The Phenomenological Analysis of Axiomatic Mathematics

Abstract:  This project proposes an investigation of the phenomenological approach to axiomatic mathematics, an approach illustrated in the works of Edmund Husserl, Hermann Weyl, Oskar Becker, Dietrich Mahnke, Felix Kaufmann, Kurt Gödel, and others. It focuses, in particular, on the related problems of mathematical understanding and conceptual change, and it aims at providing a novel, naturalistic interpretation of their phenomenological solutions.


Research Team:

Principal Investigator: Dr. Iulian D. Toader

Experienced Researcher: Prof. dr. Ilie Pârvu

Postdoctoral Researcher: Dr. Constantin C. Brîncuş

Research Assistants: Dr. Grigore Vida, Drd. Iulian Apostolescu (07.2017-12.2018)


Project Code:  PN-III-P4-ID-PCE-2016-0531

Contract nr.: 17 from 12/07/2017


Project Development

Workshops:

  1. Naturalism: From Logic to Phenomenology and Back Again, ICUB-IRH, University of Bucharest, 9 November 2019 (organized by C. Brîncuş and I. Toader)
  2. Humeanisms, The Second Bucharest-Budapest Workshop in Philosophy, Research Group for the History and Philosophy of Science, Institute of Philosophy, Hungarian Academy of Sciences, Budapest, 28-29 July 2018 (organized by I. Toader together with T. Demeter and L. Kocsis)
  3. Axiomatic Mathematics and Phenomenology, ICUB-IRH, University of Bucharest, 3-4 September 2018 (organized by I. Toader)

Talks:

  1. I. Pârvu, “Naturalizing Methods in Recent Philosophy of Science”, Naturalism: From Logic to Phenomenology and Back Again, ICUB, University of Bucharest, 9 November 2019
  2. C. Brîncuş, “Naturalizing Logic?”, Naturalism: From Logic to Phenomenology and Back Again, ICUB, University of Bucharest, 9 November 2019
  3. G. Vida, “Translating Classical Phenomenology of Mathematics”, Naturalism: From Logic to Phenomenology and Back Again, ICUB, University of Bucharest, 9 November 2019
  4. I. Toader, “Is a Naturalistic Phenomenology of Mathematics Possible?”, Naturalism: From Logic to Phenomenology and Back Again, ICUB, University of Bucharest, 9 November 2019
  5. I. Toader, “Why the Stone-von Neumann Theorem is Not a Categoricity Result”, EPSA 2019, University of Geneva, 11-14 September 2019
  6. C. Brîncuş, “Karl R. Popper: Logical Writings”, Karl R. Popper Symposium, CLMPST 16, Prague, Czech Republic, 5–10 August 2019
  7. C. Brîncuş, ”Open-ended Quantification and Categoricity”, CLMPST 16, Prague, Czech Republic, 5–10 August 2019
  8. I. Toader, “Quantum logic against anti-exceptionalism”, Logica 2019, Klaster Hejnice, Czech Republic, 24-28 June 2019
  9. C. Brîncuş, “Open-ended Quantification and Non-standard Models”, Logica 2019, Klaster Hejnice, Czech Republic, 24-28 June 2019
  10. I. Toader, “Talking Past Each Other: Frege and Schroeder on the Modeling Problem”, 2nd International Workshop on the Philosophy of Notation, University of Bologna, May 23-24, 2019
  11. C. Brîncuş, “Open-ended Quantification and Alternative Models”, Workshop “Formal Logic and Philosophy of Science”, University of Salzburg, Austria, 4 May 2019
  12. I. Toader, “Epistemically Dispensable Idealizations in Mathematics”, Philosophy of Science Conference, Dubrovnik, 15-19 April 2019
  13. C. Brîncuş, “Are the Open-Ended Rules for Negation Categorical?”, Proof-Theoretic Semantics Assessment and Future Perspectives, Third Tübingen Conference on Proof-Theoretic Semantics, Tübingen, Germany, 27-30 March 2019
  14. I. Toader, “Structuralism, Formal Semantics, and the Ghost of Modality”, Modality in Structural/Naturalist  Ontologies, Lingnan University, Hong Kong, 21-22 March 2019
  15. C. Brîncuş & I. Toader, “Categoricity and the Elimination of Negation”, Spanish Society for Logic, Methodology and Philosophy of Science, Madrid, 13-16 November 2018
  16. I. Toader, “What Emmy Noether said to Weyl about axiomatics”, Women in the History of Logic, Pader- born University, 18-19 October 2018.
  17. C. Brîncuş, “Are the Open-Ended Rules for Negation Categorical?”, Philosophical Perspectives. The 13th conference of the Italian Society for Analytic Philosophy, Novara, 4-7 September 2018
  18. I. Pârvu, “Theoretical Naturalism and Transcendental Philosophy”, Axiomatic Mathematics and Phenomenology, ICUB-IRH, University of Bucharest, 3-4 September 2018
  19. C. Brîncuş, “Finitism and Phenomenology: The Benefits of a Fully Formalized Logic”, Axiomatic Mathematics and Phenomenology, ICUB-IRH, University of Bucharest, 3-4 September 2018
  20. I. Toader, “Predicativism, evidence, and the ω-rule”, Axiomatic Mathematics and Phenomenology, ICUB-IRH, University of Bucharest, 3-4 September 2018
  21. I. Pârvu, “Einstein and Hume: Theoretical Similarities”, Humeanisms, Institute of Philosophy, Budapest, 28-29 July
  22. C. Brîncuş & M. Flonta, “Rethinking the Humean Internal Sense-Reason Correlation”, Humeanisms, Institute of Philosophy, Budapest, 28-29 July
  23. C. Brîncuş & I. Toader, “Categoricity and the Elimination of Negation”, Logica 2018, Klášter Hejnice, Czech Republic, 18-22 June 2018
  24. I. Toader, “The Transcendental Worth and Dignity of Science”, Phenomenological Approaches to Physics, University of Graz, 14-16 June 2018
  25. I. Toader, “What is Scientific Metaphysics and What Should it Be”, Institute of Philosophy, Hungarian Academy of Sciences, Budapest, 27 April 2018
  26. I. Pârvu, “The new philosophy of science”, Dialogues, University of Bucharest, 27 April 2018
  27. C. Brîncuş, “Formalism and Intuitionism: How Does Categoricity Mediate between Intuitive and Axiomatic Concepts?”, ERGO. The First Edition of the Conference of Philosophy and Humanities. Forms, Formalism and Uniqueness, Cluj-Napoca, April 20-21, 2018
  28. C. Brîncuş, “Some Remarks on Logical Negation. Do we Really Need It?”, Research Seminar of the Department of Theoretical Philosophy, Faculty of Philosophy, University of Bucharest , April 18, 2018.
  29. C. Brîncuş & I. Toader, “Non-normal Interpretations of Positive Logic”, Karl Popper and the Philosophy of Mathematics, University of Klagenfurt, 5-7 April 2018
  30. I. Pârvu, “On the goal of philosophical activity”, Department of Theoretical Philosophy, University of Bucharest, 14 March 2018
  31. C. Brîncuş, “Why is Logic Special? or What Might the Tortoise Have Said to Anti-exceptionalists?”, The nature of the normative – ontology, semantics, logic, Institute of Philosophy, Czech Academy of Sciences, Villa Lanna, Prague, 16-17 October 2017
  32. C. Brîncuş & I. Toader, “The Reception of Hilbert’s Axiomatic Method in Romania”, International Conference on the History and Philosophy of Computing, Masaryk University, Brno, 3-7 October 2017

Publications and Work in Progress or Forthcoming:

  1. I. Pârvu, The Theoretical Construction of Science, monograph, vol. 1: The New Philosophy of Science, Romanian Academy Press, in progress
  2. I. Toader, Humeanisms, special issue of Synthese, guest-edited with T. Demeter and L. Kocsis, in progress
  3. G. Vida and I. Toader, The Phenomenology of Mathematics. Classical Texts, edited for Ratio & Revelatio Press, translation by Grigore Vida, preface by I. Pârvu, in progress
  4. I. Pârvu, “Philosophical and Theoretical Naturalism”, in Romanian Journal of Analytical Philosophy, forthcoming
  5. C. Brîncuş, “Does Human Nature Entail A Unique System of Values?”, co-authored with Mircea Flonta, in progress
  6. C. Brîncuş, “Open-ended Quantification and Non-Standard Models”, in progress
  7. C. Brîncuş, “Simion Stoilow on the Limits of Formal Axiomatics: The Epistemological Significance of Categorical Formal Concepts”, in progress
  8. C. Brîncuş, “Finitism and Phenomenology: The Benefits of a Fully Formalized Logic”, in progress
  9. C. Brîncuş, “Are the Open-Ended Rules for Negation Categorical?”, under review for Synthese
  10. C. Brîncuş, “Philosophical Accounts of First-Order Logical Truths”, in Acta Analitica, 34/3, 2019, pp. 369–383
  11. C. Brîncuş, “Categoricity and Negation. A Note on Kripke’s Affirmativism”, in Logica 2018 Yearbook, eds. Igor Sedlar and Martin Blicha, College London Publications, 2019, pp. 57-66. (with I. Toader)
  12. C. Brîncuş, “Non-normal Interpretations of Positive Logic”, in Karl Popper and the Philosophy of Mathematics , Proceedings of the Conference held in Klagenfurt, 5 – 7 April, 2018, Edited by Reinhard Neck, Alpen-Adria-Universität Klagenfurt, 2018, pp. 8-12 (with I. Toader)
  13. I. Toader, “Is a Naturalistic Phenomenology of Mathematics Possible?”, in progress
  14. I. Toader, “Predicativism, Evidence, and the ω-rule”, in progress
  15. I. Toader, “Talking Past Each Other: Frege and Schroeder on Notation Modeling”, invited for a special issue of Logique et Analyse, in progress
  16. I. Toader, “Talking Past Each Other: Mach and Husserl on Thought Economy”, in Ernst Mach – Life, Work, Influence, ed. by Friedrich Stadler, Institute Vienna Circle Yearbook, 22, 2019, pp. 213-221