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Ernst Schröder on Algebra and Logic Numbers

Ernst Schröder on Algebra and Logic : Numbers [English translation of the first chapter of Ernst Schröder’s Lehrbuch der Arithmetik und Algebra für Lehrer und Studirende. Schröder discusses the nature of numbers in general and of the natural numbers in particular, treating numbers as “arbitrary signs created by us for a wide variety of purposes.” His notion that natural numbers “serve as measures of the numerousness of things” leads him to discuss one-to-one correspondences at some length. He also explores the fundamental properties of equality, inequality, and logical subordination (the relation that holds, for example, between a species and its genus). Schröder’s interest in logical topics is evident in his reflections on “general number-signs” or, as we would now say, universally quantified variables.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Ernst Schröder on Algebra and Logic Numbers

Part of the Synthese Library Book Series (volume 465)
Editors: Pollard, Stephen
Pollard, Stephen
Ernst Schröder on Algebra and Logic — Apr 24, 2022
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Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
ISBN
978-3-031-05670-3
Pages
1 –46
DOI
10.1007/978-3-031-05671-0_1
Publisher site
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Abstract

[English translation of the first chapter of Ernst Schröder’s Lehrbuch der Arithmetik und Algebra für Lehrer und Studirende. Schröder discusses the nature of numbers in general and of the natural numbers in particular, treating numbers as “arbitrary signs created by us for a wide variety of purposes.” His notion that natural numbers “serve as measures of the numerousness of things” leads him to discuss one-to-one correspondences at some length. He also explores the fundamental properties of equality, inequality, and logical subordination (the relation that holds, for example, between a species and its genus). Schröder’s interest in logical topics is evident in his reflections on “general number-signs” or, as we would now say, universally quantified variables.]

Published: Apr 24, 2022

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