Growth of Mathematical Knowledge

Inbunden, Engelska, 2000

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Beskrivning

Inspired by Hilbert, Wittgenstein, Cavailles and Lakatos, this work aims 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. It is organized 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.

Produktinformation

Utgivningsdatum:2000-01-31
Mått:155 x 235 x 30 mm
Vikt:875 g
Format:Inbunden
Språk:Engelska
Serie:Synthese Library
Antal sidor:416
Upplaga:2000
Förlag:Kluwer Academic Publishers
ISBN:9780792361510

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Recensioner i media

'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)

Innehållsförteckning

Knowledge of Functions in the Growth of Mathematical Knowledge.- Huygens and the Pendulum: From Device to Mathematical Relation.- An Empiricist Philosophy of Mathematics and Its Implications for the History of Mathematics.- The Mathematization of Chance in the Middle of the 17th Century.- Mathematical Empiricism and the Mathematization of Chance: Comment on Gillies and Schneider.- The Partial Unification of Domains, Hybrids, and the Growth of Mathematical Knowledge.- Hamilton-Jacobi Methods and Weierstrassian Field Theory in the Calculus of Variations.- On Mathematical Explanation.- Mathematics and the Reelaboration of Truths.- Penrose and Platonism.- On the Mathematics of Spilt Milk.- The Growth of Mathematical Knowledge: An Open World View.- Controversies about Numbers and Functions.- Epistemology, Ontology, and the Continuum.- Tacit Knowledge and Mathematical Progress.- The Quadrature of Parabolic Segments 1635–1658: A Response to Herbert Breger.- Mathematical Progress: Ariadne’s Thread.- Voir-Dire in the Case of Mathematical Progress.- The Nature of Progress in Mathematics: the Significance of Analogy.- Analogy and the Growth of Mathematical Knowledge.- Evolution of the Modes of Systematization of Mathematical Knowledge.- Geometry, the First Universal Language of Mathematics.- Mathematical Progress.- Some Remarks on Mathematical Progress from a Structuralist’s Perspective.- Scientific Progress and Changes in Hierarchies of Scientific Disciplines.- On the Progress of Mathematics.- Attractors of Mathematical Progress: the Complex Dynamics of Mathematical Research.- On Some Determinants of Mathematical Progress.