Logic: The Basics

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.

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.