- Ernst Schröder
:"For the actor, see

Ernst Schröder (actor) ."**Ernst Schröder**(25 November ,1841 Mannheim, Germany –16 June ,1902 Karlsruhe Germany ) was a German mathematician mainly known for his work onalgebraic logic . He is a major figure in the history ofmathematical logic (a term he may have invented), by virtue of summarizing and extending the work ofGeorge Boole ,Augustus De Morgan ,Hugh MacColl , and especiallyCharles Peirce . He is best known for his monumental "Vorlesungen über die Algebra der Logik", 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 offormal logic of the day.**Life**Schröder learned mathematics at

Heidelberg ,Königsberg , andZürich , under Hesse,Kirchhoff , and Franz Neumann. After teaching school for a few years, he moved to theTechnische Hochschule Darmstadt in 1874. Two years later, he took up a chair in mathematics at the Polytechnische Schule inKarlsruhe , 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 andAugustus De Morgan . Instead, his sources were texts by Ohm, Hankel,Hermann Grassmann , andRobert Grassmann , all written in the tradition of Germancombinatorial algebra andalgebraic analysis (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 toCharles Peirce , including subsumption andquantification .Schröder also made original contributions to

algebra ,set theory ,lattice theory ,ordered set s andordinal number s. Along withGeorg Cantor , he codiscovered theCantor–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 andChristine Ladd-Franklin both warmly cited this short book of Schröder's, andCharles Peirce used it as a text while teaching atJohns 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 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, seeClarence Irving Lewis (1918). Therelation al concepts that pervade "Principia Mathematica " are very much owed to the "Vorlesungen", cited in "Principia"'s Preface and inBertrand Russell 'sPrinciples 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

Charles Peirce , however,Hilary Putnam (1982) writes:cquote|When I started to trace the later development of logic, the first thing I did was to look at Schröder's "Vorlesungen über die Algebra der Logik", ... [whose] third volume is on the logic of relations ("Algebra und Logik der Relative", 1895). The three volumes immediately became the best-known advanced logic text, and embody what any mathematician interested in the study of logic should have known, or at least have been acquainted with, in the 1890s.

While, to my knowledge, no one except Frege ever published a single paper in Frege's notation, many famous logicians adopted Peirce-Schröder notation, and famous results and systems were published in it. Löwenheim stated and proved the Löwenheim theorem (later reproved and strengthened by

Thoralf Skolem , whose name became attached to it together with Löwenheim's) in Peircian notation. In fact, there is no reference in Löwenheim's paper to any logic other than Peirce's. To cite another example, Zermelo presented hisaxiom s for set theory in Peirce-Schröder notation, and not, as one might have expected, in Russell-Whitehead notation.One can sum up these simple facts (which anyone can quickly verify) as follows: Frege certainly discovered the quantifier first (four years before

Oscar Howard Mitchell , going by publication dates, which are all we have as far as I know). ButLeif Ericson probably discovered America "first" (forgive me for not counting the native Americans, who of course really discovered it "first"). If the effective discoverer, from a European point of view, isChristopher Columbus , that is because he discovered it so that it stayed discovered (by Europeans, that is), so that the discovery became known (by Europeans). Frege did "discover" the quantifier in the sense of having the rightful claim to priority; but Peirce and his students discovered it in the effective sense. The fact is that until Russell appreciated what he had done, Frege was relatively obscure, and it was Peirce who seems to have been known to the entire world logical community. How many of the people who think that "Frege invented logic" are aware of these facts?**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 Pierce 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 [*http://www.math.ucla.edu/%7Easl/bsl/0504/0504-001.ps here*] or [*http://www-fakkw.upb.de/institute/philosophie/Personal/Peckhaus/Schriftenverzeichnis/Text__19th_century_logic.html 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. [*http://www.jfsowa.com/peirce/putnam.htm 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

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**Ernst Schroder**— Ernst Schröder Pour les articles homonymes, voir Schröder. Ernst Schröder Ernst Schröder (25 novembre … Wikipédia en Français**Ernst Schröder**— Saltar a navegación, búsqueda Ernst Schröder Ernst Schröder ( Mannheim, 25 de noviembre de 1841 – Karlsruhe, 16 de junio de 1902) fue un matemático alemán, conocido especialmente por … Wikipedia Español**Ernst Schröder**— ist der Name folgender Personen: Ernst Schröder (Mathematiker) (1841–1902), deutscher Mathematiker Ernst Schröder (Politiker) (1893–1976), deutscher Politiker Ernst Schröder (Schauspieler) (1915–1994), deutscher Schauspieler Ernst Schroeder… … Deutsch Wikipedia**Ernst Schröder**— Pour les articles homonymes, voir Schröder. Ernst Schröder Ernst Schröder (25 novembre 1841 à Mannheim – 16 juin 1902 à Karlsruhe) est un mathématicie … Wikipédia en Français**Ernst Schröder (Schauspieler)**— Ernst Schröder (* 27. Januar 1915 in Eickel oder Wanne; † 26. Juli 1994 in Berlin) war ein deutscher Schauspieler und Regisseur. Inhaltsverzeichnis 1 Leben 2 Theater 3 … Deutsch Wikipedia**Ernst Schröder (acteur)**— Ernst Schröder (27 janvier 1915 à Eickel; 26 juillet 1994 à Berlin) était un acteur allemand. Sommaire 1 Biographie 2 Théâtre 3 Filmographie 4 Télévision … Wikipédia en Français**Ernst Schröder (Mathematiker)**— Ernst Schröder Ernst Schröder (* 25. November 1841 in Mannheim; † 16. Juni 1902 in Karlsruhe; vollständiger Name Ernst Friedrich Wilhelm Karl Schröder) war ein deutscher Mathematiker und Logiker … Deutsch Wikipedia**Ernst Schröder (Politiker)**— Ernst Schröder (* 11. Februar 1893 in Krefeld; † 20. Februar 1976 in Wiesbaden) war ein deutscher Gartenarchitekt und Politiker (DVP, später FDP). Inhaltsverzeichnis 1 Leben und Beruf 2 Politik … Deutsch Wikipedia**Ernst Schröder (actor)**— Infobox actor bgcolour = name = Ernst Schröder imagesize = caption = birthname = birthdate = birth date|1915|1|27|df=y location = Herne, Germany deathdate = death date and age|1994|7|26|1915|1|27|df=y deathplace = Berlin, Germany othername =… … Wikipedia**Rolf Ernst Schröder**— (* 23. Dezember 1940 in Flensburg; † 31. August 2005 in Sörup bei Flensburg; Signatur: R.E.S.), Bildender Künstler (Bundesverband bildender Künstler BBK), Designer Keramiker (Arbeitsgemeinschaft des Kunsthandwerks Hamburg AdK). Leben Von 1960 bis … Deutsch Wikipedia