Numbers, Infinity, and Reality: An Interdisciplinary Undergraduate Philosophy of Mathematics Course – Context and Background

The setting for the course Numbers, Infinity, and Reality is Converse University, which is a small, private university in Spartanburg, South Carolina. The co-instructors of this course are Kevin DeLapp and Jessica Sorrells. Jessica Sorrells, an associate professor of mathematics, holds a PhD in mathematics and has no formal training in the field of philosophy beyond a minor obtained during undergraduate studies. Kevin DeLapp is a professor of philosophy, holds a PhD in philosophy, and has no formal training in mathematics outside of philosophical logic.

Figure 2. Wilson Hall at Converse University. By PegasusRacer28, CC BY-SA 4.0, via Wikimedia Commons.

Numbers, Infinity, and Reality has been offered twice to date, once in a four-week January term in 2019 and once in a thirteen-week Spring term in 2021. In January 2019 the course was traditional, and in Spring 2021 it was designated as an honors course under Converse's Nisbet Honors Program. In both cases the course drew mathematics majors, philosophy majors, and students who were neither. Both iterations of the course were offered for three credit hours. Students could choose whether they received general education credit (in either mathematics or philosophy), credit toward their mathematics or philosophy degrees, and/or honors program credit.

To date, the design of the course has been as follows: A typical class day consists of a combination of lecture and discussion. Students are assigned required reading for nearly every class meeting, with occasional films and videos integrated as in-class supplements. The instructors meet outside of class approximately once per week in order to prepare the subsequent week's activities, compare disciplinary perspectives on a topic, and share on their own reflections on the readings. Most days, course preparation loosely follows a four-step plan:

• First, initial reactions to the day's reading are briefly solicited from the entire class.
• Second, the instructors expound upon some key historical, conceptual, or technical aspect of the reading. Both instructors are involved in this task during each class meeting, although different readings usually necessitate one instructor taking more of the lead, with the other instructor contributing supplemental observations. This division of labor tends to be approximately 60/40 and alternates equally from day to day or unit to unit.
• Third, based on this exposition from the instructors, the students engage in an activity such as think-pair-share or a short problem set.
• Finally, class meetings conclude by reopening discussion and debate to the entire class, with occasional time also devoted to setting up any terminology or context that would be important for the next session's reading.