ABOUT THIS BOOK

Throughout the twentieth century, the classical logic of Frege and Russell dominated the field of formal logic. But, as Ross Brady argues, a new type of weak relevant logic may prove to be better equipped to present new solutions to persistent paradoxes. Universal Logic begins with an overview of classical and relevant logic and discusses the limitations of both in analyzing certain paradoxes. It is the first text to demonstrate how the main set-theoretic and semantic paradoxes can be solved in a systematic way and as such will be of great interest to both scholars and students of logic.

AUTHOR BIOGRAPHY

Ross Brady is senior lecturer in philosophy at La Trobe University in Australia.

REVIEWS

"This book presents an original contribution to the celebrated relevant logic enterprise initiated by Alan Ross Anderson and Nuel Belnap. . . . It summarizes and in a way systematizes the author's work carried out in this field over a period of about three decades."

— Mathematical Reviews

TABLE OF CONTENTS

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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