Logic: A God-Centered Approach to the Foundation of Western Thought

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Article number: 9781433532290, B18
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Author: Vern Sheridan Poythress

A strong understanding of logic is of utmost importance for the well-rounded Christian, especially considering that logic is foundational for all human thought and communication. In his latest book, Vern Poythress undertakes a radical recasting of the study of logic and critiques the commonly-used Aristotelian approach. With over 30 years of writing and teaching experience, Poythress successfully presents a revolutionary work on the study of logic from a Christian worldview. This book will interest anyone who believes that Christians need to assess how our thinking should differ from the thinking of “the world,” and will be useful in high school, homeschool, college, and graduate-level classrooms.

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Part I.A: Introducing Logic and Argument

  1. Logic in Tension
  2. Why Study Logic?
  3. What Do We Trust?
  4. Formal Logic
  5. Inductive Logic
  6. The Importance of Formal Logic

Part I.B: God in Logic

  1. Logic Revealing God
  2. Logic as Personal
  3. Logic within Language
  4. Suppressing the Truth
  5. Logic and the Trinity
  6. The Absoluteness of God
  7. Logic and Necessity
  8. Transcendence and Immanence
  9. Reflections on the Mediation of Human Knowledge of Logic
  10. Fallacies and God

Part I.C: The Problem of Classification

  1. Analogy
  2. Unity and Diversity
  3. Stability of Meaning
  4. Form and Meaning
  5. Context for Meaning
  6. Persons and Logic
  7. Logic and Religious Antithesis
  8. Theistic Proofs
  9. Rethinking Western Thought

Part I.D: Aristotelian Syllogisms

  1. Theistic Foundations for a Syllogism
  2. Venn Diagrams
  3. Syllogisms of the First Figure
  4. Checking Validity by Venn Diagrams


Part II.A: Truth in Logic

  1. Truth in Logic: Truth Functions
  2. Divine Origin of Logical Functions
  3. Complex Expressions

Part II.B: Perspectives on Truth in Logic

  1. Venn Diagrams for Truth Functions
  2. Other Representations of Logical Truth and Falsehood
  3. Boolean Algebra
  4. Truth-functional Equivalence
  5. Harmony in Truth
  6. Perspectives on Truth Functions

Part II.C: Propositional Logic

  1. Introducing Propositional Logic
  2. Axioms of Propositional Logic
  3. Alternate Axioms
  4. Dispensing with Axioms
  5. Perspectives on Propositional Logic
  6. Soundness and Completeness of Propositional Logic
  7. Imitations of Transcendence


Part III.A: Predicate Logic

  1. Introducing Predicate Logic
  2. Theistic Foundations for Predicates

Part III.B: Quantification

  1. Quantification
  2. The Theistic Foundation for Quantification
  3. Axioms and Deductions for Quantification
  4. Soundness of Quantification

Part III.C: Including Equality and Functions

  1. Equality
  2. Functions

Part III.D: Introducing Formal Systems

  1. Troubles in Mathematics
  2. Axiomatizing Mathematics
  3. Studying Proofs
  4. Theistic Foundations for Proof Theory
  5. A Computational Perspective
  6. Theistic Foundations of Computation
  7. Models
  8. Theistic Foundations for Models

Part III.E: Special Logics and More Enriched Logics

  1. Higher-order Quantification
  2. Multivalued Logic
  3. Intuitionistic Logic
  4. Modal Logic
  5. Theistic Foundations for Modal Logic
  6. Models for Modal Logic
  7. Conclusion


Part IV.A: Supplements to Elementary Logic

A1. Antinomies with Sets: The Set of All Sets and Russell’s Paradox

A2. Deriving Syllogisms of the First Figure

A3. Syllogisms of the Second Figure

A4. Syllogism

Part IV.B: Supplementary Proofs for Propositional Logic

B1. Some Proofs for Boolean Algebra

B2. Deriving Whitehead and Russell’s Axioms

B3. Practice in Proofs

B4. The Rule of Replacement

B5. Reasoning toward the Completeness of Propositional Logic

Part IV.C: Proofs for Quantification

C1. Deductions of Rules for Quantification

C2. Natural Deduction of Syllogisms

Part IV.D: Proofs for Formal Systems

D1. Introducing Gödel’s First Incompleteness Theorem

D2. Simple Proofs within a Formal System

D3. Deriving Natural Deduction and the Associative Axiom

D4. Helping Lemmas

Part IV.E: Other  Proofs

E1. The Halting Problem for Computer Programs

E2. Diagonalization

Part IV.F: Philosophy and Logic

F1. Kantian Subjectivism

F2. The Role of Logic in Philosophy

F3. A View of Modern Logic

F4. Modal Ontological Argument

F5. Reforming Ontology and Logic

736pp. Paperback.

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