This book honors the original and influential work by Göran Sundholm in the fields of the philosophy and history of logic and mathematics. Borne from two conferences held in Paris and Leiden on the occasion of Göran Sundholm’s retirement in 2019, the contributions collected in this volume represent work from leading logicians and philosophers. Reflecting Sundholm’s contributions to the history and philosophy of logic, this book is divided into two parts: the architecture and archaeology of...

This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory (CTT). The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion.One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simp...

In this extraordinarily original and profound work, Noam Chomsky discusses themes in the study of language and mind since the end of the sixteenth century in order to explain the motivations and methods that underlie his work in linguistics, the science of mind, and even politics. This edition includes a new and specially written introduction by James McGilvray, contextualising the work for the twenty-first century. It has been made more accessible to a larger audience; all the French and ...

'what can be said at all can be said clearly; and of what one cannot talk, about that one must be silent' Wittgenstein's Tractatus Logico-Philosophicus, first published in German in 1921 and in English translation in 1922, is one of the most influential philosophical texts of the twentieth century. It played a fundamental role in the development of analytic philosophy, and its philosophical ideas and implications have been fiercely debated ever since. This new tra...

'Nagel and Newman accomplish the wondrous task of clarifying the argumentative outline of Kurt Godel's celebrated logic bomb.' – The GuardianIn 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of physicist Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system. The impo...

Digital objects, in their simplest form, are data. They are also a new kind of industrial object that pervades every aspect of our life today—as online videos, images, text files, e-mails, blog posts, Facebook events.Yet, despite their ubiquity, the nature of digital objects remains unclear.On the Existence of Digital Objects conducts a philosophical examination of digital objects and their organizing schema by creating a dialogue between Martin Heidegger and Gilbert Simon...

The Cambridge Companion to Heidegger's 'Being and Time' contains seventeen chapters by leading scholars of Heidegger. It is a useful reference work for beginning students, but also explores the central themes of Being and Time with a depth that will be of interest to scholars. The Companion begins with a section-by-section overview of Being and Time and a chapter reviewing the genesis of this seminal work. The final chapter situates Being and Time in the context of Heidegger's later work. ...

Join original Vienna Circle member Victor Kraft in his discussion of the movement for an exclusive insider’s view of this important point in philosophical history. In this in-depth philosophical study, Victor Kraft explores the role the Vienna Circle had on the international philosophical movement. The Vienna Circle constituted a point of departure for the reawaking, rebirth, and reformation of positivism and empiricism, leading to the creation of the Neo-positivism movement. At the time o...

An accessible history and philosophical commentary on our notion of infinity.How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that ...

Phenomenology, together with Marxism, pragmatism, and analytic philosophy, dominated philosophy in the twentieth century—and Edmund Husserl is usually thought to have been the first to develop the concept. His views influenced a variety of important later thinkers, such as Heidegger and Merleau-Ponty, who eventually turned phenomenology away from questions of knowledge. But here Tom Rockmore argues for a return to phenomenology's origins in epistemology, and he does so by locating its root...

Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book...

The History of Philosophical and Formal Logic introduces ideas and thinkers central to the development of philosophical and formal logic. From its Aristotelian origins to the present-day arguments, logic is broken down into four main time periods:Antiquity and the Middle Ages (Aristotle and The Stoics)The early modern period (Bolzano, Boole)High modern period (Frege, Peano & Russell and Hilbert)Early 20th century (Godel and Tarski)Each new time...