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

iographiesixJohannes Hafner is Assistant Professor of Philosophy at North Carolina StateUniversity and formerly lecturer at the University of Vienna. After receiving hisMagister degree in philosophy he pursued graduate studies in philosophy andlogic at CUNY and at U.C. Berkeley (Ph.D. in Logic, 2005). He has a stronginterest in the history of logic and has in particular worked on the emergence ofmodel-theoretic methods within the Hilbert school and on Bolzano’s conceptof indirect proof. Other research interests include ontological issues within thephilosophy of mathematics in particular Putnam’s argument for antirealism inset theory and the concept of mathematical explanation.Michael Hallett is Associate Professor of Philosophy at McGill University inMontreal. His main interests are in the philosophy and history of mathematics.He is the author of Cantorian Set Theory and Limitation of Size (Oxford,Clarendon Press, 1984), a study of Cantor’s development of set theory and ofthe subsequent axiomatization. Much more of his recent work has centred onHilbert’s treatment of the foundations of mathematics and what distinguishes itfrom other major foundational figures, e.g. Frege and Gödel. He is a GeneralEditor (along with William Ewald, Ulrich Majer, and Wilfried Sieg) of asix-volume series (to be published by Springer) containing many importantand hitherto unpublished lecture notes of Hilbert on the foundations ofmathematics and physics. Volume 1: David Hilbert’s Lectures on the Foundations ofGeometry, 1891–1902, co-edited by Hallett and Ulrich Majer, appeared in 2004.Volume 3: David Hilbert’s Lectures on Arithmetic and Logic, 1917–1933, editedbyWilliam Ewald and Wilfried Sieg, will appear in 2008.Colin McLarty is the Truman P. Handy Associate Professor of Philosophy,and of Mathematics, at Case Western Reserve University. He is the author ofElementary Categories, Elementary Toposes (OUP 1996) andworksoncategorytheory especially in logic and the foundations of mathematics. His currentproject is a philosophical history of current methods in number theory andalgebraic geometry, which largely stem from Grothendieck. The historyincludes Poincaré’s topology, Noether’s abstract algebra and her influence ontopology, and Eilenberg and Mac Lane’s category theory. He has publishedarticles on these and on Plato’s philosophy of mathematics.Paolo Mancosu is Professor of Philosophy at U.C. Berkeley. His maininterests are in logic, history and philosophy of mathematics, and historyand philosophy of logic. He is the author of Philosophy of Mathematics andMathematical Practice in the Seventeenth Century (OUP 1996) and editor of FromBrouwer to Hilbert. The debate on the foundations of mathematics in the 1920s