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 Enlightenment 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 Reason 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 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 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 Frederic Fitch 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 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 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.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 Teilhard de Chardin 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 Jeffrey Bada 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 Gregory Chaitin Jean-Pierre Changeux Arthur Holly Compton John Conway 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 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 David Foster Joseph Fourier Philipp Frank Steven Frautschi Edward Fredkin 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 J. B. S. Haldane Stuart Hameroff Augustin Hamon Sam Harris Hyman Hartman John-Dylan 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 William R. Klemm Christof Koch Simon Kochen Hans Kornhuber Stephen Kosslyn Ladislav Kovàč Leopold Kronecker Rolf Landauer Alfred Landé Pierre-Simon Laplace David Layzer Joseph LeDoux Benjamin Libet Seth Lloyd Hendrik Lorentz Josef Loschmidt Ernst Mach Donald MacKay Henry Margenau James Clerk Maxwell Ernst Mayr John McCarthy Warren McCulloch George Miller Stanley Miller Ulrich Mohrhoff Jacques Monod Emmy Noether Alexander Oparin 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 Juan Roederer Jerome Rothstein David Ruelle Tilman Sauer Jürgen Schmidhuber Erwin Schrödinger Aaron Schurger Claude Shannon Charles Sherrington David Shiang Herbert Simon Dean Keith Simonton B. F. Skinner Lee Smolin Ray Solomonoff 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 Stephen Wolfram H. Dieter Zeh Ernst Zermelo Wojciech Zurek Konrad Zuse Fritz Zwicky Presentations Biosemiotics Free Will Mental Causation James Symposium |
Contingency
All facts about the world are (necessarily?) empirical and a posteriori, and thus contingent.
Modal logic is the analysis and qualification of statements or propositions as asserting or denying necessity, possibility, impossibility, and, most problematic, contingency.
The use of "necessity" and "impossibility" to describe the physical world should be guarded and understood to describe events or "states of affairs" that have extremely high or low probability. The term certainty, when used about knowledge of the physical world, normally represents only extremely high probability.
Possibility and contingency are not easily constrained to the binary values of true and false. To begin with, possibility is normally understood to include necessity. If something is necessary, it is a fortiori possible. Contingency must be defined as the subset of possibility that excludes necessity.
The modal operators are a box '◻' for necessity and a diamond ' ◇ ' for possibility. Impossibility is the negation of possibility, ¬◇, and contingency must negate necessity and also negate impossibility, so it is the logical conjunction of "not necessity" and "possibility" (¬◻ ∧ ◇).
Mathematically, contingency is a continuum of values between impossibility and necessity, the open interval between 0 and 1 that represents all the probabilities (excluding the certainties. It is the negation of the logical disjunction of necessity and impossibility, neither necessary nor impossible. (¬ (◻ ∨ ¬◇)).
But physically, contingency is the closed interval, including the endpoints of necessity (1) and impossibility (0). Theoretical physics today is often described as probabilistic and statistical, which is sometimes misunderstood to exclude perfect certainties like 0 and 1, but this is not the case. Even quantum physics, the basis of ontological chance in the universe, sometimes predicts certain outcomes, as explained by Paul Dirac.
With its four modes, necessity, possibility, impossibility, and contingency, modal analyses simply contain more than can be confined to two-valued truth-functions, whether in logic, usually called a priori truths, or language analysis, usually called analytic truths, nor in supposed metaphysical truths.
Truth is a binary relation of ideas, true or false. Facts of the matter have a continuous value somewhere between 0 and 1, with plus or minus estimates of the standard deviation of probable errors around that value.
In analytic language philosophy, we need more than the "truth" of statements and propositions with their apparent claims about "necessary" facts in the world. The logical empiricists equate necessity in the first-order logic of their "object language" with analyticity in their higher-order "metalanguage" of propositional functions.
Although we distinguish the a priori truths of logic from the analytic truths of language philosophy, many such "truths" were discovered long before modern methods were invented to demonstrate their "proofs.' In that sense, knowledge is usually discovered a posteriori and ultimately all knowledge is synthetic in the Kantian sense.
Since facts about the world are empirical and a posteriori, and thus contingent, it is best to restrict the use of the concept "truth" to logic and to analytic discourse about statements and propositions. Truth is an appropriate concept in "ideal" formal systems like philosophical logic and mathematics where the extremes of necessity and impossibility are defined parts of the system. But the world itself cannot be confined to a Procrustean bed of true and false.
We therefore conclude that the logical empiricist's idea that the laws of nature can be described with linguistic statements or propositions is simply wrong. This is particularly the case for the laws of modern physics, which are now irreducibly probabilistic in view of the indeterministic nature of quantum mechanics, the uncertainty principle, etc.
The "evidence" that "verifies" or validates a physical theory is gathered from a very large number of experiments. No single measurement can establish a fact in the way that a single valid argument can assert the "truth" of an analytic statement. The large number of measurements means that evidence is statistical. Indeed, physical theories make predictions that are probabilities. Theories are confirmed when the a priori probabilities match the a posteriori statistics.
Probability is a theory, statistics are the results of experiments.
Information philosophy considers claims such as "If P, then P is true" to be redundant, adding no information to the (true) assertion of the statement or proposition "P." Further redundancies are equally vacuous, such as "If P is true, then P is necessarily true" and "If P is true, then P is necessarily true in all possible worlds."
Logically necessary and analytic statements are tautological and carry no new information. This is the paradox of analyticity. The statement "A is A" tells us nothing. The statement "A is B" is informative.
Adding "is true" and the like also add no new information. They cannot change the fundamental nature of a statement. For example, they cannot change a contingent statement into a necessary one. Consider the statement "x is contingently y" Prepending the necessity operator, we have "Necessarily, x is contingently y." It changes nothing.
Consider Q(x = y), where "'Q' (for questionable) is a contingency operator parallel to ' ◻' and ' ◇ ' Can we interchange the operators in ◻Q(x = y) to get Q◻(x = y)? Would it change the meaning from x is possibly y and possibly not y?
Future Contingency
Diodorus Cronus (Διόδωρος Κρόνος, Cronus was a nickname, the old 'crone') was a member (or perhaps a late follower) of the Megarian School, whose arguments about the truth and falsity of statements about the future may have influenced or been influenced by Aristotle. But they have certainly influenced modern philosophers who think that philosophical problems and facts in the world can be decided by logic and language games.
Diodorus was known as "The Dialectician," testimony to his sophistry with words, or for his ability to create paradoxes. Epictetus wrote a diatribe "Against those who embrace philosophical opinions only in words," in Book 2, Chapter 1, of his Discourses. It is our major reference to Diodorus and his famous Master Argument (the κυριεύων or κύριος λόγος).
Diodorus' Master Argument is a set of propositions designed to show that the actual is the only possible and that some true statements about the future imply that the future is already determined. This follows logically from his observation that if something in the future is not going to happen, it must have been that statements in the past that it would not happen must have been true.
The Master Argument was central in the Hellenistic debates about determinism, as shown by Cicero's descriptions in On Fate.
It is closely related to the problem of future contingency, also discussed by Diodorus, but made famous in Aristotle's example of a Sea-Battle in De Interpretatione 9. Aristotle thought that statements about the past and present must be either true or false. But statements about the future are only potentials, possibilities, so they lack any truth value until their potential becomes actual at some time in the future.
Note that there are in fact some things in the past that can be changed in the future. It is the truth value of a statement made in the past. The truth value of Aristotle's statement "there will be a sea-battle next week," can "actually" be changed if the event does not happen, showing that the concept of a "fixed past," so important in analytic language philosophy debates about free will, has some changeability. In analytical language philosophy, the "fixed past" is far from fixed.
Diodorus was a great logician and word-juggler. Like Socrates, he wrote little or nothing and preferred verbal debates. The Dialectician was a precursor of the later language game players, Ludwig Wittgenstein, Jacques Derrida, and Daniel Dennett.
Diodorus applied Democritus' great insight that much knowledge is pure convention (νόμος), but "in reality" there is only atoms and a void.
For Diodorus, language definitions were conventional and quite arbitrary. Perhaps his most famous example (also attributed to Eubulides) was the linguistic puzzle of how to define a "heap" (metaphysicians call this the Sorites puzzle, from Greek σωρείτης so-ri'-tes, meaning "heaped up"). When does a number of grains become a heap? One? No. Two? No. Three? Etc. Or, given a heap of grains, as you take grains away, at which point does it stop being a heap?
Aristotle on Contingency
That Aristotle believes in an open and ambiguous future with alternative possibilities is also shown by his denial of the logical Master Argument for determinism of Diodorus Cronus, in the form of Aristotle's famous "sea battle."
Diodorus argued from an assumed necessity of past truths (which is understandable, if a misapplication of logic to physical reality) that something is impossible that neither is or ever will be true.
Aristotle reframed the argument as the truth or falsity of the statement that a sea battle will occur tomorrow. Despite the law of the excluded middle (or principle of bivalence), which allows no third case (or tertium quid), Aristotle concluded that the statement is neither true nor false, supporting an ambiguous future.
What is, necessarily is, when it is; and what is not, necessarily is not, when it is not. But not everything that is, necessarily is; and not everything that is not, necessarily is not. For to say that everything that is, is of necessity, when it is, is not the same as saying unconditionally that it is of necessity. Similarly with what is not. And the same account holds for contradictories: everything necessarily is or is not, and will be or will not be; but one cannot divide and say that one or the other is necessary. I mean, for example: it is necessary for there to be or not to be a sea-battle tomorrow; but it is not necessary for a sea-battle to take place tomorrow, nor for one not to take place — though it is necessary for one to take place or not to take place. So, since statements are true according to how the actual things are, it is clear that wherever these are such as to allow of contraries as chance has it, the same necessarily holds for the contradictories also. This happens with things that are not always so or are not always not so. With these it is necessary for one or the other of the contradictories to be true or false — not, however, this one or that one, but as chance has it; or for one to be true rather than the other, yet not already true or false.Aristotle never denied the law of the excluded middle, merely that the truth or falsity of statements about future events does not exist yet. Note that this implies some things in the past may be changed in the future, i.e., the truth values of past statements about the future. Normal | Teacher | Scholar |