Logic and Foundations of Mathematics Commons^™

Recognizing Mathematics Students As Creative: Mathematical Creativity As Community-Based And Possibility-Expanding, Meghan Riling

Journal of Humanistic Mathematics

Although much creativity research has suggested that creativity is influenced by cultural and social factors, these have been minimally explored in the context of mathematics and mathematics learning. This problematically limits who is seen as mathematically creative and who can enter the discipline of mathematics. This paper proposes a framework of creativity that is based in what it means to know or do mathematics and accepts that creativity is something that can be nurtured in all students. Prominent mathematical epistemologies held since the beginning of the twentieth century in the Western mathematics tradition have different implications for promoting creativity in …

Real Possibility: Modality And Responsibility, Julia Gaul

Honors Scholar Theses

Imagine: someone is backing out of a parking space and does not look in their rear view mirror. They subsequently hit a car that was passing by. One could argue that they simply could have avoided the accident had they looked in their mirror. This non-actual possibility, that they could have looked in the mirror, seems legally and morally relevant. One could also argue that they could have avoided the accident had they stuck their feet out of their window and sung La Marseillaise.

My leading questions is: how do we distinguish possibilities that are legally and morally relevant from …

Logical Pluralism And Vicious Regresses, Daniel Boyd

Dissertations, Theses, and Capstone Projects

This material in this dissertation will be divided into two parts. The first part is a preliminary discussion of vicious regress arguments in the philosophy of logic in the 20th century. The second part will focus on three different versions of logical pluralism, i.e., the view that there are many correct logics. In each case an argument will be developed to show that these versions of logical pluralism result in a vicious regress.

The material in part one will be divided into three chapters, and there are a few reasons for having a preliminary discussion of vicious regress arguments in …