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date: 27 January 2020

(p. 851) Subject Index

(p. 851) Subject Index

ability
relation to manifestation 604–6, 612, 616
reproductive 603–6, 609, 612, 617, 618
survival 603–6, 616, 618
abstract formulae 20
accuracy 39, 60, 118, 138, 183, 204, 212–5, 217, 232, 243, 292, 355, 371–3, 442, 484–5, 504
arguments 261–3, 271–3, 678
Brier Score explication of 143–4, 261 (n.24), 371, 489
domination 261–3, 629–30
and precision 204, 212–7, 232, 234, 243, 293, 484
achievement 716, 718, 728
action-guiding 710, 796 (n.13)
additivity
additivity axiom 6, 284, 351
axiom of dual additivity 257
countable, sigma, σ- 18, 105, 156, 205
finite 6, 156, 159–60, 205, 351
subadditivity 234, 259, 510
aggregation
attitude 537
judgement 536–7
opinion 510, 512, 519–21, 525, 526, 536, 539
utility 537, 706, 721, 728
algebra (see also ‘field’) 17
algebraic analysis 57
Boolean 555–60
sigma (σ-) 17, 21, 100, 105, 156, 163–4, 167, 176, 205–6, 217, 239, 460–1
Heyting 270
aleatory contracts 43–5
Allais’ paradox 367, 810
ambiguity aversion 300–2, 303, 308, 349, 483, 490
annuities
life 44
anonymity
and expert judgement 510
and utility aggregation 720
anti-realism 143–5, 248, 270, 427, 431
assertibility 775–776, 777 (n.7), 780
astronomy, evidence in 39, 42
attitude
de dicto 676
de re 675–6
doxastic 625
propositional 250
averaging, axiom of 269
axiom of choice 18, 20, 157
axioms 6, 17
axiomatization of probability
Kolmogorov 17–19, 156, 351, 356
nonclassical 256–7, 259
Popperian 160, 173, 251 (n.7), 279–82
axiomatizations, immanent versus logical 272
backgammon 74
base rate 9–10, 390
neglect 10, 11 (n.4), 390, 392–3, 507
Bayes factor 377, 378, 385
Bayes’ theorem 8–9, 15, 18, 24, 169, 183–5, 266, 286, 287, 384, 511, 738, 745, 752, 768
Bayesian method 88, 91, 131, 136, 139, 143, 207, 341 (n.2)
Bayesian network (Bayes net)
definition 184–5
(p. 852) Bayesianism 382–6
objective 136, 139, 145, 335, 384, 440, 592 (n. 17), 635
types of 132, 139, 142, 145, 146, 147, 386, 402, 440, 635
behaviour, as manifestation of a propensity 133–4, 408–9, 606, 611, 612, 617, 619
belief
conditional 779, 780
degree of (see also ‘credence’) 33, 133, 138, 142, 143, 161, 168, 180, 212, 229, 253, 255, 261, 267, 322, 330, 360–2, 365, 371–3, 379, 382, 384, 393, 394, 423, 461, 477, 502, 779, 802
full (binary) 155, 253, 255, 626, 627, 767
partial 155, 255, 262, 625–7
rational constraints on 627–37
belief function
Dempster-Shafer 160, 228, 258, 300, 304, 643
Berkson’s paradox 13–4, 16
Bernoulli trials 75
Bernoulli’shypothesis 790
Bernoulli’s theorem (see also ‘law of large numbers’) 50
best system analysis 4, 423–37
bet (betting) 45–6
one-side 305
betterness(for a person, individual, relation) 706, 711, 714–30
bias (biases)
anchoring 481–3, 486, 503, 508
catch-all underestimation bias 482
cognitive 478–9, 481, 483, 485, 489, 500, 501, 503, 507–9, 513–4
confirmation 481
in judgment formation 507–10
motivational 501, 513
overconfidence/apparent overconfidence 484–5, 509
packing 508
prior distribution 746, 754, 755–7
pruning 508
sampling (selection effect) 14, 190, 191, 395, 400, 481, 485
sequence 444–6, 448
zero sum 483–4
Bienaymé-Chebyshev inequality 90, 93, 94, 103, 104, 105
billiards 83, 593
bills of mortality, London, 39, 75
Biometrika 119, 121–5
biometry 117–126
binomial distribution 23, 28, 29, 71, 321, 419
normal approximation to 77, 79, 82, 83
Poisson approximation to 77, 79
binomial expansion 62, 78, 79, 80
binomial method of the unciæ 76
binomial theorem 70, 72, 75–6
biological practice 618
birth rates 75, 88, 318
bivalence 249
blame 708
Boltzmann equation 106, 573–4
Boltzmann’s H-function 576, 578, 581–3
borderline cases 250
Borel paradox 179
Borel set 21
bounded rationality 479
Brier score 143–4, 261 (n.24), 371, 489
Brownian motion 98, 100, 107–9
calibration 226, 371, 372 (n.15), 484–5, 499, 505–7, 511, 629–30
chart 499, 505
graph 505
cardinal utility 365, 713, 791
casuistry 36–8, 45
causal discovery 822, 823 (n.4)
causal graph 189, 820, 822
causal inference 819, 822
causal model 819–22
causal power 826, 826 (n.7)
causal relevance 817–8
causal strength 815, 823, 824, 825
causality (see also ‘causation’) 41, 133, 137, 141, 145, 148, 415–6, 568
deterministic 415–6, 427, 820
indeterministic 826
quasi-deterministic 576–8
(p. 853) causation (see also ‘causality’) 91, 116, 416, 423, 430, 434, 435, 793, 815–30
actual 827–30
probabilistic 4, 91, 148, 188, 417, 815–30
cause, interacting 817–8
centered proposition 635–6, 669–70, 671–7
centered world 666–8, 675
central limit theorem (see also ‘limit theorems’) 29, 87, 100–1
certainty 255
anti-certainty 255–6
degree of (see also ‘credence’, ‘degree of belief’) 36, 51, 60, 318
moral 36–7
certainty factor 188
certainty-loss framework 674
Chapman-Kolmogorov equation 107
characteristic function 22
chi-squared (χ2) 119, 123, 386
Choquet capacities 303
Church of England 72
circularity problem 605–6, 608, 610, 618
circulation of blood 70, 72
classical mechanics, classical physics 163, 453–5, 462–3, 467, 545, 575, 580, 593, 652
indeterminism in 453–4
chaotic dynamics in classical statistical mechanics 454
classical theory of probability 3, 77, 452
cognitive loading 255, 261, 262, 263, 272, 273
coherence
and accuracy 371–3
and rationality 373–4
strict (see also ‘regularity’) 363, 631
coin tossing 147, 420
collective, Kollektiv 99
comparative probability 224–31, 277–9, 299
completeness
axiom 225, 300
informational 147
interpersonal 716–9, 725, 726, 729
rule 289, 291
compositionality 773, 775, 777, 783, 785
concentration 102
conditional 168–9
counterfactual 710, 774, 794
indicative 682, 691, 693, 699, 774–6, 778, 779–80
conditional assertion 779–81
conditional excluded middle 777
conditional independence 11, 185–6, 195, 821
conditional probability 7–9, 18, 34, 88, 100, 156–7, 160–2, 167–81, 184–6, 188, 206, 263–7, 272–3, 279, 281–2, 323, 327, 356, 361, 363, 384, 392–3, 397, 461, 485–7, 631, 637–9, 684, 686, 688–9, 691–2, 694–5, 774–9, 784, 793, 815–6
comparative 278–82, 284, 293
fallacies involving 485–7
and non-classical logics 263–7, 272–3
in quantum mechanics 550, 553
and conditionals 168–9, 181, 682, 684, 774–9, 784
conditionality principle 385
conditionalization, conditioning (see also ‘updating’) 9, 11, 146, 170, 174–7, 204, 214, 248, 263–5, 279–85, 303, 306–7, 361–4, 374–7, 384, 402, 404, 431, 503, 633–8, 667–78, 750, 753, 755
compartmentalized 672–5
for imprecise probabilities 306
for indeterminate probabilities 306
Jeffrey 316, 332, 361–4, 373, 377, 378, 667, 678
shifted 670–1
(p. 854) confidence 3, 8, 243, 251–2
comparative 277–8
interval 124, 213, 396, 484–5
over- 484–5, 509
confirmation 10, 175
absolute 651
bias 481
degree of 131, 282, 293–4, 650, 741
and the fine tuning argument 742–3, 746, 755, 757
incremental 651
relations 490
theory 3, 175, 267, 273, 402, 650–65
conflict aversion 479, 490
conflicting information 479
conglomerability 177–81
conjecture 51, 59–60, 62, 63
conjunction 167, 173, 249, 252, 254, 257, 521, 526
fallacy 478, 485–7, 490
probability of 7, 259, 688
connective 257, 259, 264–5, 684, 686, 690–1, 775, 777, 780
consequence
logical 681–9, 691, 692, 695–7, 699
no-drop characterisation of 257–8, 274
nonclassical logical 252–6, 273
rational 283
special consequence condition 652
consequentialism 706, 711–2, 714, 797
rule 731–3
consistency theorem 100, 109
constraint-based learning 192, 196
constraint semantics 783–5
constraint
synchronic 627, 631, 632, 635, 636, 666
diachronic 627, 634, 637, 667
context dependency 144, 146, 387, 486, 488, 603 (n.3), 778
continuity
axiom 306, 706, 713, 724, 726, 729
monotone 205
semantics 692, 698
contractualism 711–2, 731, 724, 729
contradiction 20, 174, 175, 248, 252, 254, 280–1, 289, 521, 778
convergence
almost sure 28, 238, 241, 347, 575, 765
in distribution 25, 95, 99, 100–102, 108, 199
in probability 28, 88, 105, 139, 204, 214, 318, 347–8, 371, 409, 575, 693
of relative frequencies 135–138, 143, 199, 204, 233, 235, 241–3, 347, 353, 575
convex combination of truth values 251, 253, 256, 257, 258, 261, 262, 272, 274
correlation 10–6, 41, 104, 116–22, 170, 190–1, 374, 478, 526, 534, 536, 562–4, 617, 658, 793, 816, 818–820, 823, 828
coefficient, measure 104, 116–22, 564
conditional 11–4, 16
positive, negative 10–11, 14, 16, 563, 658, 819
spurious 216–7, 816, 818, 823, 828
cost-benefit analysis 20, 66
counterfactual (see also ‘conditional’) 710, 774, 794
and causation 423, 430, 434–5, 822, 825, 828
conditional probability 175
priors 374–5
probability 470
probability logic of 693–4
credal sets 304–305
credence (see also ‘degree of belief’) 8
base 264
conditional 173, 595, 627, 631–4, 637, 639, 667 (n.4), 668, 676, 740
function 174, 252, 432, 433, 464, 628–32, 633
fuzzy vs. sharp 640–1, 643
indeterminate 163
profile 255 (n.3)
self-locating 636, 666–78
unconditional 173, 627, 630, 634, 667 (n.4), 676 (n.26), 794
cumulative distribution function 24
joint 25
cyclical preferences 367–9
de Moivre theorem 83, 107
decision-making with imprecise probabilities 307–8
(p. 855) decision-making with indeterminate probabilities 307–8
decision rule, Jeffrey 268
‘definitely’ operator 260 (n.23)
degree of belief (see also ‘credence’) 33, 133, 138, 142, 143, 161, 168, 180, 212, 229, 253, 255, 261, 267, 322, 330, 360–2, 365, 371–3, 379, 382, 384, 393, 394, 423, 461, 477, 502, 779, 802
Dempster rule 300
Dempster-Shafer theory 300
density function 23
deontology 712, 733–4
dependence
causal 10, 732
counterfactual 825
probabilistic 10, 425, 732, 821
“radical” 778
sample space (partition) 392, 400, 482–3, 488
determinism 89, 97, 147, 415, 429, 455, 460–3, 465–6, 469, 471–2, 574–5
desirability 268–9, 272
desire 797
consistency of 799, 800, 802
interpreting 801–810
satisfaction 366, 711, 773, 795, 797, 801
dialetheism/dialetheic/dialethic 252
Diamond’s example 721–2
dice
biased, loaded (see also ‘bias, process’) 10, 74, 407–8
games 45–6
dicing problem, probability of the sum of the faces that show 70, 79
diffusion process 107–8
directed acyclic graph (DAG) 184–5, 819
discounting 191
disjunction 17
dispersion 102–3
disposition 4, 408–9, 411, 413, 420, 423, 424, 605–6
partial 424, 431
distribution
binomial 23, 28, 29, 71, 321, 419
definition 22
identical 22
joint 22–3, 187, 545, 546, 586
normal (Gaussian) 24, 29, 89, 90, 94, 95, 101, 115, 118, 120, 121, 330, 419
of propensities for reproductive success 607, 609–11, 613–6, 618
uniform 24, 27, 179 (n.4), 229, 389, 468, 469, 586, 744, 746, 747, 754, 763
distribution function 99, 101–2, 105, 106–107, 392, 499
cumulative 238–9, 245, 399, 503, 505, 511, 514
stable 102
division of stakes problem 46, 70, 76, 77
dogmatism 642–3, 650 (n.2)
dominance 306, 722, 798, 818
strict 722
weak 722
Duhem-Quine thesis 656
duration of play problem 77–8
Dutch book
definition 215
argument 262–3, 265, 272, 363–4, 369, 379, 628, 634, 678
theorem 282
e-admissibility 308
effect size 393–4, 401–2
elicitation, probability 210, 214–5, 297, 484–5, 487–9, 497–518, 800–1
Ellsberg’s paradox 299
embedding 780, 782, 784
empirical support (see also ‘confirmation’, ‘evidence’) 421
empiricism 40, 135, 137, 142, 146, 147
English Statistical School 112–26
ensemble approach to statistical mechanics 95–7, 586–7, 588–9
environment 603–18, 742
(p. 856) epidemiology 342, 416, 497, 815, 823–4
epistemic modal 773
epistemic utility 635
equality (moral) 721–3
principle 722
equiprobability 47, 75, 88, 92, 99, 315, 317, 356 (n.18), 456, 556, 566, 569, 588, 717–8, 776
ergodicity 96–8, 108, 448 (n.4), 583
error statistics 399
error
type I and type II 387–8, 395, 400
estimation
of probability or frequency 147, 149, 188–9, 198–9, 209–10, 213, 301, 410, 415, 434, 478, 483–4, 486, 488–90, 502, 507–8, 512, 519
theory 90, 93–5, 116, 123–4, 330, 391, 396
of truth 372–3, 773
ethical theory 72, 705
ethics 705–34
eugenics 114, 117, 120, 122, 124, 604 (n.5)
evaluation
of an act 707–10
of an agent 708
event 6, 17, 20
decision theory 791
measure theory 17
single 28, 356, 407, 409–15, 482, 490, 827
types 20
evidence 10
admissible 464
centered 674
confirming 652
empirical 565, 584
historical 40
imprecise or incomplete 811
in astronomy 39, 42
law of 34–6
legal standard of 825
measure of 385
medical 40
problem of old 175, 373–5
same 171
statistical 383, 386, 393, 397, 401–2
total 636–7
exchangeability 131, 142, 143, 302, 306, 307, 316, 324–6, 328
partial 329
expectation 25–26, 52–8, 61–6, 71–3, 76, 105–6, 178, 365, 369, 506, 576, 587, 593–4, 759–61, 764–6, 790–1, 795–7
lower and upper 232, 243, 298, 300, 302, 304–5, 307–8
of truth value 251, 253, 256, 267
expected goodness 714–5
expected utility
axioms 712–3
experimental arrangement 134, 408, 412, 548, 567, 569
expert
judgment, opinion 484, 497–501, 510, 519
principle 267, 433
system 188, 300
explanation 137–8, 807
expressivism 691, 780
fairness 55, 706, 721–2, 729
of a bet/betting system 143, 628, 641
faithfulness condition 192–7, 821, 823
embedded 197
fallacy
base rate 10, 11 (n.4), 390, 392–3, 507
conjunction 478, 485–7, 490
gambler’s 27
falsehood, logical 251, 254, 257, 262
falsifiability
methodological 419–21
favouring 11
field (see also ‘algebra’) 17
Borel (see also σ-field) 351
σ- (sigma; see also ‘σ-algebra’) 17, 18, 24, 27, 164
fortune 57, 74, 316–7
fraction
attributable 825
etiological 826
excess 824–6
population-attributable 826–7
freedom
degrees of 97, 547–8, 575, 577, 580, 581, 585, 586, 587
moral/political 711, 725
frequency
finite 342–3
hypothetical (limiting relative) 28, 343–58, 444, 448, 453, 575
relative 28, 43, 64–5, 197–9, 213
frequentism 132–8, 341–58, 382–402, 444, 451–3, 457
conditional 402
finite 342–3
frequentist inference 382, 395–6, 402
hypothetical 343–58
fuzzy credence 640–1
fuzzy logic 265, 301, 479
fuzzy set, fuzzy membership 216 (n.20), 258, 486, 488
gambler’s fallacy 27
gambling manuals 74, 80
game
against nature 732
against other people 732–3
coordination 731–2
sequential 732
simultaneous 732
game of chance
coin toss, fair 454
dice 2, 21–3, 33, 45–6, 59, 65
equity or fairness in (aequa ratione) 56
premature ends of, division of stakes 46, 58, 70, 76–7, 790
game theory 478
generating condition 134, 408
generating function 77, 79, 89
genetics 113, 121, 124, 467, 468, 601, 604, 607
God 2, 42, 738–40
God’s foreknowledge 61, 66
pragmatic arguments for belief 757–67
probabalistic arguments for 738
goodness of fit test 119, 386
gradational accuracy 371–2
half-proof 35–6
Harsanyi’s theorem 718–21, 725, 727, 728–9
hazard
environmental 823–5
jeux de 53
heredity 113–6, 118–23
heuristic (see also ‘bias’)
affect 482
anchoring-and-adjustment 481–2
availability 482, 507
frugal 479
representativeness 507
higher-order probability (see also ‘second-order probability’) 685–6
historical evidence 40
Humphreys’ paradox 161, 169–71, 415–7, 417 (n.7)
hypothesis of elementary errors 90
hypothesis test (see also ‘significance test’) 42, 387–8, 391, 402
hypothetico-deductivism 402
ideal agent 249, 270, 274, 282, 707, 730, 802, 809
identification, causal 823
impartiality 717–9, 721–2
implicature 776, 781
imprecise probabilities 171–3, 181, 297–312
IncExc axiom 257, 258, 259, 260, 265 (n.30)
incommensurability 724
incompleteness 712, 717
indices of guilt, in Roman law 35
independence
axiom 306, 366
causal 732, 821
conditional 11, 185–6, 195, 821
definition 10
eventwise 524–7
generalisation 19
for imprecise probabilities 303, 307
(p. 858) and identically distributed (i.i.d.) trials or variables 23, 27, 29, 91, 93, 233, 237–8, 240, 242, 329–30, 347, 352, 385, 389, 394, 451, 456
for indeterminate probabilities 303, 307
of infinite collections of events 10
probabilistic 10, 11, 19, 22, 143, 267, 302, 512
of random variables 22, 105
indeterminacy 155, 163, 203–4, 210, 214, 216, 232–4, 235, 297–308
indeterminate probabilities 297–312
indeterminism 453–5
indexicals 670–1, 676
indicator function 22
indifference principle 3, 319–20, 322, 588
induction
by enumeration 135–7, 323, 325, 331, 353
Goodman’s new riddle of 656
principle of 135
problem of 40–2
rule of 353
inductive logic 131–2, 657, 683
inference
causal 821–2
inductive 41, 47, 323, 325, 386, 401–2
logical 249, 697, 699
probabilistic 183, 387
statistical 42, 87, 114, 122, 143, 328, 341 (n.2), 382–402, 420–1, 428
infinitely divisible distribution 103, 108
information cost 731, 799
informativeness 10, 425, 427–8, 436, 484, 505–6, 715–6, 746, 752, 801, 804–5
inheritance, biological 113–6, 118–23
insurance
pricing of 43–5, 53
interpretations of probability 3–4
best system 4, 423–437
classical theory 3, 77, 452
frequency/frequentist 3–4, 132, 134–5, 341–58, 382–402, 442, 575
hypothetical 343–58, 444, 448, 453, 575
logical 3, 131, 360, 374, 384
propensity theory 406–21
intersection 19, 164, 167, 205 (n.2), 521
intuitionism 20, 251 (n.7), 258
irrationality 726
Islamic law
of contracts 43
of inheritance 56
of partnerships 56
Jeffrey conditionalization 316, 332, 361–4, 373, 377, 378, 667, 678
Jesus of Nazareth 73
just noticeable difference 715
kinetic theory of gases 95–8, 573, 578–9
Kochen-Specker theorems 270, 555, 561, 563, 564–5, 569
Kolmogorov complexity 456
prefix-free complexity 450
compressibility 449
Kolmogorov Zero-One Law 236, 240
label space 99, 521, 639
Laplacian approximation method 88
law
court trials 47, 91, 208–9, 825 (n.5)
Islamic 43, 56
legal arguments 34–6, 47
of torts 825
Roman 35–6, 43
law of excluded middle 250–2, 254, 273
law of iterated logarithm 104
law of large numbers 26–7, 50–1, 60–3, 66
empirical 344, 346–7
strong 26, 238
weak 27
law of total probability 7, 18
lawn bowling 77
leases on lives 81
least squares 89–90, 93
Lebesgue measure 447
Leviathan 72
leximin 717
Lindley’s paradox 394–5, 396, 399, 400 (n.13), 401
life expectancy 53, 410
life table 81–2
likelihood 8
law of 655, 741, 744
likelihood principle 384, 384–5, 641–642
maximum likelihood method 90, 122–3
ratio 386, 388, 399, 654
likelihoodism 386, 650 (n.1), 738, 752–4, 767
limit theorems 27–9, 87–89, 91, 95–5, 98, 100–1, 106
Lindeberg condition 102
logic 20, 248–76, 681–704
algebraic 270–2
choice of 255
default 699
fuzzy 265, 301, 479
intuitionist 20, 251 (n.7), 258
Łukasiewicz 258
many-valued 265, 536–7
modal 218–24, 688
paraconsistent 20, 252 (n.10), 253
probabilistic 300–2, 681–99
quantum 248 (n.1), 270, 273, 565
revision of 565
strong Kleene 254
supervaluational 249 (n.2), 251, 252, 258, 259 (n.19), 260, 265 (n.30), 266, 269, 725
symmetric 254, 258
three-valued 253–6
logicism 130–2
lot (sors) 54–7
lower expectations 304–5
lower previsions 305
lower probabilities 303–4
Markov chain 105–6
Markov condition 186–7, 189–98, 819–21
causal 820–1
Markov property 108
Martingale 106
maximality 308
maximal options 308
maximin 717
measurable sets 17
measure theory 16–19
measurement
evaluative 726–8
theory 204, 215
medical evidence 40
mentalese (mental language) 250, 270
method of moments 117–22
minimality condition 821
minimax options 308
minimum description length (MDL) principle 192
miracles 40, 41, 83, 738
mismatch problem 605–6, 610, 618
modal
epistemic 773
logic 249, 258, 688
probability 218, 223–4, 423
metaphysical 463, 470
modus ponens 776
moment problem 94, 99
moments 611, 614
method of 117–22
theorem 322
theory of 94–5
money pump 369
monotonicity, axiom of 251, 252, 256, 699
cautious 697
Monty Hall paradox 14–6
Myerson’sexample 721–2
(p. 860) natural selection 123, 374, 601, 603–4, 606 (n.9), 607, 610, 613–4, 616, 617, 618
nearestand dearest objection 731
necessity 28
contractual 63
hypothetical 63
institutional 63
physical 63, 423
negation 17
negation rule 6
neutral existence 720
Newcomb’sproblem 732, 793, 794
Newtonian mechanics 163, 453–5, 462–3, 467, 545, 575, 580, 593, 652
non-expectedutility theory 726
nonidentityproblem 720
non-measurable sets 18, 20
non-monotonicity 283, 651–2
non-negativity, axiom of 6, 156, 163, 205, 251
normal distribution 24, 29, 89, 90, 94, 95, 101, 115, 118, 120, 121, 330, 419
normalization, axiom of 156, 158, 233, 251, 269
normalization objection 747–9
normativity 711
normed sums 102–3, 105–6
“not by chance” arguments 42
objectivity 134, 137, 140, 143, 357–8, 387, 401–2, 431
occupancy problem 77
odds 499, 502
offspring 115, 118, 605, 606, 607–10, 614–5, 617, 618
old evidence, problem of 175
omniscience 61, 253, 256, 373, 375, 739
omniscience, credal 256
one-sided betting 305
one-sided testing problem 391–3, 399
ordering
complete 306, 307, 712
comparative probabilistic 224–5
partial 306, 308, 556
preorder 712, 725
probabilistic 694
problem of 453
organism 601–19
outcome 20
fecund and sterile 62
space (see also ‘sample space’) 21, 22, 28, 329, 453, 546, 740
overconfidence 484–5, 509
p-values 383, 391–402
paraconsistency 20, 252 (n.10), 253
paradox 11–16
Allais’ 367, 810
Berkson’s 13–14, 16
Borel 179
Ellsberg’s 299, 307, 811
for finite additivity 159–60
Humphreys’ 161, 169–71, 415–7, 417 (n.7)
Lindley’s 394–5, 396
lottery 688
Monty Hall 14–16
preface 626
purported paradox in probability 333–6
raven 656
Robartes’s (Roberts’s) 75–6
Simpson’s 11–13
sorites 123, 212, 232, 248 (n.1)
St. Petersburg 26–7, 66, 790
parameter estimation 391
Pareto 718
ex ante 708–9
equality-neutral 722
parish clerks, company of 75
partial entailment 657–9
partiality 717–9, 721–2
partition 7
infinite 18
partition dependence 482–3, 488
principle of 260 (n.22, 23)
(p. 861) partnerships or companies 55–7
penalty methods 144 (n.28)
permutation postulate 131, 324, 326, 329
permutations and combinations 50, 52, 53, 58, 73, 231, 453, 718
phase space 96, 467, 580–3, 585–9, 593, 595
place selection 132, 344–6, 445–6, 452, 477
pluralism 147, 402, 468, 657, 659
pool, problem of the 77–8
population
size 613–4, 706
statistics 88
variable 719–21
possibility measures 304
power set 17, 241, 521, 690
pragmatic loading 262, 263, 273
pragmatism 141–6, 431
non-pragmatism 370
preemption 826–8, 830
preference 794–796
partially ordered 306
rational 628–9, 707, 712–3, 726, 789, 799
satisfaction 716, 729, 730
preorder 712, 725
presumption 35–6
prevention 818, 824
primary intensions 20
principal principle 432–5, 463–5, 632–4, 639
principle of indifference 319–20, 322, 588, 740, 764
prior probability 8–9, 139, 140, 184–5, 293, 383, 384, 387, 528, 530, 534, 538–9, 740, 755–6
improper 176–77
reference prior 402
prioritarianism (priority view, priority to the worse-off) 705, 723–4, 727, 729
probabilis 51
probabilism 261–3, 369, 373–4, 627–30, 640–1
moral theological 37–8
radical 142–8
probabilistic logic 300–2, 681–99
probability
axioms of 6–11
bearers of 19–20, 269–71
convex-combination characterisation of 253
decomposition of assessment of 503
probability, interpretations of 3–4
best system 4, 423–437
classical theory 3, 77, 452
frequency/frequentist 3–4, 132, 134–5, 341–58, 382–402, 442, 575
hypothetical 343–58, 444, 448, 453, 575
logical 3, 131, 360, 374, 384
propensity theory 406–21
probability of specific occurrences
causation 825–6
ruin 78
probability, types of
additive (see also ‘additivity’) 6, 284, 351
comparative 224–231, 277–9, 299
evidential 3, 271, 440, 637–40, 782
extrinsic and intrinsic 38
higher-order (see also ‘second-order’) 685–6
indeterminate 297–312
inverse 118, 122, 125, 139
lower 303
nonclassical 256–61
posterior 8–9, 384
quantum 545–69
qualitative 2, 35, 207, 277
second-order 502, 685
single-case (singular) 4, 343–4, 354, 407, 412–5, 451–3, 574
stochastic/factual 33, 51, 93, 101, 103, 105, 106–9, 126, 237, 428, 441, 548
sub-additive 234, 259, 369, 510
that sum to more than one 162
unquantified 47
upper 303
verbal 487–9
probability elicitation 210, 214–5, 297, 484–5, 487–9, 497–518, 800–1
probability function 17, 19, 28, 138, 162, 167–81, 277, 293, 316, 538–9, 592, 631, 640, 650, 707–8, 791–2
probability intervals 147, 211–2, 302–3, 488
probability judgement 497–514
probability kinematics (see also ‘conditionalization’, ‘updating’) 332–3, 361
probability space 17, 21, 156, 375–6, 378, 545, 560, 561, 563, 569, 773, 777, 816
infinite 17, 100
probability theory, generalizations of 555–60
probability tree 503
probability weighting function 479–80
probability wheel 499, 502, 513, 514
propensity theory of probability 406–21
proportional syllogism (statistical syllogism or argument from frequencies) 42–3
propositions 6, 20
fine-grained vs. coarse-grained 250, 269–71
prospect theory 367, 806, 807
cumulative 480
quality of experience 711, 716
quality of life 711
quandary 255 (n.13)
quantum mechanics 545–572
Copenhagen interpretation 677 (n.29)
Everettian interpretation 677 (n.29)
radical interpretation 728
raffle 74, 76, 772–3, 782–3
Ramsey test 774, 777
random drift 601, 606, 618
random variable
definition 21, 178 (n.3)
range of 21
unbounded 26
vector-valued 21
randomization (see also ‘randomness, process’) 316
randomized control experiment (RCE) 189
randomness
algorithmic 444
as evidence for chance 456–7
as typicality 446–9
as ungoverned by a rule 444–6
process 442
product 441
pseudorandomness 443
random sequences (see also ‘randomness, product’) 344–5, 442–3
(p. 863) random walk 448
reduction of chance to 442, 452, 457
rank-dependent expected utility theory 480
rational preferences 628–9, 707, 712–3, 726, 789, 799
rationality (see also ‘irrationality’) 143, 224–5, 250–3, 260–1, 361, 366, 373, 634–5, 726, 796–803, 807–11
bounded 479
Humean 707–8, 797, 805
real number values 18, 21, 162–3, 165, 213–4, 252–3, 255, 263, 366, 740
extended 760, 762–3
recarving, principle of 259–60, 272
recurring series 78
reference class problem 42, 354–6, 638
reflection principle 631, 678, 686
regression 116, 118–20, 122
rejection
and credence 255–6
and significance 387, 389, 400, 419
relevance-limiting thesis 673–4
reparation rule 376–8
repeatable conditions 409, 412–5, 418, 611
representation theorem 143, 145, 273, 291, 324, 328–30, 365–6, 369, 791–5
reproductive success 605–6, 608–15, 618
repugnant conclusion 721
resources 725
responsibility 708, 827
reversions (see also ‘regression’) 81–2, 166
risk
attitudes to 66, 628, 790
difference 824–6
and ethics 711, 714–6, 720, 723, 724, 727–9
evaluations of 482, 490, 497, 823
and insurance 43–5
ratio 824–6
relative 824
versus uncertainty 298–9, 503, 717
robust Bayesian statistics 300
robustness/resiliency 297–300, 776
robustness analysis 300
Royal Oak lottery 74
Royal Society 76, 82–3, 114, 119
Royal Statistical Society (also Statistical Society of London) 113–4, 120–1
ruin, probability of 78
rule of mixture 52
runs, problem of 79
Saint Petersburg paradox 26–7, 66, 790
satisficing 479
screening off 655 (n.8), 816, 818–20, 829
second-order probability 502, 685
selection bias 14, 190–1, 395, 400, 401, 485
self-locating credence 636, 666–78
self-reference 248, 733
semantics
classical 249, 279 (n.5)
constraint 783–5
nonclassical 249–50, 253–6
for high probability conditionals 690–6
truth conditional 777–9
sentences 19
set theory 20
sets of states 20
severity 388, 396–9
sex ratio 75
share (pars, portio) in division of stakes problem 79
sharpenings 725
σ-algebra (sigma algebra) 17, 21, 100, 105, 156, 163–4, 167, 176, 205–6, 217, 239, 460–1
σ-field (sigma field) 17
significance test (see also ‘hypothesis test’) 115, 118, 388–94, 396, 401, 448
null hypothesis significance test (NHST) 387, 389, 391, 394, 397
simplicity (of theories) 39
Simpson’s paradox 11–13
single case
problem of 4, 343, 412, 414
skew-symmetric bilinear (SSB) theory 367–9
(p. 864) sleeping beauty problem 636, 677–8
social contract 711
social welfare
ex ante 708–9
ex post 708–9
SRI protocol 513–4
Stalnaker’s thesis 777–8
standard deviation 26–7
statements 20
statistical evidence 383, 386, 393, 397, 401–2
statistical inference 87, 382–3, 394, 397, 402, 428–9
statistical physics 87, 92, 97, 98
Statistical Society of London (also Royal Statistical Society) 113–4, 120–1
statistical syllogism (proportional syllogism or argument from frequencies) 42–3
stochastic convergence (see also ‘law of large numbers’) 105–6
stochastic process (see also ‘randomness, process’) 47, 100, 103, 106–9, 126, 237
with continuous time parameter 106
with independent increments 107
stochastics 51
Stieltjes integral 99, 100
stopping
optional 383, 385 (n.4), 399
rule 400–1
sufficiency principle 385
supertruth/supertrue 252 (n.9), 258
supposition 774, 777, 781, 793, 794
suspension of judgement 255, 317
Szpilrajn’stheorem 725
Talmud 35, 43
tautology (see also ‘truth, logical’) 254
tennis
handicaps in, calculation of 63
probability applied to 63
time average 97, 204, 236, 237, 238, 241, 591
topics, in rhetoric, as ways or organizing arguments 59
torture 35
total evidence 168, 170, 273, 333, 464, 633 (n.28), 638–9, 640
requirement of 636–7
transmission, transmission failure 643–4
triviality results 169, 691, 777, 779
trolley problem 733, 734
truncation of random variable 101
truth
conditions 272, 775, 777, 779, 782
deflationism concerning 255
logical (see also ‘tautology’) 251, 361, 373
truth-functional connective 775, 776
truth status
cognitive loading of 255, 261, 262, 263, 272, 273
Kleene truth status assignment 253, 254, 255, 256, 257, 258, 264, 265, 267, 274
pragmatic loading of 262, 263, 273
truth values
convex combinations of 251, 253, 256, 257, 258, 261, 262, 272, 274
designated 256, 258
drop in 256, 272
estimation of 372–3, 773
expectation of 257
truth-value gaps 249 (n.2), 250
typicality
measure theoretic approach to 446–448, 452
effective measure one properties and 447
unanimity 519, 523, 524, 525, 528, 529, 530, 534, 537, 709
union 17, 164, 205 (n.2), 351, 521
uniqueness thesis 639
unpredictability 443, 454
(p. 865) updating (see also ‘conditionalization’) 9, 144, 204, 263, 361, 363, 364, 364 (n.10), 528, 530 (n.9), 531, 538, 635, 667–76, 677–8, 765, 766
on de se information, on centered propositions 635–6, 669–77
demonstrative scheme 669, 675–7
shifting scheme 669–71
stable base scheme 671–5
upper expectations 304–5
upper previsions 297, 305
upper probabilities 303
utilitarianism 706, 718, 726, 727, 731, 732, 733
utility
epistemic 635
expected