Philosophers
Mortimer Adler Rogers Albritton Alexander of Aphrodisias Samuel Alexander William Alston Anaximander G.E.M.Anscombe Anselm Louise Antony Thomas Aquinas Aristotle David Armstrong Harald Atmanspacher Robert Audi Augustine J.L.Austin A.J.Ayer 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 BoisReymond Hilary Bok Laurence BonJour George Boole Émile Boutroux F.H.Bradley C.D.Broad Michael Burke Lawrence Cahoone C.A.Campbell Joseph Keim Campbell Rudolf Carnap Carneades Ernst Cassirer David Chalmers Roderick Chisholm Chrysippus Cicero Randolph Clarke Samuel Clarke Anthony Collins Antonella Corradini Diodorus Cronus Jonathan Dancy Donald Davidson Mario De Caro Democritus Daniel Dennett Jacques Derrida René Descartes Richard Double Fred Dretske John Dupré John Earman Laura Waddell Ekstrom Epictetus Epicurus Herbert Feigl Arthur Fine 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 Gorgias Nicholas St. John Green H.Paul Grice Ian Hacking Ishtiyaque Haji Stuart Hampshire W.F.R.Hardie Sam Harris William Hasker R.M.Hare Georg W.F. Hegel Martin Heidegger Heraclitus R.E.Hobart 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 Christoph Lehner Keith Lehrer Gottfried Leibniz Jules Lequyer Leucippus Michael Levin George Henry Lewes C.I.Lewis David Lewis Peter Lipton C. Lloyd Morgan John Locke Michael Lockwood E. Jonathan Lowe John R. Lucas Lucretius 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 G.E.Moore Thomas Nagel Otto Neurath Friedrich Nietzsche John Norton P.H.NowellSmith Robert Nozick William of Ockham Timothy O'Connor Parmenides David F. Pears Charles Sanders Peirce Derk Pereboom Steven Pinker Plato Karl Popper Porphyry Huw Price H.A.Prichard Protagoras Hilary Putnam Willard van Orman Quine Frank Ramsey Ayn Rand Michael Rea Thomas Reid Charles Renouvier Nicholas Rescher C.W.Rietdijk Richard Rorty Josiah Royce Bertrand Russell Paul Russell Gilbert Ryle JeanPaul Sartre Kenneth Sayre T.M.Scanlon Moritz Schlick Arthur Schopenhauer John Searle Wilfrid Sellars Alan Sidelle Ted Sider Henry Sidgwick Walter SinnottArmstrong J.J.C.Smart 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 Voltaire G.H. von Wright David Foster Wallace R. Jay Wallace W.G.Ward Ted Warfield Roy Weatherford C.F. von Weizsäcker William Whewell Alfred North Whitehead David Widerker David Wiggins Bernard Williams Timothy Williamson Ludwig Wittgenstein Susan Wolf Scientists Michael Arbib Walter Baade Bernard Baars Leslie Ballentine Gregory Bateson John S. Bell Mara Beller 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 JeanPierre Changeux Arthur Holly Compton John Conway John Cramer E. P. Culverwell Olivier Darrigol Charles Darwin Richard Dawkins Terrence Deacon Lüder Deecke Richard Dedekind Louis de Broglie Max Delbrück Abraham de Moivre Paul Dirac Hans Driesch John Eccles Arthur Stanley Eddington Gerald Edelman Paul Ehrenfest Albert Einstein Hugh Everett, III Franz Exner Richard Feynman R. A. Fisher Joseph Fourier Philipp Frank Lila Gatlin Michael Gazzaniga GianCarlo Ghirardi J. Willard Gibbs Nicolas Gisin Paul Glimcher Thomas Gold A.O.Gomes Brian Goodwin Joshua Greene Jacques Hadamard Mark Hadley Patrick Haggard Stuart Hameroff Augustin Hamon Sam Harris Hyman Hartman JohnDylan Haynes Donald Hebb Martin Heisenberg Werner Heisenberg John Herschel Art Hobson Jesper Hoffmeyer E. T. Jaynes William Stanley Jevons Roman Jakobson Pascual Jordan Ruth E. Kastner Stuart Kauffman Martin J. Klein Simon Kochen Hans Kornhuber Stephen Kosslyn Ladislav Kovàč Leopold Kronecker Rolf Landauer Alfred Landé PierreSimon Laplace David Layzer Benjamin Libet Seth Lloyd Hendrik Lorentz Josef Loschmidt Ernst Mach Donald MacKay Henry Margenau James Clerk Maxwell Ernst Mayr John McCarthy Ulrich Mohrhoff Jacques Monod Emmy Noether Abraham Pais 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 Jürgen Renn/a> Juan Roederer Jerome Rothstein David Ruelle Tilman Sauer Erwin Schrödinger Aaron Schurger Claude Shannon David Shiang Herbert Simon Dean Keith Simonton B. F. Skinner Lee Smolin Roger Sperry John Stachel Henry Stapp Tom Stonier Antoine Suarez Leo Szilard Max Tegmark William Thomson (Kelvin) Giulio Tononi Peter Tse Vlatko Vedral 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 Konrad Zuse Fritz Zwicky Presentations Biosemiotics Free Will Mental Causation James Symposium 
The Recurrence Problem
The idea that the macroscopic conditions in the world will repeat after some interval of time is an ancient idea, but it plays a vital role in modern physics as well.
The Great Year should not be confused with the time that the precession of the equinoxes takes to return the equinoxes to the same position along the Zodiac  although this time (about 26,000 years) is of the same order of magnitude as one famous number given by Babylonian astronomers for the Great Year (36,000 years).
Ancient middle eastern civilizations called it the Great Year. They calculated it as the time after which the planets would realign themselves in identical positions in the sky. Many societies have the concept of the Great Year, but none did calculations as carefully as the Babylonians. But since the planets orbital periods are not really commensurate, they kept increasing the time for the Great Year in the search for a better recurrence time. The Greek and Roman Stoics thought the Great Year was a sign of the rule of law in nature and the God of reason that lay behind nature.
Nietsche's Eternal Return
In modern philosophy, Friedrich Nietzsche described an eternal return in his Also Sprach Zarathustra.
Zermelo's Paradox
Zermelo's paradox was a criticism of Ludwig Boltzmann's HTheorem, the attempt to derive the increasing entropy required by the second law of thermodynamics from basic classical dynamics.
It was the second "paradox" attack on Boltzmann. The first was Josef Loschmidt's claim that entropy would be reduced if time were reversed. This is the problem of microscopic reversibility. Ernst Zermelo was an extraordinary mathematician. He was (in 1908) the founder of axiomatic set theory, which with the addition of the axiom of choice (also by Zermelo, in 1904) is the most common foundation of mathematics. The axiom of choice says that given any collection of sets, one can find a way to unambiguously select one object from each set, even if the number of sets is infinite. Before this amazing work, Zermelo was a young associate of Max Planck in Berlin, one of many German physicists who opposed the work of Boltzmann to establish the existence of atoms. Zermelo's criticism was based on the work of Henri Poincaré, an expert in the threebody problem, which, unlike the problem of two particles, has no exact analytic solution. Where twobodies can move in paths that may repeat exactly after a certain time, three bodies may only come arbitrarily close to an initial configuration, given enough time. Poincaré had been able to establish limits or bounds on the possible configurations of the three bodies from conservation laws. Planck and Zermelo applied some of Poincaré's thinking to the n particles in a gas. They argued that given a long enough time, the particles would return to a distribution in "phase space" (a 6n dimensional space of possible velocities and positions) that would be indistinguishable from the original distribution. This is called the Poincaré "recurrence time." Thus, they argued, Boltzmann's formula for the entropy would at some future time go back down, vitiating Boltzmann's claim that his measure of entropy always increases  as the second law of thermodynamics requires. Poincaré' described his view in 1890.
A theorem, easy to prove, tells us that a bounded world, governed only by the laws of mechanics, will always pass through a state very close to its initial state. On the other hand, according to accepted experimental laws (if one attributes absolute validity to them, and if one is willing to press their consequences to the extreme), the universe tends toward a certain final state, from which it will never depart. In this final state, which will be a kind of death, all bodies will be at rest at the same temperature. Boltzmann replied that his argument was statistical. He only claimed that entropy increase was overwhelmingly more probable than Zermelo's predicted decrease. Boltzmann calculated the probability of a decrease of a very small gas of only a few hundred particles and found the time needed to realize such a decrease was many orders of magnitude larger than the presumed age of the universe. The idea that a macroscopic system can return to exactly the same physical conditions is closely related to the idea that an agent may face "exactly the same circumstances" in making a decision. Determinists maintain that given the "fixed past" and the "laws of nature" that the agent would have to make exactly the same decision again.
The Extreme Improbability of Perfect Recurrence
In a classical deterministic universe, such as that of Laplace, where information is constant, Zermelo's recurrence is mathematically possible. Given enough time, the universe can return to the exact circumstance of any earlier instant of time, because it contains the same amount of matter, energy, and information.
But, in the real universe, David Layzer has argued that information (and the material content of the universe) expands from a minimum at the origin, to ever larger amounts of information. Consequently, it is statistically and realistically improbable (if not impossible) for the universe as a whole to return to exactly the same circumstance of any earlier time.
Arthur Stanley Eddington was probably the first to see that the expanding universe provides a resolution to Zermelo's objection to Boltzmann. By accepting the theory of the expanding universe we are relieved of one conclusion which we had felt to be intrinsically absurd. It was argued that every possible configuration of atoms must repeat itself at some distant date. But that was on the assumption that the atoms will have only the same choice of configurations in the future that they have now. In an expanding space any particular congruence becomes more and more improbable. The expansion of the universe creates new possibilities of distribution faster than the atoms can work through them, and there is no longer any likelihood of a particular distribution being repeated. If we continue shuffling a pack of cards we are bound sometime to bring them into their standard order — but not if the conditions are that every morning one more card is added to the pack. H. Dieter Zeh also sees that the age of the universe being much less than the Poincaré recurrence time may invalidate the recurrence objection. Another argument against the statistical interpretation of irreversibility, the recurrence objection (or Wiederkehreinwand), was raised much later by Ernst Friedrich Zermelo, a collaborator of Max Planck at a time when the latter still opposed atomism, and instead supported the 'energeticists', who attempted to understand energy and entropy as fundamental 'substances'. This argument is based on a mathematical theorem due to Henri Poincaré, which states that every bounded mechanical system will return as close as one wishes to its initial state within a sufficiently large time. The entropy of a closed system would therefore have to return to its former value, provided only the function F(z) is continuous. This is a special case of the quasiergodic theorem which asserts that every system will corne arbitrarily close to any point on the hypersurface of fixed energy (and possibly with other fixed analytical constants of the motion) within finite time.
