, Volume 60, Issue 1, pp 1-121
Date: 26 Oct 2005

The Rise of non-Archimedean Mathematics and the Roots of a Misconception I: The Emergence of non-Archimedean Systems of Magnitudes

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Communicated by J. J. Gray
Portions of this work were presented at the Pittsburgh Center for Philosophy of Science in November 1998 as part of a conference on Philosophical Problems in the Historiography of Science jointly sponsored by the Center and the Division of Logic, Methodology, and Philosophy of Science of the International Union of History and Philosophy of Science, at Northwestern University in September 1999 as part of the Northwestern University History and Philosophy of Science Seminar Series, and at the International History and Philosophy of Mathematics Meeting in Seville, Spain in September 2003. We are very grateful to the various organizers for affording us those opportunities. Thanks are owed also to the National Science Foundation for supporting the early development of this research (Scholars Award #SBR 9602154). We also wish to express our gratitude to Scott Carson and Kathleen Evans-Romaine, who from time to time served as knowledgeable and helpful sounding boards for our translations of the German, French and Italian texts. Finally, we are especially grateful to Jeremy Gray and Henk Bos, each of whom provided valuable suggestions for improving the exposition.
Throughout the text we follow the convention of only providing the original German, French and Italian texts in the cases of translations of substantial quotations.
The companion to the present paper referred to in the text is a continuation of the present work that will focus on the emergence of non-Archimedean geometry. It is the author's intention to submit the latter paper for publication in the Archive in the not too distant future.