Acknowledgment
Foreword

Section A. Sentential Logic

Introduction
The Purpose of Logic
Truth and Validity
The Laws of Thought

Chap. I. Informal Fallacies

Chap. II. The Argument
Argument Forms
Identification of Premises and Conclusions in Arguments

Chap. III. Propositions, Syllogisms and Valid Inferences
Categorical Propositions
Symbolizing Categorical Propositions
Complement Terms
New Notation and Symbolism
Venn Diagrams
The Syllogism
The Rules of Syllogisms
Translating Arguments into Syllogisms
Determining the Validity of a Syllogism
Valid Inferences - Assuming the Existential Import
Valid Inferences - Not Assuming the Existential Import
Study Questions

Chap. IV. Truth Table Analysis and Argument Forms
Truth Functions
Sentences and Sentence Forms
Truth Table Formula
Truth-Functional Sentence Connectives
Truth-Table Analysis
Tautologies, Contradictions and Contingencies
Shortcuts in Truth-Table Analysis
Symbolizing Sentences
Argument Forms and their Substitution Instances
Study Questions
The Rules of Inference and Replacement

Chap. V. Proofs of Validity and the Inconsistency of Premises
Formal Proof of Validity
Conditional Proofs
The Method of Indirect Proof (IP)
Proving Premises Inconsistent
Proving Premises Consistent
Study Questions

Section B. Predicate Logic

Chap. VI. Atomic Sentences and Quantifiers
The Structure of Atomic Sentences
Quantifiers
Predicates and Quantifiers
The Universal Quantifier
The Existential Quantifier
Relationships between Quantifiers
Multiple Universal Quantifiers
Multiple Existential Quantifiers
Multiple Universal and Existential Quantifiers
A Notation for Predicate Ruling
Free and Bound Variables
Mixed Quantifiers
Expansion of Quantified Sentences
Study Questions

Chap. VII. Quantification Theory and Proof of Validity
Quantification Principles
Universal Instantiation (UI)
Universal Generalization (UG)
Existential Generalization (EG)
Existential Instantiation (El)
Using Quantifier Rules
Study Questions

Chap. VIII. Introduction to the Logic of Relations and Modality
Symbolizing Some Types of English Sentences
Proving Invalidity in Expanded and Quantified Arguments
Consistency of Premises
Logical Truths Involving Quantifiers
Identity
Proofs Involving Identity
Symbolizing Quantities
Symbolizing Definite Descriptions
Introduction to Modal Logic
Modality and Validity
Study Questions

Section C. Essays on Philosophical Logic

Chap. IX. Reflections on Truth

Chap. X. Paradoxes

Chap. XI. Aaron Sloman on Neccesary, Apriori and Analytic Propositions

Chap. XII. Logic, Language and Truth: An Ontological Analysis

Chap. XIII. Interderivation of ‘If-Then’ and ‘Implies’: Some Critical and Ontological Comments

Chap. XIV. The Ontology of Counterfactual Causality and Conditional

Chap. XV. Logic and Critical Thinking: Among Professional Artisans

Chap. XVI. Inductive and Deductive Logic

Chap. XVII. Apriori and Aposteriori Knowledge

Chap. XVIII. Appearance and Reality

Chap. XIX. Philosophical Questions in Logic and Mathematics

Chap. XX. The Logic of Truth and Predication in Igbo Epistemology

Answers
Bibliography
Index
About the author
Symbolic and Philosophical Logic
Maduabuchi F. Dukor
ISBN: 978-1-9996138-2-2
Paperback: 300 p
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Description
Table of contents
Table of contents
Description
About the author
Answers
Bibliography
Index
Acknowledgment
Foreword
Introduction
     The Purpose of Logic
     Truth and Validity
     The Laws of Thought

Chap. I. Informal Fallacies

Chap. II.  The Argument
     Argument Forms
     Identification of Premises and Conclusions in Arguments

Chap. III.  Propositions, Syllogisms and Valid Inferences
     Categorical Propositions
     Symbolizing Categorical Propositions
     Complement Terms
     New Notation and Symbolism
     Venn Diagrams
     The Syllogism
     The Rules of Syllogisms
     Translating Arguments into Syllogisms
     Determining the Validity of a Syllogism
     Valid Inferences - Assuming the Existential Import
     Valid Inferences - Not Assuming the Existential Import
     Study Questions

Chap. IV.  Truth Table Analysis and Argument Forms
     Truth Functions
     Sentences and Sentence Forms
     Truth Table Formula
     Truth-Functional Sentence Connectives
     Truth-Table Analysis
     Tautologies, Contradictions and Contingencies
     Shortcuts in Truth-Table Analysis
     Symbolizing Sentences
     Argument Forms and their Substitution Instances
     Study Questions
     The Rules of Inference and Replacement

Chap. V.  Proofs of Validity and the Inconsistency of Premises
     Formal Proof of Validity
     Conditional Proofs
     The Method of Indirect Proof (IP)
     Proving Premises Inconsistent
     Proving Premises Consistent
     Study Questions
15
15
16
17

19

29
29
30

57
57
57
57
58
58
60
63
64
65
70
72
73

77
77
77
79
79
83
84
88
90
91
98
100

103
103
106
112
116
117
118
Chap. VI.  Atomic Sentences and Quantifiers
     The Structure of Atomic Sentences
     Quantifiers
     Predicates and Quantifiers
     The Universal Quantifier
     The Existential Quantifier
     Relationships between Quantifiers
     Multiple Universal Quantifiers
     Multiple Existential Quantifiers
     Multiple Universal and Existential Quantifiers
     A Notation for Predicate Ruling
     Free and Bound Variables
     Mixed Quantifiers
     Expansion of Quantified Sentences
     Study Questions

Chap. VII.  Quantification Theory and Proof of Validity
     Quantification Principles
     Universal Instantiation (UI)
     Universal Generalization (UG)
     Existential Generalization (EG)
     Existential Instantiation (El)
     Using Quantifier Rules
     Study Questions

Chap. VIII.  Introduction to the Logic of Relations and Modality
     Symbolizing Some Types of English Sentences
     Proving Invalidity in Expanded and Quantified Arguments
     Consistency of Premises
     Logical Truths Involving Quantifiers
     Identity
     Proofs Involving Identity
     Symbolizing Quantities
     Symbolizing Definite Descriptions
     Introduction to Modal Logic
     Modality and Validity
     Study Questions
125
125
126
127
128
129
129
131
131
132
134
138
140
141
143

145
148
150
150
152
153
157
164

165
165
169
172
173
175
176
177
178
179
181
185
Chap. IX.       Reflections on Truth

Chap. X.        Paradoxes

Chap. XI.       Aaron Sloman on Neccesary, Apriori and Analytic   
                       Propositions

Chap. XII.      Logic, Language and Truth: An Ontological Analysis

Chap. XIII.     Interderivation of ‘If-Then’ and ‘Implies’:
                       Some Critical and Ontological Comments

Chap. XIV.     The Ontology of Counterfactual
                       Causality and Conditional

Chap. XV.      Logic and Critical Thinking:
                       Among Professional Artisans

Chap. XVI.     Inductive and Deductive Logic

Chap. XVII.    Apriori and Aposteriori Knowledge

Chap. XVIII.   Appearance and Reality

Chap. XIX.     Philosophical Questions in Logic and Mathematics

Chap. XX.      The Logic of Truth and Predication in Igbo 
                       Epistemology
191

195


201

207


213


221


229

237

243

251

259


277
289
293
297
Maduabuchi Frank Dukor is Professor of Philosophy at the Nnamdi Azikiwe University, Nigeria. He visited many universities as researcher, professor and external examiner, including the University of Ghana, Legon (1999 - 2002), and has published over 120 articles in national and foreign journals including “Secularism, Fundamentalism and Freedom” (Contemporary Philosophy, Vol. XXVI, No. 3, the University of Mane Presque Isle, U.S.A) and “The Great Debate: Deconstruction, Recognition and Cognition of African Philosophy” (Philosophical Quarterly of Isreal, Springer, Netherlands). Professor Dukor has published four volumes on African Philosophy: Theistic Humanism in African Philosophy; African Freedom; African Philosophy in the Global Village and Scientific Paradigm in African Philosophy (Lambert, Germany, 2010) and edited anthologies, such as: Philosophy and Politics: Discourse on Values Politics and Power in Africa (Malthouse, 2003), and M.C. Ali’s Federal Republic of Nigerian Army (Symposium on Sage Philosophy, Malthouse, 2018).

In 2013, a Special Issue on African Contribution to Philosophy in the Globalized World in the Light of Professor Maduabuchi Dukor’s for Great Works on African Philosophy was issued by the Open Journal of Philosophy (Vol. 3, No. 1A) to honour him as a philosopher, poet and writer.

Professor Maduabuchi Dukor is also the President/Editor-in-Chief of “Essence Library - The Cultural and Scientific Development Centre”.
An introductory text to symbolic and philosophical logic, with illustrations, examples, models of problem solving and essays.

The study of philosophy should have its background in logic, which, besides the other core disciplines like metaphysics, epistemology and ethics, endows individuals with the rigour of critical thinking in the pursuit of greater horizons of knowledge.

The ever-increasing relevance of logic to computer science and the modern age is a challenge to students in all domains. As a discipline of an infinity of possible worlds, logic probes and pushes forward the horizons of knowledge.

This book is intended not only as a textbook but also as an introductory guide to the study of symbolic logic.
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