Abstract: The seventeenth-century philosopher and mathematician G.W. Leibniz has sometimes been seen as uninterested in the foundations of mathematics. In fact Leibniz has a subtle and original position in the philosophy of mathematics. This talk gives a brief tour of Leibniz's philosophy of mathematics by considering how his view of the infinite as "actual" and "syncategorematic" is related to his view of limits as "ideal entities" and "fictions," with special attention to two simple puzzles about motion that he considers in his writings of 1676 (just after completing his major work on the infinitesimal calculus).
This talk will be accessible to undergraduates.