Table of Contents

I BACKGROUND IDEAS 1. Consequences 1.1 Relations of support 1.2 Logical consequence: the basic recipe 1.3 Valid arguments and truth 1.4 Summary, looking ahead, and reading 2. Language, Form, and Logical Theories 2.1 Language 2.2 Atoms, connectives, and molecules 2.3 Connectives and form 2.4 Validity and form 2.5 Language and formal languages 2.6 Logical theories: rivalry 3. Set-theoretic Tools 3.1 Sets 3.2 Ordered sets: pairs and n-tuples 3.3 Relations 3.4 Functions 3.5 Sets as tools. II BASIC CONNECTIVES 4. Classical Theory 4.1 Cases: complete and consistent 4.2 Classical 'truth conditions' 4.3 Basic classical consequence 4.4 Motivation: precision 4.5 Formal picture 4.6 Defined connectives 4.7 Some notable valid forms 4.8 Summary and looking ahead 5. A Paracomplete Theory 5.1 Apparent unsettledness 5.2 Cases: incomplete 5.3 Paracomplete truth and falsity conditions 5.4 Paracomplete consequence 5.5 Formal picture 5.6 Defined connectives 5.7 Some notable forms 5.8 Summary and looking ahead 6. A Paraconsistent Theory 6.1 Apparent overdeterminacy 6.2 Cases: inconsistent 6.3 Paraconsistent 'truth conditions' 6.4 Paraconsistent consequence 6.5 Formal picture 6.6 Defined connectives 6.7 Some notable forms 6.8 Summary and looking ahead. III INNARDS, IDENTITY, AND QUANTIFIERS 7. Atomic Innards 7.1 Atomic innards: names and predicates 7.2 Truth and falsity conditions for atomics 7.3 Cases, domains, and interpretation functions 7.4 Classical, paracomplete and paraconsistent 7.5 A formal picture 7.6 Summary and looking ahead 8. Identity 8.1 Logical expressions and logical form 8.2 Validity involving identity 8.3 Identity: informal sketch 8.4 Truth conditions: informal sketch 8.5 Formal picture 8.6 Summary and looking ahead 9. Everything and Something 9.1 Validity involving quantifiers 9.2 Quantifiers: an informal sketch 9.3 Truth and falsity conditions 9.4 A formal picture 9.5 Paraconsistent, paracomplete, classical 9.6 Summary and looking ahead. IV FREEDOM, NECESSITY, AND BEYOND 10. Speaking Freely 10.1 Speaking of non-existent 'things' 10.2 Existential import 10.3 Freeing our terms, expanding our domains 10.4 Truth conditions: an informal sketch 10.5 Formal picture 11. Possibilities 11.1 Possibility and necessity 11.2 Towards truth and falsity conditions 11.3 Cases and consequence 11.4 Formal picture 11.5 Remark on going beyond possibility 12. Glimpsing Different Logical Roads 12.1 Other conditionals 12.2 Other negations 12.3 Other alethic modalities: actuality 12.4 Same connectives, different truth conditions 12.5 Another road to difference: consequence. A List of Common Abbreviations. References.

About the Author

Jc Beall is Professor of Philosophy at the University of Connecticut, USA, where he is Director of the UConn Logic Group. His books include Possibilities and Paradox: An Introduction to Modal and Many-Valued Logic with Bas van Fraassen, Logical Pluralism with Greg Restall, and Spandrels of Truth.

Reviews

'This is an excellent introduction to logic: it is clear, careful, and concise. Every student of logic should find it helpful. What makes the book particularly valuable is the development of paracomplete and paraconsistent logics alongside classical logic. This distinctive approach will deepen students' appreciation and understanding of logic.' -- David Efird, University of York, UK 'Beall provides a unique and refreshing introduction both to classical logic and to some of the interesting issues that motivate going beyond classical logic. This text contains one of the most accessible introductions to paracomplete and paraconsistent logics available. As such, it fills an important gap in the literature.' -- James R. Beebe, University at Buffalo, USA 'This textbook is superb for a wide range of courses. I am immediately adopting it as the main text for introductory logic as the style is accessible and engaging while the content puts forward philosophical logic as the exciting and creative field that it is. I also have used it as a strongly recommended text for a graduate-level course in non-classical logic. The text is perfect background reading for those who have only had a basic course in logic. While other books simply rush through the formal aspects of non-classical systems, this book motivates them in ways that seem natural to those not already 'in the know'.' - Aaron Cotnoir, NIP, University of Aberdeen 'A pluralist perspective right from the beginning makes Logic: The Basics a special contribution to the universe of introductory logic texts. Beall introduces in a remarkably clear and accessible style the bare bones of classical, paracomplete and paraconsistent logical theory within a common conceptual framework. The book and its exercises are also well suited to self-study for students with some basic knowledge of classical logic who want to learn about alternative logics.' - Georg Brun, ETH Zurich 'A wonderful introduction to classical and nonclassicalalogics.aMy students and I appreciated the clarity, rigour, brevity, and breadth - truly a rare combination! Excellent for a one-semester course, or for individuals who have heard that contemporary logic is pluralistic, and want to know more.' - Tim Rogalsky, Canadian Mennonite University 'Beall has achieved a rare combination of lucidity and sophistication. This book is a marvelous introduction to philosophical logic that engages the issues without getting bogged down in formalities. Anyone looking to explore what lies beyond a first course in logic must read this book.' - Colin Caret, University of St Andrews