Cover
Contents
Preface
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 DJdQ
1.7 The Addition of Classical Sentences
1.8 The Solution of Paradoxes
2.1 The Routley–Meyer Truth-Functional Semantics
2.2 The Semantics of Meaning Containment
2.3 Quantified Content Semantics
3.1 Natural Deduction Systems
3.2 Gentzen Systems
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
6.1 The Simple Consistency Proof
6.2 The Practical Maximality of TNdQ
6.3 Non-triviality of Dialectical Class Theory
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
9.1 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
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