I am currently working on my dissertation, "Logic in Accounts of the Potential and Actual Infinite," sponsored by Professors Haim Gaifman and Achille Varzi. The project is composed of two parts: (i) a new defense of logical pluralism, the view that there are many equally good accounts of logical consequence, based on a view of theory choice where logical theories are judged based on their ability to satisfy a range of theoretical virtues; and (ii) an historical investigation into views of the potential and actual infinite. I connect the two by arguing that charitable interpretations of the historical views of the infinite leave one with several viable theories of the infinite, since disagreement seems to be epistemically irresolvable for agents like us. I argue that one ought to take a pluralistic view of the accounts of the infinite, and further, that this leads to a natural pluralism about logical consequence under my account of theory choice and the corresponding theoretical virtues.
A large part of this project is an historical investigation into philosophical, mathematical, and scientific views of the infinite, and the project covers three periods : (i) ancient and medieval views on potential and actual infinity, (ii) early modern developments re: method of indivisibles and actual parts assumptions, and (iii) the development of set theory and modern mathematical logic. I take the work to be split equally between (i) an investigation into the history of mathematics and science, and (ii) a full defense of a contemporary account of logical pluralism.
I am also interested in several other topics that include: Aristotle's philosophy of mathematics, ancient and medieval metaphysics and philosophy of science (especially the tradition of commentary on the Posterior Analytics), the historical relationship between mathematics and science, and American pragmatism.