Abstractionism is a research program in foundations of mathematics which aims to show that truths of arithmetic and real analysis are logical and linguistic truths in disguise. Abstractionism is also a form of mathematical platonism, the view that the mathematical reality is every bit as real as the concrete reality. Abstractionism has been a successful program from a formal point of view. However, its metaphysical tenets are controversial. Most pointedly, abstractionists propose a linguistic and formal notion of object which strikes many as excessively anti-realistic. In my dissertation, I address this concern by showing that the familiar objects of everyday experience are objects exactly in the same sense that the abstractionist proposes. Therefore, numbers have much in common with ordinary objects such as cups and chairs (except that they are not concrete!).
Here is a break-down of my dissertation papers. Click for abstracts. Email me for drafts.
Sortalism and the Meta-ontology of Abstraction
An Abstractionist Solution to the Problem of the Many
Some of my work in progress are offshoots of my dissertation. In these, I assess the consequences of my view for issues surrounding the applicability of mathematics and indeterminacy of reference to abstracta.
The future direction of my research is to assess the consequences of my view for personal identity and agency.
My other philosophical projects are focused on the meaning of logical connectives in different contexts:
Logical Pluralism and Meaning-Variance
My research in 2020-2021 was supported by the Josephine de Karman Fellowship Trust. In 2019-2020, I was a visiting fellow at the MIT Philosophy Department.