David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Kluwer Academic Publishers (2000)
This book draws its inspiration from Hilbert, Wittgenstein, Cavaillès and Lakatos and is designed to reconfigure contemporary philosophy of mathematics by making the growth of knowledge rather than its foundations central to the study of mathematical rationality, and by analyzing the notion of growth in historical as well as logical terms. Not a mere compendium of opinions, it is organised in dialogical forms, with each philosophical thesis answered by one or more historical case studies designed to support, complicate or question it. The first part of the book examines the role of scientific theory and empirical fact in the growth of mathematical knowledge. The second examines the role of abstraction, analysis and axiomatization. The third raises the question of whether the growth of mathematical knowledge constitutes progress, and how progress may be understood. Readership: Students and scholars concerned with the history and philosophy of mathematics and the formal sciences.
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Craig Fraser, Hamilton-Jacobi Methods and Weierstrassian Field Theory in the Calculus of Variations: A Study in the Interaction of Mathematics and Physics.
Donald Gillies, An Empiricist Philosophy of Mathematics and its Implications for the History of Mathematics.
Emily R. Grosholz, The Partial Unification of Domains, Hybrids, and the Growth of Mathematical Knowledge.
Michael Liston, Mathematical Empiricism and the Mathematization of Chance: Comment on Gillies and Schneider.
Madeline M. Muntersbjorn, The Quadrature of Parabolic Segments 1635–1658: A Response to Herbert Breger.
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Brendan Larvor (2012). How to Think About Informal Proofs. Synthese 187 (2):715-730.
Jessica Carter (2013). Handling Mathematical Objects: Representations and Context. Synthese 190 (17):3983-3999.
Mark Zelcer (2013). Against Mathematical Explanation. Journal for General Philosophy of Science 44 (1):173-192.
Brendan Larvor (2008). What Can the Philosophy of Mathematics Learn From the History of Mathematics? Erkenntnis 68 (3):393 - 407.
Michèle Friend (2010). Confronting Ideals of Proof with the Ways of Proving of the Research Mathematician. Studia Logica 96 (2):273-288.
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