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, Oskar Becker, Dietrich Mahnke, Felix Kaufmann, Kurt Gödel, Gian-Carlo Rota, 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

Project Code:  PN-III-P4-ID-PCE-2016-0531
Contract nr.: 17 from 12/07/2017

Project Development
Workshops:
  1. The Second Bucharest-Budapest Workshop in Philosophy: Humeanisms, Hungarian Academy of Sciences, Research Group for the History and Philosophy of Science, Institute of Philosophy, Budapest, 28-29 July (organized by I. Toader together with T. Demeter and L. Koksis)
  2. Axiomatic Mathematics and Phenomenology, IRH, University of Bucharest, 3-4 September 2018 (organized by I. Toader)
Talks:
  1. C. Brincus & I. Toader, “Categoricity and the Elimination of Negation”, Spanish Society for Logic, Methodology and Philosophy of Science, Madrid, 13-16 November 2018
  2. C. Brincus, “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
  3. I. Parvu, “Theoretical Naturalism and Transcendental Philosophy”, Axiomatic Mathematics and Phenomenology, IRH, University of Bucharest, 3-4 September 2018
  4. C. Brincus, “Finitism and Phenomenology: The Benefits of a Fully Formalized Logic”, Axiomatic Mathematics and Phenomenology, IRH, University of Bucharest, 3-4 September 2018
  5. I. Toader, “Predicativism, evidence, and the ω-rule”, Axiomatic Mathematics and Phenomenology, IRH, University of Bucharest, 3-4 September 2018
  6. I. Parvu, “Einstein and Hume: Theoretical Similarities”, Humeanisms, Hungarian Academy of Sciences, Research Group for the History and Philosophy of Science, Institute of Philosophy, Budapest, 27-28 July
  7. C. Brincus & M. Flonta, “Rethinking the Humean Internal Sense-Reason Correlation”, Humeanisms, Hungarian Academy of Sciences, Research Group for the History and Philosophy of Science, Institute of Philosophy, Budapest, 27-28 July
  8. I. Toader, “Von Neumann’s Use of the Principle of Permanence of Forms”, HOPOS 12, University of Groningen, 9-12 July 2018
  9. C. Brincus & I. Toader, “Categoricity and the Elimination of Negation”, Logica 2018, Klášter Hejnice, Czech Republic, 18-22 June 2018
  10. I. Toader, “The Transcendental Worth and Dignity of Science”, Phenomenological Approaches to Physics, University of Graz, 14-16 June 2018
  11. I. Toader, “What is Scientific Metaphysics and What Should it Be”, Institute of Philosophy, Hungarian Academy of Sciences, Budapest, 27 April 2018
  12. I. Parvu, “The new philosophy of science”, Dialogues, University of Bucharest, 27 April 2018
  13. C. Brincus, “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
  14. C. Brincus, “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.
  15. C. Brincus & I. Toader, “Non-normal Interpretations of Positive Logic”, Karl Popper and the Philosophy of Mathematics, University of Klagenfurt, 5-7 April 2018
  16. I. Parvu, “On the goal of philosophical activity”, Department of Theoretical Philosophy, University of Bucharest, 14 March 2018
  17. C. Brincus, “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
  18. C. Brincus & 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:
  1. I. Toader, “Talking Past Each Other: Mach and Husserl on Thought Economy”, in Ernst Mach: Life, Work, and Influence, Vienna Circle Institute Yearbook (forthcoming)
  2. C. Brincus & I. Toader, “The Categoricity Problem for Classical Positive Logic” (under review)
  3. C. Brincus, “Philosophical Accounts of First-Order Logical Truths” (under review)
  4. C. Brincus, “Are the Open-Ended Rules for Negation Categorical?” (under review)
  5. I. Parvu, “Theoretical Naturalism and Transcendental Philosophy” (in progress)
Translations:
  1. G. Vida — E. Husserl, Philosophie der Arithmetik, 1891 (selection)
  2. G. Vida — E. Husserl, “Doppelvortrag”, 1901
  3. G. Vida — O. Becker, Beiträge zur phänomenologischen Begründung der Geometrie und ihrer physikalischen Anwendungen, 1923 (selection)
  4. G. Vida — D. Mahnke, “Von Hilbert zu Husserl: Erste Einfuehrung in die Phaenomenologie, besonders der formalen Mathematik”, 1923
  5. G. Vida — O. Becker, Mathematische Existenz, 1928 (selection)
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