Reflections On The Foundations Of Mathematics

Author : Stefania Centrone
Publisher : Springer Nature
ISBN 13 : 3030156559
Total Pages : 511 pages
Book Rating : 4.58/5 ( download)

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Download or read book Reflections on the Foundations of Mathematics written by Stefania Centrone and published by Springer Nature. This book was released on 2019-11-11 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Wilfried Sieg
Publisher : Cambridge University Press
ISBN 13 : 1316998819
Total Pages : pages
Book Rating : 4.16/5 ( download)

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Download or read book Reflections on the Foundations of Mathematics written by Wilfried Sieg and published by Cambridge University Press. This book was released on 2017-03-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the fifteenth publication in the Lecture Notes in Logic series, collects papers presented at the symposium 'Reflections on the Foundations of Mathematics' held in celebration of Solomon Feferman's 70th birthday (The 'Feferfest') at Stanford University, California in 1988. Feferman has shaped the field of foundational research for nearly half a century. These papers reflect his broad interests as well as his approach to foundational research, which emphasizes the solution of mathematical and philosophical problems. There are four sections, covering proof theoretic analysis, logic and computation, applicative and self-applicative theories, and philosophy of modern mathematical and logic thought.

Author : Matthias Baaz
Publisher : Cambridge University Press
ISBN 13 : 1139498436
Total Pages : 541 pages
Book Rating : 4.32/5 ( download)

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Download or read book Kurt Gödel and the Foundations of Mathematics written by Matthias Baaz and published by Cambridge University Press. This book was released on 2011-06-06 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.

Author : Jeff Murugan
Publisher : Cambridge University Press
ISBN 13 : 0521114403
Total Pages : 453 pages
Book Rating : 4.00/5 ( download)

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Download or read book Foundations of Space and Time written by Jeff Murugan and published by Cambridge University Press. This book was released on 2012-07-19 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Encapsulates the latest debates on this topic, giving researchers and graduate students an up-to-date view of the field.

Author : Joseph Kouneiher
Publisher : Springer
ISBN 13 : 3319648136
Total Pages : 441 pages
Book Rating : 4.32/5 ( download)

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Download or read book Foundations of Mathematics and Physics One Century After Hilbert written by Joseph Kouneiher and published by Springer. This book was released on 2018-05-26 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the rich and deep interplay between mathematics and physics one century after David Hilbert’s works from 1891 to 1933, published by Springer in six volumes. The most prominent scientists in various domains of these disciplines contribute to this volume providing insight to their works, and analyzing the impact of the breakthrough and the perspectives of their own contributions. The result is a broad journey through the most recent developments in mathematical physics, such as string theory, quantum gravity, noncommutative geometry, twistor theory, Gauge and Quantum fields theories, just to mention a few. The reader, accompanied on this journey by some of the fathers of these theories, explores some far reaching interfaces where mathematics and theoretical physics interact profoundly and gets a broad and deep understanding of subjects which are at the core of recent developments in mathematical physics. The journey is not confined to the present state of the art, but sheds light on future developments of the field, highlighting a list of open problems. Graduate students and researchers working in physics, mathematics and mathematical physics will find this journey extremely fascinating. All those who want to benefit from a comprehensive description of all the latest advances in mathematics and mathematical physics, will find this book very useful too.

Author : Jose Ferreiros
Publisher : Springer Science & Business Media
ISBN 13 : 9783764357498
Total Pages : 472 pages
Book Rating : 4.95/5 ( download)

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Download or read book Labyrinth of Thought written by Jose Ferreiros and published by Springer Science & Business Media. This book was released on 2001-11-01 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: "José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)

Author : Charles Parsons
Publisher : Harvard University Press
ISBN 13 : 0674419499
Total Pages : 365 pages
Book Rating : 4.90/5 ( download)

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Download or read book Philosophy of Mathematics in the Twentieth Century written by Charles Parsons and published by Harvard University Press. This book was released on 2014-03-10 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these selected essays, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the past century: Brouwer, Hilbert, Bernays, Weyl, Gödel, Russell, Quine, Putnam, Wang, and Tait.

Author : Raymond G. Ayoub
Publisher : American Mathematical Society
ISBN 13 : 1470458543
Total Pages : 301 pages
Book Rating : 4.46/5 ( download)

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Download or read book Musings of the Masters written by Raymond G. Ayoub and published by American Mathematical Society. This book was released on 2004-06-01 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: The anthology is a collection of articles contiguous to the humanities written by renowned mathematicians of the twentieth century. The articles cover a variety of topics that, for want of a better name, shall be referred to as humanistic. An important criterion, thereby limiting the choice, is that the articles should be accessible to the literate reader who may or may not have technical knowledge of mathematics. The articles span roughly a century in time and a wide range in subject. They are by mathematicians acknowledged by their peers as outstanding creators whose work has added richly to the discipline. Each article is preceded by a brief biographical sketch of the author and a brief indication of the content. The material is accessible to a wide audience, lay as well as academic.

Author : Arthur B. Powell
Publisher : SUNY Press
ISBN 13 : 9780791433515
Total Pages : 466 pages
Book Rating : 4.1X/5 ( download)

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Download or read book Ethnomathematics written by Arthur B. Powell and published by SUNY Press. This book was released on 1997-01-01 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the emerging field of ethnomathematics from a critical perspective, challenging particular ways in which Eurocentrism permeates mathematics education and mathematics in general.

Author : Thomas Augustin
Publisher : Springer Nature
ISBN 13 : 3031154363
Total Pages : 350 pages
Book Rating : 4.62/5 ( download)

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Download or read book Reflections on the Foundations of Probability and Statistics written by Thomas Augustin and published by Springer Nature. This book was released on 2023-01-14 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift celebrates Teddy Seidenfeld and his seminal contributions to philosophy, statistics, probability, game theory and related areas. The 13 contributions in this volume, written by leading researchers in these fields, are supplemented by an interview with Teddy Seidenfeld that offers an abbreviated intellectual autobiography, touching on topics of timeless interest concerning truth and uncertainty. Indeed, as the eminent philosopher Isaac Levi writes in this volume: "In a world dominated by Alternative Facts and Fake News, it is hard to believe that many of us have spent our life’s work, as has Teddy Seidenfeld, in discussing truth and uncertainty." The reader is invited to share this celebration of Teddy Seidenfeld’s work uncovering truths about uncertainty and the penetrating insights they offer to our common pursuit of truth in the face of uncertainty.