Logic: The Basics is an accessible introduction to several core areas of logic. The first part of the book features a self-contained introduction to the standard topics in classical logic.

Table of Contents

• Preface
• Acknowledgments
• PART 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 further reading
• 1.5 Exercises
• 2 Models, modeled, and modeling
• 2.1 Models
• 2.2 Models in science
• 2.3 Logic as modeling
• 2.4 A note on notation, metalanguages, and so on
• 2.5 Summary, looking ahead, and further reading
• 2.6 Exercises
• 3 Language, form, and logical theories
• 3.1 Language and formal languages
• 3.2 Languages: syntax and semantics
• 3.3 Atoms, connectives, and molecules
• 3.4 Connectives and form
• 3.5 Validity and form
• 3.6 Logical theories: rivalry
• 3.7 Summary, looking ahead, and further reading
• 3.8 Exercises
• 4 Set-theoretic tools
• 4.1 Sets
• 4.2 Ordered sets: pairs and n-tuples
• 4.3 Relations
• 4.4 Functions
• 4.5 Sets as tools
• 4.6 Summary, looking ahead, and further reading
• 4.7 Exercises
• PART II THE BASIC CLASSICAL THEORY
• 5 Basic classical syntax and semantics
• 5.1 Cases: complete and consistent
• 5.2 Classical ‘truth conditions’
• 5.3 Basic classical consequence
• 5.4 Motivation: precision
• 5.5 Formal picture
• 5.6 Defined connectives
• 5.7 Some notable valid forms
• 5.8 Summary, looking ahead, and further reading
• 5.9 Exercises
• 6 Basic classical tableaux
• 6.1 What are tableaux?
• 6.2 Tableaux for the basic classical theory
• 6.3 Summary, looking ahead, and further reading
• 6.4 Exercises
• 7 Basic classical translations
• 7.1 Atoms, punctuation, and connectives
• 7.2 Syntax, altogether
• 7.3 Semantics
• 7.4 Consequence
• 7.5 Summary, looking ahead, and further reading
• 7.6 Exercises
• PART III FIRST-ORDER CLASSICAL THEORY
• 8 Atomic innards: unary
• 8.1 Atomic innards: names and predicates
• 8.2 Truth and falsity conditions for atomics
• 8.3 Cases, domains, and interpretation functions
• 8.4 Classicality
• 8.5 A formal picture
• 8.6 Summary, looking ahead, and further reading
• 8.7 Exercises
• 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 Summary, looking ahead, and further reading
• 9.6 Exercises
• 10 First-order language with any-arity innards
• 10.1 Truth and falsity conditions for atomics
• 10.2 Cases, domains, and interpretation functions
• 10.3 Classicality
• 10.4 A formal picture
• 10.5 Summary, looking ahead, and further reading
• 10.6 Exercises
• 11 Identity
• 11.1 Logical expressions, forms, and sentential forms
• 11.2 Validity involving identity
• 11.3 Identity: informal sketch
• 11.4 Truth conditions: informal sketch
• 11.5 Formal picture
• 11.6 Summary, looking ahead, and further reading
• 11.7 Exercises
• 12 Tableaux for first-order logic with identity
• 12.1 A few reminders
• 12.2 Tableaux for polyadic first-order logic
• 12.3 Summary, looking ahead, and further reading
• 12.4 Exercises
• 13 First-order translations
• 13.1 Basic classical theory with innards
• 13.2 First-order classical theory
• 13.3 Polyadic innards
• 13.4 Examples in the polyadic language
• 13.5 Adding identity
• 13.6 Summary, looking ahead, and further reading
• 13.7 Exercises
• PART IV NONCLASSICAL THEORIES
• 14 Alternative logical theories
• 14.1 Apparent unsettledness
• 14.2 Apparent overdeterminacy
• 14.3 Options
• 14.4 Cases
• 14.5 Truth and falsity conditions
• 14.6 Logical consequence
• 14.7 Summary, looking ahead, and further reading
• 14.8 Exercises
• 15 Nonclassical sentential logics
• 15.1 Syntax
• 15.2 Semantics, broadly
• 15.3 Defined connectives
• 15.4 Some notable forms
• 15.5 Summary, looking ahead, and further reading
• 15.6 Exercises
• 16 Nonclassical first-order theories
• 16.1 An informal gloss
• 16.2 A formal picture
• 16.3 Summary, looking ahead, and further reading
• 16.4 Exercises
• 17 Nonclassical tableaux
• 17.1 Closure conditions
• 17.2 Tableaux for nonclassical first-order logics
• 17.3 Summary, looking ahead, and further reading
• 17.4 Exercises
• 18 Nonclassical translations
• 18.1 Syntax and semantics
• 18.2 Consequence
• 18.3 Summary, looking ahead, and further reading
• 18.4 Exercises
• 19 Speaking freely
• 19.1 Speaking of nonexistent ‘things’
• 19.2 Existential import
• 19.3 Freeing our terms, expanding our domains
• 19.4 Truth conditions: an informal sketch
• 19.5 Formal picture
• 19.6 Summary, looking ahead, and further reading
• 19.7 Exercises
• 20 Possibilities
• 20.1 Possibility and necessity
• 20.2 Towards truth and falsity conditions
• 20.3 Cases and consequence
• 20.4 Formal picture
• 20.5 Remark on going beyond possibility
• 20.6 Summary, looking ahead, and further reading
• 20.7 Exercises
• 21 Free and modal tableaux
• 21.1 Free tableaux
• 21.2 Modal tableaux
• 21.3 Summary, looking ahead, and further reading
• 21.4 Exercises
• 22 Glimpsing different logical roads
• 22.1 Other conditionals
• 22.2 Other negations
• 22.3 Other alethic modalities: actuality
• 22.4 Same connectives, different truth conditions
• 22.5 Another road to difference: consequence
• 22.6 Summary, looking behind and ahead, and further reading
• 22.7 Exercises
• References