26. Anaximander of Miletus Discovers Infinity in a Boundless Universe

Anaximander of Miletus was a Presocratic philosopher who said that the apeiron was the arche of the universe
Anaximander Holding a Sundial, Ancient Roman Mosaic, 3rd Century AD

Anaximander, a student of Thales, was known for wearing ostentatious clothes.1 Like Thales, he was a multifaceted character. He was the first person to make a map of the world and thus was the first geographer. Anaximander also speculated that the earth was free-floating in space and not suspended by anything, whereas Thales said that it rested on water. He is said to have predicted an earthquake, something that modern science still cannot do.2

He took the concept of arche that was passed down to him and took it in a completely different direction.3 The arche of the universe is that fundamental principle from which everything originates. (See Post 26 for a further discussion of the term arche.) Unlike Thales and the other Presocratics, he deviated from the pattern of looking for a material cause as the first principle or arche. Rather, he chose something more abstract. 

He also wrote a book called Peri Phuseos or On Nature, a quotation of which was recorded by Simplicius in the 6th century AD, making the book the first recorded words of philosophy ever in the West: 

“Whence things have their origin, thence also destruction happens, as is the order of things; for they execute the sentence upon one another – the condemnation for the crime – in conformity with the ordinance of time.”4  

The Infinite as the Principle of the Universe

So, what was his idea of the arche? He simply said that the arche was the apeiron or the infinitean abstract concept rather than a material entity.

According to The History of Philosophy by Grayling, to put the above poem in modern speak, “He said that the apeiron, ‘the infinite’ or ‘indefinite,’ is that from which everything comes into being and into which everything finally reverts, by a process which is like reciprocity or compensation.”5 

Grayling then goes on to quote Plutarch’s interpretation of Anaximander’s words: “The infinite is the universal cause of the generation and destruction of the universe. From it, the heavens were separated off and in general all the worlds, infinite in number. He asserted that destruction, and, much earlier, generation, occur from the immemorial, all the same things being removed.”6 

Additionally, Anaximander said that the universe operated in a balanced fashion.7 When something upsets that balance, a correction occurs by which balance is restored. He put this restoration process in terms of justice, that things are “executing the sentence upon one another.” 

The important question we now ask in relation to Anaximander’s quest for the arche is what did he mean by the apeiron being the principle or origin of all things? We can translate apeiron not only as “infinite” or “indefinite,” but also as “boundless.”8

In ancient times, people weren’t quite sure what he meant by the term.9 Even now, scholars debate the meaning of apeiron. Did Anaximander mean boundless in space or time or both? Or could he have meant boundless in terms of without limits to everything so that it became an inexhaustible term? The Greeks were concerned with limit and order so the term apeiron, meaning without limit, had a negative connotation, whereas the idea of limit had a positive one.  

Anaximander, Aristotle, and the Infinite

Just like with Thales, very little remains from his writings. Much of what has come down to us from him has come down through Aristotle and other philosophers. The following is an excerpt from Aristotle’s Physics (203b3-203b15) concerning Anaximander and this idea of the boundless having no origin: 

“It is clear then from these considerations that the inquiry concerns the student of nature. Nor is it without reason that they all make it a principle. We cannot say that the infinite exists in vain, and the only power which we can ascribe to it is that of a principle. For everything is either a principle or derived from a principle. But there cannot be a principle of the infinite, for that would be a limit of it. Further, as it is a principle, it is both uncreatable and indestructible. For there must be a point at which what has come to be reaches its end, 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.”10

In his physics, Aristotle lists at least five reasons that philosophers believe in the infinite.11 The first argument goes as follows, but is note really relevant to Anaximander – “From the nature of time, for it is infinite.” The second argument is neither relevant to Anaximander for it came post Zeno, but it goes as follows -“From the division of magnitudes, for the mathematicians also use the notion of the infinite.” The other three following elements below are indeed relevant to the discussion of Anaximander.

Aristotle is saying that the infinite has no origin, for if it did, it would have an end. All things that have an origin come to the point of reaching their end and passing away. Aristotle says that the majority of physicists, including Anaximander, identify the infinite with the Divine. Anaximander took the concept of the immortal Homeric gods and developed the concept further when he deemed the infinite as impersonal and having no origin. Thales believed a similar thing. He is quoted as saying, “What is the Divine? That which has no origin or no end,” (Τι το θείον; το μήτε αρχήν έχον μήτε τελευτήν).12

Another way of looking at the same argument above is from the other way around. Instead of saying that the infinite has no origin, rather it can be said that the origin must be infinite. Again to use a quote from Aristotle’s Physics“If coming to be and passing away do not give out, it is only because that from which things come to be is infinite.”13 

Aristotle gives yet a fifth argument for infinity or boundlessness.14 The argument goes something like this: If the infinite could be found in the elements – air, water, earth, fire – since there are opposites involved (e.g., water is cold and fire is hot), if any one of the elements were infinite, then the other elements would have long ceased to be. Therefore, the infinite is different from the elements and is their source. If there were such a body of the infinite to be found, then it would have been present in our world alongside the other elements. Since it is not, it must be their source. 

With Anaximander’s apeiron, Aristotle saw the beginnings of his unmoved mover.15

Anaximander in Raphael's School of Athens said that infinity was the arche of the universe.
Anaximander in Raphael’s School of Athens Painting   

Plato makes the same argument in Phaedo, section 72.16 Since he believed that souls were immortal and always existed in the underworld, he believed that living souls came from the realm of the dead and that living souls die and return to that realm so that the two processes always beget one another and balance each other. He states, “If the two processes of becoming did not always balance each other as if they were going round in a circle, but generation proceeded from one point to its opposite in a straight line and it did not turn back again to the other opposite or take any turning, do you realize that all things would ultimately be in the same state, be affected in the same way, and cease to become?” 

So, if the living soul was preeminent over the dead or vice versa, then the preeminent entity would obliterate the other. 

Anaximander, Friedrich Nietzsche, and the Infinite

And finally, if we think what the Presocratics believed and taught is too obscure to be of any relevance to the modern world, Friedrich Nietzsche credited Anaximander for this theory of eternal recurrence. Nietzsche said that “everything has returned.”17 This was at the heart of his belief system. Furthermore, he believed that all events in the world repeat themselves in a series of endless cycles. 

The Greeks were correct in stating that there had to be an organizing principle or arche to the universe. And Anaximander was not too far off the mark when he proposed the infinite as the arche – he was just a step away from God Himself. Aristotle saw in Anaximander’s apeiron an outline of what he would later term the “unmoved mover” and what Thomas Aquinas said all men call God.18 In addition, I think he was closer than the other Presocratics in trying to find the arche because he did not look for it in the material universe. 

In another way, too, his arche resembles the Judeo-Christian account of creation. Not only is the infinite the cause of everything, but Anaximander’s apeiron is also called the “indefinite.” So, the indefinite can be considered “nothing,” which reminds us of the Christian idea of creation ex nihilo – that God created the universe out of nothing. 

But where he and the Greeks missed the mark was in seeing events in the universe as an endless series of repeating events. This relates to what I wrote in Post 21entitled “The Purpose of History.” When we abandon the linear view of history revealed to us through the Old Testament Hebrews starting with Abraham, by default we end up seeing history as a purposeless repetition of cycles.

In the modern age, we have returned to the Greek view of history, albeit with a much more pessimistic flavour. This pessimism became endemic in the West beginning in the 20th century. Nietzsche rightly grasped this meaninglessness as the only conclusion to life if indeed, as he said, “God is dead.” 

Moreover, with his Apeiron, Anaximander did give us the concept of the utter transcendence which could be found later in Plato’s concept of the Good and eventually applied to God by the Hellenistic Jewish philosopher Philo.

Friedrich Nietzsche developed his Eternal Recurrence argument from the philosophy of Anaximander.
Friedrich Nietzsche

So, let’s take a look at Anaximander’s argument as restated by Aristotle:

“Some make this (namely, that which is additional to the elements) the Boundless, but not air or water, lest the others should be destroyed by one of them, being boundless; for they are opposite to one another (the air, for instance, is cold, the water wet, and the fire hot). If any of them should be boundless, it would long since have destroyed the others; but now there is, they say, something other from which they are all generated.”19

The next quote is Nietzsche’s “Eternal Recurrence” argument that he credited to Anaximander:

“If the world had a goal, it would have been reached. If there were for it some unintended final state, this also must have been reached. If it were at all capable of a pausing and becoming fixed, if it were capable of “being,” if in the whole course of its becoming it possessed, even for a moment, this capability of “being,” then again all becoming would long since have come to an end.”20 

Finally, consider the following question:

How do you think that the idea of eternal recurrence, i.e. not having an end goal for history, has affected the modern West? Leave a comment below and please subscribe. Thank you!

Deo Gratias

Featured Book

From Amazon: “Throughout the long centuries of Western metaphysics the problem of the infinite has kept surfacing in different but important ways. It had confronted Greek philosophical speculation from earliest times. This was appeared in the definition of the divine attributed to Thales in Diogenes Laertius (I, 36) under the description “that which has neither beginning nor end. ” It was presented on the scroll of Anaximander with enough precision to allow doxographers to transmit it in the technical terminology of the unlimited (apeiron) and the indeterminate (aoriston). The respective quanti­tative and qualitative implications of these terms could hardly avoid causing trouble. The formation of the words, moreover, was clearly negative or privative in bearing.

Yet in the philosophical framework the notion in its earliest use meant something highly positive, signifying fruitful content for the first principle of all the things that have positive status in the universe. These tensions could not help but make themselves felt through the course of later Greek thought. In one extreme the notion of the infinite was refined in a way that left it appropriated to the Aristotelian category of quantity. In Aristotle (Phys. III 6-8) it came to appear as essentially re­ quiring imperfection and lack. It meant the capacity for never-ending increase. It was always potential, never completely actualized.”


  1. Couprie, Dirk L., “Anaximander (c. 610—546 B.C.E.)”, Internet Encyclopedia of Philosophy, https://iep.utm.edu/anaximan
  2. Shelley, Cameron. “The Influence of Folk Meteorology in the Anaximander Fragment.” Journal of the History of Ideas, vol. 61, no. 1, 2000, pp. 1–17. JSTOR
  3. Jones, E. Michael, Logos Rising, a History of Ultimate Reality, pp. 156-157, Fidelity Press, South Bend, Indiana, 2020 
  4. Keta, Nachi, “Apeiron of Anaximander,” https://medium.com/literary-impulse/apeiron-of-anaximander-5042173a002c
  5. Grayling, A.C., The History of Philosophy, p.15, Penguin Press, New York, 2019
  6. Ibid.
  7. Freudenthal, Gad. “The Theory of the Opposites and an Ordered Universe: Physics and Metaphysics in Anaximander.” Phronesis, vol. 31, no. 3, 1986, pp. 197–228. JSTOR
  8. Couprie, Dirk L., “Anaximander (c. 610—546 B.C.E.),” section 2
  9. Gottschalk, H. B. “Anaximander’s ‘Apeiron.’” Phronesis, vol. 10, no. 1, 1965, pp. 37–53. JSTOR
  10. Aristotle, Physics, pp. 64-5, David Bostock, author, translated by Robin Waterfield, 1st ed., Oxford University Press, Oxford, England, 2008
  11. Sweeney, Leo, Infinity in the Presocratics, A Bibliographical and Philosophical Study, p. 56, The Catholic University of America, Martinus Nijhoff, The Hague, Netherlands, 1972
  12. “Thales of Miletus, Θαλής ο Μιλήσιος, 643-548 BC , Ancient Greek philosopher,” from website The Best Quotations, https://best-quotations.com/authquotes.php?auth=145
  13. Sweeney, Leo, Infinity in the Presocratics, A Bibliographical and Philosophical Study, p. 56
  14. Ibid.
  15. Aristotle, Physics, 203b3-14, p. 64, David Bostock, author, translated by Robin Waterfield, 1st ed., Oxford University Press, Oxford, England, 2008
  16. Plato, Five Dialogues, Euthyphro, Apology, Crito, Meno, Phaedo, second ed., pp. 109-110, translated by G.M.A. Grube, revised by John M. Cooper, Hackett Publishing Company, Inc., Indianapolis/Cambridge, 2002
  17. Löwith, Karl. “Nietzsche’s Doctrine of Eternal Recurrence.” Journal of the History of Ideas, vol. 6, no. 3, 1945, pp. 273–284. JSTOR
  18. Jones, E. Michael, Logos Rising, a History of Ultimate Reality, p. 156
  19. Aristotle, Physics, 203b 6-10, pp. 64-65, David Bostock, author, translated by Robin Waterfield, 1st ed., Oxford University Press, Oxford, England, 2008
  20. Couprie, Dirk L., Heaven and Earth in Ancient Greek Cosmology, from Thales to Heraclitus Ponticus, p. 92, Springer Publishers, New York, 2011

Bibliography and Sources:

Aristotle, On the Soul, translated by Fred D. Miller, Jr., Oxford University Press, Oxford World Classics, Oxford, England, 2018

Aristotle, The Metaphysics, translated by Hugh Lawson-Tancred, Penguin Books, London, 1998, reprint 2004

Aristotle, Physics, David Bostock, author, translated by Robin Waterfield, 1st ed., Oxford University Press, Oxford, England, 2008

Copleston, Frederick, A History of Philosophy, Book 1, Image Press, Cicero, N.Y., 1981

Couprie, Dirk L., Heaven and Earth in Ancient Greek Cosmology, from Thales to Heraclitus Ponticus, Springer Publishers, New York, 2011

Dawson, Christopher, The Dynamics of World History, public domain

Grayling, A.C., The History of Philosophy, Penguin Press, New York, 2019

Hollis, Christopher, The Noble Castle, Longmans, Green and Co., London, New York, Toronto, 1941

Jones, E. Michael, Logos Rising, a History of Ultimate Reality, Fidelity Press, South Bend, Indiana, 2020 

Plato, Five Dialogues, Euthyphro, Apology, Crito, Meno, Phaedo, second ed., translated by G.M.A. Grube, revised by John M. Cooper, Hackett Publishing Company, Inc., Indianapolis/Cambridge, 2002

Sweeney, Leo, Infinity in the Presocratics, A Bibliographical and Philosophical Study, The Catholic University of America, Martinus Nijhoff, The Hague, Netherlands, 1972

Voegelin, Eric, Order and History, Vol. 2: The World of the Polis, classic reprint, hardcover, Forgotten Books, London, 2018

Waterfield, Robin, The First Philosophers: The Presocratics and Sophists, 1st ed., Oxford University Press, Oxford, 2009

Internet Sources:

Adamson, Peter, Lecture 1 “Infinity and Beyond: Anaximander and Anaximenes, December 23, 2010, History of Philosophy Without Any Gaps, King’s College, London, https://historyofphilosophy.net/anaximander-anaximenes

Couprie, Dirk L., “Anaximander (c. 610—546 B.C.E.),”Internet Journal of Philosophy, https://iep.utm.edu/anaximan/

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