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Kant's Philosophy of Mathematics: Volume 1, The Critical Philosophy and its Roots
The late 1960s saw the emergence of new philosophical interest in Kant's philosophy of mathematics, and since then this interest has developed into a major and dynamic field of study. In this state-of-the-art survey of contemporary scholarship on Kant's mathematical thinking, Carl Posy and Ofra Rechter gather leading authors who approach it from multiple perspectives, engaging with topics including geometry, arithmetic, logic, and metaphysics. Their essays offer fine-grained analysis of Kant's philosophy of mathematics in the context of his Critical philosophy, and also show sensitivity to its historical background. The volume will be important for readers seeking a comprehensive picture of the current scholarship about the development of Kant's philosophy of mathematics, its place in his overall philosophy, and the Kantian themes that influenced mathematics and its philosophy after Kant.
Mathematical Intuitionism
L. E. J. Brouwer, the founder of mathematical intuitionism, believed that mathematics and its objects must be humanly graspable. He initiated a program rebuilding modern mathematics according to that principle. This book introduces the reader to the mathematical core of intuitionism - from elementary number theory through to Brouwer's uniform continuity theorem - and to the two central topics of 'formalized intuitionism': formal intuitionistic logic, and formal systems for intuitionistic analysis. Building on that, the book proposes a systematic, philosophical foundation for intuitionism that weaves together doctrines about human grasp, mathematical objects and mathematical truth.
Computability
Computer scientists, mathematicians, and philosophers discuss the conceptual foundations of the notion of computability as well as recent theoretical developments. In the 1930s a series of seminal works published by Alan Turing, Kurt Gödel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics. In the decades since, the theory of computability has moved to the center of discussions in philosophy, computer science, and cognitive science. In this volume, distinguished computer scientists, mathematic...
Kant on Causality, Freedom, and Objectivity
Kant on Causality, Freedom, and Objectivity was first published in 1984. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. Kant's account of causation is central to his views on objective truth and freedom. The Second Analogy of Experience, in the Critique of Pure Reason,where he provides his defense of the causal principle, has long been the focus of intense philosophical research. In the past twenty years, there have been two major periods of interest in Kantian themes, The first coincided with a general turn away from positivism by analytic philosoph...
Mathematical Knowledge, Objects and Applications
This book provides a survey of a number of the major issues in the philosophy of mathematics, such as ontological questions regarding the nature of mathematical objects, epistemic questions about the acquisition of mathematical knowledge, and the intriguing riddle of the applicability of mathematics to the physical world. Some of these issues go back to the nascent years of mathematics itself, others are just beginning to draw the attention of scholars. In addressing these questions, some of the papers in this volume wrestle with them directly, while others use the writings of philosophers such as Hume and Wittgenstein to approach their problems by way of interpretation and critique. The contributors include prominent philosophers of science and mathematics as well as promising younger scholars. The volume seeks to share the concerns of philosophers of mathematics with a wider audience and will be of interest to historians, mathematicians and philosophers alike.
Humanizing Mathematics and its Philosophy
This Festschrift contains numerous colorful and eclectic essays from well-known mathematicians, philosophers, logicians, and linguists celebrating the 90th birthday of Reuben Hersh. The essays offer, in part, attempts to answer the following questions set forth by Reuben himself as a focus for this volume: Can practicing mathematicians, as such, contribute anything to the philosophy of math? Can or should philosophers of math, as such, say anything to practicing mathematicians? Twenty or fifty years from now, what will be similar, and what will, or could, or should be altogether different: About the philosophy of math? About math education? About math research institutions? About data proces...
Rethinking Kant 5
The series Rethinking Kant, now in its fifth volume, has become a mirror of Kantian studies in North America. It gathers papers presented at the various study groups of the North American Kant Society, along with contributions from hosts, session chairs, and keynote speakers. Because of its broad and unique composition, it offers a sample of a whole generation of Kantian thought, ranging from recent PhD recipients, to up-and-coming young scholars, to some well-established and influential players in the field. Contributions are subjected to strenuous peer-review, and are, without exception, examples of the most innovative and cutting-edge research done in this area. As such, this collection will appeal to anyone interested in taking the pulse of contemporary Kantian scholarship and engaging in the humbling, but rewarding task of rethinking Kant.
Kant’s Philosophy of Mathematics
Kant's views about mathematics were controversial in his own time, and they have inspired or infuriated thinkers ever since. Though specific Kantian doctrines fell into disrepute earlier in this century, the past twenty-five years have seen a surge of interest in and respect for Kant's philosophy of mathematics among both Kant scholars and philosophers of mathematics. The present volume includes the classic papers from the 1960s and 1970s which spared this renaissance of interest, together with updated postscripts by their authors. It also includes the most important recent work on Kant's philosophy of mathematics. The essays bring to bear a wealth of detailed Kantian scholarship, together with powerful new interpretative tools drawn from modern mathematics, logic and philosophy. The cumulative effect of this collection upon the reader will be a deeper understanding of the centrality of mathematics in all aspects of Kant's thought and a renewed respect for the power of Kant's thinking about mathematics. The essays contained in this volume will set the agenda for further work on Kant's philosophy of mathematics for some time to come.
Wittgenstein
In Wittgenstein's Way of Seeing, Judith Genova provides a an illuminating introduction to two surprisingly neglected aspects of his work: his conception of philosophy and his search for a style to embody his revolutionary practice. Genova examines the nuances, contours, and texture of logical twists of language. She elucidates Wittgenstein's reliance on the work of Kant and Freud, and presents how words are acts for Wittgenstein.
Kant’s Practical Philosophy Reconsidered
That Kant's ideas remain vitally present in ethical thinking today is as impossible to deny as it is to overlook their less persisting aspects and sometimes outdated idiom. The essays in this volume attempt to reassess some crucial questions in Kant's practical philosophy both by sketching the lines for new systematic interpretations and by examining how Kantian themes apply to contemporary moral concerns. In the previous decade, when Kant was primarily read as an answer to utilitarianism, emphasis was mainly laid on the fundamentals of his moral theory, stressing such concepts as universalization, duty for its own sake, personal autonomy, unconditional imperatives or humanity as end-in-itse...
