Logic: A God-Centered Approach to the Foundation of Western Thought
Article number: | 9781433532290, B18 |
Availability: | In stock |
Logic
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: ELEMENTARY LOGIC
Part I.A: Introducing Logic and Argument
- Logic in Tension
- Why Study Logic?
- What Do We Trust?
- Formal Logic
- Inductive Logic
- The Importance of Formal Logic
Part I.B: God in Logic
- Logic Revealing God
- Logic as Personal
- Logic within Language
- Suppressing the Truth
- Logic and the Trinity
- The Absoluteness of God
- Logic and Necessity
- Transcendence and Immanence
- Reflections on the Mediation of Human Knowledge of Logic
- Fallacies and God
Part I.C: The Problem of Classification
- Analogy
- Unity and Diversity
- Stability of Meaning
- Form and Meaning
- Context for Meaning
- Persons and Logic
- Logic and Religious Antithesis
- Theistic Proofs
- Rethinking Western Thought
Part I.D: Aristotelian Syllogisms
- Theistic Foundations for a Syllogism
- Venn Diagrams
- Syllogisms of the First Figure
- Checking Validity by Venn Diagrams
PART II: ASPECTS OF PROPOSITIONAL LOGIC
Part II.A: Truth in Logic
- Truth in Logic: Truth Functions
- Divine Origin of Logical Functions
- Complex Expressions
Part II.B: Perspectives on Truth in Logic
- Venn Diagrams for Truth Functions
- Other Representations of Logical Truth and Falsehood
- Boolean Algebra
- Truth-functional Equivalence
- Harmony in Truth
- Perspectives on Truth Functions
Part II.C: Propositional Logic
- Introducing Propositional Logic
- Axioms of Propositional Logic
- Alternate Axioms
- Dispensing with Axioms
- Perspectives on Propositional Logic
- Soundness and Completeness of Propositional Logic
- Imitations of Transcendence
PART III: ENRICHING LOGIC
Part III.A: Predicate Logic
- Introducing Predicate Logic
- Theistic Foundations for Predicates
Part III.B: Quantification
- Quantification
- The Theistic Foundation for Quantification
- Axioms and Deductions for Quantification
- Soundness of Quantification
Part III.C: Including Equality and Functions
- Equality
- Functions
Part III.D: Introducing Formal Systems
- Troubles in Mathematics
- Axiomatizing Mathematics
- Studying Proofs
- Theistic Foundations for Proof Theory
- A Computational Perspective
- Theistic Foundations of Computation
- Models
- Theistic Foundations for Models
Part III.E: Special Logics and More Enriched Logics
- Higher-order Quantification
- Multivalued Logic
- Intuitionistic Logic
- Modal Logic
- Theistic Foundations for Modal Logic
- Models for Modal Logic
- Conclusion
PART IV: SUPPLEMENTS
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.