Deductive Logic in Natural Language
  • Publication Date: November 13, 2002
  • ISBN: 9781551114453 / 1551114453
  • 300 pages; 7" x 9"

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Deductive Logic in Natural Language

  • Publication Date: November 13, 2002
  • ISBN: 9781551114453 / 1551114453
  • 300 pages; 7" x 9"

This text offers an innovative approach to the teaching of logic, which is rigorous but entirely non-symbolic. By introducing students to deductive inferences in natural language, the book breaks new ground pedagogically. Cannon focuses on such topics as using a tableaux technique to assess inconsistency; using generative grammar; employing logical analyses of sentences; and dealing with quantifier expressions and syllogisms. An appendix covers truth-functional logic.

Preface
Acknowledgments
Abbreviations

I. Fundamentals

  1. Propositions and sentences—the basic units of logic and language
  2. Truth and (declarative) sentences
  3. Consistency and sets of sentences
  4. Validity and arguments
    Exercises

II. Stories and Situations

  1. Reference and truth
  2. Meaning and truth
  3. Might have beens
  4. Truth with respect to a situation
    Exercises

III. Establishing Inconsistency with Tableaux

  1. Obvious inconsistency
  2. Semantic tableaux: dividing and conquering
  3. Efficiencies in tableaux
  4. A tableau that closes
    Exercises

IV. Extending the Tableau Technique

  1. Counter sets and validity
  2. Resolving reference
  3. Additional constructions
  4. When can a sentence be checked?
    Exercises

V. Generative Grammar

  1. What we mean by a grammar
  2. Phrase-structure grammars; Phrase-markers
  3. Transformations
  4. Syntactic ambiguity
    Exercises

VI. Logical Analysis of Complex Sentences

  1. “If s,” “And’s,” or “But’s”: Conjunctions and sentence connectives
  2. Rule-governed sentence connectives in tableaux
  3. Transformations in logical analysis; Grouping
  4. The reach of rules; Negated conditionals
  5. Tableaux constructed by rules
    Exercises

VII. Logical Analysis of Simple Sentences: Identity and Other Relations

  1. Designators and predicates
  2. Properties and relations; Types of relations
  3. The peculiar relation of identity
  4. Tableau rules for identity
    Exercises

VIII. Logical Analysis of Simple Sentences: One-Word Quantifiers

  1. Quantifiers in general
  2. The simplest quantifiers: “everyone,” “someone,” and “no one”
  3. Tableau rules for the simplest quantifiers
  4. The simplest quantifiers in tableaux
  5. “Anyone,” quantifier scope, and anaphoric pronouns
    Exercises

IX. Quantifier Expressions and Syllogisms

  1. The universal quantifier
  2. Relative pronouns, and the existential and nihilistic quantifiers
  3. Tableaux for syllogisms and other arguments
  4. “Anyone” and logical equivalence
  5. Things, times, and places
    Exercises

Appendix: Truth-Functional Logic

  1. Review: Tableau rules for sentence connectives
  2. Three levels of symbolization
  3. Symbolic languages for algebra
  4. Truth-functions and their computational tables
  5. Truth tables and calculating truth-values
  6. Constructing an arbitrary function; Normal form
    Exercises

For Reading and Reference

Index

Douglas Cannon is a professor in the Department of Philosophy at the University of Puget Sound.