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Joan Bertran-San-Millán, Stephen Pollard. Ernst Schröder on Algebra and Logic, Philosophia Mathematica, Volume 32, Issue 3, October 2024, Pages 379–384, https://doi.org/10.1093/philmat/nkae012
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Extract
It is widely accepted that Ernst Schröder’s works on logic have been understudied. The fact that virtually none of Schröder’s writings have been translated into English has certainly played a part in this neglect. Until recently, only Brady’s From Peirce to Skolem [2000] had introduced Schröder to English readership with translations of parts of the third volume of Vorlesungen über die Algebra der Logik [1895] (hereafter, Vorlesungen). In this respect, the publication of Pollard’s volume, containing English translations of the most prominent of Schröder’s early works, is a welcome and necessary contribution to the field.
After a brief Translator’s Introduction, Ernst Schröder on Algebra and Logic provides translations of Lehrbuch der Arithmetik und Algebra für Lehrer und Studirende [1873] (hereafter, Lehrbuch), Der Operationskreis des Logikkalkuls [1877a] (hereafter, Operationskreis), and ‘Note über den Operationskreis des Logikcalculs’ [1877b]. The Lehrbuch, as its title indicates, was conceived as a mathematics textbook, but also engages in philosophical reflection. It presents number theory as the main constituent of pure mathematics. The Operationskreis inaugurates Schröder’s focus on logic, and specifically on the algebra of logic: it is a short reformulation of Boolean logic. These works show clear and explicit influence from Grassmann’s Lehrbuch der Arithmetik für höhere Lehranstalten [1861], and the 1877 treatise from Boole’s An Investigation of the Laws of Thought [1854].1 Their historical relevance is probably overshadowed, however, by the monumental Vorlesungen. Nevertheless, Schröder’s Lehrbuch and Operationskreis also contain substantial contributions, as I will elaborate in what follows.
