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Ernst Schröder
Ernst Schröder
For the actor, see Ernst Schröder (actor). Ernst Schröder ( 27 January 1915 &ndash 26 July 1994) was a popular German theatre film and TV actor

Ernst Schröder (25 November 1841 Mannheim, Germany – 16 June 1902 Karlsruhe Germany) was a German mathematician mainly known for his work on algebraic logic. Events 1034 - Máel Coluim mac Cináeda, King of Scots dies Donnchad, the For the game see 1841 (board game. Year 1841 ( MDCCCXLI) was a Common year starting on Friday (link Mannheim is a City in Germany. With 327318 inhabitants it is the second-largest city in the state of Baden-Württemberg after the capital Stuttgart Events 1487 - Battle of Stoke Field, the last dying breath of the Wars of the Roses. Year 1902 ( MCMII) was a Common year starting on Wednesday (link will display calendar of the Gregorian calendar (or a Common year starting Karlsruhe (ˈkaɐ̯lsʁuːə population 285812 in 2006 is a city in the south west of Germany, in the Bundesland Baden-Württemberg, located near Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. In Mathematical logic, algebraic logic formalizes logic using the methods of Abstract algebra. 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. Mathematical logic is a subfield of Logic and Mathematics with close connections to Computer science and Philosophical logic. George Boole (buːl ( November 2, 1815 &ndash December 8, 1864) was a British Mathematician and Philosopher. Augustus De Morgan ( 27 June, 1806 &ndash 18 March, 1871) was a British Mathematician and Logician. Hugh MacColl (1837-1909 was a Scot who trained as a Mathematician and evolved into a Logician. Charles Sanders Peirce (pronounced purse) (September 10 1839 &ndash April 19 1914 was an American Logician mathematician, philosopher 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 of formal logic of the day. The twentieth century of the Common Era began on Mathematical logic is a subfield of Logic and Mathematics with close connections to Computer science and Philosophical logic.

Contents

Life

Schröder learned mathematics at Heidelberg, Königsberg, and Zürich, under Hesse, Kirchhoff, and Franz Neumann. Heidelberg is a city in Baden-Württemberg, Germany. As of 2006 over 140000 people live within the city's area Königsberg (Karaliaučius Low German: Königsbarg; Królewiec see also other names) was until 1946 the name of Kaliningrad. Zürich (, Zürich German: Züri, Zurich, Zurigo; in English generally Zurich) is the largest city in Switzerland and capital of the Franz Ernst Neumann ( September 11, 1798 - May 23, 1895) was a German Mineralogist, Physicist and Mathematician After teaching school for a few years, he moved to the Technische Hochschule Darmstadt in 1874. The Darmstadt University of Technology, whose official name (also its official English name) is "Technische Universität Darmstadt" (abbreviated TU Darmstadt) in Year 1874 ( MDCCCLXXIV) was a Common year starting on Thursday (link will display the full calendar of the Gregorian calendar (or a Common Two years later, he took up a chair in mathematics at the Polytechnische Schule in Karlsruhe, where he spent the remainder of his life. Karlsruhe (ˈkaɐ̯lsʁuːə population 285812 in 2006 is a city in the south west of Germany, in the Bundesland Baden-Württemberg, located near 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. George Boole (buːl ( November 2, 1815 &ndash December 8, 1864) was a British Mathematician and Philosopher. Augustus De Morgan ( 27 June, 1806 &ndash 18 March, 1871) was a British Mathematician and Logician. Instead, his sources were texts by Ohm, Hankel, Hermann Grassmann, and Robert Grassmann, all written in the tradition of German combinatorial algebra and algebraic analysis (Peckhaus 1997: 233-296). Hermann Günther Grassmann ( April 15, 1809, Stettin ( Szczecin) &ndash September 26, 1877, Stettin) was a 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 Peirce, including subsumption and quantification. Charles Sanders Peirce (pronounced purse) (September 10 1839 &ndash April 19 1914 was an American Logician mathematician, philosopher Quantification has two distinct meanings In Mathematics and Empirical science, it refers to human acts known as Counting and Measuring

Schröder also made original contributions to algebra, set theory, lattice theory, ordered sets and ordinal numbers. Algebra is a branch of Mathematics concerning the study of structure, relation, and Quantity. In Mathematics, a lattice is a Partially ordered set (also called a poset) in which every pair of elements has a unique Supremum (the elements' Ordered set is used with distinct meanings in Order theory. A set with a Binary relation R on its elements that is reflexive (for In Set theory, an ordinal number, or just ordinal, is the Order type of a Well-ordered set. Along with Georg Cantor, he codiscovered the Cantor–Bernstein–Schröder theorem, although the proof in Schröder (1898) is flawed. Georg Ferdinand Ludwig Philipp Cantor ( – January 6 1918) was a German Mathematician, born in Russia. In set theory, the Cantor–Bernstein–Schroeder Theorem, named after Georg Cantor, Felix Bernstein, and Ernst Schröder, states Felix Bernstein (1878-1956) subsequently corrected the proof as part of his Ph. Felix Bernstein ( February 24, 1878, Halle, Germany – December 3[[ 956]] Zurich, Switzerland) was a German D. dissertation.

title page of first printing of "Über die formalen Elemente der absoluten Algebra"
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 Peirce used it as a text while teaching at Johns Hopkins University. See also John Venn (regicide. John Venn FRS ( HullYorkshire, August 4, 1834 &ndash Cambridge Christine Ladd-Franklin ( December 1, 1847 &ndash March 5, 1930) was an American Psychologist and Logician. Charles Sanders Peirce (pronounced purse) (September 10 1839 &ndash April 19 1914 was an American Logician mathematician, philosopher

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:

“ . . . to design logic as a calculating discipline, especially to give access to the exact handling of relative concepts, and, from then on, by emancipation from the routine claims of natural language, to withdraw any fertile soil from "cliché" in the field of philosophy as well. A spoken language is a human Natural language in which the Words are uttered through the Mouth. Philosophy is the study of general problems concerning matters such as existence knowledge truth beauty justice validity mind and language This should prepare the ground for a scientific universal language that looks more like a sign language than like a sound language. A universal language is a hypothetical historical or mythical language said to be spoken and understood by all or most of the world's populationor in some circles is said to be understood ”

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. In Mathematical logic, predicate logic is the generic term for symbolic Formal systems like First-order logic, Second-order logic, Many-sorted Friedrich Ludwig Gottlob Frege ( 8 November 1848, Wismar, Grand Duchy of Mecklenburg-Schwerin  &ndash 26 July 1925 Giuseppe Peano ( August 27, 1858 &ndash April 20, 1932) was an Italian Mathematician, whose work was of exceptional For an example of the influence of Schröder's work on English-speaking logicians of the early 20th century, see Clarence Irving Lewis (1918). Clarence Irving Lewis ( April 12, 1883 Stoneham Massachusetts - February 3, 1964 Cambridge Massachusetts) usually 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. The Principia Mathematica is a 3-volume work on the Foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell Bertrand Arthur William Russell 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970 was a British Philosopher, Historian

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:

“ 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, . Charles Sanders Peirce (pronounced purse) (September 10 1839 &ndash April 19 1914 was an American Logician mathematician, philosopher Hilary Whitehall Putnam (born July 31 1926 is an American Philosopher who has been a central figure in Western philosophy since the 1960s especially in Philosophy The history of logic traces the development of the science of valid inference ( Logic) . . [whose] third volume is on the logic of relations (Algebra und Logik der Relative, 1895). Relational algebra, an offshoot of First-order logic (and of Algebra of sets) deals with a set of relations closed under Operators 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. Leopold Löwenheim (1878 Krefeld Germany - 1957 Berlin) was a German Mathematician, known for his work in Mathematical logic. Thoralf Albert Skolem ( May 23, 1887 – March 23, 1963) (ˈtɔɾɑlf ˈskuləm was a Norwegian Mathematician known In fact, there is no reference in Löwenheim's paper to any logic other than Peirce's. To cite another example, Zermelo presented his axioms for set theory in Peirce-Schröder notation, and not, as one might have expected, in Russell-Whitehead notation. Ernst Friedrich Ferdinand Zermelo ( July 27 1871, Berlin, German Empire – May 21 1953, Freiburg im Breisgau In traditional Logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject

One can sum up these simple facts (which anyone can quickly verify) as follows: Frege certainly discovered the quantifier first (four years before O. H. Mitchell, going by publication dates, which are all we have as far as I know). But Leif Ericson probably discovered America "first" (forgive me for not counting the native Americans, who of course really discovered it "first"). Leif Ericson ( Old Norse: Leifr Eiríksson) (c 970 – c 1020 was a Norse Explorer who was probably the first European to land in The Americas are the lands of the Western hemisphere or New World, consisting of the Continents of North America and South America For indigenous peoples in the United States other than Hawaii and Alaska see also Native Americans in the United States. If the effective discoverer, from a European point of view, is Christopher Columbus, that is because he discovered it so that it stayed discovered (by Europeans, that is), so that the discovery became known (by Europeans). Christopher Columbus (1451 &ndash May 20 1506 was an Italian Navigator, colonizer 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?

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References

External links

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