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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 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
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
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
David Hume
Ferenc Huoranszki
Frank Jackson
William James
Lord Kames
Robert Kane
Immanuel Kant
Tomis Kapitan
Walter Kaufmann
Jaegwon Kim
William King
Hilary Kornblith
Christine Korsgaard
Saul Kripke
Thomas Kuhn
Andrea Lavazza
Christoph Lehner
Keith Lehrer
Gottfried Leibniz
Jules Lequyer
Leucippus
Michael Levin
Joseph Levine
George Henry Lewes
C.I.Lewis
David Lewis
Peter Lipton
C. Lloyd Morgan
John Locke
Michael Lockwood
Arthur O. Lovejoy
E. Jonathan Lowe
John R. Lucas
Lucretius
Alasdair MacIntyre
Ruth Barcan Marcus
Tim Maudlin
James Martineau
Nicholas Maxwell
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.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
C.F. von Weizsäcker
William Whewell
Alfred North Whitehead
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
E. T. Jaynes
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
James Clerk Maxwell
Ernst Mayr
John McCarthy
Warren McCulloch
N. David Mermin
George Miller
Stanley Miller
Ulrich Mohrhoff
Jacques Monod
Vernon Mountcastle
Emmy Noether
Donald Norman
Alexander Oparin
Abraham Pais
Howard Pattee
Wolfgang Pauli
Massimo Pauri
Wilder Penfield
Roger Penrose
Steven Pinker
Colin Pittendrigh
Walter Pitts
Max Planck
Susan Pockett
Henri Poincaré
Daniel Pollen
Ilya Prigogine
Hans Primas
Zenon Pylyshyn
Henry Quastler
Adolphe Quételet
Pasco Rakic
Nicolas Rashevsky
Lord Rayleigh
Frederick Reif
Jürgen Renn
Giacomo Rizzolati
Emil Roduner
Juan Roederer
Jerome Rothstein
David Ruelle
David Rumelhart
Tilman Sauer
Ferdinand de Saussure
Jürgen Schmidhuber
Erwin Schrödinger
Aaron Schurger
Sebastian Seung
Thomas Sebeok
Franco Selleri
Claude Shannon
Charles Sherrington
David Shiang
Abner Shimony
Herbert Simon
Dean Keith Simonton
Edmund Sinnott
B. F. Skinner
Lee Smolin
Ray Solomonoff
Roger Sperry
John Stachel
Henry Stapp
Tom Stonier
Antoine Suarez
Leo Szilard
Max Tegmark
Teilhard de Chardin
Libb Thims
William Thomson (Kelvin)
Richard Tolman
Giulio Tononi
Peter Tse
Alan Turing
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

Biosemiotics
Free Will
Mental Causation
James Symposium
 
Jacques Hadamard
Jacques Hadamard was a great mathematician who studied his thought processes in solving mathematical problems. He interviewed many other leading mathematicians and scientists, including Henri Poincaré, many of whom shared Hadamard's experience that solutions to problems often came suddenly and completely, generally after long reflections on the problem.

In his 1945 book Psychology of Invention in the Mathematical Field, Hadamard described the Synthèse conference in Paris in 1936 to study creativity. In Chapter III, Hadamard described how the combination of random ideas could lead to a choice of the best combination. Chance alone is not enough.

Combination of Ideas. What we just observed concerning the unconscious in general will be seen again from another angle, when speaking of its relations with discovery. We shall see a little later that the possibility of imputing discovery to pure chance is already excluded by Poincaré's observations, when more attentively considered.

On the contrary, that there is an intervention of chance but also a necessary work of unconsciousness, the latter implying and not contradicting the former, appears, as Poincaré shows, when we take account not merely of the results of introspection, but of the very nature of the question.

Indeed, it is obvious that invention or discovery, be it in mathematics or anywhere else, takes place by combining ideas.1 Now, there is an extremely great number of such combinations, most of which are devoid of interest, while, on the contrary, very few of them can be fruitful. Which ones does our mind — I mean our conscious mind — perceive? Only the fruitful ones, or exceptionally, some which could be fruitful.

However, to find these, it has been necessary to construct the very numerous possible combinations, among which the useful ones are to be found.

It cannot be avoided that this first operation take place, to a certain extent, at random, so that the role of chance is hardly doubtful in this first step of the mental process. But we see that that intervention of chance occurs inside the unconscious: for most of these combinations — more exactly, all those which are useless — remain unknown to us.

Moreover, this shows us again the manifold character of the unconscious, which is necessary to construct those numerous combinations and to compare them with each other.

The Following Step. It is obvious that this first process, this building up of numerous combinations, is only the beginning of creation, even, as we should say, preliminary to it. As we just saw, and as Poincaré observes, to create consists precisely in not making useless combinations and in examining only those which are useful and which are only a small minority. Invention is discernment, choice.

To Invent Is to Choose. This very remarkable conclusion appears the more striking if we compare it with what Paul Valéry writes in the Nouvelle Revue Française: "It takes two to invent anything. The one makes up combinations; the other one chooses, recognizes what he wishes and what is important to him in the mass of the things which the former has imparted to him.

"What we call genius is much less the work of the first one than the readiness of the second one to grasp the value of what has been laid before him and to choose it."

We see how beautifully the mathematician and the poet agree in that fundamental view of invention consisting of a choice.

Esthetics in Invention. How can such a choice be made? The rules which must guide it "are extremely fine and delicate. It is almost impossible to state them precisely; they are felt rather than formulated. Under these conditions, how can we imagine a sieve capable of applying them mechanically?"

Though we do not directly see this sieve at work, we can answer the question, because we are aware of the results it affords, i.e., the combinations of ideas which are perceived by our conscious mind. This result is not doubtful. "The privileged unconscious phenomena, those susceptible of becoming conscious, are those which, directly or indirectly, affect most profoundly our emotional sensibility.

"It may be surprising to see emotional sensibility invoked à propos of mathematical demonstrations which, it would seem, can interest only the intellect. This would be to forget the feeling of mathematical beauty, of the harmony of numbers and forms, of geometric elegance. This is a true esthetic feeling that all real mathematicians know, and surely it belongs to emotional sensibility."

That an affective element is an essential part in every discovery or invention is only too evident, and has been insisted upon by several thinkers; indeed, it is clear that no significant discovery or invention can take place without the will of finding. But with Poincaré, we see something else, the intervention of the sense of beauty playing its part as an indispensable means of finding. We have reached the double conclusion:

that invention is choice
that this choice is imperatively governed by the sense of scientific beauty.

Hadamard described Poincaré as the source of the basic idea, but he credited Paul Valéry with the idea that there are two stages in creativity, perhaps even two entities - one to generate random alternative_possibilities, and the other to select or choose the best alternative.

These suggestions of Hadamard's were a major influence on Daniel Dennett's 1978 two-stages model of decision making which were later dubbed "Valerian." Dennett quotes the Valéry "It takes two to invent anything...," and then imagines the two stages in one mind.

Hadamard quoted Mozart to show that the first stage involves ideas that just "come to us" freely.

When I feel well and in a good humour, or when I am taking a drive or walking after a good meal, or in the night when I cannot sleep, thoughts crowd into my mind as easily as you could wish. Whence and how do they come? I do not know and I have nothing to do with it. Those which please me I keep in my head and hum them; at least others have told me that I do so....Then my soul is on fire with inspiration.
Hadamard and Poincaré both describe ideas that "present themselves" as William James described it.

Hadamard and Irreversibility
In 1906 Hadamard wrote a review of Josiah Willard Gibbs' Elementary Principles of Statistical Mechanics. (Bulletin of the American Mathematical Society, 12, p.194-210) He called it pure mathematics, applying the calculus of probabilities (of Laplace and others) to mechanics.

He wrote:

It remains to address the most important and most delicate that raises the study of the distribution phase. What happens to this distribution in the course of the movement, when part of any state: it tends, for example, to move closer to the canonical distribution or any distribution with similar properties?

This is, in short, the vital issue for kinetic theories. The paradox related and which seems at first to determine in advance any theory of this kind is as follows. How can the equations of dynamics, which are all reversible, lead to irreversible laws, to the growth of entropy? (p.201)

[Il reste à traiter la question la plus importante et la plus délicate que soulève cette étude de la distribution en phase. Que devient cette distribution au cours du mouvement, lorsqu'on part d'un état quelconque: tend-elle, par exemple, à se rapprocher de la distribution canonique ou d'une distribution présentant des propriétés analogues?

C'est, en somme, la question vitale pour les théories cinétiques. Le paradoxe qui s'y rattache et qui semble, au premier abord, miner par avance toute théorie de cette nature est eu effet le suivant. Comment, eu partant d'équations de la dynamique, toutes réversibles, parviendra-t-on à des lois irréversibles, à la croissance de l'entropie?]

We develop an answer in our treatment of micro-irreversibility.

Chapter 1.5 - The Philosophers Chapter 2.1 - The Problem of Knowledge
Home Part Two - Knowledge
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