The Growth of Mathematical Knowledge

ISBN-13: 9789048153916 / Angielski / Miękka / 2010 / 416 str.

Emily Grosholz; Herbert Breger

Opis

This book draws its inspiration from Hilbert, Wittgenstein, Cavailles 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.

Recenzje

`The print and paper are of highly quality. Overall it is a rich and thought-provoking contribution to a relatively undeveloped area of research. The philosophy of the growth of mathematical knowledge has few canonical texts as yet. This book may become one.'
Philosophia Mathematica, 10:1 (2002)

Spis treści

Acknowledgments. Introduction. Notes on Contributors. Part I: The Question of Empiricism. The Role of Scientific Theory and Empirical Fact in the Growth of Mathematical Knowledge. 1. Knowledge of Functions in the Growth of Mathematical Knowledge; J. Hintikka. Huygens and the Pendulum: From Device to Mathematical Relation; M.S. Mahoney. 2. An Empiricist Philosophy of Mathematics and Its Implications for the History of Mathematics; D. Gillies. The Mathematization of Chance in the Middle of the 17th Century; I. Schneider. Mathematical Empiricism and the Mathematization of Chance: Comment on Gillies and Schneider; M. Liston. 3. The Partial Unification of Domains, Hybrids, and the Growth of Mathematical Knowledge; E. Grosholz. Hamilton-Jacobi Methods and Weierstrassian Field Theory in the Calculus of Variations; C. Fraser. 4. On Mathematical Explanation; P. Mancosu. Mathematics and the Reelaboration of Truths; F. de Gandt. 5. Penrose and Platonism; M. Steiner. On the Mathematics of Spilt Milk; M. Wilson. Part II: The Question of Formalism. The Role of Abstraction, Analysis, and Axiomatization in the Growth of Mathematical Knowledge. 1. The Growth of Mathematical Knowledge: An Open World View; C. Cellucci. Controversies about Numbers and Functions; D. Laugwitz. Epistemology, Ontology, and the Continuum; C. Posy. 2. Tacit Knowledge and Mathematical Progress; H. Breger. The Quadrature of Parabolic Segments 1635-1658: A Response to Herbert Breger; M.M. Muntersbjorn. Mathematical Progress: Ariadne's Thread; M. Liston. Voir-Dire in the Case of Mathematical Progress; C. Mclarty. 3. The Nature of Progress in Mathematics: The Significance of Analogy; H. Sinaceur. Analogy and the Growth of Mathematical Knowledge; E. Knobloch. 4. Evolution of the Modes of Systematization of Mathematical Knowledge; A. Barabashev. Geometry, the First Universal Language of Mathematics; I. Bashmakova, G.S. Smirnova. Part II: The Question of Progress. Criteria for and Characterizations of Progress in Mathematical Knowledge. 1. Mathematical Progress; P. Maddy. Some Remarks on Mathematical Progress from a Structuralist's Perspective; M.D. Resnik. 2. Scientific Progress and Changes in Hierarchies of Scientific Disciplines; V. Peckhaus. On the Progress of Mathematics; S. Demidov. Attractors of Mathematical Progress: The Complex Dynamics of Mathematical Research; K. Mainzer. On Some Determinants of Mathematical Progress; C. Thiel.