A Philosophical Introduction to Higher-order Logics
A Philosophical Introduction to Higher-order Logics by Andrew Bacon is a comprehensive textbook published by Routledge in August 2023. This 464-page edition is designed specifically for graduate students in philosophy, providing an introduction to higher-order logic. The book covers formal aspects such as model theory, proof theory, and λ-abstraction, while also exploring philosophical applications related to modality and propositional granularity. It emphasizes non-extensional higher-order logics, making it particularly suitable for foundational metaphysics.
Readers will find that the book is organized into 18 chapters divided into four main parts, focusing on typed language, higher-order languages, general higher-order languages, and higher-order model theory. Each chapter includes a range of exercises that progress from basic to more complex, facilitating both comprehension and long-term learning. Additionally, the book features two appendices that discuss the Curry-Howard isomorphism and its applications. With its structured approach and emphasis on exercises, this textbook serves as a valuable resource for both classroom use and self-study in the fields of logic, philosophy, and computer science.
Official synopsis Publisher
This is the first comprehensive textbook on higher-order logic that is written specifically to introduce the subject matter to graduate students in philosophy. The book covers both the formal aspects of higher-order languages–their model theory and proof theory, the theory of λ-abstraction and its generalizations–and their philosophical applications, especially to the topics of modality and propositional granularity. The book has a strong focus on non-extensional higher-order logics, making it more appropriate for foundational metaphysics than other introductions to the subject from computer science, mathematics, and linguistics.
A Philosophical Introduction to Higher-order Logics assumes only that readers have a basic knowledge of first-order logic. With an emphasis on exercises, it can be used as a textbook though is also ideal for self-study.
Author Andrew Bacon organizes the book’s 18 chapters around four main parts:
I. Typed Language
II. Higher-Order Languages
III. General Higher-Order Languages
IV. Higher-Order Model Theory
In addition, two appendices cover the Curry-Howard isomorphism and its applications for modeling propositional structure. Each chapter includes exercises that move from easier to more difficult, strategically placed throughout the chapter, and concludes with an annotated suggested reading list providing graduate students with most valuable additional resources.
Key Features:
- Is the first comprehensive introduction to higher-order logic as a grounding for addressing problems in metaphysics
- Introduces the basic formal tools that are needed to theorize in, and model, higher-order languages
- Offers an abundance of
– Simple exercises throughout the book, serving as comprehension checks on basic concepts and definitions
– More difficult exercises designed to facilitate long-term learning - Contains annotated sections on further reading, pointing the reader to related literature, learning resources, and historical context
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