Full Description
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.
Contents
Preface
Acknowledgments
Abbreviations
I. Fundamentals
Propositions and sentences—the basic units of logic and language
Truth and (declarative) sentences
Consistency and sets of sentences
Validity and arguments
Exercises
II. Stories and Situations
Reference and truth
Meaning and truth
Might have beens
Truth with respect to a situation
Exercises
III. Establishing Inconsistency with Tableaux
Obvious inconsistency
Semantic tableaux: dividing and conquering
Efficiencies in tableaux
A tableau that closes
Exercises
IV. Extending the Tableau Technique
Counter sets and validity
Resolving reference
Additional constructions
When can a sentence be checked?
Exercises
V. Generative Grammar
What we mean by a grammar
Phrase-structure grammars; Phrase-markers
Transformations
Syntactic ambiguity
Exercises
VI. Logical Analysis of Complex Sentences
"If s," "And's," or "But's": Conjunctions and sentence connectives
Rule-governed sentence connectives in tableaux
Transformations in logical analysis; Grouping
The reach of rules; Negated conditionals
Tableaux constructed by rules
Exercises
VII. Logical Analysis of Simple Sentences: Identity and Other Relations
Designators and predicates
Properties and relations; Types of relations
The peculiar relation of identity
Tableau rules for identity
Exercises
VIII. Logical Analysis of Simple Sentences: One-Word Quantifiers
Quantifiers in general
The simplest quantifiers: "everyone," "someone," and "no one"
Tableau rules for the simplest quantifiers
The simplest quantifiers in tableaux
"Anyone," quantifier scope, and anaphoric pronouns
Exercises
IX. Quantifier Expressions and Syllogisms
The universal quantifier
Relative pronouns, and the existential and nihilistic quantifiers
Tableaux for syllogisms and other arguments
"Anyone" and logical equivalence
Things, times, and places
Exercises
Appendix: Truth-Functional Logic
Review: Tableau rules for sentence connectives
Three levels of symbolization
Symbolic languages for algebra
Truth-functions and their computational tables
Truth tables and calculating truth-values
Constructing an arbitrary function; Normal form
Exercises
For Reading and Reference
Index
