Citation for this page in APA citation style.           Close


Mortimer Adler
Rogers Albritton
Alexander of Aphrodisias
Samuel Alexander
William Alston
Louise Antony
Thomas Aquinas
David Armstrong
Harald Atmanspacher
Robert Audi
Alexander Bain
Mark Balaguer
Jeffrey Barrett
William Belsham
Henri Bergson
George Berkeley
Isaiah Berlin
Richard J. Bernstein
Bernard Berofsky
Robert Bishop
Max Black
Susanne Bobzien
Emil du Bois-Reymond
Hilary Bok
Laurence BonJour
George Boole
Émile Boutroux
Michael Burke
Joseph Keim Campbell
Rudolf Carnap
Ernst Cassirer
David Chalmers
Roderick Chisholm
Randolph Clarke
Samuel Clarke
Anthony Collins
Antonella Corradini
Diodorus Cronus
Jonathan Dancy
Donald Davidson
Mario De Caro
Daniel Dennett
Jacques Derrida
René Descartes
Richard Double
Fred Dretske
John Dupré
John Earman
Laura Waddell Ekstrom
Herbert Feigl
John Martin Fischer
Owen Flanagan
Luciano Floridi
Philippa Foot
Alfred Fouilleé
Harry Frankfurt
Richard L. Franklin
Michael Frede
Gottlob Frege
Peter Geach
Edmund Gettier
Carl Ginet
Alvin Goldman
Nicholas St. John Green
H.Paul Grice
Ian Hacking
Ishtiyaque Haji
Stuart Hampshire
Sam Harris
William Hasker
Georg W.F. Hegel
Martin Heidegger
Thomas Hobbes
David Hodgson
Shadsworth Hodgson
Baron d'Holbach
Ted Honderich
Pamela Huby
David Hume
Ferenc Huoranszki
William James
Lord Kames
Robert Kane
Immanuel Kant
Tomis Kapitan
Jaegwon Kim
William King
Hilary Kornblith
Christine Korsgaard
Saul Kripke
Andrea Lavazza
Keith Lehrer
Gottfried Leibniz
Michael Levin
George Henry Lewes
David Lewis
Peter Lipton
C. Lloyd Morgan
John Locke
Michael Lockwood
E. Jonathan Lowe
John R. Lucas
Alasdair MacIntyre
Ruth Barcan Marcus
James Martineau
Storrs McCall
Hugh McCann
Colin McGinn
Michael McKenna
Brian McLaughlin
John McTaggart
Paul E. Meehl
Uwe Meixner
Alfred Mele
Trenton Merricks
John Stuart Mill
Dickinson Miller
Thomas Nagel
Friedrich Nietzsche
John Norton
Robert Nozick
William of Ockham
Timothy O'Connor
David F. Pears
Charles Sanders Peirce
Derk Pereboom
Steven Pinker
Karl Popper
Huw Price
Hilary Putnam
Willard van Orman Quine
Frank Ramsey
Ayn Rand
Michael Rea
Thomas Reid
Charles Renouvier
Nicholas Rescher
Richard Rorty
Josiah Royce
Bertrand Russell
Paul Russell
Gilbert Ryle
Jean-Paul Sartre
Kenneth Sayre
Moritz Schlick
Arthur Schopenhauer
John Searle
Wilfrid Sellars
Alan Sidelle
Ted Sider
Henry Sidgwick
Walter Sinnott-Armstrong
Saul Smilansky
Michael Smith
Baruch Spinoza
L. Susan Stebbing
Isabelle Stengers
George F. Stout
Galen Strawson
Peter Strawson
Eleonore Stump
Francisco Suárez
Richard Taylor
Kevin Timpe
Mark Twain
Peter Unger
Peter van Inwagen
Manuel Vargas
John Venn
Kadri Vihvelin
G.H. von Wright
David Foster Wallace
R. Jay Wallace
Ted Warfield
Roy Weatherford
William Whewell
Alfred North Whitehead
David Widerker
David Wiggins
Bernard Williams
Timothy Williamson
Ludwig Wittgenstein
Susan Wolf


Michael Arbib
Bernard Baars
Gregory Bateson
John S. Bell
Charles Bennett
Ludwig von Bertalanffy
Susan Blackmore
Margaret Boden
David Bohm
Niels Bohr
Ludwig Boltzmann
Emile Borel
Max Born
Satyendra Nath Bose
Walther Bothe
Hans Briegel
Leon Brillouin
Stephen Brush
Henry Thomas Buckle
S. H. Burbury
Donald Campbell
Anthony Cashmore
Eric Chaisson
Jean-Pierre Changeux
Arthur Holly Compton
John Conway
John Cramer
E. P. Culverwell
Charles Darwin
Terrence Deacon
Louis de Broglie
Max Delbrück
Abraham de Moivre
Paul Dirac
Hans Driesch
John Eccles
Arthur Stanley Eddington
Paul Ehrenfest
Albert Einstein
Hugh Everett, III
Franz Exner
Richard Feynman
R. A. Fisher
Joseph Fourier
Lila Gatlin
Michael Gazzaniga
GianCarlo Ghirardi
J. Willard Gibbs
Nicolas Gisin
Paul Glimcher
Thomas Gold
Brian Goodwin
Joshua Greene
Jacques Hadamard
Patrick Haggard
Stuart Hameroff
Augustin Hamon
Sam Harris
Hyman Hartman
John-Dylan Haynes
Martin Heisenberg
Werner Heisenberg
John Herschel
Jesper Hoffmeyer
E. T. Jaynes
William Stanley Jevons
Roman Jakobson
Pascual Jordan
Ruth E. Kastner
Stuart Kauffman
Simon Kochen
Stephen Kosslyn
Ladislav Kovàč
Rolf Landauer
Alfred Landé
Pierre-Simon Laplace
David Layzer
Benjamin Libet
Seth Lloyd
Hendrik Lorentz
Josef Loschmidt
Ernst Mach
Donald MacKay
Henry Margenau
James Clerk Maxwell
Ernst Mayr
Ulrich Mohrhoff
Jacques Monod
Emmy Noether
Howard Pattee
Wolfgang Pauli
Massimo Pauri
Roger Penrose
Steven Pinker
Colin Pittendrigh
Max Planck
Susan Pockett
Henri Poincaré
Daniel Pollen
Ilya Prigogine
Hans Primas
Adolphe Quételet
Juan Roederer
Jerome Rothstein
David Ruelle
Erwin Schrödinger
Aaron Schurger
Claude Shannon
David Shiang
Herbert Simon
Dean Keith Simonton
B. F. Skinner
Roger Sperry
Henry Stapp
Tom Stonier
Antoine Suarez
Leo Szilard
William Thomson (Kelvin)
Peter Tse
Heinz von Foerster
John von Neumann
John B. Watson
Daniel Wegner
Steven Weinberg
Paul A. Weiss
John Wheeler
Wilhelm Wien
Norbert Wiener
Eugene Wigner
E. O. Wilson
H. Dieter Zeh
Ernst Zermelo
Wojciech Zurek


Free Will
Mental Causation
James Symposium

Anaximander of Miletus, a student of Thales, described a first principle (archē) as a sort of indefinite and unbounded moving element, the apeiron (ἄπειρον). Unlike the other presocratics, Anaximander did not name a known specific element as the origin of all matter, like water (Thales), fire (Heraclitus), or air (Anaximenes). Anaximander may have been the first natural scientist, describing principles about the creation and destruction of order as an arrangement of things in time, which are created and later perish.

We have only one major fragment of Anaximander, and a couple of important phrases. They come from Theophrastus (c. 370-290 BCE), the successor to Aristotle as head of the Peripatetic school, and Simplicius (c. 490-560 CE.), who is quoting from Theoprastus.

ἀρχὴ ... τῶν ὄντων τὸ ἄπειρον ... ἐξ ὧν δὲ ἡ γένεσίς ἐστι τοῖς οὖσι͵ καὶ τὴν φθορὰν εἰς ταῦτα γίνεσθαι κατὰ τὸ χρεών· διδόναι γὰρ αὐτὰ δίκην καὶ τίσιν ἀλλήλοις τῆς ἀδικίας κατὰ τὴν τοῦ χρόνου τάξιν.

Ἀθάνατον [...] καὶ ἀνώλεθρον.

Kathleen Freeman's translations are:
The Non-Limited is the original material of existing things; further, the source from which existing things derive their existence is also that to which they return at their destruction, according to necessity; for they give justice and make reparation to one another for their injustice, according to the arrangement of Time.

(The Non-Limited) is immortal [ἀ + θάνατον] and indestructible [ἀν + ὂλεθρον. N.B., φθορὰν is another word for destruction].

Kirk and Raven translate the version given by Theophrastus as

...some other apeiron nature, from which come into being all the heavens and the world in them. And the source of coming-to-be for existing things is that into which destruction, too, happens. 'according to necessity [translating κατὰ τὸ χρεών]; for they pay penalty [translating διδόναι δίκην] and retribution to each other for their injustice according to the assessment of Time [personified as Chronos].

Martin Heidegger cited this "Anaximander Fragment" as the introduction of Being (and perhaps Time?) into philosophy, after which he claims that Being (Existence itself or perhaps the noumenal Idea of Being outside space and time?) is forgotten as philosophical and scientific thought concentrates on the multitude of beings (existing things).

Friedrich Nietzsche had also cited this ancient fragment in his posthumous Philosophy in the Tragic Age of the Greeks. Much of Heidegger's work and even his terminology can be traced back to Nietzsche.

We can read ἀρχὴ as both beginning and principle, with its important relatives ἄρχω (of time, to begin) and ἄρχων (a ruler, king).

There is no "material" obvious at the beginning of the fragment, so it is better to read ἀρχὴ as a cosmological "origin" of existing things in general, of things (τῶν ὄντων) that have "being" (τὸ ὀν).

We can read ἄπειρον as without a limit (ἀ + πεῖρας), but even more deeply, see the relative πειρα as an attempt, an experiment, and as "experience." This is the root of our "empirical," from ἐν "in" + πειρα "experiment." So apeiron can mean "without experience," or, in the context of an origin, "before experience." This is then Immanuel Kant's distinction between onto-theology (discovering God from thinking about the concept alone) and cosmo-theology (discovering God based on our experiences).

Anaximander's mention of χρεών is etymologically related to χρῆματα, things for which man is the measure, according to Protagoras. These are material and useful things of value (χρῆματα, or πράγματα).

διδόναι δίκην ("giving justice") is a similar idiom "suffer punishment, make amends"

The German translation given in the first edition of the Fragmente der Vorsokratiker of Hermann Diels (1903) translates τῶν ὄντων as Dinge. A better translation would be simple "beings" or "things that exist." Diels translates κατὰ τὸ χρεών as nach der Notwendigkeit, which is too strong, implying the determinism of the later atomists and materialists.

Anfang der Dinge ist das Unendliche. Woraus aber ihnen die Geburt ist, dahin geht auch ihr Sterben nach der Notwendigkeit. Denn sie zahlen einander Strafe und Buße für ihre Ruchlosigkeit nach der Zeit Ordnung.

Notwendigkeit is the strong concept of necessity that implies determinism. It was introduced in Greek thought a century later by atomists such a Leucippus. Dinge implies material "things" and not "beings" - let alone the Being" that Martin Heidegger is looking for.

Leucippus said about necessity...

"Nothing occurs at random, but everything for a reason and by necessity." (Leucippus, Fragment 569 - from Fr. 2 Actius I, 25, 4)

οὐδὲν χρῆμα μάτην γίνεται, ἀλλὰ πάντα ἐκ λόγου τε καὶ ὑπ’ ἀνάγκης

A better translation for the idiom κατὰ τὸ χρεών· is "according to that which must be," according to what is due, or just "needed," and not the "necessity" = ἀν + ανκη of Leucippus. The χρῆμα of Leucippus and the plural χρῆματα of Protagoras are the everyday "things of which man is the measure," not Parmenides "things that exist," let alone "Being itself"

In Plato, Phaedrus (255a), του χρόνου ἣ τε ἡλικἰα και τὸ χρεών, is translated in the Loeb Plato as "in time, at an age, according to destiny."

In the sixth edition of the Fragmente der Vorsokratiker, now edited by Walther Kranz, we find a surprisingly different German translation, described as "in direct speech."

1. (In direkter Rede:) Anfang und Ursprung der seienden Dinge ist das Apeiron (das grenzenlos-Unbestimmbare). Woraus aber das Werden ist den seienden Dingen, in das hinein geschieht auch ihr Vergehen nach der Schuldigkeit; denn sie zahlen einander gerechte Strafe und Buße für ihre Ungerechtigkeit nach der Zeit Anordnung.

2. Das Apeiron ist ohne Alter.

3. Das Apeiron ist ohne Tod und ohne Verderben.

Here Kranz inserts "seienden Dinge, "things that are, "being things"" rather than just "things." And he replaces Diels' Notwendigkeit with Schuldigkeit or Duty.

The latest modern compilation of the Fragments, sixty years after the latest Diels-Kranz, is by Daniel W. Graham, a philosopher with classical training, but not a classicist. Here are full excerpts from ancient Anaximander quotations by Simplicius, via Theophrastus, by Hippolytus, and by Aristotle. Anaximander's own words are bolded.

9. Simplicius Physics 24.13-25, Theophrastus fr. 226A Fortenbaugh (A9, B1)

9 [report of the interpretation of Theophrastus:] Of those who say the source is one and in motion and boundless, Anaximander, the son of Praxiades, of Miletus, the successor and student of Thales, said the source and element of existing things was the boundless, being the first one to apply this term to the source. And he says it is neither water nor any other of the so-called elements, but some other boundless nature, from which come to be all the heavens and the world-orders in them:

Note that coming-to-be and destruction are now thought to be Simplicius' addition, as first suspected by John Burnet in the 1890's and as Heidegger knew. Even ἀρχὴ is a later term, and Graham drops it, γένεσίς, and φθορὰν
[F1] From what things existing objects come to be, into them too does their destruction take place, according to what must be: for they give recompense and pay restitution to each other for their injustice according to the ordering of time, expressing it in these rather poetic terms.

[comment by Simplicius:] It is clear that, observing the change of the four elements into each other, he did not think it appropriate to make one of them the substratum of the others, but something else besides them. And he did not derive generation from the alteration of some element, but from the separation of contraries due to everlasting motion. That is why Aristotle classified him with the followers of Anaxagoras.

10 Hippolytus Refutation 1.6.1-2 (A11, B2)

10 Anaximander, was the student of Thales. Anaximander, son of Praxiades, of Miletus. He said the source and element of existing things was a certain nature of the boundless, from which come to be the heavens and the world-order in them. [Fa] And this is everlasting and ageless [translating ἁίδιον (ἁείδιον) εῖναι καὶ ἀγήρω], and it also surrounds all the world- orders. He speaks of time as though there were a determinate period of coming to be and existing and perishing. (2) He has said the source and element of existing things is the boundless, being the first to call the source by term. Furthermore, motion is everlasting, as a result of which the heavens come to be.

16 Aristotle Physics 203b6-28 (A15+, B3)

16 Everything is either a source or derives from a source, but there is no source of the boundless or infinite, for then there would be a boundary of it. Furthermore, it would be without coming to be and perishing insofar as it is a source; for what comes to be must reach an end, and there is an end of every perishing. For that reason, as we say, there is no source of the infinite, but [F3] this seems to be a source of everything else and to contain all things and steer all things, as everyone claims who does not posit some cause beyond the boundless, as for instance mind or love. (B3) And this is the divine, for it is deathless and imperishable [translating ἁθάνατον γάρ καὶ ἀνώλεθρον], as Anaximander says, together with the majority of the natural philosophers.

The belief in some infinite principle would seem to arise especially from five considerations: [1] from the concept of time (for this is infinite), [2] from the division in magnitudes (for mathematicians employ the concept of infinity), [3] and again from the fact that only in this way will coming to be and perishing not cease: so long as there is something infinite from which what comes to be is subtracted. [4] And again from the fact that what is limited always meets some limit, so that there must be no limit if everything is limited by something else. [5] But the main and chief reason, is what causes a general problem for everyone: because we cannot imagine an end of the series, number seems infinite, and likewise mathematical magnitudes and also what is outside the heaven. And if what is outside the heavens is infinite, so, we tend to believe, are body and the world-orders themselves. For why should there be more void in one place than in another? So if there is body in one place it must be everywhere.

17 Aristotle Physics 204b22-29 (A16)

17 But it is not possible for the boundless body to be one and simple - neither as some say something besides the elements, from which they generate them, nor without qualification. For there are some who posit a boundless, not air or water, in order that other things may not be destroyed by the infinite amount of their opposite; for each of these has a character contrary to the others, for instance air is cold, water moist, fire hot. So if any one of these was infinite, the rest would already have been destroyed. But it is really something else, they say, from which these things arise.

For Teachers
For Scholars

Chapter 1.4 - The Philosophy Chapter 1.6 - The Scientists
Home Part Two - Knowledge
Normal | Teacher | Scholar