Logic  30576

An Introduction to Elementary Logic

  • Introduction
  • Consistency
    1. Consistent Sets of Beliefs
  • Expressing Beliefs in Sentences
    1. Beliefs and Words
    2. Declarative Sentences
    3. Ambiguity
  • When is a Sentence True?
    1. Truth and References
    2. Borderline Cases and Bizarre Situations
    3. Misleading Statements
    4. Possible Situations and Meanings
  • Testing for Consistency and Validity
    1. Consistent Sets of Short Sentences
    2. The Tableau Technique
    3. Arguments
  • How are Complex Sentences Built Up?
    1. Phrase-classes
    2. Phrase-markers
    3. Scope
    4. Context-free Grammars
  • Logical Analysis
    1. Sentence-functors and Truth-functors
    2. Some Basic Truth-functors
    3. Special Problems with ‘→’ and ‘^’
    4. Analysis of Complex Sentences
  • Sentence Tableaux
    1. Sentence Tableaux
    2. Interpretations
  • Propositional Calculus
    1. A Formal Language
    2. Truth-tables
    3. Properties of Semantic Entailment
    4. Formal Tableaux
  • Designators and Identity
    1. Designators and Predicates
    2. Purely Referential Occurrences
    3. Two Policies on Reference
    4. Identity
  • Relations
    1. Satisfaction
    2. Binary Relations
    3. Same, at least and more
    4. Equivalence Relations
  • Quantifiers
    1. Quantification
    2. All and some
    3. Quantifier Rules
  • Predicate Logic
    1. Logical Scope
    2. Analyses Using Identity
    3. Predicate Interpretations
    4. Predicate Tableaux
    5. Formalization Again
  • Horizons of Logic
    1. Likelihood
    2. Intension
    3. The Quest for Ingredient X
  • Answers to Exercises
  • Tableau Rules
  • Empty Domains
  • A Note on Notation
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