Synthese Library

Univalent Foundations, Set Theory and General Thoughts

By: Deborah Kant (Editor), Stefania Centrone (Editor), Deniz Sarikaya (Editor)

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Paperback | 20 November 2019

At a Glance

Paperback
524 Pages

Dimensions(cm)
23.5 x 15.5 x 3.18

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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.

Industry Reviews

"The volume succeeds in presenting a pleasantly non-biased, balanced, and multi-faceted selection of papers which does not convey the impression that any one particular approach or school would be too dominant. ... The volume is well-edited and curated. The many cross-references amongst the contributions help one appreciate the volume as something more than the mere sum of its parts, after all, conveying the feel of an actual ongoing discussion." (Hans-Christoph Kotzsch, Philosophia Mathematica, Vol. 30 (1), February, 2022)

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