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A Philosophical Introduction to Higher-order Logics book cover

1st Edition

A Philosophical Introduction to Higher-order Logics

By Andrew Bacon Copyright 2023
482 Pages 57 B/W Illustrations
by Routledge

482 Pages 57 B/W Illustrations
by Routledge

482 Pages 57 B/W Illustrations
by Routledge
Also available as eBook on:
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... Read more

Introduction

Part I: Typed Languages

1. Typed Languages
2. An Informal Introduction to Abstraction
3. λ-Languages

Part II: Higher-Order Languages

4 Higher-Order Languages
5 Higher-Order Logics
6 Application: Higher-Order Logic and Granularity
7 Application: Modal Logicism
8 Application: Consequences and Strengthenings of Classicism

Part III: General Higher-Order Languages

9 General λ-Languages
10. Curry Typing
11. Application: Structure I
12. Application: Structure II
13. Application: Structure III

Part IV: Higher-Order Model Theory

14. Applicative structures
15. Models of Higher-Order Languages
16. Logical Relations
17. Modalized Sets, M-Sets and Cartesian Closed Categories
18. The Model Theory of Classicism

Part V: Appendices

A The Curry-Howard Isomorphism
B Definability semantics

Biography

Andrew Bacon is Associate Professor at the University of Southern California. He is the author of Vagueness and Thought (Oxford UP, 2018) and has written numerous articles applying logical methods to topics in metaphysics, epistemology, and language.

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