Universal logic /
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| Author / Creator: | Brady, Ross, 1943- |
|---|---|
| Imprint: | Stanford, Calif. : CSLI Publications, c2006. |
| Description: | xii, 346 p. ; 24 cm. |
| Language: | English |
| Series: | CSLI lecture notes ; no. 109 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/5822080 |
Table of Contents:
- Preface
- 1. Philosophical Support for the Logic DJ[superscript d]Q
- 1.1. Classical Logic
- 1.2. Some Problems with Classical Logic
- 1.3. Relevant Logic
- 1.4. Some Problems with Relevant Logic
- 1.5. Setting up the Semantics of Meaning Containment
- 1.6. Constraints on DJ[superscript d]Q
- 1.7. The Addition of Classical Sentences
- 1.8. The Solution of Paradoxes
- 2. Semantics for the Logic DJ[superscript d]Q
- 2.1. The Routley-Meyer Truth-Functional Semantics
- 2.2. The Semantics of Meaning Containment
- 2.3. Quantified Content Semantics
- 3. Proof Theory for the Logic DJ[superscript d]Q
- 3.1. Natural Deduction Systems
- 3.2. Gentzen Systems
- 4. Properties of the Logic DJ[superscript d]Q
- 4.1. Rules and Derived Rules
- 4.2. Meta-Completeness Properties
- 4.3. Depth Relevance
- 4.4. The Addition of Classical Formulae
- 5. Philosophical Support for the Theories of Classes and Sets
- 5.1. The Naive Theory of Classes
- 5.2. Classicality and the Theory of Sets
- 5.3. Indeterminability
- 5.4. Consistent and Dialectical Approaches
- 5.5. Non-ad hoc Solution to the Set-Theoretic Paradoxes
- 6. Simple Consistency of the Class Theory
- 6.1. The Simple Consistency Proof
- 6.2. The Practical Maximality of TN[superscript d]Q
- 6.3. Non-triviality of Dialectical Class Theory
- 7. Simple Consistency of the Class Theory Combined with the Set Theory and Other Theories
- 7.1. Combining the Class Theory and the Set Theory
- 7.2. The Simple Consistency of the Combined Theory CST
- 7.3. The Simple Consistency of CST, Together with Other Mathematical Theories
- 8. Simple Consistency of the Higher-Order Predicate Logic
- 8.1. The Predicate Logic
- 8.2. Simple Consistency of the Predicate Logic
- 8.3. Solution of the Semantic Paradoxes
- 9. Formal Development of the Axiomatic Theories
- 9.1. The Class Theory
- 9.2. The Set Theory
- 9.3. The Combined Theory of Classes and Sets
- 9.4. Arithmetical Theories
- 9.5. The Higher-Order Predicate Logic
- 10. Conclusion
- References
- Index