Mancosu - Philosophy of Mathematical Practice (Oxford, 2008).pdf

BiographiesJeremy Avigad is an Associate Professor of Philosophy at Carnegie MellonUniversity. He received a B.A. in Mathematics from Harvard in 1989, andaPh.D. in Mathematics from the University of California, Berkeley in 1995.Hisresearch interests include mathematical logic, proof theory, automated reasoning,formal verification, and the history and philosophy of mathematics. He isparticularly interested in using syntactic methods, in the tradition of the Hilbertschool, towards obtaining a better understanding of mathematical proof.Michael Detlefsen is Professor of Philosophy at the University of NotreDame and long time editor of the Notre Dame Journal of Formal Logic. Hisscholarly work includes a number of projects concerning (i) Gödel’s incompletenesstheorems (and related theorems) and their philosophical implications,(ii) Hilbert’s ideas in the foundations of mathematics, (iii) Brouwer’s intuitionism,(iv) Poincaré’s conception of proof, and (v) the history and philosophyof formalist thinking from the 17th century to the present. Recently, hehas been thinking about the classical distinction between problems and theoremsand the role played by algebra in shaping the modern conception ofproblem-solving. Throughout his work, he has sought to illuminate meaningfulhistorical points of connection between philosophy and mathematics. Hiscurrent projects include a book on formalist ideas in the history of algebra,another on constructivism, and a third (with Tim McCarthy) on Gödel’stheorems.Marcus Giaquinto studied philosophy for a B.A. at University CollegeLondon (UCL), then mathematical logic for an M.Sc. taught by John Bell,Christopher Ferneau, Wilfrid Hodges, and Moshé Machover. Further study oflogic at Oxford under the supervision of Dana Scott was followed by turningto philosophy of mathematics for a Ph.D. supervised by Daniel Isaacson.Giaquinto is a Professor in UCL’s Philosophy Department and an associatemember of UCL’s Institute of Cognitive Neuroscience. He has writtentwo books, The Search for Certainty: a Philosophical Account of Foundations ofMathematics (OUP 2002), and Visual Thinking in Mathematics: an EpistemologicalStudy (OUP 2007). The research for this work and for Giaquinto’s articles inthis volume was funded by a British Academy two-year readership.