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Analysis and Synthesis in Mathematics : History and Philosophy - Marco Panza

Analysis and Synthesis in Mathematics

History and Philosophy

By: Marco Panza (Editor), M. Otte (Editor)

Paperback

Published: 30th November 2001
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Time and again, philosophy, in trying to untangle the issues surrounding the an- alytic-synthetic distinction, has doubted that such a distinction can significantly be drawn at all. We think, in face of the varied and age-old discussions on it, that such reflections amount only to one more documentation of the tenacity of the problems behind this distinction. We could even be justified in promoting the thesis that this distinction refers to the complex relationship between the universe of meanings and the universe of objects and thus concerns each domain of human thinking where a form of objectivity is pursued. If one accepts such a thesis, one will find it very natural that this distinction has so frequently occurred in the history of mathematics and in philosophical discussions about mathematics. Since Plato, we may encounter quite a number of interpretations of the ideas of analysis and synthesis, which are related in one sense or other with mathematical thought. Mathematicians of all ages have ap- pealed to them in order to distinguish different forms and styles in their argumen- tation and expositions. Philosophers have referred to them for clarification of the specific character of mathematics in its relations to knowledge in general. In the present volume various instances of the analytic-synthetic distinction are discussed in relation to the history and philosophy of mathematics, and some new perspectives about possible interpretations and consequences are suggested.

`... is to be recommended to anyone interested in the history and philosophy of mathematics... historians of modern mathematics and even historians of modern science in general will greatly enjoy some of the excellent articles in its historial section.'
ISIS, 91:1 (2000)

Introduction
History
The Analytical Method in Descartes' GFomFtrie
Arcanum artis inveniendi: Leibniz and Analysis
The Background to and Early Emergence of Euler's Analysis
Jacob Bernoulli on Analysis, Synthesis, and the Law of Large Numbers
Mathematical Analysis and Analytical Science
The Analysis of the Synthesis of the Analysis ... Two Moments of a Chiasmus: ViTte and Fourier
Styles of Argumentation in Late 19th Century
Philosophy
From backward Reduction to Configurational Analysis
Analysis, Hermeneutics, Mathematics
Science within Reason: Is There a Crisis of the Modern Sciences?
Mathematics as an Activity and the Analytic-Synthetic Distinction
Mathematical Acts of Reasoning as Synthetic a priori
Analysis and Synthesis in Mathematics from the Perspective of
History and Philosophy
Classical Sources for the Concepts of Analysis and Synthesis
Bibliography
Index of Names
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9781402002557
ISBN-10: 1402002556
Series: Boston Studies in the Philosophy of Science (Paperback)
Audience: General
Format: Paperback
Language: English
Number Of Pages: 450
Published: 30th November 2001
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.62 x 15.34  x 2.67
Weight (kg): 0.66
Edition Type: New edition