Synthese Library
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Reflections on the Foundations of Mathematics

Univalent Foundations, Set Theory and General Thoughts

Editors: Centrone, Stefania, Kant, Deborah, Sarikaya, Deniz (Eds.)

  • Presents some of the most important scholars in the fields of set theory, univalent foundations and philosophy of mathematics
  • Considers criteria for a suitable foundation in mathematics, fostering interdisciplinary discussion
  • Brings readers up to date with contemporary work in mathematics, philosophy and computer science
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eBook $79.99
price for USA in USD (gross)
  • The eBook version of this title will be available soon
  • Due: August 15, 2019
  • ISBN 978-3-030-15655-8
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover $139.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week).
  • Due: July 18, 2019
  • ISBN 978-3-030-15654-1
  • Free shipping for individuals worldwide
About this book

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.

About the authors

Stefania Centrone is currently Privatdozentin at the University of Hamburg and was deputy Professor of Theoretical Philosophy at the Georg-August-Universität Göttingen. In 2012 she was awarded a DFG-Eigene Stelle for the project Bolzanos und Husserls Weiterentwicklung von Leibnizens Ideen zur Mathesis Universalis at the Carl-von-Ossietzky University of Oldenburg. She is author/editor, among others, of the volume Logic and philosophy of Mathematics in the Early Husserl (Springer 2010) and Studien zu Bolzano (Academia Verlag 2015).


Deborah Kant studied mathematics at Free University and Humboldt University in Berlin, and specialized in set theory and logic. At the DMV Students' Conference 2015 in Hamburg, her talk about her master's thesis “Cardinal Sequences in ZFC” was being awarded. Since 2015, she is a PhD student at the Humboldt University Berlin under the supervision of Karl-Georg Niebergall with a project on naturalness in set theory.


Deniz Sarikaya is PhD-Student of Philosophy (BA: 2012, MA: 2016) and studies Mathematics (BA: 2015) at the University of Hamburg with experience abroad at the Universiteit van Amsterdam and Universidad de Barcelona. He stayed a term as a Visiting Student Researcher at the University of California, Berkeley developing a project on the Philosophy of Mathematical Practice concerning the Philosophical impact of the usage of automatic theorem prover and as a RISE research intern at the University of British Columbia. He is mainly focusing on philosophy of mathematics and logic.

Buy this book

eBook $79.99
price for USA in USD (gross)
  • The eBook version of this title will be available soon
  • Due: August 15, 2019
  • ISBN 978-3-030-15655-8
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover $139.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week).
  • Due: July 18, 2019
  • ISBN 978-3-030-15654-1
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Reflections on the Foundations of Mathematics
Book Subtitle
Univalent Foundations, Set Theory and General Thoughts
Editors
  • Stefania Centrone
  • Deborah Kant
  • Deniz Sarikaya
Series Title
Synthese Library
Series Volume
407
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-15655-8
DOI
10.1007/978-3-030-15655-8
Hardcover ISBN
978-3-030-15654-1
Edition Number
1
Number of Pages
X, 535
Number of Illustrations
25 b/w illustrations
Topics