The Type Theory Of Law

This volume presents a Type Theory of Law (TTL), claiming that this is a unique theory of law that stems from the philosophical understanding of Jung’s psychological types applied to the phenomenon of law. Furthermore, the TTL claims to be a universal, general and descriptive account of law. To prove that, the book first presents the fundamentals of Jungian psychological types, as they had been invented by Jung and consequently developed further by his followers. The next part of the book describes how the typological structure of an individual determines their understanding of law. It then addresses the way in which inclusive legal theory can be understood based on this typology. Finally, the book describes the TTL in general and descriptive terms and puts it into context. All in all, the book shows how the integral or inclusive approach to understanding the nature of law is not only in tune with our time, but also relevant for presenting a more persuasive picture of law than the older exclusivist or dualist approaches of strict natural law and rigid legal positivism did.

Reprint of the second revised and enlarged edition, a complete revision of the first edition published in 1934. A landmark in the development of modern jurisprudence, the pure theory of law defines law as a system of coercive norms created by the state that rests on the validity of a generally accepted Grundnorm, or basic norm, such as the supremacy of the Constitution. Entirely self-supporting, it rejects any concept derived from metaphysics, politics, ethics, sociology, or the natural sciences. Beginning with the medieval reception of Roman law, traditional jurisprudence has maintained a dual system of "subjective" law (the rights of a person) and "objective" law (the system of norms). Throughout history this dualism has been a useful tool for putting the law in the service of politics, especially by rulers or dominant political parties. The pure theory of law destroys this dualism by replacing it with a unitary system of objective positive law that is insulated from political manipulation. Possibly the most influential jurisprudent of the twentieth century, Hans Kelsen [1881-1973] was legal adviser to Austria's last emperor and its first republican government, the founder and permanent advisor of the Supreme Constitutional Court of Austria, and the author of Austria's Constitution, which was enacted in 1920, abolished during the Anschluss, and restored in 1945. The author of more than forty books on law and legal philosophy, he is best known for this work and General Theory of Law and State. Also active as a teacher in Europe and the United States, he was Dean of the Law Faculty of the University of Vienna and taught at the universities of Cologne and Prague, the Institute of International Studies in Geneva, Harvard, Wellesley, the University of California at Berkeley, and the Naval War College. Also available in cloth.

In recent years, several formalisms for program construction have appeared. One such formalism is the type theory developed by Per Martin-Löf. Well suited as a theory for program construction, it makes possible the expression of both specifications and programs within the same formalism. Furthermore, the proof rules can be used to derive a correct program from a specification as well as to verify that a given program has a certain property. This book contains a thorough introduction to type theory, with information on polymorphic sets, subsets, monomorphic sets, and a full set of helpful examples.

The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.

This book provides an overview of type theory. The first part of the book is historical, yet at the same time, places historical systems in the modern setting. The second part deals with modern type theory as it developed since the 1940s, and with the role of propositions as types (or proofs as terms. The third part proposes new systems that bring more advantages together.

Intuitionistic type theory can be described, somewhat boldly, as a partial fulfillment of the dream of a universal language for science. This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution. Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book.

"The old logic put thought in fetters, while the new logic gives it wings." For the past century, philosophers working in the tradition of Bertrand Russell - who promised to revolutionise philosophy by introducing the 'new logic' of Frege and Peano - have employed predicate logic as their formal language of choice. In this book, Dr David Corfield presents a comparable revolution with a newly emerging logic - modal homotopy type theory. Homotopy type theory has recently been developed as a new foundational language for mathematics, with a strong philosophical pedigree. Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy offers an introduction to this new language and its modal extension, illustrated through innovative applications of the calculus to language, metaphysics, and mathematics. The chapters build up to the full language in stages, right up to the application of modal homotopy type theory to current geometry. From a discussion of the distinction between objects and events, the intrinsic treatment of structure, the conception of modality as a form of general variation to the representation of constructions in modern geometry, we see how varied the applications of this powerful new language can be.