Deductive Logic in Natural Language

Douglas Cannon (Autor)

Buch | Softcover

302 Seiten

2002
Broadview Press Ltd (Verlag)
978-1-55111-445-3 (ISBN)

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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.

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

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

Erscheint lt. Verlag	30.11.2002
Sprache	englisch
Maße	178 x 229 mm
Gewicht	488 g
Themenwelt	Schulbuch / Wörterbuch ► Wörterbuch / Fremdsprachen
Themenwelt	Geisteswissenschaften ► Philosophie ► Logik
ISBN-10	1-55111-445-3 / 1551114453
ISBN-13	978-1-55111-445-3 / 9781551114453
Zustand	Neuware