:''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

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

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.

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

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

Schröder's equation

References

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

http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/Schrdr.htm (requires login, unprovided)

Category:1841 births Category:1902 deaths Category:19th-century mathematicians Category:German mathematicians Category:Logicians Category:People from Mannheim Category:People from the Grand Duchy of Baden

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Andreas Scholl (born 10 November 1967) is a German countertenor, a male classical singer in the alto vocal range. He specialises in Baroque music. His range is the same as that of the celebrated 18th century alto castrato, Senesino, for whom Handel wrote his greatest alto roles. ''Fanfare Magazine'' says: "There are more excellent countertenors before the public today than ever before, but one stands out above all others, as Caruso among tenors a century ago: Andreas Scholl". In 2005, Scholl became the first countertenor (and the first German) to appear as a solo performer at ''The Last Night of the Proms'' in London.

Childhood

Scholl was born on 10 November 1967 in Eltville, Germany, and grew up in neighboring Kiedrich. All of his family members were singers. He was enrolled at the age of seven into the Kiedricher Chorbuben (Kiedrich Choir-Boys) — which was first documented in 1333 as "a schola of men assisting the priests on all Sundays, singing the Gregorian chant." At age 13, Andreas Scholl sang the second boy (his sister Elisabeth sang the first boy) in Mozart's ''Die Zauberflöte'' at the Hessisches Staatstheater Wiesbaden. That same year, he was one of 20,000 choristers from all over the world gathered in Rome for a festival where Scholl was chosen to sing solo at Mass on 4 January 1981 and met Pope John Paul II. Along with his fellow choristers, Andreas Scholl was an extra in the film ''The Name of the Rose'', playing a young monk standing alongside Sean Connery in scenes shot at Eberbach Abbey, near Kiedrich.

Musical education

Scholl was 17 when the extent of his ability was recognized by the ''Chorbuben's'' voice coach from the Darmstadt Music Academy. He then sang for the tenor/countertenor Herbert Klein, who advised him that there were only two places he should study: either in London or at the early music conservatoire in Basel, the Schola Cantorum Basiliensis. Since an uncle had introduced Scholl to the voices of Paul Esswood and James Bowman, the leading European countertenors of the day, Scholl chose Bowman as a role model. Scholl sent a demo tape to René Jacobs to evaluate his talent. This resulted in Jacobs inviting Scholl to visit the Schola Cantorum Basiliensis. However, Scholl had no first degree. Although the Schola Cantorum Basiliensis only offered post-graduate courses, Scholl was subsequently offered admission on the strength and quality of his voice after singing a Schubert song for the admissions board — which included René Jacobs.

At the Schola, Andreas Scholl's teacher was Richard Levitt, followed by Jacobs in his second year. Violinist Chiara Banchini and soprano Emma Kirkby were major influences, as Scholl began to specialise in the music of the Baroque. Scholl additionally studied with soprano Evelyn Tubb and lutenist Anthony Rooley. In addition to the Diploma of Ancient Music, for which his external examiner was James Bowman, Andreas Scholl garnered prizes from the Council of Europe and the Foundation Claude Nicolas Ledoux, and awards from Switzerland's Association Migros and Ernst Göhner Foundation.

Andreas Scholl has been teaching interpretation in the Schola Cantorum Basiliensis, succeeding his own teacher, Richard Levitt, and is in much demand for master classes.

Early performances

In 1988 Scholl performed Bach's ''Christmas Oratorio'' in Rüdesheim. In 1991 he appeared in Bach's ''St John Passion'', conducted by Philippe Herreweghe in Antwerp. In 1993, Scholl stood in for René Jacobs at Jacobs' request at the Théâtre Grévin in Paris, causing a sensation. This performance of Bach’s ''Johannespassion'' was broadcast on Good Friday to a radio audience which included William Christie. Shortly thereafter, Christie and Scholl met on a train. The 1994 recording of Handel's ''Messiah'' with Les Arts Florissants resulted directly from this meeting.

Scholl performed Bach's ''Mass in B minor'' in 1995, conducted by Jacobs, and sang Purcell on a tour in France. In 1998 Scholl and his sister performed in Bach's ''St Matthew Passion'', with Max Ciolek as the Evangelist and Max van Egmond as the Vox Christi, in St. Martin, Idstein. Scholl made his debut on the opera stage in Handel's ''Rodelinda'' at the Glynde­bourne Festival and performed the title role of ''Solomon'' at The Proms. He gave recitals in Wigmore Hall and at the Brighton Festival.

Recordings

The bulk of Scholl's recording career has been with Harmonia Mundi and Decca. By 1998 his CDs dominated Harmonia Mundi's hit list at numbers one, three, four, five and ten, and they are still among Harmonia Mundi's best sellers. His discography amounts to more than sixty CDs, all but two being music of the European Baroque or Renaissance. Recordings in which he has collaborated, including all but one of his solo recordings, have won awards. His personal accolades include the Diapason d'Or, multiple Gramophone Awards, 10 de Repertoire, ffff Telerama and Choc du Mond de la Musique, the ECHO award and Prix de l'Union de la Presse Musicale Belge. In an extremely rare departure from its normally austere approach, ''Fanfare'' magazine described his recording of Dowland's ''A Musicall Banquet'' as 'perfect'. The recording of Bach's ''St John Passion'' conducted by Philippe Herreweghe on which Andreas Scholl sings was nominated for a Cannes Classical Award in 2003. He was Germany's Kultur Radio Artist of the Year in 1998. He has revealed, to German audiences in particular, some little-known masterworks of German Baroque composers and has thereby made a significant contribution to the modern rediscovery of the Baroque repertoire. His 2001 album of folk songs, ''Wayfaring Stranger'', was a personal project, well-received by the CD-buying public but not universally acclaimed by his fellow musicians, some of whom regarded it as an inappropriate departure.

Collaborations

Andreas Scholl has worked with the majority of contemporary Baroque specialists, including Chiara Banchini, William Christie, Christophe Coin, Michel Corboz, Paul Dyer, John Eliot Gardiner, Reinhard Goebel, Philippe Herreweghe, Christopher Hogwood, René Jacobs, Konrad Junghänel, Robert King, Paul McCreesh, Nicholas McGegan, Roger Norrington, Christophe Rousset, Jos van Veldhoven, Dominique Veillard and Roland Wilson. He took part in the project of Ton Koopman and the Amsterdam Baroque Orchestra & Choir to record the complete vocal works of Bach. His regular solo partners include cemballist Markus Märkl and the virtuoso lutenist Edin Karamazov. Ensembles with whom he performs include the Netherlands Bach Choir, Cantus Coelln, the Orchestra of the Age of Enlightenment, Musica Antiqua Köln, the Akademie für Alte Musik Berlin, the Freiburger Barockorchester, the Australian Brandenburg Orchestra and Accademia Bizantina.

The composer Marco Rosano has created a new Stabat Mater for Andreas Scholl; he sang the first complete performance of this work on 22 February 2008 at the City Recital Hall, Angel Place, Sydney, accompanied by the Australian Brandenburg Orchestra under Paul Dyer.

Opera

Scholl describes himself as a singer who does opera. His major roles have been those written for the 18th century alto castrato Senesino: Bertarido in Handel's ''Rodelinda'' (Glyndebourne, 1998, 1999, 2002 as well as The Metropolitan Opera, 2006 and planned 2011) and the title role in Handel's ''Giulio Cesare'' in the Royal Danish Opera production (2002, 2005). ''Rodelinda'' was a huge success and he 'stopped the show' (''Sunday Times''). According to James Bowman, who describes himself as an unqualified admirer, 'people went into a kind of trance' when he sang ''Dove Sei''. ''The Financial Times'' said of his ''Vivi tiranno'': '… such intelligent virtuosity … time stands still and you feel he is speaking to you.' In February 2002, ''Le Monde'' called him 'Le Roi Scholl' after his reprise of the role of King Bertarido in the Paris production of the Glyndebourne ''Rodelinda''. He reprised his Giulio Cesare in Paris (2007) and Lausanne (2008). He sang the role of Arsace in Handel's ''Partenope'' for the Royal Danish Opera in 2008. In 2010 he sang again ''Giulio Cesare'', this time with Cecilia Bartoli as Cleopatra.

Popular music

Scholl has always written songs as well as music for ballet and theatre and has his own professional sound studio in Basel, Switzerland. His ''White as Lilies'', based on ideas of John Dowland, is on the 1995 CD ''The Countertenors'' (with Dominique Visse and Pascal Bertin). It was a hit in Korea when used in a TV commercial and was later released there in an orchestrated version. In December 2003, he gave his first public performance in popular music, an eclectic programme of electronic and orchestral works which included his own compositions. Alongside Andreas Scholl was fellow Baroque countertenor, Roland Kunz, who specialises in setting Elizabethan English poems to his own electronic music. The two countertenors duetted in Scholl's and Kunz's songs, backed by Kunz's band ''die Unerlösten'' and the Rundfunk-Sinfonieorchester Saarbrücken under Rick Stengårds.

Concerts

In 2011 Scholl made his debut at the Rheingau Musik Festival in three events, an interview, a trip to three churches with different concert programs, and an opera recital with his sister Elisabeth at Eberbach Abbey. In the Christopheruskirche of Wiesbaden-Schierstein he appeared with harpsichordist Tamar Halperin, in Hallgarten with members of the Accademia Bizantina, in the romanesque Basilika St. Aegidius of Mittelheim with the vocal trio White Raven. The opera recital with the chamber orchestra Accademia Bizantina contained works of Handel and Purcell, such as Handel's ''Rodelinda'', Purcell's ''King Arthur'', closing with the final love duet "Caro! Bella!" from ''Giulio Cesare in Egitto''.

References

External links

Andreas Scholl Website

The Andreas Scholl Society not-for-profit independent site with future concerts, past performances, extended biography, full discography, list of all recorded tracks indexed by composer, photo archive, early music links, index of world countertenors, audio samples, message board

Andreas Scholl Harrison Parrott artist management

Scholl's MySpace page with audio clips from his own studio.

Andreas Scholl sings from Mozart's Mitridate

Germany special: The Rhine Valley Interview with Andreas Scholl by Kieran Falconer, ''The Independent'', 9 April 2006

Andreas Scholl' Dan Shorer, "on-line meetings at U-Sophia, where minds meet on-line"

Category:1967 births Category:Living people Category:German opera singers Category:Operatic countertenors Category:Performers of early music Category:Schola Cantorum Basiliensis alumni Category:Schola Cantorum Basiliensis faculty

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Domenico Mazzocchi (1592– 21 January 1665, aged 72) was an Italian baroque composer of the generation after Claudio Monteverdi. He was a composer of only vocal music, motets, oratorios and madrigals which have continuo, similar to the late Monteverdi's ones.

He is associated with providing music for the popes, particularly Cardinal Maffeo Barberini, later Pope Urban VIII.

His younger brother Virgilio Mazzocchi was also a Roman composer who had a similar career as a Vatican music provider.

Works

Operas

''La catena d'Adone'' (1626)

References

Entry under Domenico Mazzocchi in the ''Grove Dictionary of Music and Musicians''.

Cardinali A., 1926, ''Cenni biografici di Domenico e Virgilio Mazzocchi''.

External links

Category:1592 births Category:1665 deaths Category:Baroque composers Category:Italian composers

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