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This book presents a collection of important new chapters on topics at the intersection of philosophy of language, philosophy of mind, and philosophical logic. The starting-point for the chapters is the brilliant work of the British philosopher Gareth Evans before his untimely death in 1980 at the age of 34. Evans's work on reference and singular thought transformed the Fregean approach to the philosophy of thought and language, showing how seemingly technical issues in philosophical semantics are inextricably linked to fundamental questions about the structure of our thinking about ourselves and about the world. The chapters, all newly written for this book, explore different aspects of Evans's philosophical legacy, showing its importance to central areas in contemporary analytic philosophy. The book includes an introduction that introduces the principal themes in Evans's thought and places the chapters in context.

A language is second‐order, or higher‐order, if it has bound variables that range over properties or sets of the items in the range of the ordinary, first‐order variables. This book presents a formal development of second‐ and higher‐order logic and an extended argument that higher‐order systems have an important role to play in the philosophy and foundations of mathematics. The development includes the languages, deductive systems, and model‐theoretic semantics for higher‐order languages, and the basic and advanced results in its meta‐theory: completeness, compactness, and the Löwenheim–Skolem theorems for Henkin semantics, and the failure of those results for standard semantics. Argues that second‐order theories and formalizations, with standard semantics, provide better models of important aspects of mathematics than their first‐order counterparts. Despite the fact that Quine is the main opponent of second‐order logic (arguing that second‐order logic is set‐theory in disguise), the present argument is broadly Quinean, proposing that there is no sharp line dividing mathematics from logic, especially the logic of mathematics. Also surveys the historical development in logic, tracing the emergence of first‐order logic as the de facto standard among logicians and philosophers. The connection between formal deduction and reasoning is related to Wittgensteinian issues concerning rule‐following. The book closes with an examination of several alternatives to second‐order logic: first‐order set theory, infinitary languages, and systems that are, in a sense, intermediate between first order and second order.

Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. This book describes and practices a particularly austere form of naturalism called ‘Second Philosophy’. Without a definitive criterion for what counts as ‘science’ and what doesn't, Second Philosophy can't be specified directly — ‘trust only the methods of science!’ or some such thing — so the book proceeds instead by illustrating the behaviors of an idealized inquirer called here the ‘Second Philosopher’. This Second Philosopher begins from perceptual common sense and progresses from there to systematic observation, active experimentation, theory formation, and testing, working all the while to assess, correct, and improve methods along the way. ‘Second Philosophy’ is then the result of the Second Philosopher's investigations. This book delineates the Second Philosopher's approach by tracing reactions to various familiar sceptical and transcendental views (Descartes, Kant, Carnap, late Putnam, van Fraassen), comparing methods to those of other self-described naturalists (especially Quine), and examining a prominent contemporary debate (between disquotationalists and correspondence theorists in the theory of truth) to extract a properly second-philosophical line of thought. The book then undertakes to practice Second Philosophy in its reflections on the ground of logical truth, the methodology, ontology, and epistemology of mathematics, and the general prospects for metaphysics naturalized.

This book is an examination of Wittgenstein’s early and late philosophies of logic in relation to accounts of logic and its philosophical significance in early and middle analytic philosophy, with particular reference to Frege, Russell, Carnap, and Strawson. It argues that not only the early but also the later Wittgenstein sought to further develop the logical-philosophical approaches of Frege and Russell. Throughout his career Wittgenstein’s aim was to resolve problems with and address the limitations of Frege’s and Russell’s accounts of logic and their logical methodologies so as to achieve the philosophical progress that originally motivated the logical-philosophical approach. By re-examining the roots and development of analytic philosophy, the book seeks to open up covered-up paths for the further development of analytic philosophy. It explains how Wittgenstein extends logical methodology beyond calculus-based logical methods and how his novel account of the status of logic enables one to do justice to the complexity and richness of language use and thought while retaining rigour and ideals of logic such as simplicity and exactness. The book also outlines the new kind of non-empiricist naturalism developed in Wittgenstein’s later work as well as explaining how Wittgenstein’s account of logic can be used to dissolve the longstanding methodological dispute between the ideal and ordinary language schools of analytic philosophy.

When a legal rule requires us to drive on the right, notarize our wills, or refrain from selling bootleg liquor, how are we to describe and understand that requirement? In particular, how does the logical form of such a requirement relate to the logical form of other requirements, such as moral requirements, or the requirements of logic itself? When a general legal rule is applied or distinguished in a particular case, how can we describe that process in logical form? Such questions have come to preoccupy modern legal philosophy as its methodology, drawing on the philosophy of logic, becomes ever more sophisticated. This book gathers together some of the most prominent legal philosophers in the Anglo-American and civil law traditions to analyse the logical structure of legal norms. They focus on the issue of defeasibility, which has become a central concern for both logicians and legal philosophers in recent years. The book is divided into four parts. Part One is devoted to unravelling the basic concepts related to legal defeasibility and the logical structure of legal norms, focusing on the idea that law, or its components, are liable to implicit exceptions, which cannot be specified before the law's application to particular cases. Part Two aims to disentangle the main relations between the issue of legal defeasibility and the issue of legal interpretation, exploring the topic of defeasibility as a product of certain argumentative techniques in the law. Part 3 of the volume is dedicated to one of the most problematic issues in the history of jurisprudence: the connections between law and morality. Finally, Part 4 of the volume is devoted to analysing the relationships between defeasibility and legal adjudication.

This book is both a history of philosophy of logic told from the Kantian viewpoint and a reconstruction of Kant’s theory of logic from a historical perspective. Kant’s theory represents a turning point in a history of philosophical debates over the following questions: (1) Is logic a science, instrument, standard of assessment, or mixture of these? (2) If logic is a science, what is the subject matter that differentiates it from other sciences, particularly metaphysics? (3) If logic is a necessary instrument to all philosophical inquiries, how is it so entitled? (4) If logic is both a science and an instrument, how are these two roles related? Kant’s answer to these questions centers on three distinctions: general versus particular logic, pure versus applied logic, pure general logic versus transcendental logic. The true meaning and significance of each distinction becomes clear, this book argues, only if we consider two factors. First, Kant was mindful of various historical views on how logic relates to other branches of philosophy (viz. metaphysics and physics) and to the workings of common human understanding. Second, he first coined “transcendental logic” while struggling to secure metaphysics as a proper “science,” and this conceptual innovation would in turn have profound implications for his mature theory of logic. Against this backdrop, the book reassesses the place of Kant’s theory in the history of philosophy of logic and highlights certain issues that are still debated today, such as normativity of logic and the challenges posed by logical pluralism.