Synopses & Reviews
Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods, including algorithms and epitheory, and offers a brief treatment of Markov's approach to algorithms, explains elementary facts about lattices and similar algebraic systems, and more. 1963 edition.
Synopsis
Comprehensive account of constructive theory of first-order predicate calculus. Covers formal methods including algorithms and epi-theory, brief treatment of Markov's approach to algorithms, elementary facts about lattices and similar algebraic systems, more. Philosophical and reflective as well as mathematical. Graduate-level course. 1963 edition. Exercises.
Synopsis
Comprehensive graduate-level account of constructive theory of first-order predicate calculus covers formal methods: algorithms and epitheory, brief treatment of Markov's approach to algorithms, elementary facts about lattices, logical connectives, more. 1963 edition.
Synopsis
This book is a thoroughly documented and comprehensive account of the constructive theory of the first-order predicate calculus. This is a calculus that is central to modern mathematical logic and important for mathematicians, philosophers, and scientists whose work impinges upon logic.
Professor Curry begins by asking a simple question: What is mathematical logic? If we can define logic as -the analysis and criticism of thought- (W. E. Johnson), then mathematical logic is, according to Curry, -a branch of mathematics which has much the same relation to the analysis and criticism of thought as geometry does to the science of space.-
The first half of the book gives the basic principles and outlines of the field. After a general introduction to the subject, the author discusses formal methods including algorithms and epitheory. A brief treatment of the Markov treatment of algorithms is included here. The elementary facts about lattices and similar algebraic systems are then covered. In the second half of the book Curry investigates the possibility for a formulation that expresses the meaning to be attached to the logical connectives and to develop the properties that follow from the assumptions so motivated. The author covers positive connectives: implication, conjunction, and alternation. He then goes on to negation and quantification, and concludes with modal operations. Extensive use is made in these latter chapters of the work of Gentzen. Lists of exercises are included.
Haskell B. Curry, Evan Pugh Research Professor, Emeritus, at Pennsylvania State University, was a member of the Institute for Advanced Study, Princeton; a former Director of the Institute for Foundational Research, the University of Amsterdam; and President of the Association for Symbolic Logic. His book avoids a doctrinaire stance, presenting various interpretations of logical systems, and offers philosophical and reflective as well as mathematical perspectives.
Synopsis
This comprehensive graduate-level account of constructive theory of first-order predicate calculus covers formal methods including algorithms and epitheory, a brief treatment of Markov's approach to algorithms, elementary facts about lattices and similar algebraic systems, logical connectives, and more. 1963 edition.
Table of Contents
Preface; Explanation of Conventions
Chapter 1. Introduction
1. The nature of mathematical logic
2. The logical antinomies
3. The nature of mathematics
4. Mathematics and logic
5. Supplementary topics
Chapter 2. Formal Systems
1. Preliminaries
2. Theories
3. Systems
4. Special forms of systems
5. Algorithms
6. Supplementary topics
Chapter 3. Epitheory
1. The nature of epitheory
2. Replacement and monotone relations
3. The theory of definition
4. Variables
5. Supplementary topics
Chapter 4. Relational logical algebra
1. Logical algebras in general
2. Lattices
3. Skolem lattices
4. Classical Skolem lattices
5. Supplementary topics
Chapter 5. The Theory of Implication
1. General principles of assertional logical algebra
2. Propositional algebras
3. The systems LA and LC
4. Equivalence of the systems
5. L deducibility
6. Supplementary topics
Chapter 6. Negation
1. The nature of negation
2. L systems for negation
3. Other formulations of negation
4. Technique of classical negation
5. Supplementary topics
Chapter 7. Quantification
1. Formulation
2. Theory of the L systems
3. Other forms of quantification theory
4. Classical epitheory
5. Supplementary topics
Chapter 8. Modality
1. Formulation of necessity
2. The L theory of necessity
3. The T and H formulations of necessity
4. Supplementary topics
Bibliography; Index