Index

abduction: as argument form, 249, 271; and Darwin, 249, 253–54; and Einstein, 253, 305–12; examples in science, 248, 262–65, 273–76; as form of induction, 19; formal and material approaches, 251, 260; and inference to the best explanation, 247; no universal account of, 248; and notions of explanation, 247–49, 253, 257–58; and Peirce, 253–55; two-step scheme, 251, 267–69, 273, 310, 319, 323, 330. See also inference to the best explanation

abductive inference. See abduction

Accum, Frederick, 41–42

Adams, John, 209

additivity: of calculi, 383, 396, 435; and chance values, 537; and completely neutral support, 353; countable, 470, 472, 508, 598–99, 593–94; in credences, 15, 396, 398; deviations from, 400, 401–02; divergence additivity, 419; finite, 472, 474–75, 597, 474–80, 508; of a probability measure, 14, 601, 641; of strengths, 379; subadditivity, 399–04, 420; superadditivity, 358, 399–04, 420; violated, 345, 352, 396, 466, 601. See also credences

Aharonov, Yakir, 582

AIC. See Akaike Information Criterion

Akaike Information Criterion: and coin tosses, 234–39, 243–46; correcting for overfitting, 232; described, 229–30; and d-parameter model, 239; as elaboration of Maximum Likelihood Criterion, 226, 228–30; failure of, 242–43; and material theory of induction, 240–41; and model selection, 224–25, 242; and one-parameter model, 236, 238–40, 243; and probability distribution, 231–32; and simplicity, 12, 243; and zero-parameter model, 239–40

Akaike, Hirotogu, 228–29. See also Akaike Information Criterion

analogical inferences: distinguishing good from bad, 119, 122; as facts, 11, 51, 60, 120, 132–33; good, 120; negative analogy, 125–26, 128, 133, 141; positive analogy, 125–26, 128, 133, 140; prior association, 128; source to target, 125–28, 131–33; as warrants, 11. See also analogy

analogy: as argument form, 10–11, 60, 121; articulation model, 127–30; bare analogy, 119, 121, 124; as criterion for explanation, 258–59; facts of, 60, 135, 142; as form of inference, 51, 120; logic of, 127; material analogy, 129; and material theory of induction, 131; principle of similarity, 133, 142; problems with articulation model, 131–32; problems with two-dimensional approach, 128–29; reasoning by, 119, 122–124, 128; two-dimensional approach, 124–126, 128–29. See also analogical inferences; formal approach to analogy

Aquinas, Thomas, 184

Aristotle, 10, 119, 184

astrology, 154

astronomy: Copernican, 161, 223; as domain of inference, 47, 160; fitting orbits, 175; geocentric and heliocentric, 155–56, 160; Ptolemaic, 223. See also Copernicus; Copernican system; Ptolemaic system; Ptolemy;

asymptotic stability, 437, 459–61, 463–64

atoms: atomic theory, 85; liquid drop model of nucleus, 11; model of, 163; as propositions, 438, 445–48, 450, 455–59, 461; radioactive decay of, 590–91

Atwood, Kimball, 97

axiom of choice, 507–08, 521, 546, 547n, 554–56, 567

Bacon, Francis, 322

Banach-Tarski paradox, 547, 548n, 556

barium chloride: monoclinic form, 25; separation from radium chloride, 17, 27; similarity to radium chloride, 27–30, 44–47, 49

barium sulphate, 44. See also barium chloride

Bartha, Paul, 119, 125, 127–28, 130, 475, 477

Bayes property, 383. See also Bayes’ theorem; Bayesian approach

Bayes’ theorem: and deductive inferences, 7; and posterior probabilities, 15, 32–33, 66, 76–78, 335–36; and prior probabilities, 3–4, 15, 32–37, 58, 66, 75–79, 335; and probability calculus, 7, 38, 66, 335; ratio form of, 441. See also Bayesian approach; Bayesian epistemology

Bayesian analysis. See Bayesian approach

Bayesian approach: account of induction, 7; applicability of, 8, 14, 75–76, 80; complications with, 66, 79; and crystallography, 31; distinctiveness of, 14; and Dutch book arguments, 363–64; failure of, 34–39, 76–77, 341–43; inductive incompleteness of, 15, 58; for matching DNA samples, 4; objective, 77–78, 338, 340–42, 381–82, 480; preference for simpler hypotheses, 440; present dominance of, 3, 13, 58; problem of priors, 436–37, 465–66; simplicity, 436, 440–41; subjective, 4, 77–78, 338, 340–42, 382, 465, 485; varieties, 340. See also Bayes’ theorem; Bayesian epistemology

Bayesian epistemology, 335–36, 338–39. See also Bayes’ theorem; Bayesian approach

Bayesianism. See Bayesian approach

beliefs. See credences

Benci, Vieri, 472

Benétreau-Dupin, Yann, 348, 357–58

Besso, Michele, 110

betting: behaviors, 359, 366–67, 373, 375; fair bets, 364, 367, 371–72, 374; quotients, 364–65, 367–75; refusing to bet, 366, 368–69; scenarios, 4, 359, 363, 368, 372, 374–75

Big Bang: and cosmic background radiation, 159–60, 247, 250, 262, 275, 312–19, 341; evidence for, 4, 159–60, 318; and relativistic cosmology, 604; versus steady-state theory, 316–17, 319. See also cosmology

black hole, 604

Blackwell, David, 521, 558, 563

Blatt, John, 140–42

Bohm, David, 582

Bohr, Niels, 139, 163

Bondi, Hermann, 16, 520–21, 539–41, 546. See also cosmology; steady-state cosmology

Boolean algebra, 446–47, 451–52, 458

Boolean operators, 446, 464

Born, Max, 306, 309

Bosch, Carl, 81

Brandom, Robert, 85–86

Brewster, David, 327

Bridgman, Percy, 365

Brier score, 389–96, 399, 401, 407, 409–10, 421

Brier, Glenn, 390–93

Brigandt, Ingo, 86

British Medical Journal, 114

Byrd, R., 112

calculi of inductive inference: alternatives to probability calculus, 469; appeal of, 438–40; completeness, 436–37; failure of ideal of completeness, 444–45, 465–67; ideal of completeness, 443–44; lack of universality, 467, 469, 603; necessity of incompleteness, 437, 466; neutral initial state, 435–36; non-trivial, 435–36, 465–66; probabilistic, 451–52

“Cathode Rays” (paper by J. J. Thomson), 289–90, 293, 296–97. See also cathode rays; particle theory; Thomson, J. J.

cathode rays: as charged particles, 290–91, 293–95; as example of abduction, 276, 289–303; as waves, 290, 292–96; nature of, 289–90. See also “Cathode Rays”; particle theory; Thomson, J. J.

causation, 129–30; multiplicity of causal factors, 179–80

celestial mechanics: eccentric orbits, 203–05; ellipses, 203–05; gravitation theory, 204; hyperbolas, 203–05; orbital trajectories, 203–04; parabolas, 203–05; perturbations, 208–09; perturbed ellipses, 208–09. See also curve fitting; Newtonian gravitation theory; orbital trajectories

Chibnall, John, 113

childbed fever: cause of, 13, 261, 265–67

COBE satellite, 314

Coherent Admissibility, 411

coin tosses: accumulated results of, 4; and Akaike Information Criterion, 234–39, 243–46; invariances involving, 352; and nonmeasurable sets, 16–17, 521–22, 558–66; and probabilities, 37, 47–48, 352, 485–86; as probabilistic randomizer, 505–09; principle of indifference, 347; repeated scenarios of, 370

cold fusion, 93, 96, 98–106

comets: energy of, 206–07; orbital trajectories of, 203, 205–06

common salt. See sodium chloride

completely neutral support, 348–59; and additivity, 345, 353, 383; and background conditions, 14; and Dutch book, 368–69; and indeterministic physical systems, 604; and invariances, 17, 574, 601–02; and label independence, 520; and principle of indifference, 337

conditionalization, 76, 78, 440, 465, 592, 594

confirmation theory, 19, 253

connectives, 83–86

consilience: as criterion for explanation, 258–60, 278, 282

consistency: as criterion for theory choice, 11, 166–67, 169–71

construct validity, 94n

containment principle, 470, 504–05

continual (continuous) reaction of matter, 539–43

controlled trials, 94–95, 112, 114–15

Copernican system, 156; aesthetic superiority of, 157–58; appeal of, 156, 161; argument against by Osiander, 160; versus Ptolemaic system, 158, 223; victory over Ptolemaic, 157–58. See also Copernicus

Copernicus: On the Revolutions of the Heavenly Spheres, 157; versus Ptolemy, 156–57. See also Copernican system

corpuscular theory of light, 324–30; defined, 325. See also emission theory

cosmic background radiation: and Big Bang 159–60, 247, 250, 275, 312–19, 341; competing theories for, 314–19; as example of abduction, 312–19; Penzias and Wilson, 159; thermal character of, 312–15, 317–18

cosmic matter distribution, 584–88

cosmological principle, 80

cosmology: continual creation of matter, 539–43; and cosmic background radiation, 275; and cosmological principle, 80; eternal inflation, 471, 509–10, 512–14; inflationary, 16, 480, 509, 512–14; Newtonian, 17, 583–88, 596–97, 607–10; pre-inflationary, 604; and simplicity, 173. See also Big Bang; steady-state cosmology

Coulomb electrostatics, 129

Cournot’s Principle, 486

Cox, Richard, 338, 360, 377–80

credences: accuracy of, 14–15, 388, 395, 397, 407–08; and additivity, 15, 404, 425, 429; dominating, 396–98, 400–02, 406–07; eliciting, 393–95; “immodest,” 417–18; non-additive, 404; non-probabilistic, 388–89, 394–97, 412–14, 417–18; probabilistic, 388–89, 394–97, 408–15, 417–18, 420; and probabilities, 8–9, 14, 359; and probability calculus, 396; and strengths of inductive support, 341; subadditive, 399–04, 408, 412, 420, 426, 429–30; superadditive, 399–04, 408, 412, 420, 426, 429–30. See also additivity

criteria for explanation: analogy, 258–59; consilience, 258–60; simplicity, 258–59. See also notions of explanation; Thagard, Paul

crystallographic forms: cubic system, 24–26; dimorphism, 33, 42; and enumerative induction, 57; fluorspar, 24–25; Haüy’s account, 40–42; heavy spar, 44; isomorphism, 30, 44–47; monoclinic system, 25–26, 30, 39n, 66; octahedral, 24–25; polymorphism, 33, 42–43, 45, 47, 51; process of cleavage, 24–25; properties of, 9; regular system, 24; system of classification, 23–24; trimorphism, 42

Curie, Marie: 1911 Nobel Prize address, 30; doctoral dissertation, 27; extraction of radium, 26–28, 39n, 40; generalization about radium, 46–47; hypothesis about radium, 36; inference from radium sample, 9, 28–30, 37–38, 59, 65; observations about radium, 44–47. See also radium chloride

Curie, Pierre, 27

curve fitting: constant, 189, 190, 202; cubic, 190, 200–01, 232–34; defined, 196; error model, 196–98; linear, 189–90, 200–02, 232–34; and material theory of induction, 195–98; and model selection, 225, 227; and Moody chart, 182; and orbital trajectories, 202–11; order hierarchy, 202; overfitting, 12, 190; parametrization, 199–202; polynomial curves, 189–90, 200, 202, 232; problems with, 193; quadratic, 189–90, 200–02, 232; quartic, 190, 200–01, 232–33; and simplicity, 175, 189, 191, 193; sinusoidal curves, 12; and theory of relativity, 211. See also simplicity; orbital trajectories; tides

Czech book, 367

Darwin, Charles: and abduction, 249, 253–54; account of the eye, 274, 279–80; defense of abduction, 252, 256, 288; description of natural selection, 277–78; influence of Lyell on, 285, 287; influence of wave theory on, 324; influence of Whewell on, 278; and intelligent creation, 13, 276, 279–82; and notions of explanation, 282–83; voyage on the Beagle, 285. See also natural selection; On the Origin of Species

Davisson, Clinton, 302

Dawid, Richard, 594

Dawkins, Richard, 113; The God Delusion, 113

Day, Timothy, 249

de Broglie waves, 302

Decomposition, 419–20

deduction: all-some schema, 5; and analogical inferences, 127, 132, 135; contrast with inductive inferences, 56, 62–63; deductions from the phenomena, 51, 269; and deductive arguments, 136; and deductive validity, 50–51; deductive fallacy, 109, 124; distinguishing good from bad, 82; good, 5, 82; with hidden premise, 65; and hypothetico-deductive confirmation, 160; logic of, 82, 85, 91, 106n, 124; non-contextual, 83, 85; universal principle of, 5, 6, 91–92; validity of, 50–51; warrants for, 5–8, 46. See also hypothetico-deductive confirmation

deductive inferences. See deduction

deductive structure, 437, 445–48, 455, 465

de Finetti, Bruno: and betting scenarios, 359, 363–65, 374–75; and Dutch book arguments, 337, 360; and infinite lottery, 485, 504; and probabilities, 393, 471–72; as subjective Bayesian, 340

De Morgan’s laws, 83

De Vito, Scott, 242

Department of Energy (US), 100–01

determinism, 573; general idea of, 575; temporal, 576

deterministic physical systems, 575–76

deuterium, 99, 101, 103–06

Diaconis, Persi, 521, 558, 563

Dirac, Paul, 195

Divergence Additivity, 419

Divergence Continuity, 419–20

dome: as example of indeterminism, 576–77, 594–95; as Newtonian system, 577

dominance: condition of, 409–11; dominance argument, 388, 394–98, 401, 414–17; dominance relations, 399, 406–07, 424–28; theorem, 14

dominoes: infinite domino cascade, 17, 573, 579–81; toppling of, 605–07

Douglas, Heather, 153n

Drake, Stillman, 70, 74

Dutch book arguments, 14, 363–77

Earman, John, 576

Ehrenfest’s theorem, 303

Einstein, Albert: and abduction, 253, 306; and anomalous motion of Mercury, 305–12; appraisal of Miller experiment, 106n, 108–10; arguments against Newton, 161–62; Herbert Spencer Lecture, 192; as mathematical Platonist, 71–72, 191–92; and notion of simplicity, 191, 193–95

—theory of relativity: completion of, 305; complexity of, 252–53; cosmological constant, 584; and the ether, 122 and Mercury, 4, 210–11, 253; and von Neumann, John 195; special relativity, 107, 329; versus zodiacal light, 274–75

electrons: and atoms, 138–39; discovery of, 289; and ellipses, 12, 203–05; orbit of, 141; as spin-half particles, 82, 164; spin of, 17, 82, 469; wave-like properties of, 275; as waves, 302–05; and perturbed ellipses, 208–09. See also celestial mechanics

emission theory of light, 274, 325–30; defined, 325; and evidential debt, 330; versus wave theory, 325–30. See also corpuscular theory; wave theory

Energy Research Advisory Board (ERAB), 100–01, 103–05

enthymeme, 50, 65

enumerative induction: authorizing too much, 59; of breathtaking scope, 9; contrast with all-some schema, 6, 22; and crystallography, 50; early attempt at, 5; failure of, 438; and Haüy’s principle, 68; and Marie Curie, 38; schema of, 29–31, 39, 47, 57

epistemic values and virtues, 11; and skepticism, 162; and Thomas Kuhn, 168; as criteria for theory choice, 154–55, 169; and evidential relations, 159; and inductive support, 158, 161; and material theory of induction, 158; as means and ends, 154; as surrogates for facts, 155, 159; role in assessing evidence, 153; role in inductive inference, 162; as warrants for induction, 159. See also theory choice; values; value judgments

eternal inflation: defined, 509–10; and label independence, 509; measure problem, 471, 509–15

ether, 107–10, 122

ether-wave theory. See wave theory

Euclid, 72

Euclidean geometry, 195

Euclidean space, 584

Eva, Benjamin, 348

evidential debt: and abduction, 268; and Charles Lyell, 289; defined, 251; and inference to the best explanation, 268; and natural selection, 278–79, 282–83; and Newtonian theory, 311; and theory of relativity, 307, 310–11; and wave theory, 330

evolution, 1, 2

explanatory virtues: Lipton, Peter, 310; loveliness, 310–12; oxygen and phlogiston, 321, 323

Extension Theorem, 527

external considerations, 15. See also external inductive content

external inductive content, 34, 36, 442–43, 466. See also external considerations

fallacies: analogical, 122–23; deductive, 50, 109, 124; gambler’s streak, 595–96; inductive, 6

Feyarabend, Paul, 7

Fleischmann, Martin, 99, 102

fluid flow in pipes, 181–83, 198. See also Reynolds analogy

Ford, William 42, 44

formal approach to analogy: and bare analogy, 124, 128; development of, 119, 124; and material approach, 130, 142; problems with, 122, 129, 131–32, 142; requirement for success, 129–31. See also analogy

Forster, Malcolm, 223, 242–43

Fourier analysis, 202, 211–12

frequencies of outcomes: and chance, 488, 495, 498–502; and probabilities, 470, 497, 502–03, 554, 592; relative frequencies, 16, 474, 479, 494–95, 594

Fresnel, Augustin, 326

Freundlich, Erwin, 307–09

Frisch, Otto, 139

Galilean spaces, 161–62

Galileo, Galilei: The Assayer, 71; and invariance under units of time, 10, 74–75; law of fall, 70–73, 80, 181; mountains on moon, 11, 120–22, 133–137; Siderius Nuncius, 133; Two New Sciences, 70, 72, 74–75

Galton, Francis, 111

gambler’s streak, 595–96

gauge systems, 582–83, 601–02

Germer, Lester, 302

The God Delusion, 113. See also Dawkins, Richard

Gödel, Kurt, 444

Goedel’s theorem, 557

Gold, Thomas, 16, 520–21, 539. See also cosmology; steady-state cosmology

Goldstein, Eugen, 293

Grand Unified Theory, 508

gravitational potential, 17

Guth, Alan, 509–14

H. pylori, 93, 96–97

Haber-Bosch process, 81

Haber, Fritz, 81

Hacking, Ian, 312–13

Hájek, Alan, 367

Hale, George Ellery, 193

Hall, Asaph, 210, 308–09; modified law of attraction, 210

Harman, Gilbert, 255

Harmonic functions, 587–88

Harper, William, 242

Harris, William, 112

Haüy, René Just, 29, 40–41; account of crystalline shapes, 40–42. See also Haüy’s Principle

Haüy’s Principle, 9, 43, 63, 68; strong, 50, 51; weakened, 39n, 43, 59, 65. See also Haüy, René Just

Hawking, Stephen, 114

Hempel, Carl, 265

Herschel, John, 322–23

Hertz, Heinrich, 290, 292–93, 295, 297

Hesse, Mary, 119, 124–127, 129

Hilbert space, 359

History of the Inductive Sciences, 29, 326–27. See also Whewell, William

Hooke’s laws, 578

Horsten, Leon, 472, 477

Hoyle, Fred, 16, 520–21. See also cosmology; steady-state cosmology

Hubble, Edwin, 269–70

Hutter, Marcus, 79

Hutton, James, 285

Huygens, Christiaan, 74–75, 325

hydrogen: atoms of, 98, 138–39, 483; bombs, 98; and deuterium, 99

hyperbolas, 12, 203–05. See also celestial mechanics; orbital trajectories

hypotheses: competing, 12–13, 60, 76–77, 173; descriptive simplicity of, 175–78; evaluating probability of, 32–33

—favored hypotheses: adequate to the evidence, 12, 60, 268; authorized inference to, 273; competing foils, 275–76, 330–31; establishing superiority of, 275–76, 330–31; and evidential debt, 251; failure of competitor, 13, 60; falsity of, 3; multiple, 77; preference for simpler hypotheses, 439–40, 442–44

hypothetico-deductive confirmation: as account of induction, 159; augmenting, 452; basic notion of, 451; defined, 159; problem with, 155, 160–62; repairing, 159–62. See also deduction

implicit definitions, 449–54

imprecise probabilities, 14, 344–46, 356–60

indeterminism: among components of a system, 581–88, 596–99; and degrees of freedom, 578, 581; elimination of, 577; and physics, 595–96; without physics, 583. See also indeterministic physical systems

indeterministic physical systems, 17, 469, 515; common characteristic, 573; commonness of, 576; and degrees of freedom, 573; and empirical observation, 594–96; of infinite three-dimensional crystals, 578; and probabilities, 594–96. See also indeterminism

induction: and abduction, 12, 247–48; account by Bayesian analysis, 7, 38, 79, 339, 341–43; ampliative nature of, 9, 19, 56, 61–62, 65; analogy as form of, 58, 119, 131; axioms governing, 570; and bare analogy, 123, 128; and belief, 335–36; of breathtaking scope, 26; calculus governing, 342–43; appeal of, 438–40; example of, 448–52; failure of universal, 437, 469, 603; formal analysis within, 36; in particular domains, 466–67, 469; and restrictions, 346; comprehensive account of, 153; concerning crystalline forms, 43–45; concerning genetic mutations, 616–20; concerning spin of electrons, 615, 618–21; conclusions of, 6; contextual nature of, 8, 47; contrast with deductive inferences, 56, 62–63; and controlled trials, 94; and countably infinite sets, 519; dependence on background assumptions, 302; as distinct from deductive inferences, 42, 50–52; distinguishing good from bad, 23, 30, 61, 142; and epistemic values and virtues, 155, 162, 261; and factual propositions, 7; failure of universal schemas of, 22, 57–59, 653; formal approaches to, 21–23, 29, 119–20, 142, 187, 654; foundational problems of, 382, 436; general inductive principles of, 109, 115; good, 30, 50, 55, 61; and Hume’s problem, 654; and imprecise probability, 359; and indeterministic systems, 581–83, 589; and inductive risk, 48, 64, 123, 186; and inference to the best explanation, 12, 247–48, 266, 270; and the law of fall, 70–72, 75; licit, 52, 57, 59; limitations of, 132, 557–58, 569, 575; literature on, 2, 10, 52; local character of, 7, 16, 47, 56, 68; modern accounts of, 22; mystery of, 61–62; and nonmeasurable sets, 521; non-trivial, 599; no universal rules for, 7, 159, 335, 653; powers of, 55–56, 61–62; premises of, 6, 51, 63, 65; and probabilistic facts, 48; and probabilistic logic, 618; and probability calculus, 443–45, 466, 469, 575; probability measures in, 548, 604–05; qualitative and quantitative approaches to, 9; and replicability, 90; and reproducibility, 112; schemas for, 5, 10; and simplicity, 60, 173–74; and skeptical relativism, 153–54; standard collections of, 59–61; and strengths of support, 581–82, 603–04; terms for, 19–20; theories of, 3, 40, 79; universal induction, 79, 90; universal principle of, 90, 109; and Vitali sets, 553; warranted by facts, 7, 23, 46, 65–68, 159, 196, 613. See also calculi of inductive inference; enumerative induction; inductive import; inductive logic; inductive risk

inductive import: confusion over, 100; determined by background facts, 93–94; and Einstein, 109; and inductive logic, 462; and Mercury, 311; replication without inductive import, 106–15. See also induction; inductive logic

inductive inferences. See induction

inductive logic: and asymptotic stability, 460–62; and completely neutral support, 353, 574, 604; constraints on, 454; and continuum-sized sets, 519–21; and deductive logic, 81–82; and deductive structure, 445; deductively definable, 454–57, 464; and density operators, 628–30, 638, 647; for entangled electrons, 647; failure of universally applicable, 56, 116, 241; formal, 283; and formal approach to induction, 22, 39; general principle of, 159; generalization, 43, 45 and Gödel, 444; and Haüy’s principle, 67 and imprecise probabilities, 360; and infinite lottery machine, 470, 481–90, 519–21, 537, 541; and label independence, 494, 539; material, 283; non-additive, 337, 601; and nonmeasurable sets, 554; non-probabilistic, 16, 346, 514, 571, 618–19; objectivity of, 637; and prior probabilities, 382; and probabilistic randomizers, 636, 508; and probability calculus, 471; and probability measure, 638–39; and problem of probabilities, 343; and replicability of experiment, 89–90; for a roulette wheel, 638; and simplicity, 187; and ultrafilter logic, 522;

—probabilistic: applicability of, 575; compared to quantum inductive logic, 614–16, 627–28, 648, 650–52; and electrons, 620; and genetic mutations, 616; necessity of, 361, 637; prevalence of, 613

—quantum: and density operators, 638; and disanalogies, 651; and electrons, 618–20, 628; and genetic mutations, 618; and violation of real-valued functions, 345; compared to probabilistic inductive logic, 613–16, 627–28, 648, 650–52; strengths of support for, 367; warranted by facts in a domain, 343, 470, 599, 620, 651; weak, 17, 532, 559, 570. See also induction; inductive inferences; material theory of induction

inductive risk: and background assumptions, 51n; in chemistry, 29; controlling, 49; in crystallography, 45; degrees of, 44n, 81; differing conclusions, 44; and Galileo, 136; inescapability of, 123, 132; and probabilistic analysis, 66; unique forms of, 47; with warranted inductive inference, 64. See also induction

Infection and Immunity (journal), 89

inference to the best explanation: as argument form, 250, 271; canonical examples, 262–65, 273–76; credentials in science, 252; and Charles Lyell, 286; and cosmic background radiation, 312–19; defined, 247–251; and Albert Einstein, 305–12; explanatory relations, 60; as form of induction, 51; and Gilbert Harman, 255–56; and material theory of induction, 271; no universally applicable schema, 273; notion of explanation, 257–58; and Peter Lipton, 13, 260–62, 274; problems with, 12–13, 22, 48, 250, 438; and Paul Thagard, 256–58; two-step scheme, 251, 267–69, 310, 319, 323, 330–31; vagueness of, 58–59; visceral appeal of, 248–49; and William Whewell 258–59. See also abduction; Lipton, Peter

infinite lottery machines: chance properties of, 470, 478, 523; and countably infinite outcomes, 469, 519, 522; difficulties with, 471–72; fairness of, 472–73, 503, 522; and label independence, 475, 477–78, 481, 489–91; in the literature, 470–71; logic of, 345, 359, 481–90, 508, 519–21, 537–39, 553–54; and non-standard calculus, 470; and probability measures, 470–71, 478–79; physical properties of, 470–71

invariances: and coin tossing, 352; from ignorance, 352–53; under negation, 351–52, 602–03; from positive warrant, 352–53; under redescription, 348–50, 601–02

Isaacs, Rufus, 535

Jaynes, Edwin, 14, 338, 342, 360, 377–82, 480

Jeffreys, Harold, 441, 443

Joyce, James, 410–12, 417–18

Jupiter, 209

Kaufman, M., 316

Kelly, Kevin, 180

Kepler’s laws: area law, 204; planetary motion, 269

Keynes, John Maynard, 347–49, 379

Khalifa, Kareem, 249

Kincaid, Harold, 249

Kolmogorov axioms, 437, 449, 450, 452

Kolmogorov, Andrey, 344–45, 486–87, 526, 560

Kuhn, Thomas: Kuhn loss, 321; Matchette Lecture, 155, 165–71; obfuscation by, 162, 165–68; and skeptical relativism, 169; and theory choice, 155; The Structure of Scientific Revolutions, 165–66, 168

Kullback-Leibler discrepancy, 230

label independence: and choosing without favor, 471–73; compatibility with probabilistic logic, 520; condition of, 470; and continuum-sized sets, 520, 522, 523; defined, 470, 473; and infinite lottery machines, 475, 477–78, 481, 489–91; metrically adapted, 520, 535–37, 539, 545, 553; and restriction on permutations, 526; and roulette wheels, 473–74; requirement of, 473, 524; unrestricted requirement, 553; weakening of, 520, 524

label permutation: and continuum-sized sets 520, 523; defined, 473; and infinite lottery machines, 476, 479, 481; and roulette wheels, 474

Laplace’s equation, 608

Lavoisier, Antoine, 320–23

Layzer, David, 316

Le Verrier, Urbain, 209

Leibovici, Leonard, 114–15

Leitgeb, Hannes, 411

Lenard, Philipp: and abduction, 275, 290, 293; argument against particle theory, 293–96; cathode rays as waves, 290, 292–96

Levi-Civita, Tullio, 195

Lipton, Peter, 260–62, 265, 267, 274, 310

Lloyd, Humphrey, 327–28

Lorentz force law, 290

Lorentz, Hendrick, 194

loveliness as explanatory virtue, 310–12

Lyell, Charles: and catastrophist theories, 286–88; and evidential debt, 289; influence on Darwin, 285; summary of approach, 286. See also Principles of Geology; uniformitarian geology

Mach, Ernst, 180–81

Maher, Patrick, 376–77

Malament, David, 609–10

Manchak, John, 578

Manhattan project, 164

masses and springs: as example indeterminism, 577–78; as Newtonian system, 577–78; temporal behavior of, 578

material theory of induction: and analogy, 60, 131–33; and background assumptions, 302; and curve fitting, 196–98; as distinct from deductive inference, 50–52; as distinct from other approaches, 5; and Dutch book argument, 367; and epistemic virtues and values, 153–55, 158–59; and formal approaches, 260; and foundational problem of induction, 382; and Hume’s problem, 654; and inductive logic, 651; and inference to the best explanation, 247, 260, 271, 273; foundational argument for, 62–68; main ideas of, 7–9, 46–50; regress problem in, 656; relation to Akaike Information Criterion, 240–43; and replication of experiment, 98; and simplicity, 166, 173, 186; and size of domains, 81; stated and illustrated, 19–20; summary of case for, 55–57; terminology, 17–18; versus formal approaches, 57, 59; and warranting facts, 61, 115–16, 188, 195, 481, 534, 574–75. See also induction; inductive logic; simplicity

Mathematical Foundations of Quantum Mechanics, 195. See also von Neumann, John

Maximum Likelihood Criterion: defined, 227; as elaboration of Akaike Information Criterion, 226, 228

McCarthy, John, 393

McMullin, Ernan, 170–71

measure theory, 506, 526

Mercury: advancing orbit of, 209

—anomalous motion: account by Erwin Freundlich, 307–09; and Newtonian gravitation theory, 305, 307; explained by theory of relativity, 4, 210–11, 253, 263, 268, 306; explained by zodiacal light, 274; perihelion of, 211, 253, 274, 305–06; perturbations of, 209–10, 310

Mill, John Stuart, 255; methods of, 255, 266–67

model selection: and Akaike Information Criterion, 225, 242; best fitting, 226–27; defined, 225; d-parameter model, 238–39; one-parameter model, 235–40; overfitting, 224–29; and simplicity, 223–26; and statistical noise, 225–26; two-parameter model, 242; zero-parameter model, 234–35, 239–40

modus ponens, 20n, 84, 124, 439

monotonicity, 352

Moody chart, 181–82, 198. See also curve fitting

Moody, Lewis, 181

Myrvold, Wayne, 242

Narlikar, Jayant, 316

National Oceanic and Atmospheric Administration (NOAA), US, 218–20

natural selection: aesthetics elegance of, 283; complexity of, 270, 277–78; and evidential debt, 278–79, 282–83; and independent creation, 279–82, 285; obstacles facing, 278–80, 282; summary of, 277–78; warranted acceptance of, 284–85. See also Darwin, Charles; On the Origin of Species

necessary conditions: for strengths of inductive support, 377–81

Neptune, 209, 311

New York Times, 193

Newcomb, Simon, 210, 308

Newton, Isaac: accused by Einstein of ad hocery, 161; and gravity, 187–88; corpuscular theory of light, 324–30; Principia, 51, 176, 187; “Rules of Reasoning in Philosophy,” 176–77, 184–87. See also Newtonian gravitation theory; Newtonian cosmology; Newtonian physics; Newtonian potentials; Newtonian systems

Newtonian cosmology, 17, 583–88, 596–97, 607–10

Newtonian gravitation theory: and elliptical orbits, 305; as example of indeterminism, 573; and gravitational constant G, 191, 582–83; and indeterministic systems, 573, 583–85; inverse square law of, 269, 309; Mercury’s motion explained by, 307; perturbations explained by, 208–09; potentials of, 588; probability of, 7. See also Newton, Isaac; Newtonian cosmology; Newtonian physics; Newtonian potentials; Newtonian systems

Newtonian physics, 311, 595

Newtonian potentials, 17, 573–74, 584, 586–88, 598, 608

Newtonian systems, 577–78

no-go results, 463–65

notions of explanation: and abduction, 253, 257–58; attempts to define, 22, 257–58; elusiveness of, 13, 251; and favored hypotheses, 330; heterogeneity of, 248–49, 260; and induction, 3; varied and vague, 58. See also criteria for explanation

nuclear reactions: fission, 98, 139–40, 142, 163; fusion, 98–99, 101–02, 104–05, 188. See also cold fusion

Ockham, William of, 183–84; Ockham’s razor 174–76, 183–84, 316

On the Origin of Species, 256; analogical reasoning in, 121; and abduction, 254; argument of, 121, 252, 256, 277–78, 281–82; as example of abduction 276–85; influence of wave theory on 324; similarity to Charles Lyell’s argument, 287–88. See also Darwin, Charles; natural selection

On the Revolutions of the Heavenly Spheres, 157. See also Copernicus

orbital trajectories: elliptical orbits, 207–08; perturbed orbits, 207–11. See also celestial mechanics; curve fitting

oxygen: oxygen chemistry, 320–24; oxygen theory, 320–21; and phlogiston, 320–24; and weight, 322; and William Whewell, 323

parabolas, 203–05, 440. See also celestial mechanics; orbital trajectories

paradoxical decompositions, 16, 521, 543–48

parsimony: aesthetic of, 158; failure of, universal principle of, 224; principle of, 175, 177–78, 180, 188, 224; of the world, 241. See also simplicity

particle theory: cathode rays, 275, 289, 295; failure of, 295; fit with experimental results, 290–91, 298–99; versus wave theory, 297–99

Partridge, Bruce, 315–17

Pauli, Wolfgang, 306, 309

Peano’s axioms, 444

Peebles, P. J. E. “Jim,” 317–18

Peirce, Charles, 253–55, 260

Penzias, Arno, 247, 275, 313, 319, 539

perfect cosmological principle, 539, 546

Pettigrew, Richard, 360, 411, 419

Philosophy of Natural Science, 265. See also Hempel, Carl

Philosophy of Science (journal), 162

phlogiston: and levity, 322–23; and oxygen, 320–24; phlogiston chemistry, 320–23; phlogiston theory, 320–22; and Whewell, 323

Physical Cosmology, 317. See also Peebles, P. J. E. “Jim”

pocket universes, 480, 510–11, 514

Poisson’s equation, 608–10

Pons, B. Stanley, 99, 102

Popper, Karl, 180

posterior probabilities: and Bayes’ theorem, 335–36, 344, 441; fixed, 465n

Precht, J., 45

Primer on Determinism, 576. See also Earman, John

Principia, 51, 176, 187. See also Newton, Isaac

principle of indifference, 346–48, 350, 355

Principles of Geology: and catastrophist theories, 286–88; as example of abduction, 276, 285–89; impact on Darwin, 285; and notions of explanation, 285–86; methodological discussion, 286. See also Lyell, Charles; uniformitarian geology

Principles of Physical Cosmology, 318. See also Peebles, Phillip

prior probabilities: and arbitrariness, 381–82; and Bayesianism, 335, 435; distribution, 340, 440–42, 466; necessity of, 382; one correct, 340; problem of, 381; ratio of, 441; unambiguous, 341; washed out, 33–34, 37, 465n

probabilistic law, 590–92, 596

probabilities: 336, 339, 348, 357–58; acceptance or rejection, 382–83; additivity of, 14, 16, 470, 483, 508, 601; and chance properties, 478; and coin tosses, 37, 47–48; conditional, 335, 648; and continuum-sized outcome sets, 520; dominance of, 395–99; necessity of, 337–38, 360–62, 382, 387–89, 395, 410–11, 423; no-memory property of, 590; as strengths of support, 574, 589–90, 599–600; and non-additive logic, 594; and nonmeasurable sets, 521; and pocket universes, 480–81; necessity of, 478; normalization, 574; representation of indeterminacy, 17; strengths of support, 575, 603–05; uniform, 574; and volumes in space, 597–99. See also prior probabilities: posterior probabilities

probability calculus: additivity of, 396, 601; axioms of, 336–38, 340, 352, 365, 369, 371–73; and Bayesianism, 335, 383; and beliefs, 364; and Brier score, 392; computational rules of, 338, 377, 379; and credences, 396; and induction, 335; as incomplete, 436; as “logic of science,” 342; limits of, 343, 435; problems with, 382; success of, 536; weakening of, 345

Probability Theory: The Logic of Science, 342. See also Jaynes, Edwin

protons, 138, 140

Pruss, Alexander, 472, 506

Ptolemaic system, 156; versus Copernican, 157, 223. See also Ptolemy

Ptolemy: versus Copernicus 156. See also Ptolemaic system

Pythagoras, 411, 535–36, 557

quantum measurement, 17, 576

quantum mechanics, 60, 114, 141, 195, 302, 615, 620

quantum theory, 17, 163, 191, 291, 302–03, 614–32, 636–38, 647–50

radioactivity, 27

radioactive decay: law of, 590; probabilistic analysis of, 591

radium chloride: and barium chloride, 27–30, 44–46, 49; crystalline form of, 44, 46, 59; crystallographic properties of, 9, 27, 38; isomorphism of, 45; monoclinic form, 39n, 66; and Marie Curie, 26–27, 36; separation from uranium, 26–28

Ramsey, Frank, 337, 360, 363, 365

randomization, 60–61, 69, 94–95, 112, 114–15

Rathmanner, Samuel, 79

Rayleigh scattering, 85

recession of galaxies, 179, 269

repeatability of experiment, 89–91, 95, 97. See also replicability; reproducibility

replicability of experiment: defined, 89–91; evidential significance of, 60; import of, 90, 93; failure of, 10, 91–93, 98–104, 106–07, 115; and induction, 51; and material analysis, 93–96; as “scientific gold standard,” 10; success of, 10, 91–93, 96–98, 111–13, 115. See also repeatability; reproducibility

reproducibility of experiment. See replicability; repeatability

Reynolds analogy: defined, 137–38; for fluid flow, 120, 133, 137, 145–46, 148–49; heat transfer, 138, 143–149; modern, 146–50; momentum transfer, 138, 143, 144–47, 149; original, 144–45; technical details, 143–50. See also fluid flow in pipes; transport phenomena

Reynolds, Osborne, 137, 145–46. See also Reynolds analogy

Roberts, Bryan, 578

Roche, William, 249

Romé de l’Isle, 29

Rosenkrantz, Roger, 409

Rosenthal, Jeffrey, 560

roulette wheel, 473–74, 595–96, 615, 638

Rudner, Richard, 155, 162–65, 168, 170–71

Runge, C., 45

Russell set, 555

Russell’s paradox, 555

Rutherford, Ernest, 28–29, 40, 45–46

Salmon, Wesley, 67

Savage, Leonard, 360, 375

saving the appearances, 156, 158. See also saving the phenomena

saving the phenomena, 156, 160–61, 322. See also saving the appearances

Schervish, Mark, 416

Schrödinger equation, 303

scoring rules: and accuracy of credences, 388; choice of, 388–89, 398–99, 408–12, 420, 423; and frequencies, 390–92; literature on, 388–90, 423; multiplicity of, 423; and probabilistic credences, 418, 423; and probabilities, 389, 418, 423; quadradic, 420–23; strictly proper, 390, 412–20, 423, 431–32; and subjective Bayesianism, 389; vindications of, 387; with 0 < n < 1, 403–05 with n = 1, 405–07; with n > 1, 399–403, 424–30

Sellars, Wilfrid, 85

Selten, Reinhard, 420–23

Semmelweis, Ignaz, 13, 261, 265–67

Shafer-Dempster theory, 358–59, 411–12, 435, 466

Shankland, R. S., 110

Shapiro, Alan, 326

Siderius Nuncius, 133. See also Galileo, Galilei

simplicity: and Bayesian analysis, 436, 440–41, 443; and counting entities, 174–76, 183, 185–86; as criterion for explanation, 258–59; as criterion for theory choice, 11, 166–67, 169–70; descriptive simplicity, 183, 188–95, 202; as economy of expression, 180–81; in evidential assessment, 58, 153; as evidential truism, 186–87; explanation for popular appeal of, 173; in Galileo’s reasoning, 70–71; as grounds for inference, 51, 60; in heuristic search, 180; of hypotheses, 175–78; inductive power of, 159; and material theory of induction, 186–87; metaphysics of, 241, 243; in model selection, 223–26; ontic simplicity, 183–84; pragmatic justifications of, 178–82; as surrogate for facts, 159, 169, 173–76, 178, 224. See also parsimony

skepticism: and cold fusion, 101; dogmatic, 34, 36; and epistemic virtues and values, 153–55, 162, 169–70; inductive, 11; and Kuhn, 155; and Thomson, 297; prior, 35; radical, 155

Smith, Cedric, 373

Snow, John, 179

Sober, Elliot, 174, 223, 242, 249

Soddy, Frederick, 45

sodium chloride, 24, 29

Solomon, Monica, 75n

Solomonoff, Ray, 79

space-time, 72, 81, 604

Space-Time-Matter, 306–07. See also Weyl, Hermann

spontaneous movement, 17, 574, 577–79, 581, 591–94, 599–600

Stanford, Kyle, 251

Stanton number, 138, 144, 147, 149

statistical mechanical systems, 60

Statistical Reasoning with Imprecise Probabilities, 373. See also Walley, Peter

steady-state cosmology, 16, 247, 276, 316–19, 483, 520–21, 539. See also cosmology; Bondi, Hermann; Hoyle, Fred; Gold, Thomas

Steinhardt, Paul, 512–14

string theory, 114

strontium sulphate, 44

The Structure of Scientific Revolutions, 165–66, 168. See also Kuhn, Thomas

Studies in History and Philosophy of Science, 52

Sturms, Edmund, 103–05

Symmetry, 409–10, 422

tail events, 558–66

temporally indeterministic systems, 575, 589–94

Thagard, Paul, 256–60, 320, 324

The Assayer, 71. See also Galileo, Galilei

theory choice, 154–55, 166–67, 169

theory of evolution, 277, 341. See also natural selection

theory of gases, 185

theory of relativity: aesthetics of, 307; complexity of, 252–53, 270; correction to Newtonian motions, 306; and curve fitting, 211; and the ether, 122; and evidential debt, 307, 310; explanation of motion of Mercury, 4, 210–11, 253, 263, 306–07, 311; explanation of curvature of space-time, 80–81; extension by Hermann Weyl, 311–12; and Miller experiment, 93; popularizations of, 194, 306; simplicity of, 310; special relativity, 107, 329; versus zodiacal light, 274–75. See also Einstein, Albert

thermal background radiation. See cosmic background radiation

Thirring, Hans, 109

Thompson, William, 212, 218

Thomson, J. J.: and abduction, 302; argument against wave theory, 292, 296; and cathode rays, 275–76, 289–303; “Cathode Rays,” 289, 293, 297; and notions of explanation, 291. See also cathode rays; particle theory

tides: astronomical effects, 217; complications in tidal analysis, 216–17; compound tides, 217; and curve fitting, 12, 211; harmonic analysis of, 175, 211–20; harmonic constituents, 218–19; neap tides, 214–15; overtides, 217; spring tides, 214; tidal bulges, 213–14, 216; tidal prediction, 211, 216–18, 220

Tolstoy, Leo, 560

transport phenomena, 11, 121, 137, 144. See also Reynolds analogy

Tribus, Myron, 378, 380, 381n

Truth-Directedness, 420

Turing machine, 79–80, 441

Two New Sciences, 70, 72, 74–75. See also Galileo, Galilei

Tyndall, John, 111, 327

ultrafilter logic, 17, 522, 568–70

ultrafilter theorem, 565, 567

unified field theory, 72

uniform probability distribution, 16, 382n, 524–25, 527–30, 534–36, 592

uniformitarian geology: and catastrophist theories, 285, 289; as example of abduction, 276, 285–89; similarity to Darwin’s argument, 287–88. See also Lyell Charles; Principles of Geology

uniformity of chance, 520, 522–24

uranium: and nuclear fission, 98, 139–40; separation of radium, 26–27

Uranus: anomalous motions of, 311; source of perturbations, 209

value judgments: as criterion for theory choice, 170; ethical judgments of scientists, 155, 162–64; irresolvable, 168. See also epistemic values and virtues; values

values: as criteria of theory choice, 168; as distinguished from facts, 154; non-epistemic, 162. See also epistemic values and virtues; value judgments

Van Fraassen, Bas, 249

Vossiche Zeitung, 108, 110

Vitali sets: and axiom of choice, 555–56; construction of, 548–52, 567; chance properties of, 553–54; defined 521; logic of 521; as simple nonmeasurable set, 548; specification of, 554–55

von Mises, Richard, 337, 353–56, 369

von Neumann, John, 195; Mathematical Foundations of Quantum Mechanics, 195

von Seeliger, Hugo, 274–75, 308–09

Vulcan, 210, 308, 310–11

Wagon, Stan, 521, 543, 545

Walker, James, 329–30

Wallace, David, 583–84, 610

Walley, Peter, 359, 373–75

War and Peace, 560. See also Tolstoy, Leo

Warren, Robin, 96

Watson, James, 205

wave theory of light: and cathode rays, 290–96; and Darwin, 324; and electromagnetic theory, 329; versus emission theory, 274, 324–30; as example of abduction, 324–330; fit with experimental results, 290, 295–96; multiple theories, 324–25; obstacles facing, 274, 329; versus particle theory, 297–99

Weak Convexity, 409–10

Weinberg, Steven, 314–15

Weintraub, Ruth, 472

Weisskopf, Victor, 140–42

Wenmackers, Sylvia, 472, 477

Weyl, Hermann, 306–07, 311

Whewell, William: and catastrophist theories, 285; and crystallography, 29, 39, 42, 44; and inference to the best explanation, 258–59; History of the Inductive Sciences, 29, 326–27; influence on Darwin, 278; oxygen and phlogiston, 323

white hole, 604

Wickramasinghe, Chandra, 316

Wiedemann, Eilhard, 293

Williamson, Timothy, 472

Wilson, Robert, 247, 275, 313, 319, 539

Worrall, John, 114

Young, Thomas, 326

Zermelo-Fraenkel set theory, 555–56

Zero-One Law, 560

zodiacal light, 210, 274, 308–09

Zorn’s lemma, 556

σ-algebras. See σ-fields

σ-fields, 526–31