Generally speaking, my interests are in the areas of metaphysics and epistemology: What is there?� And how do we find out about it?� These questions are obviously interconnected. If we circumscribe the domain of what there is to include only spatio-temporal entities causally connected to one another, then the answer as to how we found out about them seems relatively straightforward. (I say �relatively� because providing philosophical answers is never an entirely straightforward process).� We obtain knowledge about physical objects by means of observation and the methods of inquiry characterizing the natural sciences.� �However, if we enlarge the domain of existing things to include the non-spatial, non-temporal and non-causal, numbers for example, then accounting for our knowledge of all that there is becomes much more problematic.� For this reason, my general interests have inevitably led me to questions considered within the philosophy of mathematics.
Currently, I am writing my dissertation on how Kant and certain 19th century philosophers (e.g. Hermann Helmholtz, Hermann Cohen, and Gottlob Frege) answered the following questions:� What are mathematical entities?� How do we uncover the truths about such entities?� Why are the truths we uncover about mathematical entities also applicable to physical entities?� I am especially interested in how the latter three men positioned their answers relative to Kant and each other. My hope is that articulating a particular dialectic occurring among 19th century German philosophers of mathematics will help illuminate and perhaps broaden contemporary debates surrounding these issues.�