What are you going to work with at IFIKK?
I am working on an independent project on mathematical pluralism.
Pluralism is advocated in connection to many debates in the philosophy of mathematics. Central among these is the debate over mathematical existence and truth. Does every mathematical proposition have a determinate truth-value? Or are certain propositions simply not uniquely decided by our mathematical concepts? Different answers here may have consequences for one’s chosen approach to how research in mathematical logic should proceed. A monistic and pluralistic diagnosis of, for instance, the independence-results in set-theory, have led to the development of distinct research programs, where the focus is either to look new axioms to sharpen our concept of set or to develop alternative frameworks that can capture various aspects of it.
I will be investigating the conceptual foundation and development of mathematical pluralism. Specifically, I distinguish two types of pluralist theories, structuralism and conventionalism, the roots of which may both be traced back to the development of modern axiomatic geometry at the turn of the 19th century. Although these philosophical theories have generated much discussion, little attention has been paid to how they relate to each other, on the one hand – and to mathematical pluralism, on the other. This is somewhat surprising: considering their shared origin in the development of modern axiomatics, one should expect a good amount of overlap between the two conceptions. Instead, they appear to have developed in parallel, as opposing philosophical perspectives on the foundations of mathematics. I will investigate the ground for this conceptual disagreement, with the aim to determine which of them is the better framework for mathematical pluralism.
Can you tell us a bit about your research interests?
My research is focused on the history and philosophy of mathematics and logic, and certain epistemological and metaphysical issues connected to the foundations of mathematics. My philosophical interests include the philosophy of language and of science more broadly, in addition to aesthetics and political philosophy.
What do you like to do in your spare time?
I like to run and to ski. I am also fan of experimental electronic music and literature.