I work in philosophy, especially philosophy of mathematics and philosophy of logic, and in mathematical logic. From July 2019, I will be Marie Skłodowska-Curie Individual Fellow at the Department of Philosophy, University of Oslo.
In 2017, I completed a PhD in Philosophy at the University of Leeds, with a thesis on constructive mathematics and predicativity. This was my second PhD, the first, also awarded by the University of Leeds in 2000, was in Mathematical Logic, and focused on the proof theory of constructive set theory. For an exposition on constructive set theory, see my Stanford Encyclopedia of Philosophy entry: Constructive and Intuitionistic ZF.
From 2000 to 2012, I was Post Doc and then Lecturer at the Department of Mathematics, LMU Munich, Post Doc at the Department of Philosophy, University of Florence, and Post Doc at the Department of Mathematics, University of Leeds.
Philosophy of Constructive Mathematics and Predicativity
Constructive mathematics (Bishop style) is a form of mathematics that uses intuitionistic rather than classical logic and is motivated by the desire to develop a form of mathematics that is computational "by default". Predicativity is a more elusive notion, as a number of variants of predicativity have emerged in the literature. According to one characterisation, a definition is predicative if it is not viciously circular. Predicativity emerged at the beginning of the 20th century in an exchange between Poincaré and Russell, originally prompted by paradoxes as Russell’s. In my thesis, I look at the origins of predicativity, with special focus on the distinctive contributions by Poincaré and Weyl. I also consider a form of predicativity typical of constructive type theory and discuss Nelson's predicative arithmetic. I employ this analysis of predicativity to offer a new perspective on Dummett's argument for intuitionistic logic from indefinite extensibility.
A common theme in my philosophical and mathematical research is the comparison and evaluation of a variety of approaches (philosophical and/or formal) to the concept of set, with a particular eye to concepts of set which are computational or operational.
Contact: Laura.Crosilla at gmail.com