1. Introduction: Mathesis Universalis, Proof and ComputationStefania Centrone
2. Diplomacy of Trust in the European CrisisEnno Aufderheide
3. Mathesis Universalis and Homotopy Type TheorySteve Awodey
4. Note on the Benefit of Proof Representations by NameMatthias Baaz
5. Constructive Proofs of Negated StatementsJosef Berger and Gregor Svindland
6. Constructivism in Abstract MathematicsUlrich Berger
7. Addressing Circular Definitions via Systems of ProofsRiccardo Bruni
8. The Monotone Completeness Theorem in Constructive Reverse MathematicsHajime Ishihara and Takako Nemoto
9. From Mathesis Universalis to Fixed Points and Related Set-Theoretic ConceptsGerhard Jäger and Silvia Steila
10. Through an Inference Rule, DarklyRoman Kuznets
11. Objectivity and Truth in Mathematics: A Sober Non-Platonist PerspectiveGodehard Link
12. From Mathesis Universalis to Provability, Computability, and ConstructivityKlaus Mainzer
13. Analytic Equational Proof Systems for Combinatory Logic and λ-Calculus: a SurveyPierluigi Minari
14. Computational Interpretations of Classical Reasoning: From the Epsilon Calculus to Stateful ProgramsThomas Powell
15. The Concepts of Proof and GroundDag Prawitz
16. On Relating Theories: Proof-Theoretical ReductionMichael Rathjen and Michael Toppel
17. Program Extraction from Proofs: the Fan Theorem for Uniformly Coconvex BarsHelmut Schwichtenberg
18. Counting and Numbers, from Pure Mathesis to Base Conversion AlgorithmsJan von Plato
19. Point-Free Spectra of Linear SpreadsDaniel Wessel
About the Author:

Stefania Centrone is currently Privatdozentin at the University of Hamburg, teaches and does research at the Universities of Oldenburg and of Helsinki and has been in 2016 deputy Professor of Theoretical Philosophy at the University of Göttingen. In 2012 she was awarded a DFG-Eigene Stelle for the project Bolzanos und Husserls Weiterentwicklung von Leibnizens Ideen zur Mathesis Universalis and 2017 a Heisenberg grant. She is author of the volumes Logic and philosophy of Mathematics in the Early Husserl (Synthese Library 2010) and Studien zu Bolzano (Academia Verlag 2015).

Sara Negri is Professor of Theoretical Philosophy at the University of Helsinki, where she has been a Docent of Logic since 1998. After a PhD in Mathematics in 1996 at the University of Padova and research visits at the University of Amsterdam and Chalmers, she has been a research associate at the Imperial College in London, a Humboldt Fellow in Munich, and a visiting scientist at the Mittag-Leffler Institute in Stockholm. Her research interests range from mathematical logic and philosophy of mathematics to proof theory and its applications to philosophical logic and formal epistemology.

Deniz Sarikaya is PhD-Student of Philosophy and studies Mathematics 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.