|
My primary area of expertise is the works of Bernard Bolzano, specifically his mathematical works and his works on scientific methodology. In particular, I have been focussing on his highly original notion of analyticity, his ideal of scientific proof (grounding), and his notion of formal logical consequence. Inspired by Bolzano and the Classical Model of Science, I have been studying the works of Gottlob Frege. In particular, I focused on the extent to which the classical ideal of proper scientific proof is present in Frege's works. Another important theme in my work is the analytic-synthetic distinction. In my Bachelor's thesis I compared the linguistic approach to the analytic-synthetic distinction of J.J. Katz with the epistemological one of L. Bonjour. In my Master's thesis, I analyzed Bolzano's purely semantic account of analyticity, and linked it to the notion of grounding. An account of the analytic-synthetic distinction that is linked to grounding is also topic of a paper that I am currently working on (see my work in progress). In my dissertation, I will look at the currently hot topic of infinite idealizations in physics from the viewpoint of the philosophy of mathematics. Commonly in physics, a mathematics based on actual infinities is used, but the number of components in the physical world is always finite. Consequently, this mathematics is representationally inaccurate, and gives rise to various philosophical problems which became recently topic of debate in the philosophy of science. In my dissertation I investigate whether the use of a mathematics based on a different conception of infinity would solve the problems concerning infinite idealizations in physics. Additionally, I did pioneering work in exploring the potential of techniques from Digital Humanities for text-based philosophical research, and built, together with Sanne Vrijenhoek (Master student Artificial Intelligence), a computational text-analysis tool for philosophers. My research interests include: * grounding, or explanatory proofs, in contrast with non-explanatory proofs (primarily in mathematics) * foundations of mathematics * infinities and infinitesimals * infinite idealizations in physics * history of mathematics (in particular, of analysis and of set-theory) * mathematical logic and its development * constructive mathematics * mind-dependency versus mind-independency of mathematics * the (ontological) nature of mathematical concepts and truths * methods of teaching/ learning mathematics * the notion(s) of logical consequence * the benefits and limits of logical reasoning * methods of teaching/ learning mathematics * the analytic-synthetic distinction * the works of Bernard Bolzano * the works of Gottlob Frege * the Classical Model of Science * Digital Humanities, and its potential for philosophical research Home | Specialization | Publications & Talks | CV | |