Dr. Casper Storm Hansen
Areas of specialization:
Philosophy of Mathematics, Logic, Philosophy of Language, Metaphysics, Decision Theory
Areas of competence:
Epistemology, Philosophy of Science, History of Analytic Philosophy, Early Modern Philosophy
I am working on a nominalistic philosophy of mathematics. That is, I try to show that mathematics can get by without a need to assume the existence of abstract objects. I believe that a mathematical ontology consisting of possible sentences plus human beings’ ability to commit to conventional truth conditions for those sentences will suffice. However, I do not think it suffices for classical (i.e. mainstream) mathematics, just that it suffices for a mathematics that again suffices for the empirical sciences. An important part of my project is to develop this non-classical mathematics in detail. Thus, in order to do philosophy of mathematics, I do a lot of mathematics.
My philosophy of mathematics is closely connected to a conventionalist solution to the semantic paradoxes that I have developed (see my personal website for a draft paper). I can also sometimes be caught working on projects concerned with supertasks, decision theory, and principles of probability.
- The Signalman Against the Glut and Gap Theorists. Synthese, forthcoming.
- Choice Sequences and the Continuum. Erkenntnis, published online.
- Two Envelopes and Binding. Australasian Journal of Philosophy 96 (2018), 508-518.
- On Fair Countable Lotteries. Philosophical Studies 174 (2017), 2787-2794.
- Unified Grounding. Erkenntnis 81 (2016), 993-1010.