Research
Research
In mathematics, I am interested in problems at the intersection of (two or more of) geometry, partial differential equations, representation theory, and functional analysis. I am motivated primarily by the desire for unified mathematical models of abstract formal systems that admit application to diverse areas of mathematics in addition to physics, computer science, philosophy, and beyond. Accordingly, I maintain a significant interest in univalent foundations of mathematics and homotopy type theory.
I haven't any results to speak of... yet! 😄
In philosophy, I think mostly in phenomenological and epistemological terms. I am deeply concerned with the problem of subjectivity and in particular of allowing an (optimistic) epistemological foundationalism for a univocal theory of mind. I have a strong interest in the history of philosophy—in particular the 19th century—with a focus on Fichte, Schelling, Hegel, and Kierkegaard. I am also interested in 20th century continental philosophy, most notably Bataille.
Formal Systems (in progress)
I am currently in the beginning stages of a book-length project about formal systems (considered as abstract philosophical objects).
"On the Faculty of Intuition" (2020). UVM Patrick Leahy Honors College Senior Theses. 377.
In this work I present an account of the faculty of intellectual intuition as analogous to the faculties of empirical sensing (i.e. sight, touch, hearing, proprioception, &c.). I develop an abstract schema into which all of these can be understood as 'presentational' mental activity. I then offer some external criteria that help distinguish between presentational mental activity which can justify belief (like intuition or seeing) and presentational mental activity that cannot justify belief (like dreaming or hallucinating). In the second chapter, I leverage the foregoing to defend epistemological foundationalism. Finally, I leverage my account of intuition specifically to defend against philosophical skepticism.