| Preliminaries | p. 1 |
| Introduction for teachers | p. 3 |
| Purpose and intended audience | p. 3 |
| Topics in the book | p. 6 |
| Why pluralism? | p. 13 |
| Feedback | p. 18 |
| Acknowledgments | p. 19 |
| Introduction for students | p. 20 |
| Who should study logic? | p. 20 |
| Formalism and certification | p. 25 |
| Language and levels | p. 34 |
| Semantics and syntactics | p. 39 |
| Historical perspective | p. 49 |
| Pluralism | p. 57 |
| Jarden's example (optional) | p. 63 |
| Informal set theory | p. 65 |
| Sets and their members | p. 68 |
| Russell's paradox | p. 77 |
| Subsets | p. 79 |
| Functions | p. 84 |
| The Axiom of Choice (optional) | p. 92 |
| Operations on sets | p. 94 |
| Venn diagrams | p. 102 |
| Syllogisms (optional) | p. 111 |
| Infinite sets (postponable) | p. 116 |
| Topologies and interiors (postponable) | p. 126 |
| Topologies | p. 127 |
| Interiors | p. 133 |
| Generated topologies and finite topologies (optional) | p. 139 |
| English and informal classical logic | p. 146 |
| Language and bias | p. 146 |
| Parts of speech | p. 150 |
| Semantic values | p. 151 |
| Disjunction (or) | p. 152 |
| Conjunction (and) | p. 155 |
| Negation (not) | p. 156 |
| Material implication | p. 161 |
| Cotenability, fusion, and constants (postponable) | p. 170 |
| Methods of proof | p. 174 |
| Working backwards | p. 177 |
| Quantifiers | p. 183 |
| Induction | p. 195 |
| Induction examples (optional) | p. 199 |
| Definition of a formal language | p. 206 |
| The alphabet | p. 206 |
| The grammar | p. 210 |
| Removing parentheses | p. 215 |
| Defined symbols | p. 219 |
| Prefix notation (optional) | p. 220 |
| Variable sharing | p. 221 |
| Formula schemes | p. 222 |
| Order preserving or reversing subformulas (postponable) | p. 228 |
| Semantics | p. 233 |
| Definitions for semantics | p. 235 |
| Interpretations | p. 235 |
| Functional interpretations | p. 237 |
| Tautology and truth preservation | p. 240 |
| Numerically valued interpretations | p. 245 |
| The two-valued interpretation | p. 245 |
| Fuzzy interpretations | p. 251 |
| Two integer-valued interpretations | p. 258 |
| More about comparative logic | p. 262 |
| More about Sugihara's interpretation | p. 263 |
| Set-valued interpretations | p. 269 |
| Powerset interpretations | p. 269 |
| Hexagon interpretation (optional) | p. 272 |
| The crystal interpretation | p. 273 |
| Church's diamond (optional) | p. 277 |
| Topological semantics (postponable) | p. 281 |
| Topological interpretations | p. 281 |
| Examples | p. 282 |
| Common tautologies | p. 285 |
| Nonredundancy of symbols | p. 286 |
| Variable sharing | p. 289 |
| Adequacy of finite topologies (optional) | p. 290 |
| Disjunction property (optional) | p. 293 |
| More advanced topics in semantics | p. 295 |
| Common tautologies | p. 295 |
| Images of interpretations | p. 301 |
| Dugundji formulas | p. 307 |
| Basic syntactics | p. 311 |
| Inference systems | p. 313 |
| Basic implication | p. 318 |
| Assumptions of basic implication | p. 319 |
| A few easy derivations | p. 320 |
| Lemmaless expansions | p. 326 |
| Detachmental corollaries | p. 330 |
| Iterated implication (postponable) | p. 332 |
| Basic logic | p. 336 |
| Further assumptions | p. 336 |
| Basic positive logic | p. 339 |
| Basic negation | p. 341 |
| Substitution principles | p. 343 |
| One-formula extensions | p. 349 |
| Contraction | p. 351 |
| Weak contraction | p. 351 |
| Contraction | p. 355 |
| Expansion and positive paradox | p. 357 |
| Expansion and mingle | p. 357 |
| Positive paradox (strong expansion) | p. 359 |
| Further consequences of positive paradox | p. 362 |
| Explosion | p. 365 |
| Fusion | p. 369 |
| Not-elimination | p. 372 |
| Not-elimination and contrapositives | p. 372 |
| Interchangeability results | p. 373 |
| Miscellaneous consequences of notelimination | p. 375 |
| Relativity | p. 377 |
| Soundness and major logics | p. 381 |
| Soundness | p. 383 |
| Constructive axioms: avoiding not-elimination | p. 385 |
| Constructive implication | p. 386 |
| Herbrand-Tarski Deduction Principle | p. 387 |
| Basic logic revisited | p. 393 |
| Soundness | p. 397 |
| Nonconstructive axioms and classical logic | p. 399 |
| Glivenko's Principle | p. 402 |
| Relevant axioms: avoiding expansion | p. 405 |
| Some syntactic results | p. 405 |
| Relevant deduction principle (optional) | p. 407 |
| Soundness | p. 408 |
| Mingle: slightly irrelevant | p. 411 |
| Positive paradox and classical logic | p. 415 |
| Fuzzy axioms: avoiding contraction | p. 417 |
| Axioms | p. 417 |
| Meredith's chain proof | p. 419 |
| Additional notations | p. 421 |
| Wajsberg logic | p. 422 |
| Deduction principle for Wajsberg logic | p. 426 |
| Classical logic | p. 430 |
| Axioms | p. 430 |
| Soundness results | p. 431 |
| Independence of axioms | p. 431 |
| Abelian logic | p. 437 |
| Advanced results | p. 441 |
| Harrop's principle for constructive logic | p. 443 |
| Meyer's valuation | p. 443 |
| Harrop's principle | p. 448 |
| The disjunction property | p. 451 |
| Admissibility | p. 451 |
| Results in other logics | p. 452 |
| Multiple worlds for implications | p. 454 |
| Multiple worlds | p. 454 |
| Implication models | p. 458 |
| Soundness | p. 460 |
| Canonical models | p. 461 |
| Completeness | p. 464 |
| Completeness via maximality | p. 466 |
| Maximal unproving sets | p. 466 |
| Classical logic | p. 470 |
| Wajsberg logic | p. 477 |
| Constructive logic | p. 479 |
| Non-finitely-axiomatizable logics | p. 485 |
| References | p. 487 |
| Symbol list | p. 493 |
| Index | p. 495 |
| Table of Contents provided by Ingram. All Rights Reserved. |
