Polkinghorne - Meaning in Mathematics

Meaning in Mathematics

Edited by
John Polkinghorne

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Oxford University Press 2011

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First published 2011

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Library of Congress Control Number: 2011920646

Typeset by SPI Publisher Services, Pondicherry, India
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ISBN 9780199605057

1 3 5 7 9 10 8 6 4 2

In grateful memory of Peter Lipton, scholar and friend.

John Polkinghorne

Timothy Gowers

Gideon Rosen

Marcus du Sautoy

Mark Steiner

John Polkinghorne

Mary Leng

John Polkinghorne

Roger Penrose

Michael Detlefsen

Peter Lipton

Stewart Shapiro

Mary Leng

Michael Detlefsen

Michael Detlefsen

John Polkinghorne

Stewart Shapiro

Gideon Rosen

Stewart Shapiro

Gideon Rosen

Timothy Gowers

Mark Steiner

Marcus du Sautoy

Editor: John Charlton Polkinghorne, KBE, FRS, the former president of Queens College, Cambridge, and the winner of the 2002 Templeton Prize, has been a leading figure in the dialogue of science and religion for more than two decades. He resigned his professorship of mathematical physics at Cambridge University to take up a new vocation in mid-life and was ordained a priest in the Church of England in 1982. A fellow of the Royal Society, he was knighted by Queen Elizabeth II in 1997. In addition to an extensive body of writing on theoretical elementary particle physics, including Quantum Theory: A Very Short Introduction (2002), he is the editor or co-editor of four books, the coauthor (with Michael Welker) of Faith in the Living God: A Dialogue (2001), and the author of nineteen other books on the interrelationship of science and theology, including Belief in God in an Age of Science (1998), a volume composed of his Terry Lectures at Yale University, Science and Theology (1998), Faith, Science and Understanding (2000), Traffic in Truth: Exchanges between Theology and Science (2001), The God of Hope and the End of the World (2002), Living with Hope (2003), Science and the Trinity: The Christian Encounter with Reality (2004), Exploring Reality: The Intertwining of Science and Religion (2005), Quantum Physics and Theology: An Unexpected Kinship (2007), From Physicist to Priest (2007), Theology in the Context of Science (2008), and Questions of Truth: Fifty-one Responses to Questions about God, Science and Belief (2008) with Nicholas Beale

Michael Detlefsen is McMahon-Hank Professor of Philosophy at the University of Notre Dame and Distinguished Invited Professor of Philosophy at both the University of Paris 7-Diderot and the University of Nancy 2. He has held a senior chaire dexcellence of the ANR in France since 2007. His chief scholarly interests are in the history and philosophy of mathematics and logic. His current projects include a book on Gdels incompleteness theorems with Timothy McCarthy and various other projects concerning ideals of proof in mathematics.

Marcus du Sautoy is professor of mathematics and Simonyi Professor for the Public Understanding of Science at Oxford University, where he is a fellow of New College. His academic work mainly concerns group theory and number theory, and he is widely known for popularizing mathematics. He was awarded the Berwick Prize of the London Mathematical Society in 2001 and the Faraday Prize by the Royal Society in 2009. He has presented numerous series for BBC TV and radio and is the author of three books, The Music of the Primes (2003), Finding Moonshine (2007), and The Num8er My5teries: A Mathematical Odyssey through Everyday Life (2010), for general audiences.

Timothy Gowers, FRS, is Rouse Ball Professor of Mathematics at Cambridge University and a fellow of Trinity College, Cambridge. He received a Fields Medal in 1998 for his research connecting the fields of functional analysis and combinatorics. Earlier, he was awarded the Junior Whitehead Prize by the London Mathematical Society and the European Mathematical Society Prize. A fellow of the Royal Society, he is the author of Mathematics: A Very Short Introduction (2002) and the main editor of The Princeton Companion to Mathematics (2008). Launched in 2009, his Polymath Project uses the comment functionality of his blog to produce mathematics collaboratively.

Mary Leng is a lecturer in philosophy at the University of Liverpool. Her research focus is the philosophy of mathematics, with particular reference to issues raised by the applicability of mathematics in empirical science. Dr. Leng has been a visiting fellow in the Department of Logic and Philosophy of Science at the University of California at Irvine, and after a postdoctoral fellowship in the humanities at the University of Toronto, she held a research fellowship at St. Johns College, Cambridge, for four years, as well as a visiting junior fellowship at the Peter Wall Institute for Advanced Studies at the University of British Columbia. She is the co-editor (with Alexander Paseau and Michael Potter) of Mathematical Knowledge (2007), and the author of Mathematics and Reality (2010), both of which were published by Oxford University Press.

Peter Lipton was the Hans Rausing Professor and chair of the History and Philosophy of Science at Cambridge University until his death in 2008. He also had been a fellow of Kings College, Cambridge. Much of his work concerned explication and inference in science, but his interests extended broadly across many of the major areas of philosophy. A fellow of the Academy of Medical Sciences, he had been consulting editor of