Reflections on the Foundations of Mathematics

Table of Contents

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   Book Overview
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   Chapter 1 Interview With a Set Theorist
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   Chapter 2 How to Choose New Axioms for Set Theory?
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   Chapter 3 Maddy On The Multiverse
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   Chapter 4 Proving Theorems from Reflection
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   Chapter 5 Naïve Type Theory
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   Chapter 6 Univalent Foundations and the Equivalence Principle
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   Chapter 7 Higher Structures in Homotopy Type Theory
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   Chapter 8 Univalent Foundations and the UniMath Library
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    Chapter 9 Models of HoTT and the Constructive View of Theories
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    Chapter 10 Set Theory and Structures
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    Chapter 11 A New Foundational Crisis in Mathematics, Is It Really Happening?
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    Chapter 12 A Comparison of Type Theory with Set Theory
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    Chapter 13 What Do We Want a Foundation to Do?
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    Chapter 14 Formal and Natural Proof: A Phenomenological Approach
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    Chapter 15 Varieties of Pluralism and Objectivity in Mathematics
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    Chapter 16 From the Foundations of Mathematics to Mathematical Pluralism
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    Chapter 17 Does Mathematics Need Foundations?
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    Chapter 18 Foundations for the Working Mathematician, and for Their Computer
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    Chapter 19 How to Frame a Mathematician
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    Chapter 20 Formalising Mathematics in Simple Type Theory
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    Chapter 21 Dynamics in Foundations: What Does It Mean in the Practice of Mathematics?