Paradox

INDEX 391Poincaré, Henri, 325politics, 74, 85–86Polycrates, 13–14Polygnotos, 223populations, infinite, 235pragmatic paradoxes, 162–76, 206,210prayer, 166–68“Prayer to Ask God for the Good Useof Illnesses” (Pascal), 231precision, 97premises, paradoxes without, 366–68Priest, Graham, 112–14primary qualities, 298Principia Mathematica (Russell andWhitehead), 332, 349, 361principle of alternative compositionalpossibilities, 141, 143principle of bivalence, 95–96, 122principle of continuity, 243principle of contradiction, 303–15principle of indifference, 246–51principle of sufficient reason, 237–51, 291principle of the identity of indiscernibles,266principle of the substitutivity ofidenticals, 81Principles of Mathematics (Russell),328, 331Prior Analytics (Aristotle), 195probability theory, 152, 223, 227,238–40, 245–51problem of the criterion, 154–56projection thesis, 298proof of a proposition, 19“A Proof of the External World”(Moore), 279propositions, 19, 60–61, 152–53, 153,209–10Protagoras, 52–53, 62, 102, 112Protagorean relativism, 102–3Protestantism, 167, 268Pseudo-Scotus, 194–95pseudoquestions, 36, 342Ptolemy Philopator, 155Ptolemy Soter, 119Pyrrho of Elis, 149Pyrrhonism, 149–54Pythagoras, 21–27, 60Pythagorean theorem, 24–27Pythagoreans, 33, 185quantum mechanics, 128questions in philosophy, 340Quine, Willard Van Orman, 349–71Ramanujan, 362–63Ramus, Peter, 189rational numbers, 323–24rationalism, 253, 268, 294, 295, 311,322–33raven paradox, 357Rea, Michael, 140Read, Stephen, 194–95real numbers, 323–24reality, 304, 305–6reason: antinomies of pure reason,249, 287–93, 293–95, 304;appearances and, 304; Augustineon, 168, 287; Hegel on, 312;Hume on, 253; jumble argumentsand, 104–5; Kant on, 309;principle of sufficient reason,237–51; Reid on, 269, 275–76;reliance on, 164–66; rule of, 33–34; Socrates on, 125reciprocity, 22reductio ad absurdum: defined, 91–92, 169, 289; dialetheist’s contradictionsand, 114; role of, 310;