Topics in Modern Logic
Topics in Modern Logic by D. C. Makinson, published by Routledge in 2019, is a concise exploration aimed at students of philosophy with limited mathematical backgrounds. This edition, consisting of 114 pages, presents a balanced approach between philosophical and formal material, highlighting the intricate connections between the two. The author provides essential tools from set theory and arithmetic necessary for studying various systems of logic, including completeness results for multiple-valued logics and key concepts in quantificational logic.
Readers will find a thorough examination of significant philosophical topics such as entailment, the Löwenheim-Skolem theorem, and the relationship between logic and set theory. The book also delves into the nature of set theory and intuitionistic logic, making it a valuable resource for those interested in the foundational aspects of mathematics and philosophy. Exercises are included throughout the text, allowing readers to engage with the theoretical concepts presented.
Official synopsis Publisher
Originally published in 1973. This book is directed to the student of philosophy whose background in mathematics is very limited. The author strikes a balance between material of a philosophical and a formal kind, and does this in a way that will bring out the intricate connections between the two. On the formal side, he gives particular care to provide the basic tools from set theory and arithmetic that are needed to study systems of logic, setting out completeness results for two, three, and four valued logic, explaining concepts such as freedom and bondage in quantificational logic, describing the intuitionistic conception of the logical operators, and setting out Zermelo’s axiom system for set theory. On the philosophical side, he gives particular attention to such topics as the problem of entailment, the import of the Löwenheim-Skolem theorem, the expressive powers of quantificational logic, the ideas underlying intuitionistic logic, the nature of set theory, and the relationship between logic and set theory.
There are exercises within the text, set out alongside the theoretical ideas that they involve.
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