Ernst Schroeder, On the Formal Elements of the Absolute Algebra

Ernst Schröder

On the Formal Elements of the Absolute Algebra

with German Parallel Text

A cura di Davide Bondoni

Collana: «LED Bibliotheca»
15,5 x 22 cm – pagg. 152 – 2012 – € 27,00
ISBN 978-88-7916-516-7

Questo libro è disponibile con download immediato anche in versione E-book

TABLE OF CONTENTS: ALGEBRA, WHAT ELSE?: 1. The Birth of a Masterwork - 2. Commutativity and Left- and Right-Division - 3. Algorithms, Algorithms, Algorithms - 4. Formalism - 5. A Fateful Choice - 6. Overview - 7. A Strange Document - 8. Acknowledgements - 9. Tools - Notes — ON THE FORMAL ELEMENTS OF THE ABSOLUTE ALGEBRA: §. 1. Character des zu behandelnden Problems. Character of the Problem in Issue - §. 2. Einschränkungen der Aufgabe. Restrictions of our Scope - §. 3. Die Fundamentalgleichungen für nur zwei Zahlen. Algorithmen. The Fundamental Equations for only Two Numbers. Algorithms - §. 4. Vertauschungsprincipien. Principles of Permutation - §. 5. Die Fundamentalgleichungen für drei Zahlen. Elementarcyklen und Gruppen. The Fundamental Equations for Three Numbers. Elementary Cycles and Groups - §. 6. Consequenzen der Algorithmen C1; C2; C3 für drei Zahlen. Consequences of the Algorithms C1; C2; C3 for Three Numbers - §. 7. Consequenzen von C0. Consequences of C0 - §. 8. Combination der Ci. Combination of the Ci - §. 9. Das Formelsystem O1 der ordinäre Algebra. The Formal System O1 of the Usual Algebra - §. 10. Untergeordnete Algorithmen von O1: Weitere ermittelte Tragweitezahlen. Subordinate Algorithms of O1: Further Sizes — FIGURES - Notes — APPENDIX - Notes — ILLUSTRATIONS - Bibliography - Index of the Main Concepts - Index of the Illustrations.

This book is the first worldwide English translation of Schröder’s «Über die formalen Elemente der absoluten Algebra» (1874), a text as epiphanic as unknown to the general non German reader. Occasioned like a simple support for the students of the Gymnasium in Baden-Baden, this text is indeed the pivot of all Schröder’s activity in mathematics and logic which culminates in a formal algebra of connections whose elements are spoiled of any sort of (semantic) meaning. As a matter of fact, Schröder’s theory of relations arose in the broader context to build up a mathematical and formal structure in which only the relations among the elements are to survive. Given the formal character of this structure, one can search for possible interpretations of it. As easily seen, we are not so far from a naive modern model theory. Furthermore, this booklet marks the passage in Schröder’s investigations from a purely mathematical engagement to a logical-mathematical one. From this point of view, the calculus of relations is only a possible interpretation of a more general discipline (a universal algebra) and not a topic in itself. Schröder was and remained until his death a pure mathematician who used logic as a temporary tool to dig in the concept of absolute algebra, his authentic vocation (as he himself admitted one year before dying).

Davide Bondoni is an Italian independent scholar in the field of logic and algebraic logic with a particular interest in the German mathematician Ernst Schröder. For LED Edizioni he has already authored La teoria delle relazioni nell’algebra della logica schröderiana (2007), and Parafrasi schröderiane (2010). His recent paper Structural Features in Ernst Schröder’s Work is aimed to define a possibile philosophy of mathematics underlying Schröder’s various investigations.

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