General Index

σ -algebra 408, 452 belief revision 516 σ -additive probability measure 453 belief set 454, 457 stit logic 348 best-system analysis of probability Ł3 187 417 de re/de dicto distinction 533 BHK interpretation 196 sui generis epistemic probability 424 BIT 551 Kt 331 boolean algebra 184, 284 T 313 borderline vague 134 branching space-time 347 abstract situations 204 branching time 339 accessibility relation 326 Brouwer’s axiom (for modal logic) actualist frequentism 409 526 Adams’ Thesis (about conditionals) Brouwer–Heyting–Kolmogorov 395 interpretation 197 additive separation 551 admissible interpretations 151 calculus of individuals 272 AGM model 456 canonical model 312 AGM postulates 456, 460 canonical terms 320 alethic modal logic 300 categoricity (of a theory) 111 algebra 408, 452 causal decision theory 554 Allais’s paradox 565 chance 418 analyticity 301 circular time 332 antitony 486 classical negation 183 Aristotelian modality 342 coherence constraint 473 Arrow’s theorem 572 common knowledge 512, 570 aspect 346 compactness (for first-order logic) Atom Exchangeability Principle 436 110 atom of an algebra 408 Compactness (of first-order logic) 41 atomic algebra 408 complete propositional selection Axiom of Choice 109 function 475 axiomatization stage 5 completed infinity 196 axioms of modal logic 508 completeness 6 completeness (for first-order logic) backwards linear 328 110 Barcan formula 318 completeness stage 6 basic intrinsic attitude 551 Completeness Theorem (for Bayesian conditionalization 420 first-order logic) 38 Becker’s rule 304 completeness theorem for first-order being 64, 65 logic 7 belief base contraction 486 completeness theorem for modal belief basis 455 logic 309

Compositional theory of truth 363 de re attitude 89 comprehension axioms (for decidability 6, 315 second-order logic) 108 decision 544 computer simulations 21 decision procedure 315 concept 71 Dedekind continuity 335 conceptual analysis 16 Dedekind–Peano arithmetic 290 conceptual cover 535 deductively closed 310 conceptual modelling 21 deep structure 85 conditional probability 453 definite description 16, 57, 79 conditional sorites 131 definite truth 137 conditionalization 567 degree of belief 419 conditionals 383 demonstrability 301 conditioning 453 denotation 70, 78 Condorcet’s paradox 572 deontic necessity 300 connectedness 131, 151 designated values 190 Constant Exchangeability Principle dialetheism 190 436 dialethism 49 constraint 204 Diodorean modality 342 construction system 3 direct Barcan formula 318 constructive proof 196 direct control 546 contextual definition 85 direct discriminability 154 contextualism 151 direct reference theory 58 Continuum of inductive methods discreteness 335 438 disquotational theory of truth 357 contraction 458 doxastic commitments 454 converse Barcan formula 318 Dutch book argument 421 converse Dutch book theorem 421 Dutch book theorem 421 cooperative game 571 dynamically consistent 547 Coordinated Attack Problem (Halpern) 514 EFQ 189 core 493 Ellsberg’s paradox 565 correspondence 337 Email Game (Rubinstein) 514 correspondence theorem 313 empty name 80 countably additive 409 entrenchment-based severe countably additive probability space withdrawal 484 409 epistemic entrenchment 461 course of values 92 epistemic necessity 300 criterion of identity 60 epistemic paradoxes 538 Curry’s paradox 191 epistemic probability 407 cyclic negation 188 epistemic state 496 epistemic utility function 424 D4 215 epistemicism 144 de dicto attitude 89 equilibrium (in a strategic game) 255 de Finetti Representation Theorem equilibrium semantics 219 441 equivalence relation 55 De Morgan negation 213 evidential decision theory 554 De Morgan’s laws 183 evidential situation 197

Pettigrew, R., and Horsten, L. (eds) (2011) The Continuum Companion to Philosophical Logic (London: Continuum Books) © Leon Horsten, Richard Pettigrew and Contributors, 2011 ISBN: 978-1-4411-5423-1 http://philosophy.horstenpettigrew.continuumbooks.com General Index ex falso quodlibet 181 global constraint 204 existence 61, 65 grammatical mood 300 existential commitment 74 Grove connection 468 existential quantifier 34, 65 grue paradox 19, 429 expected degree of desire 558 expected utility 549, 553 Henkin model 109 expected utility interpretation 423 Henkin semantics (for second-order expected-utility analysis 553 logic) 109 explicit definition 85 Henkin, Leon 109 expressiveness 322 hereditariness property 198 expulsiveness 485 higher-order logic 44 extensive game 219 higher-order vagueness 140 historical modality 341 fair betting odds interpretation 420 history 339 falsum 199 Humphrey’s paradox 416 field 452 hypothetical frequentism 412 finite model property 315 first moment 334 identity 55 first-order logic 33 identity of indiscernibles 60 Fitch paradox 538 IF logic 218 fixed margin model 145 imaging 495 fixed point 193 implosion principle 157 FOL 33 Import–Export Principle (for nested formal language stage 4 conditionals) 387 formal necessity 301 impossible situation 204 formalization 4 impossible worlds 524 frame 328 improper description 90 free logic 67 incomplete symbol 84 Frege–Grundgesetze theory of indefinite description 79 descriptions 92 Independence-Friendly logic 218 Frege–Carnap theory of descriptions indicative conditional 384 93 indifference relation 131 Frege–Hilbert theory of descriptions indirect discriminability 154 90 indiscernibility of identicals 55 full control 546 indiscernibility of identicals with full meet contraction 459 respect to properties 56 inductive logic 428 Gödel coding 352 infinite utility 562 Gödel Incompleteness Theorem (for infinite valued logics 187 Peano Arithmetic) 41 information 203 Gödel numbering 352 information preservation 207 Gödel’s diagonal lemma 356 informational value 480 Gale–Stewart theorem 221 intensional context 56, 82 game of strategy 547 intensity of preference 545 game theory 547 interactive epistemology 510 game-theoretical semantics 221 intrinsic desire 551 generalized quantifier 100 intrinsic utility 551

Pettigrew, R., and Horsten, L. (eds) (2011) The Continuum Companion to Philosophical Logic (London: Continuum Books) © Leon Horsten, Richard Pettigrew and Contributors, 2011 ISBN: 978-1-4411-5423-1 http://philosophy.horstenpettigrew.continuumbooks.com General Index intrinsic-utility analysis 551 logical terms 42 intuitionism 49 logically perfect language 90 intuitionist logic 196 long-run propensity interpretation intuitionist mathematics 195 413 is-ness 65 lottery paradox 150 LP 190 Jeffrey conditioning 454 Łukasiewicz’s three-valued logic Johnson’s Sufficientness Principle 187 437 judgement aggregation 572 justification stage 5 main lemma 311 majoritarian methods 572 K3 186 many-valued logic 185 kernel contraction 488 margin of error 146 KK principle 526 Margin or error semantics (for Kleene’s strong three-valued logic epistemic logic) 527 185 Matching Pennies 561 knowing-wh 536 material conditional 385 Kreisel counterexample 232 mathematical modelling 1 Kreisel form 232 mathematical probability 408 Kreisel’s squeezing argument 115 maxichoice contraction 459 Kripke’s theory of truth 370 maximal consistent 310 maximal proposition 548 Löwenheim–Skolem Theorem (for Meinongian object 81 FOL) 41, 110 mereological algebra 284 last moment 334 mereological atoms 278 law of the excluded middle 48, 181 mereological complement 276 left linearity 333 mereological fusions 272 Leibniz’ law 87 mereologlical sums 272 Levi contraction 480 mereology 271 Levi identity 462 mereotopology 294 Lewis’ triviality results (for metaphysical necessity 300 Stalnaker’s hypothesis) 393 metric operator 343 liar paradox 352 minimal logic 202 liar sentence 352 minimal modal logic 304 limiting relative frequency 412 Minimax theorem 219 Lindenbaum’s lemma 311 mixed strategy (in a game) 258 linear 328 model 18 linearity 333 model (of first-order / predicate linguistic necessity 301 logic) 36 local constraint 205 model theory 182 logic of agency 348 modes of being 74 logical analysis 103 moment of context 343 logical consequence 29 moment of evaluation 343 logical form 85 Moore’s paradox 504, 538 logical necessity 301 multi-agent systems 510 logical probability 407 multiattribute-utility analysis 550

Pettigrew, R., and Horsten, L. (eds) (2011) The Continuum Companion to Philosophical Logic (London: Continuum Books) © Leon Horsten, Richard Pettigrew and Contributors, 2011 ISBN: 978-1-4411-5423-1 http://philosophy.horstenpettigrew.continuumbooks.com General Index narrow scope 87 potential relative to 311 Nash equilibrium 514, 547 practical reasoning 544 necessitation rule 304 predicate calculus 33 necessity of distinctness 319 predicative 109 necessity of identity 318 preference ranking 545 negation 181 presupposition 185 neo-Meinongian theory 81 Principal Principle 417 Newcomb’s problem 563 principle of bivalence 181 nihilism 133 principle of consistency 184 non-existent entities 67 principle of dominance 558 noncooperative game 570 principle of double negation 185 normal bimodal logic 331 Principle of Instantial Relevance 437 now 342 principle of non-contradiction 184 principle of ratification 561 Ockhamist temporal logic 340 Priorean tense logic 328 ontological commitment 74 Prisoners’ dilemma 252 operator 183 priviliged terms 320 option’s world 548 probabilism 420 probabilistic models 19 probability measure 452 package principle 422 probability space 408 paracomplete logic 156 Proof of Completeness Theorem for paraconsistent logic 157, 189 First-order Logic 39 paradox of the absent-minded driver proof theory 182 566 propensity 415 paradoxes of material implication proper description 85 208, 390 proper name 78 Parmenides’ paradox 62 property 60 part–whole relation 271 propositional calculus 31 partial definition 139 propositional choice-based revision partial information 203 function 475 partial meet contraction 458 propositional function 70 partial meet revision 463 propositional selection function 465 partition invariance 555 provability logic 316 Pasadena gamble 562 public announcement logic 518 Peano arithmetic 290 pure time preference 546 Peano arithmetic (second-order) 111 Peircean temporal logic 339 quality 60 persistent revision 471 quantified modal logic 317 Pettit, Philip 572 quantifier 77 physical probability 407 quantization 559 platonism 195 quasi-categoricity (of ZF2)114 plural logic 112 quasi-order 501 plural quantification 47 Popper function 409 R 208 possible world 315 Ramsey, F. P. 398 possible worlds models 18 rational selection function 473 potential infinity 196 reference failure 80

Pettigrew, R., and Horsten, L. (eds) (2011) The Continuum Companion to Philosophical Logic (London: Continuum Books) © Leon Horsten, Richard Pettigrew and Contributors, 2011 ISBN: 978-1-4411-5423-1 http://philosophy.horstenpettigrew.continuumbooks.com General Index reference sequence 413 set theory 115 reference type 410 severe withdrawals 460, 483 reflection principle (in set theory) sharpening of a language 166 115 signalling 241 Reichenbach’s Axiom 439 since 344 relational theory of meaning 203 single-case propensity interpretation relative frequency 410 415 relative identity 61 singular term 62, 77 relative interpretation 288 situation semantics 203 relative possibility 308, 326 Skolem form 229 relevant logic 207 Skolem functions 218 remainder set 458 Skolemization 229 replacement rule 305 Sleeping Beauty problem 567 representation theorem 423 slingshot argument 96 restricted conditional probability social choice theory 572 space 409 sorites condition 131 Revision theory of truth 378 sorites paradox 130 rigidity 320 soundness 5 risk aversion 564 soundness theorem for modal logic Robinson arithmetic 290 309 rollback equilibrium 547 sphere semantics 466 Routley Meyer semantics 215 sphere-based revision 466, 470 Routley star operator 213 St. Petersburg gamble 562 Russell’s paradox 45 Stalnaker’s Hypothesis 393 Russell’s theory of descriptions 69, standard semantics (for 83 second-order logic) 109 standard translation 337 state 553 S4 313 state description 433 S5 313 statement 91 safe contraction 488 strategic game 252 satisficing 559 strategy profile 547 saturable set 479 strengthened liar sentence 190 Savage’s representation theorem 555 strict implication 302 scope 86 strict partial ordering 328 scope indicator 86 strong completeness 331 scoring rule 424 Strong Kleene logic 160 second-order logic 107 Strong Kleene scheme 371 selection function 459 strong modal operator 326 self-ratifying 561 strongly paracomplete 158 Self-Sampling Assumption 567 strongly paraconsistent 158 semantic stage 5 subjective Nash equilibrium 571 semantical game 222 subjunctive conditional 384 sense 70 Substitution Lemma (for first-order sentential calculus 31 logic) 230 separation 551 substitutivity of identity 55 sequential game 547 supertruth 166 serial frame 334 supervaluation 341