• Primary Source (Fragments and Testimonies): H. Diels & W. Kranz, eds., Die Fragmente der Vorsokratiker, Vol. 1, chapter on Anaximander (DK 12). Contains Fragment B1 and all testimonies (A section).
• Primary Source (Testimonies): Aristotle, Physics, Book III; Aristotle, On the Heavens 295b10–16 (equilibrium argument); Aetius, Placita III.10.2 and Hippolytus, Refutation of All Heresies I.6.3 (shape testimony).
• Primary Source (Biography): Diogenes Laërtius, Lives of the Eminent Philosophers, II.1–2.
• Secondary Source (Standard Reference): G. S. Kirk, J. E. Raven, M. Schofield, The Presocratic Philosophers, 2nd ed., Cambridge UP, 1983, Ch. 4 — The standard reference, offering the most rigorous examination of Anaximander's fragments and testimonies.
• Secondary Source (Specialist Study): C. H. Kahn, Anaximander and the Origins of Greek Cosmology, Columbia UP, 1960 (repr. Hackett, 1994) — A classic monograph providing a detailed reconstruction of Anaximander's cosmology.
• Secondary Source (Philosophy of Science): K. R. Popper, Conjectures and Refutations, Routledge, 1963, Ch. 5 — Discusses Anaximander as the origin of the "rational tradition," situating early Greek philosophy within a critical-rationalist framework.
• Secondary Source (Near Eastern Comparison): M. L. West, The East Face of Helicon: West Asiatic Elements in Greek Poetry and Myth, Oxford UP, 1997 — The standard work on comparative study of Near Eastern cosmologies and Greek philosophy. Chapter 3 discusses the Milesian school's relationship with the Near East.
• Secondary Source (Recent Research): D. W. Graham, Explaining the Cosmos: The Ionian Tradition of Scientific Philosophy, Princeton UP, 2006 — An important recent work reassessing the scientific thinking of the Milesian school.