Knowledge and understanding: the students will be expected to acquire essential knowledge about the main philosophical problems raised by observation of the practice of mathematics.
Use of knowledge and understanding: while grappling with theoretical questions, the course will provide the students with tools to apply rigorous reasoning models in diverse circumstances.
Ability to draw conclusions: the course will emphasize the importance of rigorous critical argumentation. In particular, the use of logical and formal tools will be encouraged.
Communication skills: in both classroom discussion and individual writing, importance will be given to the ability to present the issues clearly and systematically, as well as to argue rigorously in presenting one's personal considerations.
Ability to learn: the course will stimulate the student’s independent reflection through the progressive verification of the knowledge acquired, while also providing didactic and bibliographical indications for further analysis of the course's topics.
none
Lectures accompanied by group discussions. The student’s active participation will be encouraged.
Written exam in (take-home) paper form and possibly class presentation. Eligible topics and criteria for the papers will be made available during the class.
The course "Philosophy of Mathematics: Epistemology and Practice" will address central problems in the philosophy of mathematics. It will do so by integrating complementary perspectives.
In this first Module (Module A - A.Sereni) the main philosophical issues raised by mathematics will be outlined, reconstructing the context and central concepts of the debate on the foundations of mathematics. The major foundational proposals concerning mathematics will be discussed, emphasizing how they answer to epistemological, logical, semantic, ontological, and metaphysical questions.
The debate on the foundations of mathematics will introduced by an outline of the crucial philosophical and mathematical developments which occurred in the XIX century. Among foundational proposals, special attention will be devoted to the logicist tradition inaugurated by Gottlob Frege and the structuralist views inaugurated by Richard Dedekind, also in connection with the formalist tradition championed by David Hilbert. These traditions will then be explored as regards their theoretical ramifications in the contemporary debate on the epistemology and ontology of mathematics, especially between neo-logicist and structuralist proposals.
Special attention will be placed on the conceptual analysis of numerical notions and on the formal and epistemic role of mathematical definitions.
The final program will be valid for both attending and non-attending students. Attendance is anyway warmly encouraged, both for a better understanding of the course topics, and for a better performance in the final paper.
Communication with the teacher will be by email at the address: andrea.sereni@iusspavia.it. Individual supervision meetings (either in- person or remote) can be scheduled by contacting the teacher by email.
Topics in this module will be integrated by issues in the philosophy of mathematical practice to be addressed in the second module of the course.
Further developments in epistemology and philosophy of mathematics will be addressed in the course "EPISTEMOLOGY AND MATHEMATICS".
