Colclough, T., Howitz, W., Mann, D., Kearns, K., & Hoffmann, D. (Forthcoming). Meanings of community: Educational developers experience care, satisfying contributions, and belonging in a collaboration across institutions. To Improve the Academy, https://doi.org/10.3998/tia.2637
Projects/articles under construction
Components of Arithmetic Theory Acceptance
Different philosophies of mathematics disagree about what accepting a formal theory involves. Recently there has been some discussion around this idea for arithmetic theories couched in terms of the implicit commitment thesis (ICT): accepting a mathematical system S implicitly commits one to additional resources R not immediately available in S. For arithmetic theories schematically axiomatized, this project offers an analysis of two components of arithmetic theory acceptance, and explores the ramifications of this account for foundational positions whose philosophies of mathematics are said to be incompatible with the ICT.
The warrant of arithmetic theory acceptance
If, on the basis of accepting a system of axioms S, we are warranted in accepting additional principles which are not immediately available in S, then what is the nature of that warrant? In this project I argue that the nature of the epistemic warrant involved in theory acceptance cannot be like any traditional epistemic notions which appear in the literature (mathematical justification, and Crispin Wright’s (2004) notion of entitlements). I propose a different kind of epistemic warrant which I suggest can solve this problem.
Epistemic routes to large cardinals
This project addresses the following main question: if one accepts a global reflection principle GRP(S) for a system of axioms S, what sort of warrant does that provide for accepting S itself? I argue that if one accepts a global reflection principle GRP(S) for S then one is entitled, purely on the basis of one's acceptance of GRP(S), to accept S itself. I also explore the extent to which the consistency of large cardinal axioms functions as an epistemic justification for those axioms.
These projects evaluate the impact of a trauma-informed approach on student learning experiences in several interdisciplinary courses. We analyze student reflections for the five themes of a trauma-informed approach, and ask: how are these themes reflected in students' experiences? Part of this work aims to shed light on common ground between STEM and disciplines that do not typically involve rigorous mathematics, in order to inform teaching approaches in courses that span these two areas, like logic courses taught in philosophy departments.