Citation for this page in APA citation style.

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 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 |
The Sorites Puzzle of the Heap
The Sorites problem was one of a number of paradoxes created by the 4th century BCE Megarian philosopher Eubulides, who was a pupil of Euclid.
The Greek word
Would you describe a single grain of wheat as a heap? Not at all. Another variation is to start with a genuinely large heap, claim that the following two premises are true, then remove grains of sand.
A million grains of sand is a heap of sand After removing enough grains, we get to the borderline cases of the paradox. The second premise shows that one grain is absolutely not a heap, because removing one grain leaves nothing, let alone a heap. Sorites problems are also called "little by little" because small changes may be indiscernible in large objects but they become obvious when applied long enough and the object becomes small. A characteristic of all Sorites puzzles is the breakdown of truth conditions at some point along the soritical chain of steps from one end to the other. This is often considered a logical paradox, but it seems to be created by our ambiguous language..
Sorites paradoxes appear to resemble proofs by mathematical induction. If F, and given any _{n+1}n where F is true, then it is true for all _{n}n.
The Stoics are said to have backed away from the strong conditional A ⇒ B to a weaker material implication where A → B is true just in the case that either A is false or B is true, or not (¬A ∨ B) . But this did hot help them.
Viewed from the point of the infinite series of mathematical induction, the problem can be found in the fact that for some n is small), while for other values of n, F is true.
_{n}
∀
But there is no particular point n along the chain where the failure is obvious, since each step seems too small to make the difference. Put another way, there is no transitivity of truth back and forth
Some philosophers regard this failure at some point midway between One semi-formal way out might be say that either/or soritical terms need a third option or even a "dialectical" acceptance of "both." This is similar but not identical to the failure of bi-valence in statements about the future that are neither true nor false. We are often somewhere in the middle between extremes, neither rich nor poor, but middle class, neither hot nor cold, but Goldilocks "just right." Accepting "both" might be statements like, "He's bald but he's not that bald."
Another workaround for sorites paradoxes might be to notice that neither/nor can be said of the truth value for situations in the vagueness gap. For example, somewhere between small and large, we might say it's neither small nor large. Then if we say that small = "not large," we can say that in the gap we have neither small nor not small is true. Since it is always true that everything is either small or not small, without knowing which, some metatheorists imagine a " The fact that large objects appear not to change when small, indiscernible changes are made is also called a vagueness problem. A classic example is Peter Unger's observation that a few water molecules at the edge of a cloud may be removed with no obvious change in the cloud.
See also David Wiggins's version of Tibbles the Cat as really 1,001 cats by selectively excluding one of Tibbles' 1,000 hairs.
Unger's conclusion was that the water molecules may compose many clouds by selectively excluding or including just a few molecules. This is known as the Problem of the Many, but Unger's first response was to say that the ambiguity meant that there are no clouds at all, a position known as mereological nihilism that is now endorsed by Peter van Inwagen.
Liar Paradox
Eubulides also created a variation on Sorites with the number of hairs on a bald man's head and the much more famous Liar's Paradox
A man says that he is lying. Is what he says true or false? A modern self-referential variation is Russell's Paradox
The statement in this box is false
Normal | Teacher | Scholar |