seventeenth century philosophy: My main area of research over the past 25 years has been seventeenth century philosophy, particularly that of Leibniz. I am currently writing a book for Polity Press on Leibniz for their Classic Thinkers series, which gives a fresh overview of his thought. I am als...
seventeenth century philosophy: My main area of research over the past 25 years has been seventeenth century philosophy, particularly that of Leibniz. I am currently writing a book for Polity Press on Leibniz for their Classic Thinkers series, which gives a fresh overview of his thought. I am also completing a larger work on Leibniz's natural philosophy and metaphysics based on his solution to the continuum problem: Ariadnean Threads . In it I offer new interpretations of Leibniz's theory of substance, his theory of the infinite and infinitesimals, and his theories of space, time, motion and continuity.
A secondary research area I have been investigating is the lively atomist tradition of the early seventeenth century and its connection with biology, theology, and the chymical tradition, particularly in the work of Daniel Sennert.
philosophy of physics: I have recently published a paper on virtual processes, showing the close relationship between them and the phenomenon of quantum tunnelling; I argue that neither can be interpreted in terms of particle transmission, since that would involve processes with imaginary mass travelling backwards in time. My main current interest is the close relationship between time and inertia, on which I have written two papers , "Time, Inertia and the Relativity Principle" (archived paper) in Minnesota, and "Time and Inertia" in Montreal. The Time and Universe (tau) Cluster, a collaborative venture with other physicists and philosophers in Canada and around the world, is on hold pending a successful bid for funding.
history and philosophy of time: I am also doing substantial work on early modern philosophy of time. I recently published a paper on Descartes's debt to Beeckman in his philosophy of time, first given at a symposium in Chicago in mid-February 2010. This is part of a projected third book project treating the interconnection of views on time, force and activity in seventeenth century natural philosophy, Matters of Moment.
philosophy of the infinite: Fourth, arising out of my work on Leibniz, I have been defending an account of the actual infinite that is a rival to the Cantorian account, but which eschews infinite sets. On this topic I have written a dialogue between Leibniz and Cantor, and five related papers: one on the development of Leibniz's early thinking on infinitesimals; a second on Leibniz's Law of Continuity; a third in which I compare Leibniz's syncategorematic interpretation of infinitesimals with that of Smooth Infinitesimal Analysis, a fourth comparing Newton and Leibniz on infinitesimals , and a fifth to be published in the Netherlands, in which (inter alia) I offer a largely sympathetic critique of Deleuze's interpretation of Leibniz's calculus with regard to the rise of structuralism.
epistemology of science, thought experiments: Fifth, I am part of a cluster of scholars interested in thought experiments. I published an article on Galileo's thought experiment on falling bodies and Jim Brown's Platonist interpretation of it, incorporating a weird dream, a partial defence of Feyerabend's views, and my interest in Diderot's materialist philosophy. More recently I published a paper on one of the world's oldest TEs, Aristotle's Wheel, perhaps originating with Archytas of Tarentum, first read at a workshop in Halifax. I also co-hosted a workshop on the (contested) expanding role of applied mathematics from the Renaissance to the Enlightenment, in Pisa in September 2010.