Steve Awodey – författare

This volume contains Carnap's Studies in Semantics, a series of three interlocking books: Introduction to Semantics (1942), Formalization of Logic (1942), and Meaning and Necessity (1947). They were extremely influential in their time, especially the third, and shaped the direction of analytic philosophy during the 1950s and 1960s. They constitute the background to a number of celebrated controversies of that period, especially those between Carnap and Quine. Most of the philosophical debates today in philosophical logic and the philosophy of language ultimately had their origins here. This new edition situates these works in their context, both within Carnap's philosophical development and within the philosophical debates they responded to and influenced.The editors' introduction explains how Carnap arrived at the project of semantics in the 1930s and how it developed into these three successive publications, how the three books fit together, and how the project developed and changed in the course of the 1940s. It also describes the reception of the books as they appeared, as well as Carnap's response. The editorial and textual notes give variant readings, Carnap's own marginal notes on these texts in his personal copies, and elucidatory commentary where Carnap's terminology or notation are no longer familiar. This will be an indispensable volume for anyone interested in the origins and preoccupations of present-day analytic philosophy, especially philosophical logic and philosophy of language.

Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership. Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists!This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.

Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership. Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists!This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.

This book introduces the category of Cartesian cubical sets and endows it with a Quillen model structure using ideas coming from Homotopy type theory. In particular, recent constructions of cubical systems of univalent type theory are used to determine abstract homotopical semantics of type theory. The celebrated univalence axiom of Voevodsky plays a key role in establishing the basic laws of a model structure, showing that the homotopical interpretation of constructive type theory is not merely possible, but in a certain, precise sense also necessary for the validity of univalence. Fully rigorous proofs are given in diagrammatic style, using the language and methods of categorical logic and topos theory. The intended readers are researchers and graduate students in homotopy theory, type theory, and category theory.

Rudolf Carnap (1891-1970) is considered the pioneer of logical positivism, but his work was thought to have been repudiated. Recently he has been undergoing a reappraisal, and this book of essays by leading philosophers, logicians, and art historians attempts to return Carnap to his rightful place. The philosopher’s early days as a utopianist, the root of his thought in neo-Kantianism, his social and political activism – all are explored in these important essays.

Rudolf Carnap (1891-1970) was the most important philosopher of the movement known as logical empiricism or logical positivism, still the basis of much modern analytic philosophy. It was long thought that this movement had been destroyed by the polemics of Quine, Popper, and Kuhn. But recently, leading philosophers have been re-appraising this verdict. It is no longer universally agreed that Quine or Popper "won" their disputes with Carnap, and some have now been arguing that Kuhn’s ideas are—as Carnap himself thought—perfectly compatible with logical empiricism.This volume presents the latest contributions to this discussion from both sides, and adds a number of new voices, who look at Carnap from a more international point of view — bringing out, for instance, the roots of his thought in Continental neo-Kantianism and Dilthey’s Lebensphilosophie, and stressing his deep commitment to political and cultural change. Carnap grew up in Jena, and in his student days was an active member there of the utopian "Sera Group", part of the German youth movement. At the same time, he was one of Frege’s few students, and was deeply influenced by him.