This collection documents the work of the Hyperuniverse Project which is a new approach to set-theoretic truth based on justifiable principles and which leads to the resolution of many questions independent from ZFC. The contributions give an overview of the program, illustrate its mathematical content and implications, and also discuss its philosophical assumptions. It will thus be of wide appeal among mathematicians and philosophers with an interest in the foundations of set theory. The Hyperuniverse Project was supported by the John Templeton Foundation from January 2013 until September 2015
This volume focuses on the importance of historical enquiry for the appreciation of philosophical problems concerning mathematics. It contains a well-balanced mixture of contributions by internationally established experts, such as Jeremy Gray and Jens Hoyrup; upcoming scholars, such as Erich Reck and Dirk Schlimm; and young, promising researchers at the beginning of their careers. The book is situated within a relatively new and broadly naturalistic tradition in the philosophy of mathematics. In this alternative philosophical current, which has been dramatically growing in importance in the last few decades, unlike in the traditional schools, proper attention is paid to scientific practices as informing for philosophical accounts.
This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The volume is divided into three sections, the first two of which focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The third section then builds on this and is centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories. This book shares the work of some of the most important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics.
Saul Kripke's Naming and Necessity was one of the most influential philosophical works of the twentieth century. In this collection of essays leading specialists explore issues arising from this and other works of Kripke's.
Innovation is central to the dynamics and success of organizations and society in the modern world, the process famously referred to by Schumpeter as 'gales of creative destruction'. This ambitious and wide ranging book makes the case for a new approach to the study of innovation. It is the editors' conviction that this approach must accomplish several objectives: it must recognise that innovation encompasses changes in organizations and society, as well as products and processes; it must be genuinely interdisciplinary and include contributes from economics, sociology, management and political science; It must be international, to reflect both different patterns or systems of innovation, and different research traditions; and it must reflect the fundamental changes taking place in science, research and knowledge creation at all levels. To this end they have gathered together a distinguished group of economists, sociologists, political scientists, and organization, innovation and institutional theorists to both assess current research on innovation, and to set out a new research agenda. This has been achieved through careful planning and development of the project, and also through the ensuing structure of the book which looks in turn at Product and Process Innovation (perhaps the best established focus of existing research on innovation), Scientific Research (assessing the changing character of basic research and science policy); Knowledge Dynamics in Context (encompassing organizational learning in all its aspects); and Institutional Change (an analysis of the institutional context that can shape, enable and constrain innovation). This carefully integrated and wide ranging book will be an ideal reference point for academics and researchers across the Social Sciences interested in all dimensions of innovation - be they in the field of Management Studies, Economics, Organization Studies, Sociology, Political Science and Science and Technology Studies.
This volume announces a new era in the philosophy of God. Many of its contributions work to create stronger links between the philosophy of God, on the one hand, and mathematics or metamathematics, on the other hand. It is about not only the possibilities of applying mathematics or metamathematics to questions about God, but also the reverse question: Does the philosophy of God have anything to offer mathematics or metamathematics? The remaining contributions tackle stereotypes in the philosophy of religion. The volume includes 35 contributions. It is divided into nine parts: 1. Who Created the Concept of God; 2. Omniscience, Omnipotence, Timelessness and Spacelessness of God; 3. God and Perfect Goodness, Perfect Beauty, Perfect Freedom; 4. God, Fundamentality and Creation of All Else; 5. Simplicity and Ineffability of God; 6. God, Necessity and Abstract Objects; 7. God, Infinity, and Pascal’s Wager; 8. God and (Meta-)Mathematics; and 9. God and Mind.
The answer to the question 'what is literature?' has not been found. This is the first book-length attempt to find the answer, by one author, since Sartre in his 1948 book with the same title. The book addresses issues such as: how does literature speak to the world; what is great writing; what is originality; what sorts of truths are there, if any, in creative writing? The book uses hundreds of literary examples, and confronts them with philosophy. The book also explores some big questions about the meaning of life, and sets them against a range of literature. It asks questions like: how does great science relate to literature? The book advances the concept of counter-intuition, as part of the basis for answering the question 'what is literature?' The book is also concerned with practical matters, such as the ways literature is involved with war, corruption, rights, suffering and hope.
Logic and Philosophy of Mathematics in the Early Husserl focuses on the first ten years of Edmund Husserl’s work, from the publication of his Philosophy of Arithmetic (1891) to that of his Logical Investigations (1900/01), and aims to precisely locate his early work in the fields of logic, philosophy of logic and philosophy of mathematics. Unlike most phenomenologists, the author refrains from reading Husserl’s early work as a more or less immature sketch of claims consolidated only in his later phenomenology, and unlike the majority of historians of logic she emphasizes the systematic strength and the originality of Husserl’s logico-mathematical work. The book attempts to reconstruct the discussion between Husserl and those philosophers and mathematicians who contributed to new developments in logic, such as Leibniz, Bolzano, the logical algebraists (especially Boole and Schröder), Frege, and Hilbert and his school. It presents both a comprehensive critical examination of some of the major works produced by Husserl and his antagonists in the last decade of the 19th century and a formal reconstruction of many texts from Husserl’s Nachlaß that have not yet been the object of systematical scrutiny. This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to analytical philosophers and phenomenologists with a background in standard logic.