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Publications
Colclough, T. (2024). Components of arithmetic theory acceptance. Synthese, 203(32). https:doi.org/10.1007/s11229-023-04465-z
Colclough, T., Howitz, W., Mann, D., Kearns, K., & Hoffmann, D. (2023). Meanings of community: Educational developers experience care, satisfying contributions, and belonging in a collaboration across institutions. To Improve the Academy: A Journal of Educational Development, 42(2): 9. https://doi.org/10.3998/tia.2637
Hooper, A., Hyder, M., Colclough, T., & Mann, D. (2023). Re-envisioning learning through a trauma-informed lens: Empowering students in their personal and academic growth. Journal of the Scholarship of Teaching and Learning, 23(3), 74-94. https://doi.org/10.14434/josotl.v23i3.35234
Projects/articles under construction
Can set theorists be intellectually virtuous?
This project explores the epistemic value of truth in discussions of intellectual virtues for the particular mathematical field of set theory. I argue set theory poses problems for intellectual virtue frameworks which hold truth above all else as an epistemic end.
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? This project is concerned with the thesis that the nature of the epistemic warrant involved in theory acceptance cannot be any traditional epistemic notions which appear in the literature (mathematical justification, and Crispin Wright’s (2004) notion of entitlements).
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.
Trauma-informed pedagogy
This project evaluates the impact of a trauma-informed approach on student learning experiences in an interdisciplinary logic course. 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.
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