Schaum's Outline of Theory And Problems Of Logic, Second Edition | Schaum's Outline

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Schaum's Outline of Theory And Problems Of Logic, Second Edition

Schaum's Outline of Theory And Problems Of Logic, Second Edition

Authors: John Nolt, Dennis Rohatyn and Achille Varzi

Published: 1998

ISBN: 9780071368681 0070466491

Contents

Chapter 1 ARGUMENT STRUCTURE

1.1 What Is an Argument?

1.2 Identifying Arguments

1.3 Complex Arguments

1.4 Argument Diagrams

1.5 Convergent Arguments

1.6 Implicit Statements

1.7 Use and Mention

1.8 Formal vs. Informal Logic

Chapter 2 ARGUMENT EVALUATION

2.1 Evaluative Criteria

2.2 Truth of Premises

2.3 Validity and Inductive Probability

2.4 Relevance

2.5 The Requirement of Total Evidence

Chapter 3 PROPOSITIONAL LOGIC

3.1 Argument Forms

3.2 Logical Operators

3.3 Formalization

3.4 Semantics of the Logical Operators

3.5 Truth Tables for Wffs

3.6 Truth Tables for Argument Forms

3.7 Refutation Trees

Chapter 4 THE PROPOSITIONAL CALCULUS

4.1 The Notion of Inference

4.2 Nonhypothetical Inference Rules

4.3 Hypothetical Rules

4.4 Derived Rules

4.5 Theorems

4.6 Equivalences

Chapter 5 THE LOGIC OF CATEGORICAL STATEMENTS

5.1 Categorical Statements

5.2 Venn Diagrams

5.3 Immediate Inferences

5.4 Categorical Syllogisms

Chapter 6 PREDICATE LOGIC

6.1 Quantifiers and Variables

6.2 Predicates and Names

6.3 Formation Rules

6.4 Models

6.5 Refutation Trees

6.6 Identity

Chapter 7 THE PREDICATE CALCULUS

7.1 Reasoning in Predicate Logic

7.2 Inference Rules for the Universal Quantifier

7.3 Inference Rules for the Existential Quantifier

7.4 Theorems and Quantifier Equivalence Rules

7.5 Inference Rules for the Identity Predicate

Chapter 8 FALLACIES

8.1 Classification of Fallacies

8.2 Fallacies of Relevance

8.3 Circular Reasoning

8.4 Semantic Fallacies

8.5 Inductive Fallacies

8.6 Formal Fallacies

8.7 Fallacies of False Premises

Chapter 9 INDUCTION

9.1 Statement Strength

9.2 Statistical Syllogism

9.3 Statistical Generalization

9.4 Inductive Generalization and Simple Induction

9.5 Induction by Analogy

9.6 Mill’s Methods

9.7 Scientific Theories

Chapter 10 THE PROBABILITY CALCULUS

10.1 The Probability Operator

10.2 Axioms and Theorems of the Probability Calculus

10.3 Conditional Probability

10.4 Application of the Probability Calculus

Chapter 11 FURTHER DEVELOPMENTS IN FORMAL LOGIC

11.1 Expressive Limitations of Predicate Logic

11.2 Higher-Order Logics

11.3 Predicate Logic with Function Symbols

11.4 Formal Arithmetic

11.5 Formal Definitions

11.6 Definite Descriptions

11.7 Modal Logic

GLOSSARY

INDEX