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Philosophers

Mortimer Adler
Rogers Albritton
Alexander of Aphrodisias
Samuel Alexander
William Alston
Anaximander
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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 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
Daniel Boyd
F.H.Bradley
C.D.Broad
Michael Burke
Lawrence Cahoone
C.A.Campbell
Joseph Keim Campbell
Rudolf Carnap
Carneades
Nancy Cartwright
Gregg Caruso
Ernst Cassirer
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Roderick Chisholm
Chrysippus
Cicero
Randolph Clarke
Samuel Clarke
Anthony Collins
Antonella Corradini
Diodorus Cronus
Jonathan Dancy
Donald Davidson
Mario De Caro
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Jacques Derrida
René Descartes
Richard Double
Fred Dretske
John Dupré
John Earman
Laura Waddell Ekstrom
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Austin Farrer
Herbert Feigl
Arthur Fine
John Martin Fischer
Frederic Fitch
Owen Flanagan
Luciano Floridi
Philippa Foot
Alfred Fouilleé
Harry Frankfurt
Richard L. Franklin
Bas van Fraassen
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
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Frank Jackson
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Robert Kane
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Jaegwon Kim
William King
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Thomas Kuhn
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Keith Lehrer
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Jules Lequyer
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Joseph Levine
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C.I.Lewis
David Lewis
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C. Lloyd Morgan
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Michael Lockwood
Arthur O. Lovejoy
E. Jonathan Lowe
John R. Lucas
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Tim Maudlin
James Martineau
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Storrs McCall
Hugh McCann
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John McTaggart
Paul E. Meehl
Uwe Meixner
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Trenton Merricks
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Dickinson Miller
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Thomas Nagel
Otto Neurath
Friedrich Nietzsche
John Norton
P.H.Nowell-Smith
Robert Nozick
William of Ockham
Timothy O'Connor
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David F. Pears
Charles Sanders Peirce
Derk Pereboom
Steven Pinker
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Nicholas Rescher
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Josiah Royce
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Paul Russell
Gilbert Ryle
Jean-Paul Sartre
Kenneth Sayre
T.M.Scanlon
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John Searle
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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
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Richard Taylor
Kevin Timpe
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John Venn
Kadri Vihvelin
Voltaire
G.H. von Wright
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R. Jay Wallace
W.G.Ward
Ted Warfield
Roy Weatherford
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David Widerker
David Wiggins
Bernard Williams
Timothy Williamson
Ludwig Wittgenstein
Susan Wolf

Scientists

David Albert
Michael Arbib
Walter Baade
Bernard Baars
Jeffrey Bada
Leslie Ballentine
Marcello Barbieri
Gregory Bateson
Horace Barlow
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
Jean Bricmont
Hans Briegel
Leon Brillouin
Stephen Brush
Henry Thomas Buckle
S. H. Burbury
Melvin Calvin
Donald Campbell
Sadi Carnot
Anthony Cashmore
Eric Chaisson
Gregory Chaitin
Jean-Pierre Changeux
Rudolf Clausius
Arthur Holly Compton
John Conway
Jerry Coyne
John Cramer
Francis Crick
E. P. Culverwell
Antonio Damasio
Olivier Darrigol
Charles Darwin
Richard Dawkins
Terrence Deacon
Lüder Deecke
Richard Dedekind
Louis de Broglie
Stanislas Dehaene
Max Delbrück
Abraham de Moivre
Bernard d'Espagnat
Paul Dirac
Hans Driesch
John Eccles
Arthur Stanley Eddington
Gerald Edelman
Paul Ehrenfest
Manfred Eigen
Albert Einstein
George F. R. Ellis
Hugh Everett, III
Franz Exner
Richard Feynman
R. A. Fisher
David Foster
Joseph Fourier
Philipp Frank
Steven Frautschi
Edward Fredkin
Benjamin Gal-Or
Howard Gardner
Lila Gatlin
Michael Gazzaniga
Nicholas Georgescu-Roegen
GianCarlo Ghirardi
J. Willard Gibbs
James J. Gibson
Nicolas Gisin
Paul Glimcher
Thomas Gold
A. O. Gomes
Brian Goodwin
Joshua Greene
Dirk ter Haar
Jacques Hadamard
Mark Hadley
Patrick Haggard
J. B. S. Haldane
Stuart Hameroff
Augustin Hamon
Sam Harris
Ralph Hartley
Hyman Hartman
Jeff Hawkins
John-Dylan Haynes
Donald Hebb
Martin Heisenberg
Werner Heisenberg
John Herschel
Basil Hiley
Art Hobson
Jesper Hoffmeyer
Don Howard
John H. Jackson
William Stanley Jevons
Roman Jakobson
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Pascual Jordan
Eric Kandel
Ruth E. Kastner
Stuart Kauffman
Martin J. Klein
William R. Klemm
Christof Koch
Simon Kochen
Hans Kornhuber
Stephen Kosslyn
Daniel Koshland
Ladislav Kovàč
Leopold Kronecker
Rolf Landauer
Alfred Landé
Pierre-Simon Laplace
Karl Lashley
David Layzer
Joseph LeDoux
Gerald Lettvin
Gilbert Lewis
Benjamin Libet
David Lindley
Seth Lloyd
Hendrik Lorentz
Werner Loewenstein
Josef Loschmidt
Ernst Mach
Donald MacKay
Henry Margenau
Owen Maroney
David Marr
Humberto Maturana
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Ernst Mayr
John McCarthy
Warren McCulloch
N. David Mermin
George Miller
Stanley Miller
Ulrich Mohrhoff
Jacques Monod
Vernon Mountcastle
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Donald Norman
Alexander Oparin
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Howard Pattee
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Max Planck
Susan Pockett
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Daniel Pollen
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Hans Primas
Zenon Pylyshyn
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Jerome Rothstein
David Ruelle
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Tilman Sauer
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Aaron Schurger
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Thomas Sebeok
Franco Selleri
Claude Shannon
Charles Sherrington
David Shiang
Abner Shimony
Herbert Simon
Dean Keith Simonton
Edmund Sinnott
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Lee Smolin
Ray Solomonoff
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John Stachel
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Tom Stonier
Antoine Suarez
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Max Tegmark
Teilhard de Chardin
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William Thomson (Kelvin)
Richard Tolman
Giulio Tononi
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Francisco Varela
Vlatko Vedral
Mikhail Volkenstein
Heinz von Foerster
Richard von Mises
John von Neumann
Jakob von Uexküll
C. S. Unnikrishnan
C. H. Waddington
John B. Watson
Daniel Wegner
Steven Weinberg
Paul A. Weiss
Herman Weyl
John Wheeler
Wilhelm Wien
Norbert Wiener
Eugene Wigner
E. O. Wilson
Günther Witzany
Stephen Wolfram
H. Dieter Zeh
Semir Zeki
Ernst Zermelo
Wojciech Zurek
Konrad Zuse
Fritz Zwicky

Presentations

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James Symposium
 
S. H. Burbury

S. H. Burburyl was one of a number of British scientists who criticized the H-Theorem of Ludwig Boltzmann, which was widely believed to have shown that the entropy in an isolated system can only increase to a maximum. Boltzmann's quantity H is the opposite of entropy (in modern terms it is the negentropy or information).

Boltzmann at first (1872) claimed to have shown that his "minimum function" H (he actually used the German letter "E" which resembles the English "H") could be shown to decrease to a minimum as a consequence of the dynamic evolution of a gas of colliding particles. Boltzmann counted the number of particles that would leave a small volume of phase space as a result of collisions and compared it to the number of particles that would enter the same volume. This was called the Stosszahlansatz (collision number estimate).

Already in the 1870's William Thomson (Lord Kelvin) and Josef Loschmidt had criticized this dynamical derivation on the grounds that if all the velocities of the particle were reversed the H function would increase (entropy would decrease). And Boltzmann had agreed with them, saying in 1877 that the only proper derivation of the H-Theorem is statistical. Systems would evolve toward macrostates with the greatest probability (the greatest number of microstates). Boltzmann's definition of entropy is proportional to the logarithm if the number of microstates W.

S = k logW

The proportionality factor k was introduced by Max Planck in 1900. He called it Boltzmann's constant.

Scientists at the 1894 meeting of the British Association for the Advancement of Science (which was attended by Boltzmann) argued that there must be something causing "molecular disorder" or chaos that is introducing the irreversibility. Edward Culverwell suggested molecular disorder might be caused by the ether that was the presumed medium for electromagnetic waves. In 1890 he wrote:

We know that by means of the aether, bodies at a distance and wholly prevented from acting on each other molecularly, come to exactly the same temperature-equilibrium without any assistance from their collisions. Hence there is every reason to suppose that it is by the molecules interacting through the aether that the temperature-equilibrium is determined.

Then in 1894 he argued that something must be preventing the reversibility, since a dynamical analysis leads to perfect reversibility.

The remarkable differences of opinion as to what the H-theorem is, and how it can be proved, show how necessary is the discussion elicited by my letter...

I say that if that proof does not somewhere or other introduce some assumption about averages, probability, or irreversibility, it cannot be valid.

S. H. Burbury used the terms "haphazard" and "chaos" to describe what is needed.

The objection that I understand to be made is that if you reverse all the velocities after collisions, the system will retrace its course with H increasing - which is supposed to be contrary to the thing proved...

I think the answer to this would be that any actual material system receives disturbances from without, the effect of which, coming at haphazard, is to produce the very distribution of coordinates which is required to make H diminish.

Sir James Jeans in 1903 agreed with Culverwell and Burbury that interaction with radiation could be dissipative and change the physics of Boltzmann's conservative dynamical system.
In the first place the distribution of energy which is given by Boltzmann's Theorem is the only distribution which is permanent under the conditions postulated by this theorem. And in the second place, this law of distribution may break down entirely as soon as we admit an interaction, no matter how small, between the molecules and the surrounding ether. That such an interaction must exist is shown by the fact that a gas is capable of radiating energy. In fact, Boltzmann's Theorem rests on the assumption that the molecules of a gas form a conservative dynamical system, and it will appear that the introduction of a small dissipation function may entirely invalidate the conclusions of the theorem.* Thus we may regard the Boltzmann distribution as unstable, in the sense that a slight deviation from perfect conservation of energy may result in a complete redistribution of the total energy.
Boltzmann largely ignored the suggestions of the British physicists, ignoring the idea of randomizing radiation interactions, arguing instead that the mean free paths of particles in a dilute gas would allow the molecules to escape to distant parts of the gas, leaving behind any correlations (molecular order) with recent collisions. For Boltzmann, molecular disorder is a statistical condition, not a dynamic process whereby molecular paths are made haphazard and thus irreversible.
If the mean free path in a gas is large compared to the mean distance of two neighboring molecules, then in a short time, completely different molecules than before will be nearest neighbors to each other. A molecular-ordered but molar-disordered distribution will most probably be transformed into a molecular-disordered one in a short time. Each molecule flies from one collision to another one so far away that one can consider the occurrence of another molecule, at the place where it collides the second time, with a definite state of motion, as being an event completely independent (for statistical calculations) of the place from which the first molecule came (and similarly for the state of motion of the first molecule). However, if we choose the initial configuration on the basis of a previous calculation of the path of each molecule, so as to violate intentionally the laws of probability, then of course we can construct a persistent regularity or an almost molecular-disordered distribution which will become an molecular-ordered at a particular time. Kirchhoff also makes the assumption that the state is molecular-disordered in his definition of the probability concept.

Boltzmann was confident that probability played the major role and he prophetically described a future physics of "average values," eerily anticipating the "expectation values" of probabilistic indeterministic quantum physics.

Since today it is popular to look forward to the time when our view of nature will have been completely changed, I will mention the possibility that the fundamental equations for the motion of individual molecules will turn out to be only approximate formulas which give average values, resulting according to the probability calculus from the interactions of many independent moving entities forming the surrounding medium - as for example in meteorology the laws are valid only for average values obtained by long series of observations using the probability calculus. These entities must of course be so numerous and must act so rapidly that the correct average values are attained in millionths of a second.
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