Logic: The Basics
Logic: The Basics
Editor/Author
Beall, J.C. and Logan, Shay A.
Publication Year: 2017
Publisher: Routledge
Single-User Purchase Price:
$115.00

Unlimited-User Purchase Price:
Not Available
ISBN: 978-1-13-885226-6
Category: Philosophy
Image Count:
34
Book Status: Available
Table of Contents
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