Contemporary Topics in Epistemology of Mathematics 3800-CTEM26-S
The aim of this seminar is to read, analyse and discuss research articles on contemporary topics in the epistemology of mathematics. The students will engage with papers ranging on different topics in the epistemology of mathematics, in the context of “epistemic foundations”. The general idea is that, through the papers of concrete topics in the epistemology of mathematics, students will have a better understanding of epistemic foundations in general, and of the concrete debates within epistemic foundations. Ideally, we will discuss broadly different but interconnected topics, but have one important main focus throughout the seminar: to better understand the concept of justification involved in epistemic foundations. with as main such as the concept of foundational stances, equivalences theses, the role played by justification.
I also provide a tentative list of articles that I’d like to discuss. Ideally, I’d like to discuss all the papers throughout the seminar, but I’d be happy to tailor the list around the topics as the seminar goes, depending on the interests of the students.
Koordynatorzy przedmiotu
Rodzaj przedmiotu
Efekty kształcenia
● Acquired knowledge: through the reading, the presentations, writing the essays, and the discussions in the seminar students will have a better understanding of contemporary philosophical topics and issues in the epistemology of mathematics. In particular, they will gain knowledge about specific contemporary research topics in epistemology of mathematics. Moreover, they will be able to locate these topics in a broader philosophical context of foundations and philosophy of mathematics.
● Acquired skills: through the reading, the presentations, discussions, and writing the essays, students improve their ability in reading, analysing, evaluating, and discussing research articles in philosophy in English. Specifically through the process of presenting, students will enhance their ability to present in English philosophical positions, and possibly also their own arguments, in a short amount of time and in a precise way. Writing the essays will definitely help the students to improve their philosophical analysis and argumentation.
● Acquired social competences: Through the discussions and presentations in the seminar, students will enhance their competence with respect to the following: a) critical discussion philosophical articles in English, b) constructive critique of articles and presentations in English.
Kryteria oceniania
The students will have the following possibilities: either i) write a longer essay on a topic related to some of the topics discussed in the seminar, or ii) give a presentation during one of the meetings on a specific topic to be discussed in the seminar and write a short essay elaborating on the presentation.
Allowed number of absences that can be excused : 2
Literatura
This is a tentative list of some of the scientific articles I’d like to be discussed in the seminar.
Shapiro, S. (2004), Foundations of Mathematics: Metaphysics, Epistemology, Structure. The Philosophical Quarterly, 54: 16-37.
Walter Dean, Arithmetical Reflection and the Provability of Soundness, Philosophia Mathematica, Volume 23, Issue 1, February 2015, Pages 31–64
Feferman, S. Does Reductive Proof Theory Have A Viable Rationale? Erkenntnis 53, 63–96 (2000).
Solomon Feferman. Logic, mathematics, and conceptual structuralism. In Penelope Rush, editor, The Metaphysics of Logic, page 7292. Cambridge University Press, 2014.
Waxman, D. Did Gentzen prove the consistency of arithmetic?
Leon Horsten, On Reflection, The Philosophical Quarterly, Volume 71, Issue 4, October 2021
Antonutti Marfori, M. Informal Proofs and Mathematical Rigour. Stud Logica 96, 261–272 (2010)
Rosen, Gideon. “Nominalism, Naturalism, Epistemic Relativism.” Philosophical Perspectives, vol. 15, 2001, pp. 69–91.
Parsons, Charles. “Mathematical Intuition.” Proceedings of the Aristotelian Society, vol. 80, 1979, pp. 145–68.