Reflections on the Foundations of Mathematics
Univalent Foundations, Set Theory and General Thoughts
Editors: Centrone, Stefania, Kant, Deborah, Sarikaya, Deniz (Eds.)
Free Preview 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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 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), nonclassical 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 GeorgAugustUniversität Göttingen. In 2012 she was awarded a DFGEigene Stelle for the project Bolzanos und Husserls Weiterentwicklung von Leibnizens Ideen zur Mathesis Universalis at the CarlvonOssietzky 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 KarlGeorg Niebergall with a project on naturalness in set theory.Deniz Sarikaya is PhDStudent 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.
 Table of contents (22 chapters)


Interview With a Set Theorist
Pages 326

How to Choose New Axioms for Set Theory?
Pages 2742

Maddy On The Multiverse
Pages 4378

Proving Theorems from Reflection
Pages 7997

Naïve Type Theory
Pages 101136

Table of contents (22 chapters)
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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
 9783030156558
 DOI
 10.1007/9783030156558
 Hardcover ISBN
 9783030156541
 Edition Number
 1
 Number of Pages
 XXVIII, 494
 Number of Illustrations
 24 b/w illustrations
 Topics
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