Ernst Schröder

For the actor, see Ernst Schröder (actor).

Ernst Schröder (25 November 1841, Mannheim, Baden, Germany – 16 June 1902, Karlsruhe, Germany) was a German mathematician mainly known for his work on algebraic logic. He is a major figure in the history of mathematical logic (a term he may have invented), by virtue of summarizing and extending the work of George Boole, Augustus De Morgan, Hugh MacColl, and especially Charles Peirce. He is best known for his monumental Vorlesungen über die Algebra der Logik (Lectures on the algebra of logic), in 3 volumes, which prepared the way for the emergence of mathematical logic as a separate discipline in the twentieth century by systematizing the various systems of formal logic of the day.

Life[link]

Schröder learned mathematics at Heidelberg, Königsberg, and Zürich, under Hesse, Kirchhoff, and Franz Neumann. After teaching school for a few years, he moved to the Technische Hochschule Darmstadt in 1874. Two years later, he took up a chair in mathematics at the Polytechnische Schule in Karlsruhe, where he spent the remainder of his life. He never married.

Work[link]

Schröder's early work on formal algebra and logic was written in ignorance of the British logicians George Boole and Augustus De Morgan. Instead, his sources were texts by Ohm, Hankel, Hermann Grassmann, and Robert Grassmann (Peckhaus 1997: 233–296). In 1873, Schröder learned of Boole's and De Morgan's work on logic. To their work he subsequently added several important concepts due to Charles Sanders Peirce, including subsumption and quantification.

Schröder also made original contributions to algebra, set theory, lattice theory, ordered sets and ordinal numbers. Along with Georg Cantor, he codiscovered the Cantor–Bernstein–Schröder theorem, although the proof in Schröder (1898) is flawed. Felix Bernstein (1878–1956) subsequently corrected the proof as part of his Ph.D. dissertation.

title page of first printing of "Über die formalen Elemente der absoluten Algebra"

Schröder (1877) was a concise exposition of Boole's ideas on algebra and logic, which did much to introduce Boole's work to continental readers. The influence of the Grassmanns, especially Robert's little-known Formenlehre, is clear. Unlike Boole, Schröder fully appreciated duality. John Venn and Christine Ladd-Franklin both warmly cited this short book of Schröder's, and Charles Sanders Peirce used it as a text while teaching at Johns Hopkins University.

Schröder's masterwork, his Vorlesungen über die Algebra der Logik, was published in three volumes between 1890 and 1905, at the author's expense. Vol. 2 is in two parts, the second published posthumously, edited by Eugen Müller. The Vorlesungen was a comprehensive and scholarly survey of "algebraic" (today we would say "symbolic") logic up to the end of the 19th century, one that had a considerable influence on the emergence of mathematical logic in the 20th century. The Vorlesungen is a prolix affair, only a small part of which has been translated into English. That part, along with an extended discussion of the entire Vorlesungen, is in Brady (2000). Also see Grattan-Guinness (2000: 159–76).

Schröder said his aim was:

Influence[link]

Schröder's influence on the early development of the predicate calculus, mainly by popularising C. S. Peirce's work on quantification, is at least as great as that of Frege or Peano. For an example of the influence of Schröder's work on English-speaking logicians of the early 20th century, see Clarence Irving Lewis (1918). The relational concepts that pervade Principia Mathematica are very much owed to the Vorlesungen, cited in Principia's Preface and in Bertrand Russell's Principles of Mathematics.

Frege (1960) dismissed Schröder's work, and admiration for Frege's pioneering role has dominated subsequent historical discussion. Contrasting Frege with Schröder and C. S. Peirce, however, Hilary Putnam (1982) writes:

See also[link]

• Schröder's equation

References[link]

• Primary
  • Schröder, E., 1877. Der Operationskreis des Logikkalküls. Leipzig: B.G. Teubner.
  • Schröder, E., 1890–1905. Vorlesungen über die Algebra der Logik, 3 vols. Leipzig: B.G. Teubner. Reprints: 1966, Chelsea; 2000, Thoemmes Press.
  • Schröder, E., 1898. "Über zwei Definitionen der Endlichkeit und G. Cantor'sche Sätze ", Abh. Kaiserl. Leop.-Car. Akad. Naturf 71: 301–362.
• Both Primary and Secondary
  • Brady, Geraldine, 2000. From Peirce to Skolem. North Holland. Includes an English translation of parts of the Vorlesungen.
• Secondary
  • Anellis, I. H., 1990–91, "Schröder Materials at the Russell Archives," Modern Logic 1: 237–247.
  • Dipert, R. R., 1990/91. "The life and work of Ernst Schröder," Modern Logic 1: 117–139.
  • Frege, G., 1960, "A critical elucidation of some points in E. Schröder's Vorlesungen über die Algebra der Logik", translated by Geach, in Geach & Black, Translations from the philosophical writings of Gottlob Frege. Blackwell: 86–106. Original: 1895, Archiv fur systematische Philosophie 1: 433–456.
  • Ivor Grattan-Guinness, 2000. The Search for Mathematical Roots 1870–1940. Princeton University Press.
  • Clarence Irving Lewis, 1960 (1918). A Survey of Symbolic Logic. Dover.
  • Peckhaus, V., 1997. Logik, Mathesis universalis und allgemeine Wissenschaft. Leibniz und die Wiederentdeckung der formalen Logik im 19. Jahrhundert. Akademie-Verlag.
  • Peckhaus, V., 1999, "19th Century Logic between Philosophy and Mathematics," Bulletin of Symbolic Logic 5: 433–450. Reprinted in Glen van Brummelen and Michael Kinyon, eds., 2005. Mathematics and the Historian's Craft. The Kenneth O. May Lectures. Springer: 203–220. Online here or here.
  • Peckhaus, V., 2004. "Schröder's Logic" in Gabbay, Dov M., and John Woods, eds., Handbook of the History of Logic. Vol. 3: The Rise of Modern Logic: From Leibniz to Frege. North Holland: 557–609.
  • Hilary Putnam, 1982, "Peirce the Logician," Historia Mathematica 9: 290–301. Reprinted in his 1990 Realism with a Human Face. Harvard University Press: 252–260. Online fragment.
  • Thiel, C., 1981. "A portrait, or, how to tell Frege from Schröder," History and Philosophy of Logic 2: 21–23.

External links[link]

• http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/Schrdr.htm (requires login, unprovided)
• O'Connor, John J.; Robertson, Edmund F., "Ernst Schröder", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Schroder.html .
• Ernst Schröder at the Mathematics Genealogy Project

Klaus Ernst in August 2005

Klaus Ernst (born 1 November 1954 in Munich) is a left-wing German politician and was a leading member of the Labour and Social Justice Party and now The Left. The certified political economist has served as a member of The Left in the Bundestag since 2005, and as of 2010 has been co-chairing the party together with Gesine Lötzsch.

At the age of 15 he left his home and school because of his violent father. In 1970 he found work as an electronics technician and was elected youth representative and member of the works council. In 1972 he became a member of the German Metalworkers' Union and in 1974 he took the chair of regional trade unions youth organization in Munich (until 1979) and became a partymember of the Social Democratic Party of Germany. From 1979 to 1984 he studied political economy at the University of Hamburg.

After his studies he became a trade union secretary in Stuttgart, responsible for organization, educational work and social plans. In 1995 Ernst was elected plenipotentiary of the IG Metall in Schweinfurt.

He took objection to the Agenda 2010, which he considered anti-social. Instead he pleaded for the establishment of a political alliance, an electoral alternative with regard to the German federal election in 2005. In the summer of 2004 the party executive decided his expulsion from the Social Democratic Party (SPD).

Ernst became chairman of the association "Wahlalternative Arbeit und soziale Gerechtigkeit e. V." which had been founded on 3 July 2004. Later he became leader of the new founded Electoral Alternative for Labor and Social Justice, which emerged from the association.

External links[link]

Media related to Klaus Ernst at Wikimedia Commons

• Website from Klaus Ernst
• Website about Klaus Ernst by IG Metall

Title page of Sonatinae, the 1692 collection which contains Albertini's only surviving music

Ignazio Albertini (Albertino) (ca. 1644 – 22 September 1685) was an Italian Baroque violinist and composer.

Very little is known about Albertini's life. He may have been born in Milan, but first surfaces in Vienna, in a letter exchange between the famous violinist Johann Heinrich Schmelzer of the Viennese court and Karl II von Liechtenstein-Kastelkorn, Prince-Bishop of Olomouc. Apparently, Albertini was guilty of some sort of misconduct, but both Schmelzer and the Prince-Bishop express their high opinion of him as a musician. The letter exchange dates from September 1671, so by that time Albertini was in Vienna; how he got there and what positions he occupied is unknown. That he was introduced to the Prince-Bishop, a well-known collector of music, and knew Schmelzer, one of the most important musicians at the court, seems to indicate that Albertini was much respected in Vienna. Nothing is known about his career, except that at some point he entered the service of Eleanor Gonzaga, widow of Ferdinand III, as chamber musician, and held that position until his death, which occurred in Vienna on 22 September 1685 when Albertini was murdered. The circumstances of the murder (Albertini was stabbed to death) are unknown.

As a composer Albertini is known by a single collection of music, the twelve Sonatinae (sonatas for violin and basso continuo) posthumously published in Vienna and in Frankfurt in 1692. The collection was prepared for publication by Albertini himself, but he did not live to see it printed, possibly because of the high cost of the copperplate engraving process. Albertini's sonatas are multi-sectional pieces, very varied in content and structure, and all of the highest quality. Some idea of the rich variety of forms found in the Sonatinae may be gleaned from the following examples: Sonata IX is a passacaglia in which the main theme is presented as a canon at the fifth in the first and the last sections; and statements of the ostinato sometimes overlap with formal sections of the sonata. Sonata XII, the last in the cycle, consists entirely of imitative movements, unlike other sonatas, in which imitative movements are either absent or are surrounded by free sections, such as slow lyrical arias, toccata-like movements with rapid passagework over sustained bass notes, etc. Albertini's sonatas are very demanding technically, with frequent instances of difficult fast passages, leaps, sudden changes of register and, particularly in the last sonata, double stopping.

Apart from the Sonatinae, two works are known by name from catalogues: Sonata hyllaris ex C à 10 (from a 1699 inventory) and a suite of 7 pieces à 4.

References[link]

• Antonicek, Theophil. "Bernardo Storace", Grove Music Online, ed. L. Macy (accessed 11 October 2006), grovemusic.com (subscription access).
• Drescher, Thomas. Liner notes to: Ignazio Albertini: Sonatas For Violin & Continuo. Performed by Héléne Schmitt (violin), Jörg-Andreas Bötticher (harpsichord & organ), Karl-Ernst Schröder (theorbo) and David Sinclair (violine). Alpha-028