Deductive Logic

Deduction - in logic, form of inference such that the conclusion must be true if the premises are true. For example, if we know that all men have two legs and that John is a man, it is then logical to deduce that John has two legs. Logicians contrast deduction with induction, in which the conclusion might be false even when the premises are true. Deduction has to do with necessity; induction Read More...

9 of the Best Books and Articles on: Deductive Logic

as selected by Questia School librarians.

1.

Deductive Logic
by Warren Goldfarb. 292 pgs.

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Title Page

Part I: Truth-Functional Logic

A Analysis

1: Statements

2: Conjunction

Contents

Preface

Introduction

3: Negation

4: Disjunction

5: Grouping

6: Truth-Functions

7: Conditional

8: Logical Paraphrase

9: Schemata and Interpretation

B: Logical Assessment

10: Validity and Satisfiability

11: Implication

12: Use and Mention

13: Equivalence

14: General Laws

C: Reflection

15: Disjunctive Normal Form

16: Expressive Adequacy

17: Formal Systems

Part II: Monadic Quantification Theory

18: Monadic Predicates and Open Sentences

A: Analysis

19: The Existential Quantifier

20: The Universal Quantifier

21: Further Notes on Paraphrase

22: Universe of Discourse

B: Logical Assessment

23: Schemata and Interpretation

24: Validity, Implication, and Equivalence

25: Testing Monadic Schemata

C: Reflection

26: Monadic Satisfiability

27: General Laws

Part III: Polyadic Quantification Theory

28: Polyadic Predicates

A: Analysis

29: Paraphrase

B: Logical Assessment

30: Schemata and Interpretation

31: Validity, Implication, and Equivalence

32: Instances

33: Deduction

34: Deduction Extended

35: Soundness

C: Reflection

36: Other Laws

37: Prenex Form

38: Completeness

39: Further Consequences

40: Decidability

Part IV: Identity and Names

41: Identity

42: Inference with Names

43: Descriptions

44: Elimination of Descriptions

Exercises

Index
2.

An Introduction to Deductive Logic (1955)
by Hugues Leblanc. 246 pgs.

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Title Page

Preface

Acknowledgments

Contents

Introduction

Chapter One: Sentential Logic

Chapter Two: Quantificational Logic

Chapter Three: Formalization of Sentential and Quantificational Logic

Chapter Four: The Logic of Identity, Classes, and Relations

Chapter Five: Sample Syntax

Exercises

Selected Bibliography

Index
3.

Logic, Deductive and Inductive (1905)
by John Grier Hibben. 442 pgs.

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Title Page

PREFACE

CONTENTS

PART I: DEDUCTIVE LOGIC

Chapter I: THE NATURE OF THOUGHT

Chapter II: THE CONCEPT

Chapter III: THE JUDGMENT

Chapter IV: THE UNIVERSAL JUDGEMENT

Chapter V: DEFINITION

Chapter VI: DIVISION AND CLASSIFICATION

Chapter VII: THE SINGULAR JUDGMENT

Chapter VIII: THE NEGATIVE JUDGMENT

Chapter IX: THE CATEGORICAL, HYPOTHETICAL, AND DISJUNCTIVE JUDGMENTS

Chapter X: THE NATURE OF INFERENCE

Chapter XI: THE LAWS OF THOUGHT

Chapter XII: INFERENCE BY OPPOSITION

Chapter XIII: ON TRANSFORMATIONS OF JUDGMENT FORMS

Chapter XIV: A GENERALIZATION OF IMMEDIATE INFERENCES

Chapter XV: MEDIATE INFERENCE -- THE SYLLOGISM

Chapter XVI: MOOD AND FIGURE

Chapter XVII: THE HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS

Chapter XVIII: EXTRA-SYLLOGISTIC REASONING

Chapter XIX: FALLACIES

PART II: INDUCTIVE LOGIC

Chapter I: INDUCTION AND DEDUCTION

Chapter II: THE ESSENTIALS OF INDUCTION

Chapter III: TYPES OF INDUCTIVE INFERENCE

Chapter V: THE METHOD OF CAUSAL ANALYSIS AND DETERMINATION

Chapter VI: MILL'S INDUCTIVE METHODS -- THE METHOD OF AGREEMENT

Chapter VII: THE METHOD OF DIFFERENCE

Chapter VIII: THE JOINT METHOD OF AGREEMENT AND DIFFERENCE

Chapter IX: THE METHOD OF CONCOMITANT VARIATIONS

Chapter X: THE METHOD OF RESIDUES

Chapter XI: PREDICTION AND VERIFICATION

Chapter XIII: ANALOGY

Chapter XIV: PROBABILITY

Chapter XV: EMIPIRICAL LAWS

Chapter XVI: INDUCTIVE FALLACIES

Chapter XVII: THE INDUCTIVE METHODS AS APPLIED TO THE VARI OUS SCIENCES

Chapter XVIII: HISTORICAL SKETCH OF INDUCTION

LOGICAL EXERCISES

INDEX
4.

Challenge and Response: Justification in Ethics (Chap. 1 "Deduction")
by Carl Wellman. 300 pgs.

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CONTENTS

PREFACE

INTRODUCTION

one WHAT IS JUSTIFICATION?.

1: Deduction

2: Induction

3: Conduction

4: Reasoning

5. Justification

6: Infinite regresses

two HOW CAN ETHICAL STATEMENTS BE JUSTIFIED?

7: Truth

8: Truth-value

9: Meaningfulness

10: Validity

1: Validity-value

12: Competence

13. Knowability

notes / selected bibliography / index

NOTES

SELECTED BIBLIOGRAPHY

INDEX
5.

Intermediate Logic (Includes discussion of deductive logic in multiple chapters)
by David Bostock. 406 pgs.

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Intermediate Logic is an ideal text for anyone who has taken a first course in logic and is progressing to further study. It examines logical theory, rather than the applications of logic, and does not assume any specific technical grounding. The author introduces and explains each concept and term, ensuring readers have a firm foundation for study. He provides a broad, deep understanding of logic by adopting and comparing a variety of different methods and approaches

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Title Page

Preface

Contents

Part I: Semantics

1: Introduction

2: Truth-Functors

3: Quantifiers

Part II: Proofs

4: Semantic Tableaux

5: Axiomatic Proofs

6: Natural Deduction

7: Sequent Calculi

Part III: Further Topics

8: Existence and Identity

References

List of Symbols

List of Axioms and Rules of Inference

Index
6.

The Rationality of Induction (Chap. X "Is Deductive Logic Empirical?")
by D. C. Stove. 234 pgs.

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Writing on the justification of certain inductive inferences, the author proposes that sometimes induction is justified and that arguments to prove otherwise are not cogent. In the first part he examines the problem of justifying induction, looks at some attempts to prove that it is justified, and responds to criticisms of these proofs. In the second part he deals with such topics as formal logic, deductive logic, the theory of logical probability, and probability and truth.

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Title Page

ACKNOWLEDGEMENTS

CONTENTS

PART ONE INDUCTION

I Induction Presupposes Angels

Ii 'the Problem of Justifying Induction'

Iii the Sceptical Thesis About Induction

Iv What Sort of Thing a Proof That Induction is Justified Would Be

V an Attempt to Prove That Induction is Justified: the Relevance of Experience

Vi Another Attempt to Prove That Induction is Justified: the Law of Large Numbers

Vii Responses to These Attempts; and Responses to Them

Viii Why These Arguments Do Not Convince

PART TWO PROBABILITY

INTRODUCTION

Ix the Myth of Formal Logic

X is Deductive Logic Empirical?

Xi is the Theory of Logical Probability Groundless?

Xii Probability and Truth

GLOSSARY OF NUMBERED ENTRIES IN THE TEXT

BIBLIOGRAPHY

INDEX OF PERSONS

INDEX OF SUBJECTS
7.

Reasoning, Necessity, and Logic: Developmental Perspectives ("'If' and Deductive Thinking" begins on p. 159)
by Willis F. Overton. 332 pgs.

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Title Page

The Jean Piaget Symposium Series Available from LEA

Contents

List of Contributors

Preface

REFERENCES

1: Competence and Procedures: Constraints on the Development of Logical Reasoning

ACKNOWLEDGMENTS

REFERENCES

2: The Role and Meaning of Structures in Genetic Epistemology

ACKNOWLEDGMENTS

REFERENCES

3: Necessity and the Logic of Entailment

REFERENCES

4: The Logic of Meaning and Meaningful Implication

REFERENCES

5: A Genetic Study of Implication

5: A Genetic Study of Implication

REFERENCES

6: Language and the Acquisition of Logical Knowledge

REFERENCES

7: The "Natural Logic" Approach to Reasoning

REFERENCES

8: The Three Faces of If

ACKNOWLEDGMENTS

REFERENCES

9: The Conversion of Truth Into Necessity

REFERENCES

10: The Development of Metalogical Understanding

CONCLUSIONS

11: Formal Operational Thought

REFERENCES

12: Reasoning, Logic, and Thought Disorder: Deductive Reasoning and Developmental Psychopathology

CONCLUSION: REASONING PATHOLOGY AND THOUGHT DISORDER

ACKNOWLEDGMENTS

REFERENCES

REFERENCES

13: Structuralism, Deconstruction, Reconstruction: The Limits of Reasoning

Author Index

Subject Index
8.

Deductive Reasoning, in Annual Review of Psychology
by P. N. Johnson-Laird. 27 pgs.
9.

Natural Deduction: The Logical Basis of Axiom Systems
by John M. Anderson, Henry W. Johnstone. 422 pgs.

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Title Page

PREFACE

CONTENTS

Part One: Introduction to Logic

Chapter 1: Proof and Rules of Inference

Chapter 2: The Proportional Rules

SUGGESTED READINGS

Chapter 3: Matrices, Normal Forms, and Duality

SUGGESTED READINGS

Chapter 4: Some Other Propositional Logics

SUGGESTED READINGS

Chapter 5: Introduction to Predicate Logic

Chapter 6: General Predicate Logic --First Order

Chapter 7 Identity and Description

Part Two: Introduction to Metatheory

Chapter 8: Axiom Systems and the Axiomatic Method

Chapter 9: The Metatheory of Propositional Logic

SUGGESTED READINGS

Chapter 11: Aspects of the Metatheory of General Predicate Logic

Chapter 12: Intuitive Set Theory

Chapter 13: Logic and Set Theory

General Index

Index of Proper Names

Index of Symbols

THE RULES FOR PROPORTIONAL LOGIC

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