The Growth of Mathematical Knowledge

Abstract

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.