Sean Ebels-Duggan Visiting Lecturer
I am interested primarily in the philosophy of logic and mathematics, with associated interests in early analytic philosophy and Kant. Ages ago, I worked on a dissertation on the normativity of logic. My published work has been on the logic of neo-Fregean abstraction. But my interests in logic are not limited to that, and my interests in general are not limited to logic.
- "Relative Categoricity and Abstraction Principles” (joint work with Sean Walsh, UC Irvine). The Review of Symbolic Logic, 8:3 (572–606), 2015.
- Many recent writers in the philosophy of mathematics have put great weight on the relative categoricity of the traditional axiomatizations of our foundational theories of arithmetic and set theory (Parsons, 1990; Parsons, 2008, sec. 49; McGee, 1997; Lavine, 1999; Väänänen & Wang, 2014). Another great enterprise in contemporary philosophy of mathematics has been Wright’s and Hale’s project of founding mathematics on abstraction principles (Hale & Wright, 2001; Cook, 2007). In Walsh (2012), it was noted that one traditional abstraction principle, namely Hume’s Principle, had a certain relative categoricity property, which here we term natural relative categoricity. In this paper, we show that most other abstraction principles are not naturally relatively categorical, so that there is in fact a large amount of incompatibility between these two recent trends in contemporary philosophy of mathematics. To better understand the precise demands of relative categoricity in the context of abstraction principles, we compare and contrast these constraints to (i) stability-like acceptability criteria on abstraction principles (cf. Cook, 2012), (ii) the Tarski-Sher logicality requirements on abstraction principles studied by Antonelli (2010b) and Fine (2002), and (iii) supervaluational ideas coming out of the work of Hodes (1984, 1990, 1991).
- “The Nuisance Principle in Infinite Settings”. Thought: A Journal of Philosophy, 4:4 (263–268), December 2015.
- Neo-Fregeans have been troubled by the Nuisance Principle (NP), an abstraction principle that is consistent but not jointly (second-order) satisfiable with the favored abstraction principle HP. We show that logically this situation persists if one looks at joint (second-order) consistency rather than satisfiability: under a modest assumption about infinite concepts, NP is also inconsistent with HP.