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Core Concepts

Actualism
Adequate Determinism
Agent-Causality
Alternative Possibilities
Causa Sui
Causal Closure
Causalism
Causality
Certainty
Chance
Chance Not Direct Cause
Chaos Theory
The Cogito Model
Compatibilism
Complexity
Comprehensive   Compatibilism
Conceptual Analysis
Contingency
Control
Could Do Otherwise
Creativity
Default Responsibility
De-liberation
Determination
Determination Fallacy
Determinism
Disambiguation
Double Effect
Either Way
Emergent Determinism
Epistemic Freedom
Ethical Fallacy
Experimental Philosophy
Extreme Libertarianism
Event Has Many Causes
Frankfurt Cases
Free Choice
Freedom of Action
"Free Will"
Free Will Axiom
Free Will in Antiquity
Free Will Mechanisms
Free Will Requirements
Free Will Theorem
Future Contingency
Hard Incompatibilism
Idea of Freedom
Illusion of Determinism
Illusionism
Impossibilism
Incompatibilism
Indeterminacy
Indeterminism
Infinities
Laplace's Demon
Libertarianism
Liberty of Indifference
Libet Experiments
Luck
Master Argument
Modest Libertarianism
Moral Necessity
Moral Responsibility
Moral Sentiments
Mysteries
Naturalism
Necessity
Noise
Non-Causality
Nonlocality
Origination
Paradigm Case
Possibilism
Possibilities
Pre-determinism
Predictability
Probability
Pseudo-Problem
Random When?/Where?
Rational Fallacy
Refutations
Replay
Responsibility
Same Circumstances
Scandal
Science Advance Fallacy
Second Thoughts
Self-Determination
Semicompatibilism
Separability
Soft Causality
Special Relativity
Standard Argument
Supercompatibilism
Superdeterminism
Taxonomy
Temporal Sequence
Tertium Quid
Torn Decision
Two-Stage Models
Ultimate Responsibility
Uncertainty
Up To Us
Voluntarism
What If Dennett and Kane Did Otherwise?

Philosophers

Mortimer Adler
Rogers Albritton
Alexander of Aphrodisias
Samuel Alexander
William Alston
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
Isaiah Berlin
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
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
John Locke
Michael Lockwood
E. Jonathan Lowe
John R. Lucas
Lucretius
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
C. Lloyd Morgan
Thomas Nagel
Friedrich Nietzsche
John Norton
P.H.Nowell-Smith
Robert Nozick
William of Ockham
Timothy O'Connor
David F. Pears
Charles Sanders Peirce
Derk Pereboom
Steven Pinker
Plato
Karl Popper
Porphyry
Huw Price
H.A.Prichard
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
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
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

Presentations

Biosemiotics
Free Will
Mental Causation
James Symposium

 
Probability
Probability was introduced as an acceptable euphemism for chance in the eighteenth century, by Pierre-Simon Laplace, for example, who called his work the "calculus of probabilities."

The root meaning of probability was originally "approbation." Something probable was deserving of belief. This connotation has been lost in modern times as the understanding of mathematical probabilities has become widespread. Although some epistemologists still connect "degrees of belief" with epistemic probabilities.

Chance, on the other hand, was associated with gambling and other disreputable ideas. Something chancy was risky and evoked disapprobation. Many religious philosophers equated belief in chance with atheism.
We can distinguish probability from statistics by reserving the term probability for the a priori or epistemic sense of the term.

Probabilities are a priori theories. Statistics are a posteriori experiments.

The a priori probability of two dice showing two sixes is 1/36. A priori probability assumes that we have no information that favors one outcome over the others. This is the principle of indifference or principle of insufficient reason. Specifically, it assumes that all outcomes are equally probable. In short, all other things being equal, things are equal.

If we did have information about a difference, we would adjust our probabilities. The increase in our information or "state of knowledge" is the essential idea in Bayesian probability.

And how might we come by such additional information? By running experimental trials and gathering data on the frequencies of real outcomes. This is the work of statistics.

In the theory of measurements and measurement errors, we find a dispersion in measurements when we are measuring the same thing over and over. These are measurement errors. It is very important to distinguish measurement errors from real variations in the thing measured. But this is not easy, because errors and the natural distribution in values of a measured property normally follow the same distribution function.

If the values of some property in a population is the consequence of independent random events, for example coin flips that result in heads instead of tails, the distribution can be shown to follow the well-known bell-shaped curve or "normal" distribution.

Pr(x) = (1/√(2π)) e-x2/2

Observational errors themselves are the result of independent random factors, so they follow the same distribution.

This distribution function was discovered in the 1720's by the French mathematician Abraham de Moivre. It was identified with measurement errors by astronomers measuring star positions in the early nineteenth century, notably by the Belgian astronomer Adolphe Quételet.

An unfortunate choice of terms led to this being called the "law of errors." Mathematicians and philosophers both jumped to the erroneous conclusion that if random events followed "laws" that they must in fact be determined by those laws.

De Moivre's work was a famous book called "The Doctrine of Chances." In the 1738 edition he found that in the limit of large numbers of tosses of a coin, the discrete binomial expansion of (p - q)n could be approximated by a continuous mathematical curve (the modern bell curve).

This was an era when mathematical analysis and continuity carried an aura of deterministic causal truth, compared to the chance nature of individual random events.

The curve was first called the "normal distribution" by Charles Sanders Peirce, who better than any other philosopher articulated the difference between a priori probabilities and a posteriori statistics.

For reasons that are philosophically and physically very deep (basically the fundamental discreteness of nature), we find a similar random distribution of many physical, biological, and social characteristics. Note that the distribution of such characteristics is ontological, not epistemic. It is not a matter of what humans can know, but how things are in a mind-independent external world..

Social scientists in the early nineteenth century argued that randomness in many populations was governed by this "law." Adolphe Quetelet was a Belgian astronomer who developed the error distribution as a way to analyze and reduce the data from astronomical observations. He then found the same distribution function in many human statistics, the number of marriages and suicides per year, for example. He found "norms for many human characteristics, such as height, and promoted the concept of the average man (l'homme moyen) . Quetelet and other social scientists mistakenly concluded that the "lawfulness" of these normal distributions affirmed the fundamental deterministic nature of the world.

To the modern sensibility, an argument that all events are determined because their characteristics are random and normally distributed seems illogical and a bit perverse. But such was the philosophical and religious commitment of nineteenth-century scientists to the many forms of determinism.

If just one single event is determined by chance, then indeterminism would be true, some philosophers say, which would undermine the very possibility of certain knowledge. Some go to the extreme of saying that chance makes the state of the world totally independent of any earlier states, which is nonsense, but it shows how anxious they are about chance.

In statistical mechanics, the state of least information (equilibrium) can be achieved in many more ways than states with recognizable information. The equilibrium macrostate has the most microstates, each assumed to have equal a priori probability. If a system begins in an initially ordered state (high information), it tends to evolve toward states of disorder (absence of microscopic information). The increase of entropy (second law of thermodynamics) is then seen to be a decrease of information. The mathematical equations for entropy and information turn out to be identical apart from their sign and arbitrary constants.

Both are proportional to the logarithm of the number W of microstates consistent with the macrostate information.

I ∝ -S ∝ lnW

Both James Clerk Maxwell and Ludwig Boltzmann were familiar with the work of Quetelet and his English colleague Thomas Buckle. Maxwell, and probably Boltzmann too, used the above law of distribution of random events in the limit of large numbers to help them derive the law for the distribution of molecular velocities in a gas.

For Teachers
For Scholars
Aristotle on Probability, Rheetoric, Book II, Chapter 24, section 10, line 1402a2
[9] ἄλλος παρὰ τὴν ἔλλειψιν τοῦ πότε καὶ πῶς, 
οἷον ὅτι δικαίως Ἀλέξανδρος ἔλαβε τὴν Ἑλένην: αἵρεσις γὰρ αὐτῇ ἐδόθη παρὰ τοῦ πατρός. οὐ γὰρ ἀεὶ ἴσως, ἀλλὰ τὸ πρῶτον: καὶ γὰρ ὁ πατὴρ μέχρι τούτου κύριος. 
ἢ εἴ τις φαίη τὸ τύπτειν τοὺς ἐλευθέρους ὕβριν εἶναι: οὐ γὰρ πάντως, ἀλλ᾽ ὅταν ἄρχῃ χειρῶν ἀδίκων. [10] ἔτι ὥσπερ ἐν τοῖς ἐριστικοῖς παρὰ τὸ ἁπλῶς καὶ μὴ ἁπλῶς, ἀλλὰ τί, γίγνεται φαινόμενος 
συλλογισμός, οἷον ἐν μὲν τοῖς διαλεκτικοῖς ὅτι ἔστι τὸ μὴ ὄν [ὄν], ἔστι γὰρ τὸ μὴ ὂν μὴ ὄν, καὶ ὅτι ἐπιστητὸν τὸ ἄγνωστον, ἔστιν γὰρ ἐπιστητὸν τὸ ἄγνωστον ὅτι ἄγνωστον, οὕτως καὶ ἐν τοῖς ῥητορικοῖς ἐστιν φαινόμενον ἐνθύμημα παρὰ τὸ μὴ ἁπλῶς εἰκὸς ἀλλὰ τὶ εἰκός. ἔστιν δὲ τοῦτο οὐ καθόλου, ὥσπερ 
καὶ Ἀγάθων λέγει

“τάχ᾽ ἄν τις εἰκὸς αὐτὸ τοῦτ᾽ εἶναι λέγοι,

βροτοῖσι πολλὰ τυγχάνειν οὐκ εἰκότα.

” γίγνεται γὰρ τὸ παρὰ τὸ εἰκός, ὥστε εἰκὸς καὶ τὸ παρὰ τὸ εἰκός, εἰ δὲ τοῦτο, ἔσται τὸ μὴ εἰκὸς εἰκός. ἀλλ᾽ οὐχ ἁπλῶς, 
ἀλλ᾽ ὥσπερ καὶ ἐπὶ τῶν ἐριστικῶν τὸ κατὰ τί καὶ πρὸς τί καὶ πῇ οὐ προστιθέμενα ποιεῖ τὴν συκοφαντίαν, καὶ ἐνταῦθα παρὰ τὸ εἰκὸς εἶναι μὴ ἁπλῶς ἀλλὰ τὶ εἰκός.

[11] ἔστι δ᾽ ἐκ τούτου τοῦ τόπου ἡ Κόρακος τέχνη συγκειμένη: “ἄν τε γὰρ μὴ ἔνοχος ᾖ τῇ αἰτίᾳ, οἷον ἀσθενὴς ὢν αἰκίας φεύγει (οὐ γὰρ εἰκός), κἂν ἔνοχος ᾖ, οἷον ἰσχυρὸς ὤν (οὐ γὰρ εἰκός, ὅτι εἰκὸς ἔμελλε δόξειν)”. ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων: ἢ γὰρ ἔνοχον ἀνάγκη ἢ μὴ ἔνοχον εἶναι τῇ αἰτίᾳ: φαίνεται μὲν οὖν ἀμφότερα εἰκότα, ἔστι δὲ τὸ μὲν εἰκός, τὸ δὲ οὐχ ἁπλῶς ἀλλ᾽ ὥσπερ εἴρηται: καὶ τὸ τὸν ἥττω δὲ λόγον κρείττω ποιεῖν τοῦτ᾽ ἔστιν. καὶ ἐντεῦθεν δικαίως ἐδυσχέραινον οἱ ἄνθρωποι τὸ Πρωταγόρου ἐπάγγελμα: ψεῦδός τε γάρ ἐστιν, καὶ οὐκ ἀληθὲς ἀλλὰ φαινόμενον εἰκός, καὶ ἐν οὐδεμιᾷ τέχνῃ ἀλλ᾽ <ἢ> ἐν ῥητορικῇ καὶ ἐριστικῇ.

[10] Further, as in sophistical disputations, an apparent syllogism arises as the result of considering a thing first absolutely, and then not absolutely, but only in a particular case. For instance, in Dialectic, it is argued that that which is not is, for that which is not is that which is not1; also, that the unknown can be known, for it can be known of the unknown that it is unknown. Similarly, in Rhetoric, an apparent enthymeme may arise from that which is not absolutely probable but only in particular cases. But this is not to be understood absolutely, as Agathon says:

“ One might perhaps say that this very thing is probable,
that many things happen to men that are not probable;

” for that which is contrary to probability nevertheless does happen, so that that which is contrary to probability is probable. If this is so, that which is improbable will be probable. But not absolutely; but as, in the case of sophistical disputations, the argument becomes fallacious when the circumstances, reference, and manner are not added, so here it will become so owing to the probability being not probable absolutely but only in particular cases. 1 The first “is” means “has a real, absolute existence”; the second “is” merely expresses the identity of the terms of the proposition, and is particular; but the sophistical reasoner takes it in the same sense as the first. The same applies to the argument about the unknown.


Chapter 3.7 - The Ergod Chapter 4.2 - The History of Free Will
Part Three - Value Part Five - Problems
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