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  • Thus the word apeiron occurs in Archimedes only nontechnically, and very rarely too.


  • We are not asserting that a Greek of the sixth or fifth centuries B.C., when encountering the word apeiron, had to go through a mental process of deciding which of the various meanings, in our vocabulary, is intended.


  • During the formative stages of their rational - ity, even still in Plato, the Greeks reacted to this difficulty by investing the word apeiron with both meanings in one, and they added a range of interme - diate and proximate meanings too.


  • Although the receptacle does not appear by name in any other of the later dialogues, it clearly has affinities to the concept of the apeiron (indefinite or indeterminate) of the metaphysical scheme in the Philebus.

    Plato's Timaeus Zeyl, Donald 2009

  • Simplicius continues: “Zeno says this because each of the many things has magnitude and is infinite [reading apeiron instead of ms. apeirôn], given that something is always in front of whatever is taken, in virtue of infinite division; this he shows after first demonstrating that none have magnitude on the grounds that each of the many is the same as itself and one” (Simp. in Ph. 139. 16-19).

    Zeno of Elea Palmer, John 2008

  • Rather, the apeiron somehow generates the opposites hot and cold.

    Presocratic Philosophy Curd, Patricia 2007

  • He replaces Anaximander's apeiron with air, thus eliminating the first stage of the coming-to-be of the cosmos (the something productive of hot and cold).

    Presocratic Philosophy Curd, Patricia 2007

  • He says that it is neither water nor any other of the so-called elements, but some other indefinite (apeiron) nature, from which come to be all the heavens and the worlds in them; and the things from which is the coming-to-be for the things that exist are also those into which is their passing-away, in accordance with what must be.

    Presocratic Philosophy Curd, Patricia 2007

  • Aristotle's associate Theophrastus, quoted by Simplicius, speculates that Anaximenes chose air because he agreed that a basic principle must be neutral (as Anaximander's apeiron is) but not so lacking in properties that it seems to be nothing at all.

    Presocratic Philosophy Curd, Patricia 2007

  • Anaximander: namely, to think finite beings as determinations, or delimitations, of “the Indefinite” or “the Unlimited” (to apeiron).

    The Kyoto School Davis, Bret W. 2006


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  • Greek for the unbounded, the indeterminate. The bete noire of the Pythagoreans, which loomed when they discovered that the square root of 2 was "irrational", i.e., could not be represented as a ratio of two integers (e.g., 1.4142..., an unending decimal).

    March 17, 2007