Ernst Schröder
Encyclopedia
- For the actor, see Ernst Schröder (actor)Ernst Schröder (actor)Ernst Schröder was a popular German theatre, film and TV actor.-Life:Born in Herne, Schröder began his acting career at the nearby Bochum Theatre in 1934, under the legendary director Saladin Schmitt. He worked there until 1936, also working as Assistant Director and Stage Designer...
.
Ernst Schröder (25 November 1841, Mannheim
Mannheim
Mannheim is a city in southwestern Germany. With about 315,000 inhabitants, Mannheim is the second-largest city in the Bundesland of Baden-Württemberg, following the capital city of Stuttgart....
, Baden
Baden
Baden is a historical state on the east bank of the Rhine in the southwest of Germany, now the western part of the Baden-Württemberg of Germany....
, Germany
German Confederation
The German Confederation was the loose association of Central European states created by the Congress of Vienna in 1815 to coordinate the economies of separate German-speaking countries. It acted as a buffer between the powerful states of Austria and Prussia...
– 16 June 1902, Karlsruhe
Karlsruhe
The City of Karlsruhe is a city in the southwest of Germany, in the state of Baden-Württemberg, located near the French-German border.Karlsruhe was founded in 1715 as Karlsruhe Palace, when Germany was a series of principalities and city states...
, Germany
German Empire
The German Empire refers to Germany during the "Second Reich" period from the unification of Germany and proclamation of Wilhelm I as German Emperor on 18 January 1871, to 1918, when it became a federal republic after defeat in World War I and the abdication of the Emperor, Wilhelm II.The German...
) was a German mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
mainly known for his work on algebraic logic
Algebraic logic
In mathematical logic, algebraic logic is the study of logic presented in an algebraic style.What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for the study of various logics and connected problems...
. He is a major figure in the history of mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
(a term he may have invented), by virtue of summarizing and extending the work of George Boole
George Boole
George Boole was an English mathematician and philosopher.As the inventor of Boolean logic—the basis of modern digital computer logic—Boole is regarded in hindsight as a founder of the field of computer science. Boole said,...
, Augustus De Morgan
Augustus De Morgan
Augustus De Morgan was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorous. The crater De Morgan on the Moon is named after him....
, Hugh MacColl
Hugh MacColl
Hugh MacColl was a Scot who trained as a mathematician and became a logician. MacColl was the youngest son of a poor highland family which was at least in part Gaelic-speaking...
, 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
Formal logic
Classical or traditional system of determining the validity or invalidity of a conclusion deduced from two or more statements...
of the day.
Life
Schröder learned mathematics at HeidelbergHeidelberg
-Early history:Between 600,000 and 200,000 years ago, "Heidelberg Man" died at nearby Mauer. His jaw bone was discovered in 1907; with scientific dating, his remains were determined to be the earliest evidence of human life in Europe. In the 5th century BC, a Celtic fortress of refuge and place of...
, Königsberg
Königsberg
Königsberg was the capital of East Prussia from the Late Middle Ages until 1945 as well as the northernmost and easternmost German city with 286,666 inhabitants . Due to the multicultural society in and around the city, there are several local names for it...
, and Zürich
Zürich
Zurich is the largest city in Switzerland and the capital of the canton of Zurich. It is located in central Switzerland at the northwestern tip of Lake Zurich...
, under Hesse, Kirchhoff
Gustav Kirchhoff
Gustav Robert Kirchhoff was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects...
, and Franz Neumann
Franz Ernst Neumann
Franz Ernst Neumann was a German mineralogist, physicist and mathematician.-Biography:Neumann was born in Joachimsthal, Margraviate of Brandenburg, located not far from Berlin. In 1815 he interrupted his studies at Berlin to serve as a volunteer in the Hundred Days against Napoleon, and was...
. 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
Karlsruhe
The City of Karlsruhe is a city in the southwest of Germany, in the state of Baden-Württemberg, located near the French-German border.Karlsruhe was founded in 1715 as Karlsruhe Palace, when Germany was a series of principalities and city states...
, 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 BooleGeorge Boole
George Boole was an English mathematician and philosopher.As the inventor of Boolean logic—the basis of modern digital computer logic—Boole is regarded in hindsight as a founder of the field of computer science. Boole said,...
and Augustus De Morgan
Augustus De Morgan
Augustus De Morgan was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorous. The crater De Morgan on the Moon is named after him....
. Instead, his sources were texts by Ohm, Hankel, Hermann Grassmann
Hermann Grassmann
Hermann Günther Grassmann was a German polymath, renowned in his day as a linguist and now also admired as a mathematician. He was also a physicist, neohumanist, general scholar, and publisher...
, 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
Quantification
Quantification has several distinct senses. In mathematics and empirical science, it is the act of counting and measuring that maps human sense observations and experiences into members of some set of numbers. Quantification in this sense is fundamental to the scientific method.In logic,...
.
Schröder also made original contributions to algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
, set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
, lattice theory, ordered set
Ordered set
In order theory in mathematics, a set with a binary relation R on its elements that is reflexive , antisymmetric and transitive is described as a partially ordered set or poset...
s and ordinal number
Ordinal number
In set theory, an ordinal number, or just ordinal, is the order type of a well-ordered set. They are usually identified with hereditarily transitive sets. Ordinals are an extension of the natural numbers different from integers and from cardinals...
s. Along with Georg Cantor
Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor was a German mathematician, best known as the inventor of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets,...
, he codiscovered the Cantor–Bernstein–Schröder theorem, although the proof in Schröder (1898) is flawed. Felix Bernstein
Felix Bernstein
Felix Bernstein was a German Jewish mathematician known for developing a theorem of the equivalence of sets in 1897, and less well known for demonstrating the correct blood group inheritance pattern of multiple alleles at one locus in 1924 through statistical analysis...
(1878–1956) subsequently corrected the proof as part of his Ph.D. dissertation.
John Venn
Donald A. Venn FRS , was a British logician and philosopher. He is famous for introducing the Venn diagram, which is used in many fields, including set theory, probability, logic, statistics, and computer science....
and Christine Ladd-Franklin
Christine Ladd-Franklin
Christine Ladd-Franklin was the first American woman psychologist, logician, and mathematician.-Early Life and Early Education:...
both warmly cited this short book of Schröder's, and Charles Sanders Peirce used it as a text while teaching at Johns Hopkins University
Johns Hopkins University
The Johns Hopkins University, commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States...
.
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 FregeGottlob Frege
Friedrich Ludwig Gottlob Frege was a German mathematician, logician and philosopher. He is considered to be one of the founders of modern logic, and made major contributions to the foundations of mathematics. He is generally considered to be the father of analytic philosophy, for his writings on...
or Peano
Giuseppe Peano
Giuseppe Peano was an Italian mathematician, whose work was of philosophical value. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much notation. The standard axiomatization of the natural numbers is named the Peano axioms in...
. For an example of the influence of Schröder's work on English-speaking logicians of the early 20th century, see Clarence Irving Lewis
Clarence Irving Lewis
Clarence Irving Lewis , usually cited as C. I. Lewis, was an American academic philosopher and the founder of conceptual pragmatism. First a noted logician, he later branched into epistemology, and during the last 20 years of his life, he wrote much on ethics.-Early years:Lewis was born in...
(1918). The relational concepts that pervade Principia Mathematica
Principia Mathematica
The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913...
are very much owed to the Vorlesungen, cited in Principias Preface and in Bertrand Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
'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
Hilary Putnam
Hilary Whitehall Putnam is an American philosopher, mathematician and computer scientist, who has been a central figure in analytic philosophy since the 1960s, especially in philosophy of mind, philosophy of language, philosophy of mathematics, and philosophy of science...
(1982) writes:
External links
- http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/Schrdr.htm (requires login, unprovided)