John P. Burgess is the John N. Woodhull Professor of Philosophy at Princeton University. He obtained his Ph.D. from the Logic and Methodology program at the University of California at Berkeley under the supervision of Jack H. Silver with a thesis on descriptive set theory. He is a very distinguished and influential philosopher of mathematics. He has written several books: A Subject with No Object (with G. Rosen, Oxford University Press, 1997), Computability and Logic (with G. Boolos and R. Jeffrey, 5th ed., Cambridge University Press, 2007), Fixing Frege (Princeton University Press, 2005), Mathematics, Models, and Modality (Cambridge University Press, 2007), Philosophical Logic (Princeton University Press, 2009), Truth (with A. G. Burgess, Princeton University Press, 2011), Saul Kripke: Puzzles & Mysteries (Polity Press, 2012), Rigor & Structure (Oxford University Press, 2015), and Set Theory (Cambridge Elements, Forthcoming). In this interview, Professor Burgess talks about how his interests in mathematics and philosophy developed and relate to each other. He then answers questions about specific themes of his philosophical work, with a focus on issues pertaining to philosophy of mathematics.