This book brings together young researchers from a variety of fields within mathematics, philosophy and logic. It discusses questions that arise in their work, as well as themes and reactions that appear to be similar in different contexts. The book shows that a fairly intensive activity in the philosophy of mathematics is underway, due on the one hand to the disillusionment with respect to traditional answers, on the other to exciting new features of present day mathematics. The book expl...

This second of a two-volume book prolongs the inquiry of volume 1 by considering other examples apt to better illustrate the ideal of epistemic economy in mathematical recasting. The new examples are drawn from second-order definitions of real numbers and allow the comparison of three different approaches to the definition of these numbers: by domain extension, as ratios of magnitudes, and as bicimal developments. These definitions are presented in detail (by often going further than any a...

This first of a two-volume book discusses the process of conceptual recasting of mathematical contents under a new and more convenient form, complying with the ideal of epistemic economy (expressing the same content by appealing to fewer or minimal conceptual resources). It accounts for this ideal and discusses its philosophical significance, also in opposition to the most frequently considered ideal of ontological parsimony, in the context of an original approach to mathematical knowledge...

This book is intended as conceptual introduction to three mathematical theories arising from the attempt to understand (actual) infinity. Though the treatment does not avoid technical aspects, it tries to explain their origins and purposes. The book is divided into three parts, each composed of two chapters and a few appendices. Each part presents in detail one of three moments in which mathematicians made a concerted effort to control the idea of infinity: Projective Geometry, Infinitesim...

This book examines three connected aspects of Frege’s logicism: the differences between Dedekind’s and Frege’s interpretation of the term ‘logic’ and related terms and reflects on Frege’s notion of function, comparing its understanding and the role it played in Frege’s and Lagrange’s foundational programs. It concludes with an examination of the notion of arbitrary function, taking into account Frege’s, Ramsey’s and Russell’s view on the subject. Composed of three chapters, this book sheds...

Alexander Grothendieck is often considered one of the greatest mathematicians of the twentieth century (if not all time), and his unique vision continues to impact and inspire many fields and researchers today. Utilizing a multidisciplinary approach, this edited volume explores the profound influence his work and ideas have had not only on mathematics, but also on logic and philosophy. Chapters are written by international scholars, and many were inspired by talks given at the conference “...

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 ...

Introduction to Phenomenology is an outstanding and comprehensive guide to phenomenology. Dermot Moran lucidly examines the contributions of phenomenology's nine seminal thinkers: Brentano, Husserl, Heidegger, Gadamer, Arendt, Levinas, Sartre, Merleau-Ponty and Derrida.Written in a clear and engaging style, Introduction to Phenomenology charts the course of the phenomenological movement from its origins in Husserl to its transformation by Derrida. It describes the ...

Truth and Method is a landmark work of 20th century thought which established Hans Georg-Gadamer as one of the most important philosophical voices of the 20th Century. In this book, Gadamer established the field of 'philosophical hermeneutics': exploring the nature of knowledge, the book rejected traditional quasi-scientific approaches to establishing cultural meaning that were prevalent after the war. In arguing the 'truth' and 'method' acted in opposition to each other, Gadamer ...

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...

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. ...

Heidegger's Being and Time: Critical Essays provides a variety of recent studies of Heidegger's most important work. Twelve prominent scholars, representing diverse nationalities, generations, and interpretive approaches deal with general methodological and ontological questions, particular issues in Heidegger's text, and the relation between Being and Time and Heidegger's later thought. All of the essays presented in this volume were never before available in an...