1st Edition

The Elements of Formal Logic

ISBN 9780367426200
Published March 31, 2021 by Routledge
420 Pages

USD $40.00

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Book Description

Originally published in 1965. This is a textbook of modern deductive logic, designed for beginners but leading further into the heart of the subject than most other books of the kind.

The fields covered are the Propositional Calculus, the more elementary parts of the Predicate Calculus, and Syllogistic Logic treated from a modern point of view. In each of the systems discussed the main emphases are on Decision Procedures and Axiomatisation, and the material is presented with as much formal rigour as is compatible with clarity of exposition. The techniques used are not only described but given a theoretical justification. Proofs of Consistency, Completeness and Independence are set out in detail. The fundamental characteristics of the various systems studies, and their relations to each other are established by meta-logical proofs, which are used freely in all sections of the book. Exercises are appended to most of the chapters, and answers are provided.

Table of Contents

Preface  1. Validity  Part 1: The Propositional Calculus: Elements and Decision Procedures  2. Some Simple Forms of Inference  3. Establishing Validity (Theory)  4. Establishing Validity (Practice)  5. Disjunction and Disjunctive Inference  6. Material Equivalence: ‘If and Only If‘  7. Valid Inference and Proof  8. The Propositional Calculus  9. Truth-tables as a Decision Procedure  10. Equivalence Transformations  11. Another Decision Procedure  Part 2: The Propositional Calculus: Axiomatic Systems  12. Operations of Inference  13. Axiomatic Systems  14. Formal Axiomatic Systems  15. The System PM (I)  16. PM (II) Substitution of Equivalents  17. PM (III) Some Further Theorems  18. PM (IV) Independence and Non-independence  19. Consistency and Completeness of PM  20. The System TB  21. Extensions of TB: The System W  22. Consistency and Completeness of W  23. The Elements of Formal Logic  Part 3: The Lower Predicate Calculus  Some General Remarks on Part 3  23. The Lower Predicate Calculus: Introduction  24. The System LPCl  25. LPCl: Decision Procedure I - The Truth-table Method  26. Universes of Discourse - Justification of Decision Procedure  27. LPCI : Decision Procedure II - Exposition  28. LPCI : Decision Procedure II - Justification  29. LPCl: Axiomatization  30. LPCl : Consistency and Completeness  31. The System LPC2: Introductory  32. LPC2: Decision Procedure I  33. LPC2: Decision Procedure II - Exposition  34. LPC2: Decision Procedure II - Justification  35. LPC2: Axiomatization  36. LPC2 and the Logic of an Empty Universe  37. Multiple Quantification I  38. Equivalence Transformations of Quantifiers  39. Multiple Quantification II  40. Multiple Quantification III  41. The Lower Predicate Calculus: Conclusion  Part 4: Syllogistic  Introductory Note  42. Résumé of Traditional Syllogistic Logic  43. Syllogistic and the Predicate Calculus  44. Syllogistic Moods under Interpretation 1: The Antilogism Theorem  45. Syllogistic and LPC1: Further Interpretations  46. Syllogistic and LPC1: Another Approach  47. The Validity of Syllogisms Reconsidered: An Extension of the Antilogism Theorem  48. Syllogistic: An Axiomatic Presentation  49. On the Meta-Iogic of AS.  Appendices

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Hughes\, G. E.; Londey\, D. G.