This Element is an exposition of second- and higher-order logic and type theory. It begins with a presentation of the syntax and semantics of classical second-order logic, pointing up the contrasts with first-order logic. This leads to a discussion of higher-order logic based on the concept of a type. The second Section contains an account of the origins and nature of type theo...(展开全部)

This book articulates and defends Fregean realism, a theory of properties based on Frege’s insight that properties are not objects, but rather the satisfaction conditions of predicates. Robert Trueman argues that this approach is the key not only to dissolving a host of longstanding metaphysical puzzles, such as Bradley’s Regress and the Problem of Universals, but also to under...(展开全部)

This book articulates and defends Fregean realism, a theory of properties based on Frege’s insight that properties are not objects, but rather the satisfaction conditions of predicates. Robert Trueman argues that this approach is the key not only to dissolving a host of longstanding metaphysical puzzles, such as Bradley’s Regress and the Problem of Universals, but also to under...(展开全部)

The higher-order evidence debate concerns how higher-order evidence affects the rationality of our first-order beliefs. This Element has two parts. The first part (Sections 1 and 2) provides a critical overview of the literature, aiming to explain why the higher-order evidence debate is interesting and important. The second part (Sections 3 to 6) defends calibrationism, the vie...(展开全部)

This book explores the role of Martin-Lof s constructive type theory in computer programming. The main focus of the book is how the theory can be successfully applied in practice. Introductory sections provide the necessary background in logic, lambda calculus and constructive mathematics, and exercises and chapter summaries are included to reinforce understanding.

This book explores the role of Martin-Lof s constructive type theory in computer programming. The main focus of the book is how the theory can be successfully applied in practice. Introductory sections provide the necessary background in logic, lambda calculus and constructive mathematics, and exercises and chapter summaries are included to reinforce understanding.

This volume explores the use of higher-order logics in metaphysics. Higher-order logics are natural extensions of the common systems of predicate logic, with a history going back to the very beginnings of formal logic. Such logics are well suited to formalize metaphysical views and arguments. Over the last decade, there has been a resurgence of interest in higher-order metaphys...(展开全部)

Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. In "Higher Topos Theory", Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and...(展开全部)

Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. In "Higher Topos Theory", Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and...(展开全部)