Part III: The original writings

A result in the small is worth more than no overview at large.

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Jan von Plato

Saved from the Cellar

Gerhard Gentzen’s Shorthand Notes on Logic and Foundations of Mathematics

Sources and Studies in the History of Mathematics and Physical Sciences

Managing Editor Jed Z. Buchwald Associate Editors J.L. Berggren J. L¨utzen J. Renn Advisory Board C. Fraser T. Sauer A. Shapiro

More information about this series at http://www.springer.com/series/4142

Sources and Studies in the History of Mathematics and Physical Sciences was inaugurated as two series in 1975 with the publication in Studies of Otto Neugebauer’s seminal threevolume History of Ancient Mathematical Astronomy, which remains the central history of the subject. This publication was followed the next year in Sources by Gerald Toomer’s transcription, translation (from the Arabic), and commentary of Diocles on Burning Mirrors. The two series were eventually amalgamated under a single editorial board led originally by Martin Klein (d. 2009) and Gerald Toomer, respectively two of the foremost historians of modern and ancient physical science. The goal of the joint series, as of its two predecessors, is to publish probing histories and thorough editions of technical developments in mathematics and physics, broadly construed. Its scope covers all relevant work from pre-classical antiquity through the last century, ranging from Babylonian mathematics to the scientific correspondence of H. A. Lorentz. Books in this series will interest scholars in the history of mathematics and physics, mathematicians, physicists, engineers, and anyone who seeks to understand the historical underpinnings of the modern physical sciences.

Jan von Plato

Saved from the Cellar Gerhard Gentzen’s Shorthand Notes on Logic and Foundations of Mathematics

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Jan von Plato Department of Philosophy University of Helsinki Helsinki, Finland

ISSN 2196-8810 ISSN 2196-8829 (electronic) Sources and Studies in the History of Mathematics and Physical Sciences ISBN 978-3-319-42119-3 ISBN 978-3-319-42120-9 (eBook) DOI 10.1007/978-3-319-42120-9 Library of Congress Control Number: 2016963638 © Springer International Publishing Switzerland 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publ