# Ernst Schröder on Algebra and Logic Rules for Linking All Our Operations

Ernst Schröder on Algebra and Logic : Rules for Linking All Our Operations [English translation of the fourth chapter of Ernst Schröder’s Lehrbuch der Arithmetik und Algebra für Lehrer und Studirende. In the first half of the chapter, Schröder lets his universally quantified variables range over the positive whole numbers and assigns his seven operations the properties they normally possess in this domain. He then identifies various conditions under which expressions featuring two or more operation-symbols are to be equated. He also offers a meticulous analysis of conventions governing the omission of parentheses. The second half of the chapter, is a contribution to formal algebra in which Schröder “investigates the laws of algebraic operations that apply to entirely general numbers in an unbounded domain making no further assumptions about their nature.” His main goal is to determine what follows from what: to distinguish “assumptions or premises as clearly as possible and investigate what each of them entails.” He further develops his class-algebra by allowing his operations to have classes as both inputs and outputs.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Ernst Schröder on Algebra and Logic Rules for Linking All Our Operations

Part of the Synthese Library Book Series (volume 465)
Editors: Pollard, Stephen
118 pages

Publisher
Springer International Publishing
© 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
171 –289
DOI
10.1007/978-3-031-05671-0_4
Publisher site
See Chapter on Publisher Site

### Abstract

[English translation of the fourth chapter of Ernst Schröder’s Lehrbuch der Arithmetik und Algebra für Lehrer und Studirende. In the first half of the chapter, Schröder lets his universally quantified variables range over the positive whole numbers and assigns his seven operations the properties they normally possess in this domain. He then identifies various conditions under which expressions featuring two or more operation-symbols are to be equated. He also offers a meticulous analysis of conventions governing the omission of parentheses. The second half of the chapter, is a contribution to formal algebra in which Schröder “investigates the laws of algebraic operations that apply to entirely general numbers in an unbounded domain making no further assumptions about their nature.” His main goal is to determine what follows from what: to distinguish “assumptions or premises as clearly as possible and investigate what each of them entails.” He further develops his class-algebra by allowing his operations to have classes as both inputs and outputs.]

Published: Apr 24, 2022