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:

Axiomatic Mathematics and Phenomenology, ICUB-IRH, University of Bucharest, 3-4 September 2018 (organized by I. Toader)

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)

Naturalism: From Logic to Phenomenology and Back Again, ICUB-IRH, University of Bucharest, 9 November 2019 (organized by C. Brîncuş and I. Toader)

Talks:

I. Pârvu, “Naturalizing Methods in Recent Philosophy of Science”, Naturalism: From Logic to Phenomenology and Back Again, ICUB, University of Bucharest, 9 November 2019

C. Brîncuş, “Naturalizing Logic?”, Naturalism: From Logic to Phenomenology and Back Again, ICUB, University of Bucharest, 9 November 2019

G. Vida, “Translating Classical Phenomenology of Mathematics”, Naturalism: From Logic to Phenomenology and Back Again, ICUB, University of Bucharest, 9 November 2019

I. Toader, “Is a Naturalistic Phenomenology of Mathematics Possible?”, Naturalism: From Logic to Phenomenology and Back Again, ICUB, University of Bucharest, 9 November 2019

I. Toader, “Why the Stone-von Neumann Theorem is Not a Categoricity Result”, EPSA 2019, University of Geneva, 11-14 September 2019

C. Brîncuş, “Karl R. Popper: Logical Writings”, Karl R. Popper Symposium, CLMPST 16, Prague, Czech Republic, 5–10 August 2019

C. Brîncuş, ”Open-ended Quantification and Categoricity”, CLMPST 16, Prague, Czech Republic, 5–10 August 2019

I. Toader, “Quantum logic against anti-exceptionalism”, Logica 2019, Klaster Hejnice, Czech Republic, 24-28 June 2019

C. Brîncuş, “Open-ended Quantification and Non-standard Models”, Logica 2019, Klaster Hejnice, Czech Republic, 24-28 June 2019

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

C. Brîncuş, “Open-ended Quantification and Alternative Models”, Workshop “Formal Logic and Philosophy of Science”, University of Salzburg, Austria, 4 May 2019

I. Toader, “Epistemically Dispensable Idealizations in Mathematics”, Philosophy of Science Conference, Dubrovnik, 15-19 April 2019

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

I. Toader, “Structuralism, Formal Semantics, and the Ghost of Modality”, Modality in Structural/Naturalist Ontologies, Lingnan University, Hong Kong, 21-22 March 2019

C. Brîncuş & I. Toader, “Categoricity and the Elimination of Negation”, Spanish Society for Logic, Methodology and Philosophy of Science, Madrid, 13-16 November 2018

I. Toader, “What Emmy Noether said to Weyl about axiomatics”, Women in the History of Logic, Pader- born University, 18-19 October 2018.

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

I. Pârvu, “Theoretical Naturalism and Transcendental Philosophy”, Axiomatic Mathematics and Phenomenology, ICUB-IRH, University of Bucharest, 3-4 September 2018

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

I. Toader, “Predicativism, evidence, and the ω-rule”, Axiomatic Mathematics and Phenomenology, ICUB-IRH, University of Bucharest, 3-4 September 2018

I. Pârvu, “Einstein and Hume: Theoretical Similarities”, Humeanisms, Institute of Philosophy, Budapest, 28-29 July

C. Brîncuş & M. Flonta, “Rethinking the Humean Internal Sense-Reason Correlation”, Humeanisms, Institute of Philosophy, Budapest, 28-29 July

C. Brîncuş & I. Toader, “Categoricity and the Elimination of Negation”, Logica 2018, Klášter Hejnice, Czech Republic, 18-22 June 2018

I. Toader, “The Transcendental Worth and Dignity of Science”, Phenomenological Approaches to Physics, University of Graz, 14-16 June 2018

I. Toader, “What is Scientific Metaphysics and What Should it Be”, Institute of Philosophy, Hungarian Academy of Sciences, Budapest, 27 April 2018

I. Pârvu, “The new philosophy of science”, Dialogues, University of Bucharest, 27 April 2018

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

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.

C. Brîncuş & I. Toader, “Non-normal Interpretations of Positive Logic”, Karl Popper and the Philosophy of Mathematics, University of Klagenfurt, 5-7 April 2018

I. Pârvu, “On the goal of philosophical activity”, Department of Theoretical Philosophy, University of Bucharest, 14 March 2018

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