Classical and nonclassical logics : an introduction to the mathematics of propositions /
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| Author / Creator: | Schechter, Eric, 1950- |
|---|---|
| Imprint: | Princeton, N.J. : Princeton University Press, c2005. |
| Description: | ix, 507 p. : ill. ; 25 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/6098429 |
Table of Contents:
- A. Preliminaries
- 1. Introduction for teachers
- Purpose and intended audience
- Topics in the book
- Why pluralism?
- Feedback
- Acknowledgments
- 2. Introduction for students
- Who should study logic?
- Formalism and certification
- Language and levels
- Semantics and syntactics
- Historical perspective
- Pluralism
- Jarden's example (optional)
- 3. Informal set theory
- Sets and their members
- Russell's paradox
- Subsets
- Functions
- The Axiom of Choice (optional)
- Operations on sets
- Venn diagrams
- Syllogisms (optional)
- Infinite sets (postponable)
- 4. Topologies and interiors (postponable)
- Topologies
- Interiors
- Generated topologies and finite topologies (optional)
- 5. English and informal classical logic
- Language and bias
- Parts of speech
- Semantic values
- Disjunction (or)
- Conjunction (and)
- Negation (not)
- Material implication
- Cotenability, fusion, and constants (postponable)
- Methods of proof
- Working backwards
- Quantifiers
- Induction
- Induction examples (optional)
- 6. Definition of a formal language
- The alphabet
- The grammar
- Removing parentheses
- Defined symbols
- Prefix notation (optional)
- Variable sharing
- Formula schemes
- Order preserving or reversing subformulas (postponable)
- B. Semantics
- 7. Definitions for semantics
- Interpretations
- Functional interpretations
- Tautology and truth preservation
- 8. Numerically valued interpretations
- The two-valued interpretation
- Fuzzy interpretations
- Two integer-valued interpretations
- More about comparative logic
- More about Sugihara's interpretation
- 9. Set-valued interpretations
- Powerset interpretations
- Hexagon interpretation (optional)
- The crystal interpretation
- Church's diamond (optional)
- 10. Topological semantics (postponable)
- Topological interpretations
- Examples
- Common tautologies
- Nonredundancy of symbols
- Variable sharing
- Adequacy of finite topologies (optional)
- Disjunction property (optional)
- 11. More advanced topics in semantics
- Common tautologies
- Images of interpretations
- Dugundji formulas
- C. Basic syntactics
- 12. Inference systems
- 13. Basic implication
- Assumptions of basic implication
- A few easy derivations
- Lemmaless expansions
- Detachmental corollaries
- Iterated implication (postponable)
- 14. Basic logic
- Further assumptions
- Basic positive logic
- Basic negation
- Substitution principles
- D. One-formula extensions
- 15. Contraction
- Weak contraction
- Contraction
- 16. Expansion and positive paradox
- Expansion and mingle
- Positive paradox (strong expansion)
- Further consequences of positive paradox
- 17. Explosion
- 18. Fusion
- 19. Not-elimination
- Not-elimination and contrapositives
- Interchangeability results
- Miscellaneous consequences of notelimination
- 20. Relativity
- E. Soundness and major logics
- 21. Soundness
- 22. Constructive axioms: avoiding not-elimination
- Constructive implication
- Herbrand-Tarski Deduction Principle
- Basic logic revisited
- Soundness
- Nonconstructive axioms and classical logic
- Glivenko's Principle
- 23. Relevant axioms: avoiding expansion
- Some syntactic results
- Relevant deduction principle (optional)
- Soundness
- Mingle: slightly irrelevant
- Positive paradox and classical logic
- 24. Fuzzy axioms: avoiding contraction
- Axioms
- Meredith's chain proof
- Additional notations
- Wajsberg logic
- Deduction principle for Wajsberg logic
- 25. Classical logic
- Axioms
- Soundness results
- Independence of axioms
- 26. Abelian logic
- F. Advanced results
- 27. Harrop's principle for constructive logic
- Meyer's valuation
- Harrop's principle
- The disjunction property
- Admissibility
- Results in other logics
- 28. Multiple worlds for implications
- Multiple worlds
- Implication models
- Soundness
- Canonical models
- Completeness
- 29. Completeness via maximality
- Maximal unproving sets
- Classical logic
- Wajsberg logic
- Constructive logic
- Non-finitely-axiomatizable logics
- References
- Symbol list
- Index
