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Classical and Nonclassical Logics : An Introduction to the Mathematics of Propositions.
So-called classical logic--the logic developed in the early twentieth century by Gottlob Frege, Bertrand Russell, and others--is computationally the simplest of the major logics, and it is adequate for the needs of most mathematicians. But it is just one of the many kinds of reasoning in everyday th...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2005.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover Page
- Half-title Page
- Title Page
- Copyright Page
- 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
- 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
- Denned 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