A Philosophical Introduction to Higher-order Logics

A Philosophical Introduction to Higher-order Logics is a textbook for graduate students in philosophy that covers the formal aspects of higher-order languages, their philosophical applications, and non-extensional higher-order logics. It assumes only a basic knowledge of first-order logic and is organized into four main parts, with two appendices covering the Curry-Howard isomorphism. The book includes exercises and annotated suggested reading lists to facilitate long-term learning.

Format: Hardback
Length: 464 pages
Publication date: 29 September 2023
Publisher: Taylor & Francis Ltd

This groundbreaking textbook is the first comprehensive resource designed specifically to introduce graduate students in philosophy to the fascinating world of higher-order logic. Covering both the formal aspects of higher-order languages, such as their model theory and proof theory, as well as their philosophical applications, particularly in the domains of modality and propositional granularity, it offers a comprehensive and accessible introduction to this complex subject.

Written by renowned expert Andrew Bacon, the book assumes only a basic knowledge of first-order logic, making it suitable for both classroom use and independent study. Organized into 18 chapters, the book is divided into four main parts:

Part I: Typed Language explores the fundamental concepts of typed languages, including type theory, lambda abstractions, and their generalizations. It provides a solid foundation for understanding higher-order logics and their applications.

Part II: Higher-Order Languages delves into the construction and analysis of higher-order languages, covering topics such as higher-order quantifiers, natural deduction, and the Curry-Howard isomorphism. It demonstrates how higher-order languages can be used to formalize and study complex philosophical concepts.

Part III: General Higher-Order Languages explores the broader landscape of higher-order logics, including various generalizations and extensions. It discusses the relationship between higher-order logic and other areas of philosophy, such as metaphysics, logic, and computer science.

Part IV: Higher-Order Model Theory provides a detailed introduction to higher-order model theory, which is the study of the logical properties of higher-order languages. It covers topics such as the semantics of higher-order models, the proof theory of higher-order logic, and the application of higher-order model theory to philosophical problems.

In addition to its comprehensive coverage, the book features numerous exercises that move from easier to more difficult, strategically placed throughout each chapter. These exercises serve as valuable comprehension checks on basic concepts and definitions, helping students to deepen their understanding of the material.

Furthermore, the book concludes with two appendices that cover the Curry-Howard isomorphism and its applications for modeling propositional structure. This isomorphism is a fundamental concept in higher-order logic and plays a crucial role in understanding the relationship between different types of formal systems.

A Philosophical Introduction to Higher-order Logics is an essential resource for anyone interested in exploring the foundations of metaphysics, logic, and computer science. With its clear and concise writing style, extensive exercises, and comprehensive coverage, it provides a solid foundation for students to advance their knowledge in these fields. Whether you are a graduate student, researcher, or simply someone passionate about philosophy, this book will undoubtedly enrich your understanding of higher-order logic and its applications.

Weight: 1050g
Dimension: 246 x 174 (mm)
ISBN-13: 9780367483029