Index

Note: Page numbers in bold refer to the primary treatment of a specific philosopher. Page numbers in italics refer to concept definitions. Page numbers with (fig) refer to illustrations.

Abelard, Peter, 203

abstraction axiom, 33031

absurdities, paradoxes as, 358

Academic Questions (Cicero), 8889

Academic Skepticism, 152, 163, 169

Academica (Cicero), 19798

Academy, 84, 85, 135

Achilles, 36667

acquired traits theory, 11

“Address to the Academie Parisienne de Mathematiques” (Pascal), 223

aerodynamics, 222

aesthetics, 74

Against the Logicians (Sextus Empiricus), 148, 156

Agathon, 11718

Albert of Saxony, 2012

Albert the Great, 199

Alexander the Great, 85, 86, 171, 208

Alexinus, 212

Alice’s Adventures in Wonderland (Carroll), 33334

allegory of the cave, 6768

Amasis, 1315

Anaxagoras, 43

Anaximander, 118, 33

Anaximenes, 208

Andronikos of Rhodes, 88

Anscombe, Elizabeth, 12122

Anselm of Canterbury, 168

anthropomorphism, 17

antinomies: antinomies of pure reason, 249, 28793, 29395, 304; premiseless antinomies, 368; Quine on, 35152

“Antinomy” (White), 302

Antipater, 86

Antisthenes of Athens, 112

Apelles, 14950

Apellikon of Teos, 8788

Apollo, 51

apostolic poverty doctrine, 19394

appearances, 29697, 303, 304

Aquinas, Thomas, 144, 17786, 199, 203

Arcesilaus, 134, 135

Archimedes, 46, 241, 269

argument against place, 52

arguments in paradoxes, 6, 9

argumentum ad hominem, 271

argumentum cornutum, 96

Aristocles (Plato), 100101. See also Plato

Ariston, 137

Aristophanes, 162

Aristotle, 11629; on Anaximander, 13; argument patterns, 354; Aspasius on, 96; on common sense, 8, 12325; condemnation of 1277, 189; Copernican paradox and, 224; ethical theory, 9798; on fatalism, 129; growing argument, 133; influence, 8788; on language, 356; on the liar paradox, 198; library, 8788; monarchy paradox, 8586; motion paradoxes, 49, 5052; on origins, 11; rules of inference, 299; spy questions, 8486; on substances and properties, 266; on time, 12122; on vacuums, 221

arithmetic. See mathematics

arithmetic machine, 21621

arrow paradox, 3067

Ars Combinatoria (Leibniz), 245

assertions, lies as, 9192

astrology, 165

astronomy, 311

atomism, 243, 28990

“The Auction of Philosophers” (Lucian), 2078

Augustine, 16276; on God’s existence, 1718; immutability of God, 178, 179; influence, 213; on the liar paradox, 197; on reason, 168, 287

axiom of infinity, 368

Babylonians, 21

Bach, Emmon, 202

balance, 22

barber paradox, 365

barometers, 22122

Basic Laws of Arithmetic (Frege), 329

Beauvoir, Simone de, 343

Beckman, Peter, 182, 183

Being and Nothingness (Sartre), 343

Bennett, Robert, 39

Berkeley, George, 217, 297, 318

Bernoulli, Daniel, 23233

Bernoulli, Nicholas, 232, 235

Berry, G. G., 332

Bertrand, Joseph Louis, 24651

Bertrand’s paradox, 246

Beyond Good and Evil (Nietzsche), 125

Bieberbach, Ludwig, 236

“The Big Rock Candy Mountain” (McClintock), 242

birthday paradox, 353

bisection argument, 352

bivalence principle, 9596, 122

Blair, Hugh, 27778

Boethius, 178

bridge paradox, 207

British empiricism, 25567

Brouwer, Luitzen, 325

Buddhism, 93

bundle theory, 266

Burali-Forti, Cesare, 32728

Burali-Forti paradox, 32728, 368

Buridan, Jean, 20615, 352

Burke, Michael, 13840, 143

calculator, 219, 220

Callisthenes, 86

Camus, Albert, 44, 343

Canadian flag, 7 (fig)

Candide (Voltaire), 242

Cantor, Georg, 5455, 57, 31718, 32228, 34647

Cardano, Gerolama, 22324

cardinality, 32324, 325

Carneades, 152

Carroll, Lewis, 4, 214, 33334, 358, 366

Carter, Brandon, 35051, 369, 370

Catholicism, 144, 167

causal theory of perception, 270

cave allegory, 6768

certainties, 169

Cervantes, Miguel de, 209

chess problems, 11617

chicken or egg paradox, 4, 11

Chisholm, Roderick, 143

Choice and Chance (Skyrms), 354

Christianity. See also God: Aquinas, 17786; Augustine, 16376; condemnation of 1277, 18790, 191, 196; divine command theory, 192; faith, 16566; freewill and, 128, 191; origins of the universe and, 10; Pascal’s evangelism, 22932

Chroust, Anton-Hermann, 85

Chrysippus, 38, 129, 13047, 196, 2078

Cicero, 8889, 129, 163, 197, 213

circumnavigator’s paradox, 21315

City of God (Augustine), 170

Clarke, Samuel, 287, 29192, 295

Clinton, Bill, 3942

The Clouds (Aristophanes), 162

Code of Canon Law (1917), 180

Cogito (Augustine), 16873

cogito ergo sum (I think, therefore I am), 170, 254, 334

coins and probability, 23840

Collegium logicum (Goethe), 309

Commentary on the Sentences (Ockham), 191

common sense: Aristotle on, 12324; inference and, 173; linguistic philosophy and, 341; Moore on, 320; nature of, 145; Reid on, 26883

compensation paradox, 1317

composition fallacy, 53

computer science, 238, 28081

The Concept of Mind (Ryle), 340

conclusions of arguments, 6

condemnation of 1277, 18790, 191, 196

cones dilemma, 5354

conflict resolution, 238

consequences, moral relevance of, 285

consistency in logic, 204, 205, 365

continuity principle, 243

Contra Academicos (Augustine), 163

contradictions, 11215, 30315, 31632, 365

Copernican paradox, 224

Copleston, Frederick, 12021

cosmology, 13337, 188

criterion problem, 15456

Critique of Pure Reason (Kant), 28485, 299, 302

Crito, 69

Cyclops of Homer’s Odyssey, 3435, 3637

d’Alembert, Jean, 232, 252

Darrow, Clarence, 12627

Darwin, Charles, 11, 242

Davies, Lady Eleanor, 228

De fallaciis (Aquinas), 199

De Fato (Cicero), 129

De Ludo Aleae (Cardano), 223

De Orbitis Planetarum (Hegel), 311

death, mortal dread of, 230

debate, 30910

Decline of the West (Spengler), 127

Dedekind, Richard, 326

definitions, 60, 79, 7982, 337

Democritus, 5354

Demophilus, 86

Demosthenes, 85, 86

Dennett, Daniel, 35758

Descartes, René: appearances and noumenal reality, 297; on belief, 229; cogito ergo sum (I think, therefore I am), 170, 254, 334; on following arguments, 27677; on metaphysical dualisms, 21621; on reason, 269; Ryle on, 34041

determinism, 12529, 29092, 3012

The Development of Logic (Kneale and Kneale), 90

diagonal argument, 32327

dialectic method of inquiry, 61, 11011

dialetheia, 11314

dice, 223

Diderot, Denis, 106, 23132

dilemma about cones, 5354

dilemma of freedom or determinism, 29092

Diodorus Cronos, 11922, 12223

Diogenes, 84, 94, 196

Diogenes Laertius, 3, 38, 76, 85, 8889, 92

Dion and Theon, 138, 13940, 14142

direct answers, 56

direct arguments, 15659

Discourse on Method (Descartes), 218

divine command theory, 192

division paradox, 22628

doctrine of apostolic poverty, 19394

doctrine of family resemblance, 347

doctrine of reminiscence, 6568

Dodgson, Charles, 33334

dogmatism, 15961, 173

dominant substances, 13940

Don Quixote (Cervantes), 209

doomsday argument, 35051, 370

Dunsany, Lord, 116

duplicates, 24344

Dutchbooks, 239

Eastern philosophy, 93

Eco, Umberto, 193

economic theory, 235

Edinburgh Review, 274

education, 196

Egyptian culture, 20, 39

Einstein, Albert, 41, 77, 369

Electra. See paradox of the veiled figure

Elements (Euclid), 23

Elenchus problem, 110, 11215

emotions, 285

empiricism, 253, 25567, 268, 294, 295

Encyclopedia of Philosophy, 11011

The End of the World (Leslie), 350

Enlightenment, 310

enthymeme, 354

Epicharmus, 130, 13536

Epictetus, 11920, 36263

Epimenides, 9495, 102

epistemology, 74

equality, 22

equiprobability, 23840

Erasmus, 163, 213

eristic method of inquiry, 62

errors of commission, 78

An Essay Concerning Human Understanding (Locke), 255

An Essay on the Foundations of Geometry (Russell), 317

essentialism, 141, 143

Eternal Questions, 334

ethics: of Aristotle, 9798; epistemology and, 74; ethical determinism, 12529; ethical theory, 9798, 235; of paradox, 9193; principles of common sense and, 273

Etienne Tempier, 18889

Euathlus, 6263

Eubulides, 8399

Euclid, 299

Euclides, 71, 7273, 74, 76, 78, 8182

Euler, Leonhard, 1067

Eurymedon, 86

Eusebius, 84

Euthydemus (Plato), 112, 192

evaluative finitism, 233

evolutionary theory, 11, 28182, 356

existence, 14142, 240

experience, 3334, 253, 303

faith, 16566. See also Christianity

fallacy of composition, 53

false identity statements, 79

falsidical paradoxes, 35154, 358

family resemblance doctrine, 347

fatalism, 11629

Fermat, Pierre, 227, 231

finite numbers, 319

finitism, evaluative, 233

flight, 222

forms, 6061, 74, 296, 337

Foundations of Statistics (Savage), 233

Fraassen, Bas van, 250

fractions, 20

Franks, Bobby, 12627

freedom, 29092

freewill, 128, 191, 29092, 3012, 336

Frege, Gottlob, 89, 329, 331, 336

fusions, 361

Gaia hypothesis, 134

Galileo, 360

gambler’s fallacy, 15

Gazzaniga, Michael, 286

gears, 22021, 220 (fig)

genetic fallacy, 181

geometry. See also mathematics: contradictions in, 317; Egyptians’ interest in, 20; geometrical probability paradoxes, 24649; independent axioms, 272; principles of common sense and, 273; probability, 24551; Rhind Papyrus, 2021

Germans, 3738

Gibbard, Allan, 140, 14546

Giles of Rome, 199

gnomons, 23, 23 (fig)

God. See also Christianity; metaphysics: Augustine’s portrayal of, 173; common sense and, 28182; existence of, 1617, 1067, 166, 21819, 24142, 273, 292, 301; immutability of, 17780; nature of, 18082; omniscience, 180, 192; thoughts of, 240

God: A Biography (Miles), 177, 18182

Gödel, Kurt, 90, 107, 36768

gods paradox, 5556

Goethe, Johann, 309

Goodman, Nelson, 15556, 35455, 36162

Goodman’s paradox, 356

gradualism about paradoxes, 36971

grammatical sophisms, 202

grandfather paradox, 118

Greek culture, 20, 37

Grelling, Kurt, 332

growing argument, 13033, 13334, 13536, 13738, 140

Halley, Edmond, 228

Hardy, G. H., 36263

Harman, Gilbert, 15960

Hatshepsut, 39

Hayes, Patrick, 281

heap paradox, 53

Hegel: A Reexamination (Findlay), 314

Hegel, Georg Wilhelm Friedrich, 30315, 319

Heidegger, Martin, 38

Hempel, Carl, 357

Heraclitus, 27, 33, 78, 131, 307, 310

Herodotus, 12, 1314, 20

Hesiod, 3

Hiappasus of Metapontum, 25

Hiappasus’s paradox, 2526

Hindu culture, 21

Hintikka, Jaakko, 106

History of England (Hume), 252

A History of (Beckman), 182

Hobbes, Thomas, 132, 314

Hodja, Nasreddin, 313

Hoffman, Albert, 151

Homer, 3435, 3637

homunculi, 89, 343

hooded man. See paradox of the veiled figure

Hume, David, 25255, 270, 27273, 278, 295

Huygens, Christian, 221

idealism, 319

ideas, 254, 266, 269

identicals, substitutivity of, 78

identity: Chrysippus, 13647; identity assumption, 141; identity paradoxes, 7172, 299; identity statement, 78, 8081; of indiscernibles, 24344; necessity of, 14546

ignorance, 74

illness, 231

imaginary numbers, 3045

In Praise of Folly (Erasmus), 16263

incompleteness theorem, 1078

inconsistency, 111

Indiana House of Representatives, 60

indiscernibles principle, 24344

induction, 35457

inference rules, 367

infinity. See also mathematics: axiom of infinity, 368; complexity of, 17; Descartes on, 218; Greeks on infinity, 20; infinite analysis, 241; infinite number of tasks, 5455; infinite numbers and, 318; infinite populations, 235; infinite sequence, 10; infinite time, 2, 23334, 235; infinite utility, 232; infinite value, 23334, 235; infinitesimals, 318; Peter of Spain on, 188; prone to paradox, 12; Wittgenstein on, 348; Zeno on, 47

inheritance theory, 11

Inquiry into the Human Mind: On the Principles of Common Sense (Reid), 26869

inquiry paradox, 6465, 80

insolubles, 19499, 2023, 21012

insurance industry, 22728

intellectual perversion, paradoxes as, 31213

intentions in conflict, 56

Introduction to Metaphysics (Heidegger), 38

Inwagen, Peter van, 14142

Jaynes, E. T., 250

John XXI, 189

John XXII, 19394

Johnson, L. S., 33031

jokes in philosophy, 340

Jones, Paula, 39, 41

Jourdain, Philip, 332

jumble arguments, 10410

justification, 15455

Kant: A Biography (Kuehn), 287

Kant, Immanuel, 284302; on antinomies, 249; Hegel on, 303, 305, 31011; metaphysics, 296, 298, 309; on peace and war, 310; on reason and appearances, 304

Kelsen, Hans, 85

Kelvin, Lord, 36970

Kenny, Anthony, 340

Kepler, Johannes, 217

kinematics, 317

Kneale, Martha, 90

Kneale, William, 90

knowledge, 7274, 164

Konig, Julius, 332

Kripke, Saul, 147, 15960, 34546

Kuehn, Manfred, 287

Lamarck, Jean, 11

Lampe, Martin, 287

Landau, Edmund, 236

Langford, C. H., 80

language: grammatical jokes, 33348; grammatical rules, 352; grammatical sophisms, 202; logic and, 32122, 33536; mathematics and, 32231; myths regarding, 3742; principles of common sense and, 273; private languages, 338, 348; Quine’s paradoxes and, 35960; semantic paradoxes, 3536, 332, 35960; timelessness and eternity, 183

Laplace, Pierre-Simon de, 238

law of averages, 1517

law of bivalence, 9596, 122

law of diminishing marginal utility of money, 233

lawyers, 63, 75

Lazarus, 144

Lazzerini, M., 246

Le Lionnais, Francois, 363

Leclerc, Georges Louis, 245

Lee, Nathaniel, 275

Leibniz, Gottfried, 23844, 24651, 266, 287, 291, 295

Leopold, Nathan, 12527

Leslie, John, 350

“Let’s Make a Deal” (television show), 22425

Lewinsky, Monica, 39

liar paradox: as an insoluble, 19496, 19799; Aristotle on, 198; Augustine on, 197; in Bible, 83; Buridan’s sophisms and, 210, 211; contempt for, 21213, 299; contingent liar paradoxes, 352; diagonal argument and, 32627; Epimenides, 9395; law of bivalence, 9596; looped liar, 332; Plato and, 102; Russell’s use of, 90

library of Aristotle, 8788

lies and assertions, 9192

Lincoln, Abraham, 337

linguistics, 3742, 202. See also language

Littlewood, J. E., 18

Lloyd, Edward, 227

Locke, John, 25559

Loeb, Richard, 12527

logic: in common sense, 273; logical sophisms, 202; prior to the plague, 190; Russell’s use of, 321, 32531; of truth-value gaps, 90

logicism, 323

London Bridge, 13233

looped liar paradox, 332

Lovelock, James, 134

Lowell, Percival, 297

Lumpl and Goliath, 140, 144, 146

Lutterell, John, 193

Lyceum, 85, 87

Mackie, J. L., 6

Mackinson, D. C., 103

Magellan, Ferdinand, 21314

The Magic Mountain (Mann), 313

Malraux, André, 343

Mani, 163

Manichees, 163, 174

Mann, Thomas, 313

map by Anaximander, 12

Marchand, Jean-Christophe, 284, 286

Marx, Karl, 12728

material constitution paradoxes, 13047

material objects, 297

“Mathematical Logic as Based on the Theory of Types” (Russell), 332

Mathematical Logic (Quine), 368

mathematics. See also geometry; infinity: arithmetic, 2021; arithmetic machine, 21621; cardinality, 32324, 325; diagonal argument, 32326; finite numbers, 319; fractions, 20; Galileo on, 360; imaginary numbers, 3045; infinite numbers, 318; interesting numbers, 36264; language of, 32223; law of averages, 1517; natural numbers, 324, 36263; negative numbers, 23, 10, 3045; ordinal numbers, 32728; probability theory, 152, 223, 227, 23840, 24551; rational numbers, 32324; real numbers, 32324; Russell’s contradiction, 32631; sets, 361; transfinite numbers, 31718, 325

Matthews, Gareth, 6

Mayan culture, 21

McCarthy, John, 281

McClintock, Harry, 242

McCulloch, Robert, 13233

McTaggart, John, 18486, 316

meaningless paradoxes, 36

Meditations (Descartes), 170, 218

Megarian paradoxes, 8890

Meinong, Alexius, 2930

Mendel, Gregor, 11

Menedemus, 212

Meno (Plato), 6367

mereological essentialism, 131, 143

metaphysics. See also God: arguments for God’s existence, 301; Aristotle on, 17879; Descartes on, 21621; Kant on, 296, 298, 309; Lord Kelvin on, 36970; McTaggart’s temporal paradoxes, 185; physics and, 298, 36970; Quine on, 361; reason and, 311; study of infinity, 235

Methods of Ethics (Sidgwick), 278

midwifery analogy, 6667

Miles, Jack, 177, 181

Mill, John Stuart, 172, 316, 354

modus ponens, 160

modus tollens, 92, 114

money and law of diminishing marginal utility of, 233

Montaigne, 213

Monty Hall problem, 22426

Moore, G. E., 80, 15758, 27980, 31920

morality, 98, 273, 285

motion paradoxes, 5, 4952, 50 (fig), 3078

Myson, 108

naive set theory, 90

The Name of the Rose (Eco), 193

Naming and Necessity (Kripke), 147

National History and Theory of the Heavens (Kant), 284

natural numbers, 324, 36263

nature, 360

The Nature of Things (Anaximander), 13

nebular hypothesis, 284

necessary beings, 293

necessity assumption, 141

necessity of identity, 14546

Needle Problem, 24546

negation and time, 3133

negative existentials, 2831, 36, 299

negative facts, 3132

negative numbers, 23, 10, 3045

negative theology, 181

Neleus of Skepsis, 8788

Neoplatonism, 163

neutrality, 158

Newton, Isaac, 172, 292, 311

Nichomachean Ethics (Aristotle), 96

Nietzsche, Friedrich, 12526, 183

nihilism, 14142

Nombres remarguables (Le Lionnais), 363

nominalism, 361

Nonexistent Objects (Parson), 3031

noumena, 297, 303, 312

numbers. See mathematics

objectivity of paradoxes, 212

obligational disputes, 2046

Ockham, William of, 187, 19196, 20910, 285

Odyssey (Homer), 34, 3637

Oedipus the King (Sophocles), 3

oldest recorded paradoxes, 1012

Omar Khayyam, 118

On Beyond Zebra (Seuss), 347

“On Denoting” (Russell), 30, 90

“On False Modesty” (Plutarch), 212

“On Referring” (Strawson), 90

opposites, battle between, 1317, 20

optics, 217

oratory, 6263

ordinal numbers, 32728

Oresme, Nicole, 214, 215

organicism, 13335

origin riddles, 13, 1012

orthodoxies, 224

Outlines of Pyrrhonism (Sextus Empiricus), 148

Outlines of the History of Greek Philosophy (Zeller), 89

pain, Wittgenstein on, 339, 347

paraconsistent logics, 114

Parade magazine, 225

paradox: definitions, 310, 35051, 358; earliest recorded paradox, 1012, 224

paradoxes. See also liar paradox: of analysis, 7982; of the arrow, 3067; of the barber, 365; of Bertrand, 246; of the birthday, 353; of the chicken or egg, 4, 11; of the circumnavigator, 21315; of compensation, 1317; of division, 22628; of the gods, 5556; of the grandfather, 118; of the heap, 53; of Hiappasus, 2526; of the horned man, 90, 9596; of identity, 90, 299; of inquiry, 6465, 80; of material constitution, 13047; of material implication, 1056; of measurement, 175; of motion, 5, 4952, 50 (fig); of plurality, 4548; of the preface, 1024; of the raven, 357; of St. Petersburg, 23234; of strict implication, 1067; of the truth-teller, 100102; of the two envelopes, 23436; of the veiled figure, 7172, 7879, 81

Parmenides, 2843; “as if” theory of physics, 123; defense of, 90; elenchus argument, 112; Euclides and, 76; on existence, 3133; on experience, 3334; on place, 52; on plurality of simple things, 142; on premises and conclusions, 91; reaction to, 3437; on reality of time, 279; on reason, 27, 3334; refutation of, 47; on semantic solutions, 35; on the senses, 5253; sorites arguments, 98; Zeno and, 45, 48

Parson, Terence, 3031

Parthenon, 109

Pascal, Blaise, 21636

Paul, 93

Pausanias, 208, 209, 223

Peano, Giuseppe, 319, 329

Peirce, C. S., 278, 325

Penrose, Roger, 89

Penrose triangle, 8, 8 (fig), 304

Pensées (Pascal), 229

perceptions, 235, 266, 270

perdurance, 77

Pericles, 4243

“Perpetual Peace” (Kant), 310

Perseus, 137

perspective, 242

Peter of Spain, 18788, 318

Peters, Stanley, 202

Phaenarete, 66

phenomena, 303

phenomenalism, 17273, 298

Philetas, 196

Philip of Macedon, 84, 85

Philo of Alexandria, 13738

philosophers, 22

Philosophical Investigations (Wittgenstein), 340

The Philosophical Lexicon (Dennett), 35758

physics: empiricism and, 268; infinity research, 235; mathematics in, 361; metaphysics and, 298, 36970; of opposites, 16; quantum mechanics, 128; thought experiments, 18990

Pierce, Charles, 156

Pillow Problems (Dodgson), 334

piousness, 192

π, 60, 182, 24546

The Pirates of Penzance, 351

place, argument against, 52

Plato, 100115; on appearance, 296; Aristotle and, 84; on astronomy, 311; Augustine and, 179; Euclides and, 71, 74; on forms, 361; on growing argument, 133; on origins, 174; paradox of analysis, 81; prayer and, 166; Socrates and, 59

Plotinus, 163, 179

plurality paradoxes, 4548, 142

Plutarch, 88

Poincaré, Henri, 325

politics, 74, 8586

Polycrates, 1314

Polygnotos, 223

populations, infinite, 235

pragmatic paradoxes, 16276, 206, 210

prayer, 16668

“Prayer to Ask God for the Good Use of Illnesses” (Pascal), 231

precision, 97

premises, paradoxes without, 36668

Priest, Graham, 11214

primary qualities, 298

Principia Mathematica (Russell and Whitehead), 332, 349, 361

principle of alternative compositional possibilities, 141, 143

principle of bivalence, 9596, 122

principle of continuity, 243

principle of contradiction, 30315

principle of indifference, 24651

principle of sufficient reason, 23751, 291

principle of the identity of indiscernibles, 266

principle of the substitutivity of identicals, 81

Principles of Mathematics (Russell), 328, 331

Prior Analytics (Aristotle), 195

probability theory, 152, 223, 227, 23840, 24551

problem of the criterion, 15456

projection thesis, 298

proof of a proposition, 19

“A Proof of the External World” (Moore), 279

propositions, 19, 6061, 15253, 153, 20910

Protagoras, 5253, 62, 102, 112

Protagorean relativism, 1023

Protestantism, 167, 268

Pseudo-Scotus, 19495

pseudoquestions, 36, 342

Ptolemy Philopator, 155

Ptolemy Soter, 119

Pyrrho of Elis, 149

Pyrrhonism, 14954

Pythagoras, 2127, 60

Pythagorean theorem, 2427

Pythagoreans, 33, 185

quantum mechanics, 128

questions in philosophy, 340

Quine, Willard Van Orman, 34971

Ramanujan, 36263

Ramus, Peter, 189

rational numbers, 32324

rationalism, 253, 268, 294, 295, 311, 32233

raven paradox, 357

Rea, Michael, 140

Read, Stephen, 19495

real numbers, 32324

reality, 304, 3056

reason: antinomies of pure reason, 249, 28793, 29395, 304; appearances and, 304; Augustine on, 168, 287; Hegel on, 312; Hume on, 253; jumble arguments and, 1045; Kant on, 309; principle of sufficient reason, 23751; Reid on, 269, 27576; reliance on, 16466; rule of, 3334; Socrates on, 125

reciprocity, 22

reductio ad absurdum: defined, 9192, 169, 289; dialetheist’s contradictions and, 114; role of, 310; Sextus Empiricus’ use of, 153; Socrates’ use of, 109

Reid, Thomas, 172, 26883, 320, 341

relativism, Protagorean, 1023

religion, 167, 181, 268, 312. See also Christianity; God

reminiscence doctrine, 6566

The Republic (Plato), 6667, 74

Rescher, Nicholas, 6, 36465

Rhind Papyrus, 2021

Richard, Jules, 332

riddles: of induction, 35457; as logical analogies, 340; mathematical riddles, 2021; origin riddles, 13, 1012; as paradoxes, 310, 349; Quine’s paradoxes and, 358; Sphinx’s riddle, 34

Robison, John, 36162

A Room of One’s Own (Woolf), 52

Rosser, Barkley, 368

rule following, 34548

rules of inference, 299, 367

Russell, Bertrand, 31632; antinomy, 351; on Aquinas, 179; on common sense, 279; on contradictions, 336; on ‘is,’ 39; on nonexistent objects, 30; paradoxes of identity, 90; religious beliefs, 167; Wittgenstein and, 7

Russell’s paradox, 32231

Ryle, Gilbert, 340

Sainsbury, R. M., 6, 104, 114

Saint Anselm of Canterbury, 167

St. Petersburg paradox, 23234, 246

The Sand Reckoner (Archimedes), 46

Sartre, Jean Paul, 34345

Sathon (Little Willy) (Antisthenes), 112

Savage, Leonard, 233

Savant, Marilyn vos, 225

Schliemann, Heinrich, 2829

scholasticism, 21215

Schopenhauer, Arthur, 31113

science, 280. See also specific fields such as physics

science fiction, 14445, 219

sciences, 36971

scientific revolution, 190

Scotus, John Duns, 168

Sedley, David, 13536

self-awareness, 230

self-deception, 34344

self-reference, 195

semantic paradoxes, 3536, 332, 35960

senses, 5254, 124

September 11 terrorist attacks, 4

sets of Quine, 36166

Sextus Empiricus, 14861; on appearance, 16869; Hume on, 254; method of equipollence, 29495; Pascal and, 230, 231; on philosophical inquiry, 337; skepticism of, 295; sorites paradox, 98; soul’s existence argument, 171

Shalit, Gene, 3031

Ship of Theseus, 132, 140, 145

Sidgwick, Henry, 278

Siger of Brabant, 18889

simplicity, 360

singular propositions, 153

Sisyphus, 44

size, 4546

skepticism, 295

Skinner, B. F., 127

Skyrms, Brian, 354

Smith, Norman Kemp, 285

Smith, Sydney, 273

Socrates, 5870; Augustine and, 164; commandments, 108, 159; on deduction, 1089; on definition, 337; dialectic debate, 6163, 7476, 111; Elenchus problem, 11012; on following arguments, 157, 276; on forms, 337; objection to Protagoras, 1023; Parmenides and, 7678; on piousness, 192; prayer and, 166; on reason, 125; on virtue, 74; Zeno and, 45, 4748

solipsism, 172

sophism, 6263, 14748, 200215, 201

Sophismata (Albert of Saxony), 2012

Sophistic Elenchi (Aristotle), 19798

Sophocles, 3

sorites: Cicero on, 88; of Democritus, 5354; Parmenidean approach and, 9699; premises, 107; Russell’s use of, 90; solution, 122; of Zeno, 5254

soundness of arguments, 105

space, Kant on, 288, 289

space-time worms, 4142, 77, 143

specious present, 175

Spengler, Oswald, 127

Sphaerus the Stoic, 155

Sphinx’s riddle, 34

Star Trek, 14445, 19798

Stevenson, Robert Louis, 339

Stilpo, 119

Stoicism, 13337, 313

Stout, G. F., 27879

Strawson, Peter, 90

Strepsiades, 162

strict conditionals, 105

The Structure of Appearances (Goodman), 361

Studies in the Hegelian Dialectic (McTaggart), 316

substitutivity of identicals, 78

superargument strategy, 249

supervaluationism, 90

swamping, 15

symmetry, 5

tautologies, 16869, 319

temporal paradoxes, 185

terrorist attacks of September 11, 2001, 4

Terspion, 71, 7273

Theaetetus (Plato), 72, 74, 7677, 79

Theodorus, 72, 7677

Theogony (Hesiod), 3

Theophrastus, 8788

theory of propositions, 20910

theory of virtue, 9697

Thomas, Henry, 254

Thomists, 184, 188

Thomson, J. F., 5455

Through the Looking Glass (Carroll), 358

Thutmose III, 39

The Timaeus (Plato), 62, 174, 311

time: Aristotle on, 12122; Augustine on, 17376; flowing and static time, 18486; as fourth dimension, 41, 121, 14344; immutability of God and, 178; infinite time, 2, 23334, 235; Kant on, 28889; negation and, 3133; Parmenides on, 279; specious present, 175; temporal paradoxes, 185; theories of, 11723; time travel, 11819, 121; timelessness and eternity, 18284

The Time Machine (Wells), 118

Timon of Philius, 47, 76

Tolstoy, Leo, 335

Topics (Aristotle), 97, 203

Torricelli, Evangelista, 22122

Tortoise, 36667

Tractatus (Wittgenstein), 335, 342

“Traitié de l’espére” (Oresme), 214

transfinite numbers, 31718, 325

“A Treatise on God as First Principle” (Scotus), 168

“Treatise on the Equilibrium of Liquids” (Pascal), 222

trichotomy law, 328

The Trinity (Augustine), 170

true identity statements, 78

truth-value gaps, 12122

truths, paradoxical, 1078

Turing, Alan, 90, 21920

Twain, Mark, 89

1277, condemnation of, 18790, 191, 196

“Two dogmas of empiricism” (Quine), 358

two envelope paradox, 23436

Tyrannion of Amisos, 88

Unger, Peter, 142

universal propositions, 6061, 15253

University of Paris, 203

unnoticed man. See paradox of the veiled figure

“The Unreality of Time” (McTaggart), 184

utilitarianism, 278

vacuums, 22122, 223, 243, 289

“Vagueness” (Russell), 90

validity, 105

veridical paradoxes, 35154, 358

vice, 74

vicious circle principle, 331

virtues, 7273, 74, 9697, 164

visual paradoxes, 89, 2223, 109

Vlastos, Gregory, 11011

Voltaire, 231, 242

Waldo, C. A., 60

Wang, Hao, 368

war, Hegel on, 310

Way of Ideas, 26970, 276, 320

Weierstrass, Karl, 318

Wells, H. G., 118

Western philosophy, 93

Wheeler, Samuel, 74, 96

White, V. Alan, 302

Whitehead, Alfred North, 56, 100, 318, 32829, 349

“Why I took to Philosophy” (Russell), 320

will, 312

Wisenberg, Solomon, 3940

Wittgenstein, Ludwig, 1, 7, 113, 33448

Woolf, Virginia, 52

world map of Anaximander, 12

Xanthippus, 42

Zeller, Eduard, 89

Zeno of Citium, 127

Zeno of Elea, 4557; arguments, 52, 107, 108, 109, 352; Cantor’s work on paradoxes, 319; debating games, 62; millet seed, 5254; ordinals in paradoxes, 327; paradox of the arrow, 3067; paradoxes of motion, 5, 3078; paradoxes of plurality, 4548, 142; reaction to, 5455

Zermello, Ernst, 332

zombie thought experiment, 220