Logic: The Basics

Editor/Author Beall, J.C. and Logan, Shay A.
Publication Year: 2017
Publisher: Routledge

ISBN: 978-1-13-885226-6
Category: Philosophy
Image Count: 34
Book Status: Pending
Predicted Release Month: June 2017
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.

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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