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

Article number:	9781433532290, B18
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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.

–––––––––– Table of Contents ––––––––––

PART I: ELEMENTARY LOGIC

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

7. Logic Revealing God
8. Logic as Personal
9. Logic within Language
10. Suppressing the Truth
11. Logic and the Trinity
12. The Absoluteness of God
13. Logic and Necessity
14. Transcendence and Immanence
15. Reflections on the Mediation of Human Knowledge of Logic
16. Fallacies and God

Part I.C: The Problem of Classification

17. Analogy
18. Unity and Diversity
19. Stability of Meaning
20. Form and Meaning
21. Context for Meaning
22. Persons and Logic
23. Logic and Religious Antithesis
24. Theistic Proofs
25. Rethinking Western Thought

Part I.D: Aristotelian Syllogisms

26. Theistic Foundations for a Syllogism
27. Venn Diagrams
28. Syllogisms of the First Figure
29. Checking Validity by Venn Diagrams

PART II: ASPECTS OF PROPOSITIONAL LOGIC

Part II.A: Truth in Logic

30. Truth in Logic: Truth Functions
31. Divine Origin of Logical Functions
32. Complex Expressions

Part II.B: Perspectives on Truth in Logic

33. Venn Diagrams for Truth Functions
34. Other Representations of Logical Truth and Falsehood
35. Boolean Algebra
36. Truth-functional Equivalence
37. Harmony in Truth
38. Perspectives on Truth Functions

Part II.C: Propositional Logic

39. Introducing Propositional Logic
40. Axioms of Propositional Logic
41. Alternate Axioms
42. Dispensing with Axioms
43. Perspectives on Propositional Logic
44. Soundness and Completeness of Propositional Logic
45. Imitations of Transcendence

PART III: ENRICHING LOGIC

Part III.A: Predicate Logic

46. Introducing Predicate Logic
47. Theistic Foundations for Predicates

Part III.B: Quantification

48. Quantification
49. The Theistic Foundation for Quantification
50. Axioms and Deductions for Quantification
51. Soundness of Quantification

Part III.C: Including Equality and Functions

52. Equality
53. Functions

Part III.D: Introducing Formal Systems

54. Troubles in Mathematics
55. Axiomatizing Mathematics
56. Studying Proofs
57. Theistic Foundations for Proof Theory
58. A Computational Perspective
59. Theistic Foundations of Computation
60. Models
61. Theistic Foundations for Models

Part III.E: Special Logics and More Enriched Logics

62. Higher-order Quantification
63. Multivalued Logic
64. Intuitionistic Logic
65. Modal Logic
66. Theistic Foundations for Modal Logic
67. Models for Modal Logic
68. 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.