Ernst Schröder

Biography

Schröder learned mathematics with Heidelberg, Königsberg, and Zurich, at Hesse, Kirchhoff, and Franz Ernst Neumann. He taught a few years in a school, then with the Technische Hochschule Darmstadt in 1874. Two years later, it obtained a pulpit of mathematics in Polytechnische Schule of Karlsruhe, where it passed the remainder of its life. It was never married.

Works

The first work of bearing Schröder on the algebra and logic was undertaken without their author knowing the English logicians George Boole and Auguste De Morgan. It was based on work of Ohm, Hankel, Hermann Grassmann, and Robert Grassmann, resulting from the German traditional school in combinative algebra and algebraic Analyze (Peckhaus 1997:233 - 296). In 1873, Schröder discovered work of Boole and Morgan on logic. It will integrate into it important ideas due to Charles Sanders Peirce in particular the concepts of Subsomption (the equivalent of inclusion for the predicates) and of Quantification.

Schröder also contributed original shares to the Algèbre, the Set theory and the theory of the ordered units like the lattice or the ordinal numbers. With Georg Cantor, he discovered the theorem of Cantor-Bernstein-Schröder, although its demonstration of 1898 was imperfect. Felix Bernstein (1878-1956) corrected it in its thesis.

In its work Der Operationskreis of Logikkalküls (operations of logical calculation) appeared in 1877, Schröder exposes in a concise way the ideas of Boole on the algebra and logic. This book helped to introduce the work of Boole in continental Europe. The influence of Grassmann, in particular of little known the Formenlehre of Robert, is clear. John Venn and Ladd-Franklin Christine quotes this court delivers of Schröder, and Charles Peirce used it as reference for his teaching to the Université Johns-Hopkins.

Chief of work of Schröder, the Vorlesungen über die Algebra der Logik , was published in three volumes between 1890 and 1905, on account of author. Volume 3 counts two parts, the second published on a purely posthumous basis, and published by Eugen Müller. The Vorlesungen constituted a complete sum on the state of “algebraic” logic (we would say “symbolic system today”) at the end of the 19th century. The work had a considerable influence on the emergence of mathematical logic at the 20th century.

Schröder qualified its objective thus:

to make logic a calculation to allow to handle the concepts concerned with precision, and then, thanks to the emancipation of the routine chains of the natural Language, to also remove from its “stereotypes” all the fertile fields of the Philosophy. This must prepare the way with a universal scientific language which would be distinguished from the whole to the whole of a universal Langue with the Volapük, but would resemble rather a language of signs that to a language of sons.

Schröder, by popularizing work of Peirce on the quantification, had on the first developments of the Calcul of the predicates an influence at least as large as those of Frege and Peano. The concept of relation of the Principia Mathematica (1908) must much with the Vorselungen . The work is quoted besides there in the foreword, like in that of the preliminary work of Bertrand Russell, the Principles off mathematics (1903).

Frege (1960), nevertheless, rejected the work of Schröder, and admiration for the pioneer role of Frege dominated the historical debate. However, comparing Frege with Schröder and Charles Sanders Peirce, Hilary Putnam writes in 1982:

When I started to study the Histoire of logic, the first thing that I made was to look at the Vorlesungen über die Algebra der Logik of Schröder, the third volume relates to the logic of the relations ( Algebra und Logik der Relative , 1895). At least three volumes became immediately the advanced text of logic most known, and includes/understands what any mathematician interested by the study of logic was to know, or to be informed, in the years 1890.

While, to my knowledge, nobody, except for Frege, published an article in the notation of Frege, of many famous logicians adopted the notation of Peirce-Schröder, and of famous results and systems were published in this one. Löwenheim stated and proved the theorem of Löwenheim (rejected and improved then by Thoralf Skolem, which left its name, associated with that with Löwenheim, with the theorem) in the notation of Peirce. Actually, there is not a reference in the article of Löwenheim to other logic only that of Peirce. To quote another example, Zermelo presented its Axiome S for the set theory in the notation of Peirce-Schröder, and not, as one could have expected it, in that of Russell-Whitehead.

These simple facts (that whoever can easily check) can be summarized as follows: Frege discovered certainly the quantifiers the first (four years before O.H. Mitchell, according to the date of the publication, which are all which one has to my knowledge). But Leif Ericsson probably discovered the America " the premier" (excuse me not to count the natives of America, who of course really discovered it " premiers"). If the effective discoverer, from the European point of view, is Christophe Colomb, it is because he discovered it and that it remained it (by Europeans, I understand), so that it was known (Europeans). Frege has indeed " découvert" quantifiers in the sense that it is founded to claim the priority; but Peirce and its students discovered it in the effective direction. The fact is that until Russell recognized what it had made, Frege was relatively obscure, and it was Peirce which seems to have been known of the community of the whole logicians of the world. How much among those which think that " Frege invented logique" , are with the current of these facts?

Random links: