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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 Bois-Reymond
Hilary Bok
Laurence BonJour
George Boole
Émile Boutroux
F.H.Bradley
C.D.Broad
Michael Burke
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
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
Keith Lehrer
Gottfried Leibniz
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
Friedrich Nietzsche
John Norton
P.H.Nowell-Smith
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
Jean-Paul Sartre
Kenneth Sayre
T.M.Scanlon
Moritz Schlick
Arthur Schopenhauer
John Searle
Wilfrid Sellars
Alan Sidelle
Ted Sider
Henry Sidgwick
Walter Sinnott-Armstrong
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
William Whewell
Alfred North Whitehead
David Widerker
David Wiggins
Bernard Williams
Timothy Williamson
Ludwig Wittgenstein
Susan Wolf

Scientists

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
A.O.Gomes
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
Martin J. Klein
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
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
Juan Roederer
Jerome Rothstein
David Ruelle
Erwin Schrödinger
Aaron Schurger
Claude Shannon
David Shiang
Herbert Simon
Dean Keith Simonton
B. F. Skinner
Roger Sperry
John Stachel
Henry Stapp
Tom Stonier
Antoine Suarez
Leo Szilard
William Thomson (Kelvin)
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

Presentations

Biosemiotics
Free Will
Mental Causation
James Symposium
 
The Strong Cosmological Principle
The first presentation of Layzer's Strong Cosmological Principle apparently was at a conference on The Nature of Time at Cornell in 1963, organized by Thomas Gold. The attendees included Hermann Bondi, Subramanyan Chandrasekhar, Richard Feynman, Gold, Martin Harwit, Roger Penrose, Philip Morrison, and John Wheeler, among others.

Five years later, Layzer presented a paper, entitled "Cosmogonic Processes," at the Brandeis Summer Institute of Theoretical Physics in 1968, published as Astrophysics and General Relativity, two volumes, edited by Max Chrétien, Stanley Deser, and Jack Goldstein, Gordon and Breach, NY, 1971.

Layzer begins with a hypothesis of Ludwig Boltzmann that depends on the universe being infinite. Since Boltzmann was attempting to explain how we could have departed from equilibrium enough to live in a universe in which entropy was low and obviously increasing, it is clearly the intellectual origin of the problem of growth of order. It also appears to have inspired Layzer's Strong Cosmological Principle.

Boltzmann's hypothesis
Boltzmann pointed out that in an infinite universe in a state of thermodynamic equilibrium every finite configuration whose structure does not violate the laws of physics has a finite probability of occurring. Hence the observable universe of Boltzmann's day could represent a statistical fluctuation in a universe that, as a whole, was in a stationary state.
Layzer's theory of the growth of order in the universe shows that "the initial state of local thermodynamic equilibrium is uniquely defined, and it is a state of zero specific information."
Subsequently, as the universe expands, the specific information must increase, and this increase defines the arrow of time — at least on the cosmological level. But can we attribute objective significance to the concept of information? Information is, after all, defined only in the context of a statistical description. The quantity n that figures in definition (2.27) is a probability density in phase space. If we had chosen to specify the state of our ideal gas through the actual occupation numbers of cells in phase space instead of through a distribution function, the specific entropy would have been precisely zero and would have remained zero for ail time. A complete microscopic description of a closed system always contains the same quantity of information, and is hence completely time-symmetric.

This argument — that the asymmetry between past and future disappears when we pass from the macroscopic to the microscopic level of description — is undoubtedly valid for closed macroscopic systems.

See the reversibility and recurrence objections to Boltzmann's H-Theorem
It has been raised against statistical theories of irreversibility in macroscopic systems since the time of Boltzmann, and even today it stands in the way of a completely satisfactory theory of macroscopic irreversibility. To avoid it, some physicists have adopted the view that irreversible processes occur only in systems that are not quite closed [allowing the environment to disturb the system and introduce disorder]. Interactions between a system and its environment give rise to genuine indeterminacy in the microstate of the system and thus afford an objective basis for a statistical description.

An alternative and equally objective basis for a statistical description not only of macroscopic systems but of the universe as a whole is provided by an assumption that I shall call the strong cosmological principle. This asserts that the universe is characterized completely by random functions and that no statistical property of the description serves to define a preferred position or direction in space. A Poisson distribution of particles filling all space is the simplest model of a universe that satisfies this postulate. For the sake of definiteness, we imagine space to be partitioned into cells of volume V. The distribution of particles among the cells is completely determined by the parameter nV, where n is the mean number density of particles. This infinite and unbounded Poisson distribution has two properties that are not shared by any finite or bounded distribution.

(a) From a single realization we can evaluate the defining parameter nV — or indeed any average quantity pertaining to the distribution with arbitrary precision.

This property depends on the law of large numbers and on the fact that the distribution occupies an infinite volume.

(b) There do not exist two distinguishable realizations of a given Poisson distribution. For the set of occupation numbers that characterizes any finite part of a given realization has a finite and calculable probability of occurrence and must therefore have an exact counterpart — indeed infinitely many exact counterparts — in a second realization of the same distribution. Thus any two realizations can be made to coincide over any finite volume. It follows that "different" realizations of the same Poisson distribution are operationally indistinguishable.

We are therefore forced to the rather startling conclusion that, for any finite value of the cell size V, a Poisson distribution of particles in an infinite Euclidian space contains ail the information needed to define it (namely, the value of n) but does not contain any "microscopic" information. The proviso that the cell size V be finite is essential. If the positions of particles were specified precisely through their coordinates, the distance between any two particles would suffice to characterize the distribution uniquely. In reality we are of course concerned with distributions of particles in phase space, whose cellular structure is guaranteed by the laws of quantum mechanics. Thus the indeterminacy resulting from the absence of microscopic information in a cosmic distribution satisfying the strong cosmological principle is closely related to the quantal indeterminacy expressed by Heisenberg's uncertainty relations. Nevertheless the two kinds of indeterminacy are distinct.

We conclude that objective significance can be attached to the growth of information in a Friedmann universe expanding from an initial state of local thermodynamic equilibrium.

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