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Encyclopedia > Friedrich Ludwig Gottlob Frege
Western Philosophy
19th-century philosophy,
Friedrich Ludwig Gottlob Frege
Name: Friedrich Ludwig Gottlob Frege
Birth: November 8, 1848
Death: 26 July 1925
School/tradition: Analytic philosophy
Main interests
Philosophy of language, mathematical logic
Notable ideas
Predicate calculus, Logicism, Sense and reference, Mediated reference theory
Influences Influenced
Giuseppe Peano, Bertrand Russell, Rudolf Carnap, Ludwig Wittgenstein Michael Dummett, George Boolos, Edward N. Zalta

Friedrich Ludwig Gottlob Frege (8 November 1848, Wismar26 July 1925, Bad Kleinen) was a German mathematician who evolved into a logician and philosopher. He helped found both modern mathematical logic and analytic philosophy. In the 18th century the philosophies of The Enlightenment would begin to have dramatic effect, and the landmark works of philosophers such as Immanuel Kant and Jean-Jacques Rousseau would have an electrifying effect on a new generation of thinkers. ... gottlob frege (uncopyrighted, from polish website) This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... November 8 is the 312th day of the year (313th in leap years) in the Gregorian Calendar, with 53 days remaining. ... 1848 is a leap year starting on Saturday of the Gregorian calendar. ... July 26 is the 207th day (208th in leap years) of the year in the Gregorian Calendar, with 158 days remaining. ... 1925 (MCMXXV) was a common year starting on Thursday (link will take you to calendar). ... Analytic philosophy is the dominant philosophical movement in University philosophy departments in English-speaking countries, although one of its founders, Gottlob Frege, was German, and many of its leading proponents, such as Ludwig Wittgenstein, Rudolf Carnap, Kurt Gödel and Karl Popper, were Austrian. ... Philosophy of language is the branch of philosophy that studies language. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... First-order predicate calculus or first-order logic (FOL) permits the formulation of quantified statements such as there exists an x such that. ... Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic. ... The distinction between Sinn and Bedeutung (usually but not always translated sense and reference, respectively) was an innovation of the German philosopher and mathematician Gottlob Frege in his 1892 paper Ãœber Sinn und Bedeutung (On Sense and Reference), which is still widely read today. ... The mediated reference theory is a semantic theory that posits that words reference something in the external world, but are mediated by some other process. ... Giuseppe Peano Giuseppe Peano (August 27, 1858 – April 20, 1932) was an Italian mathematician and philosopher best known for his contributions to set theory. ... The Right Honourable Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970), was an influential British logician, philosopher, and mathematician, working mostly in the 20th century. ... Rudolf Carnap (May 18, 1891, Ronsdorf Germany - September 14, 1970, Los Angeles) was a philosopher, active in central Europe before 1935, and in the United States thereafter. ... Ludwig Josef Johann Wittgenstein (IPA: ) (April 26, 1889 – April 29, 1951) was an Austrian philosopher who contributed several ground-breaking works to modern philosophy, primarily on the foundations of logic, the philosophy of mathematics, the philosophy of language, and the philosophy of mind. ... Sir Michael Anthony Eardley Dummett (born 1925) is a leading British philosopher. ... This article is not about George Boole, another mathematical logician. ... Edward N. Zalta is a Senior Research Scholar at the Center for the Study of Language and Information. ... November 8 is the 312th day of the year (313th in leap years) in the Gregorian Calendar, with 53 days remaining. ... 1848 is a leap year starting on Saturday of the Gregorian calendar. ... Wismar Coat of Arms Wismar is a smaller port and Hanseatic League city in northern Germany on the Baltic Sea, in the state of Mecklenburg-Vorpommern, about 45 km due east of Lübeck, and 30 km due north of Schwerin. ... July 26 is the 207th day (208th in leap years) of the year in the Gregorian Calendar, with 158 days remaining. ... 1925 (MCMXXV) was a common year starting on Thursday (link will take you to calendar). ... Mathematics is often defined as the study of topics such as quantity, structure, space, and change. ... Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... Analytic philosophy is the dominant philosophical movement in University philosophy departments in English-speaking countries, although one of its founders, Gottlob Frege, was German, and many of its leading proponents, such as Ludwig Wittgenstein, Rudolf Carnap, Kurt Gödel and Karl Popper, were Austrian. ...

Contents


Life

Frege's father was a schoolteacher whose specialty was mathematics. Frege began his studies at the University of Jena in 1869, moving to Göttingen after two years, where he received his Ph.D. in mathematics, in 1873. According to Sluga (1980), the nature of Frege's university education in logic and philosophy is still unclear. In 1875, he returned to Jena as a lecturer. In 1879, he was made associate professor, and in 1896, professor. Frege had but one student of note, Rudolf Carnap. His children all having died before reaching maturity, he adopted a son in 1905. Friedrich Schiller University of Jena (FSU) is located in Jena, Thuringia in Germany and was named for the German writer Friedrich Schiller. ... 1869 (MDCCCLXIX) is a common year starting on Friday (link will take you to calendar) of the Gregorian calendar or a common year starting on Sunday of the 12-day-slower Julian calendar. ... Landmark Gänseliesel fountain at the main market Göttingen ( (help· info)) is a city in Lower Saxony, Germany. ... Doctor of Philosophy (Ph. ... 1873 was a common year starting on Wednesday (see link for calaber). ... Jena is a town in central Germany on the River Saale. ... 1879 (MDCCCLXXIX) was a common year starting on Wednesday (see link for calendar). ... 1896 (MDCCCXCVI) was a leap year starting on Wednesday (see link for calendar). ... Rudolf Carnap (May 18, 1891, Ronsdorf Germany - September 14, 1970, Los Angeles) was a philosopher, active in central Europe before 1935, and in the United States thereafter. ...


For many years, Heinrich Scholtz at the University of Munster, where Frege's papers were deposited after his death, was the only scholar to pay Frege any respect. Much of Frege's Nachlass was lost in WWII. The first English translations of Frege appeared in 1950. Leading contemporary authorities on Frege writing in English include Michael Dummett and Hans Sluga. To date, there is no biography of Frege in English. The University of Münster (German Westfälische Wilhelms-Universität Münster, WWU) is a public university located in the city of Münster in Germany. ... A literary executor is a person with decision-making power in respect of the literary estate of an author who has died. ... German soldiers at the Battle of Stalingrad World War II was the most extensive and costly armed conflict in the history of the world, involving the great majority of the worlds nations, being fought simultaneously in several major theatres, and costing tens of millions of lives. ... Sir Michael Anthony Eardley Dummett (born 1925) is a leading British philosopher. ... Hans Sluga is Professor of Philosophy at the University of California, Berkeley. ...


Logician

Main article: Begriffsschrift

Frege is widely regarded as a very great logician, on par with Aristotle, Kurt Gödel, and Alfred Tarski. His revolutionary Begriffsschrift, or Concept Script (1879) marked the beginning of a new epoch in the history of logic. The Begriffsschrift broke much new ground, including a clean treatment of functions and variables. He invented and axiomatized predicate logic, thanks to his discovery of quantified variables, which subsequently became ubiquitous in mathematics and solved the medieval problem of multiple generality. Hence the quantification essential to Bertrand Russell's theory of descriptions and Principia Mathematica (with Alfred North Whitehead), was ultimately due to Frege. Begriffsschrift is the title of a short book on logic by Gottlob Frege, published in 1879, and is also the name of the formal system set out in that book. ... Aristotle (Ancient Greek: AristotelÄ“s 384 BC – March 7, 322 BC) was an ancient Greek philosopher, student of Plato and teacher of Alexander the Great. ... Kurt Gödel Kurt Gödel [kurt gøːdl], (April 28, 1906–January 14, 1978) was a logician, mathematician, and philosopher of mathematics. ... Alfred Tarski (January 14, 1901 in Warsaw – October 26, 1983 in Berkeley, USA) was a Polish mathematician, and widely considered one of the four greatest logicians of all time, along with Aristotle, Gottlob Frege, and Kurt Gödel. ... Partial plot of a function f. ... In computer science and mathematics, a variable is a symbol denoting a quantity or symbolic representation. ... In mathematics, axiomatization is the process of defining the basic axiomatic systems from which mathematical theories can be derived. ... ... In language and logic, quantification is a construct that specifies the extent of validity of a predicate, that is the extent to which a predicate holds over a range of things. ... Mathematics is often defined as the study of topics such as quantity, structure, space, and change. ... The problem of multiple generality names a failure in Aristotelian logic to describe certain intuitively valid inferences. ... The Right Honourable Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970), was an influential British logician, philosopher, and mathematician, working mostly in the 20th century. ... The Theory of Descriptions is one of the philosopher Bertrand Russells most significant contributions to the philosophy of language. ... The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910-1913. ... Alfred North Whitehead, OM (February 15, 1861 – December 30, 1947) was a British mathematician who evolved into a philosopher. ...


Frege was a major advocate of the view that arithmetic is reducible to logic, a form of logicism. In his Grundgesetze der Arithmetik (1893, 1903), published at its author's expense, he attempted to explicitly derive the laws of arithmetic from logic and some set theory. As the second volume was about to go to press, Frege learned of Russell's paradox from its discoverer. This paradox revealed that the Grundgesetze system was worthless because its axioms led to a contradiction. Frege acknowledged this contradiction in a last-minute appendix to volume two, pointing to the axiom he believed was at fault. Frege never succeeded in amending his axioms to his satisfaction, although Russell's theory of types, the axiomatic set theory of Ernst Zermelo and John von Neumann, and the second order logic of George Boolos (1998) all suggested ways to remedy the problem. For a modern exposition of the core of Frege's Grundgesetze system, see Hatcher (1982: chpt. 3). For an attempt to rehabilitate this system, see Boolos (1998). Arithmetic or arithmetics (from the Greek word αριθμός = number) in common usage is a branch of (or the forerunner of) mathematics which records elementary properties of certain operations on numerals, though professional mathematicians often treat arithmetic as a synonym for number theory. ... Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... Russells paradox (also known as Russells antinomy) is a paradox discovered by Bertrand Russell in 1901 which shows that the naive set theory of Frege is contradictory. ... At the broadest level, type theory is the branch of mathematics and logic that concerns itself with classifying entities into sets called types. ... Set theory is a branch of mathematics created principally by the German mathematician Georg Cantor at the end of the 19th century. ... Ernst Friedrich Ferdinand Zermelo (July 27, 1871 – May 21, 1953) was a German mathematician and philosopher. ... John von Neumann in the 1940s. ... This article is not about George Boole, another mathematical logician. ...


Frege's work in logic was little recognized in his own day, in considerable part because his peculiar diagrammatic notation had no antecedents; it has since had no imitators. His ideas spread chiefly through those he influenced, particularly his correspondents Giuseppe Peano and Russell. Giuseppe Peano Giuseppe Peano (August 27, 1858 – April 20, 1932) was an Italian mathematician and philosopher best known for his contributions to set theory. ...


Philosopher

Frege is regarded as one of the founding fathers of analytic philosophy, mainly because of his conceptual contributions to the philosophy of language, such as his: Philosophy of language is the branch of philosophy that studies language. ...

As a philosopher of mathematics, Frege loathed appeals to psychologistic or "mental" explanations for meanings (such as idea theories of meaning). His original purpose was very far from answering questions about meaning; he wanted to use modern logic to further develop the foundations of arithmetic. He first undertook to answer the question "What is a number?" or "What objects do number-words ("one", "two", etc.) refer to?" But in pursuing these matters, he eventually faced the task of analysing and explaining what meaning is, and came to several major conclusions. Proposition is a term used in logic to describe the content of assertions. ... The distinction between Sinn and Bedeutung (usually but not always translated sense and reference, respectively) was an innovation of the German philosopher and mathematician Gottlob Frege in his 1892 paper Ãœber Sinn und Bedeutung (On Sense and Reference), which is still widely read today. ... The mediated reference theory is a semantic theory that posits that words reference something in the external world, but are mediated by some other process. ... The distinction between concept and object is due to the German philosopher Gottlob Frege. ... In the philosophy of language, the context principle is a form of semantic holism holding that a philosopher should never . ... The Principle of Compositionality in semantics is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. ... Psychologism in the philosophy of mathematics is the explanation or derivation of mathematical or logical laws in terms of psychological facts. ...


Frege, despite Bertrand Russell's generous praise, was little known as a philosopher during his lifetime. Here too, his ideas spread chiefly through those he influenced, including Edmund Husserl, with whom he corresponded and debated in print, and Ludwig Wittgenstein. Had it not been for Wittgenstein -- whose major works, the Tractatus and the Philosophical Investigations, were attempts to come to terms with Frege's ideas about logic and language -- Frege's worth as a philosopher might never have been recognised. Edmund Husserl Edmund Gustav Albrecht Husserl (April 8, 1859 - April 26, 1938, Freiburg) was a German philosopher, known as the father of phenomenology. ... Ludwig Josef Johann Wittgenstein (IPA: ) (April 26, 1889 – April 29, 1951) was an Austrian philosopher who contributed several ground-breaking works to modern philosophy, primarily on the foundations of logic, the philosophy of mathematics, the philosophy of language, and the philosophy of mind. ... Tractatus Logico-Philosophicus is the only book-length work published by the philosopher Ludwig Wittgenstein in his lifetime. ... This article needs to be cleaned up to conform to a higher standard of quality. ...


References

Primary

  • Online bibliography of Frege's works and their English translations.
  • 1879. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle a. S.: Louis Nebert. Translation: Concept Script, a formal language of pure thought modelled upon that of arithmetic, by S. Bauer-Mengelberg in [[Jean Van Heijenoort], ed., 1967. From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931. Harvard University Press.
  • 1884. Die Grundlagen der Arithmetik: eine logisch-mathematische Untersuchung über den Begriff der Zahl. Breslau: W. Koebner. Translation: J. L. Austin, 1974. The Foundations of Arithmetic: A logico-mathematical enquiry into the concept of number, 2nd ed. Blackwell.
  • 1891. "Funktion und Begriff." Translation: "Function and Concept" in Geach and Black (1980).
  • 1892a. "Über Sinn und Bedeutung" in Zeitschrift für Philosophie und philosophische Kritik 100: 25-50. Translation: "On Sense and Reference" in Geach and Black (1980).
  • 1892b. "Über Begriff und Gegenstand" in Vierteljahresschrift für wissenschaftliche Philosophie 16: 192-205. Translation: "Concept and Object" in Geach and Black (1980).
  • 1893. Grundgesetze der Arithmetik, Band I. Jena: Verlag Hermann Pohle. Band II, 1903. Partial translation: Furth, M, 1964. The Basic Laws of Arithmetic. Uni. of California Press.
  • 1904. "Was ist eine Funktion?" in Meyer, S., ed., 1904. Festschrift Ludwig Boltzmann gewidmet zum sechzigsten Geburtstage, 20. Februar 1904. Leipzig: Barth: 656-666. Translation: "What is a Function?" in Geach and Black (1980).
  • Peter Geach and Max Black, eds., and trans., 1980. Translations from the Philosophical Writings of Gottlob Frege, 3rd ed. Blackwell.

Frege intended that the following three papers be published together in a book titled Logical Investigations. The English translations thereof were so published in 1975. Begriffsschrift is the title of a short book on logic by Gottlob Frege, published in 1879, and is also the name of the formal system set out in that book. ... John Langshaw Austin (March 28, 1911 - February 8, 1960) was a philosopher of language, who developed much of the current theory of speech acts. ... Peter Thomas Geach (born 1919) is one of the foremost contemporary British philosophers. ... Max Black (1909 - 1988) was a distinguished Anglo-American philosopher, who has been a leading influence in analytic philosophy in the first half of the twentieth century. ...

  • 1918-19. "Der Gedanke: Eine logische Untersuchung (Thought: A Logical Investigation)" in Beiträge zur Philosophie des Deutschen Idealismus I: 58-77.
  • 1918-19. "Die Verneinung" (Negation)" in Beiträge zur Philosophie des deutschen Idealismus I: 143-157.
  • 1923. "Gedankengefüge (Compound Thought)" in Beiträge zur Philosophie des Deutschen Idealismus III: 36-51.

Secondary

  • George Boolos, 1998. Logic, Logic, and Logic. MIT Press.
  • Michael Dummett, 1991. Frege: Philosophy of Mathematics. Harvard Uni. Press.
  • Gillies, Douglas A., 1982. Frege, Dedekind, and Peano on the foundations of arithmetic. Assen, Netherlands: Van Gorcum.
  • Ivor Grattan-Guinness, 2000. The Search for Mathematical Roots 1870-1940. Princeton Uni. Press. Fair to the mathematician, less so to the philosopher.
  • Hatcher, William, 1982. The Logical Foundations of Mathematics. Pergamon. Uses natural deduction to rederive Peano's axioms from the Grundgesetze system, recast in modern notation.
  • Hill, C. O., and Rosado Haddock, G. E., 2000. Husserl or Frege: Meaning, Objectivity, and Mathematics. Open Court. The Frege-Husserl-Cantor triangle.
  • Hans Sluga, 1980. Gottlob Frege. Routledge.

This article is not about George Boole, another mathematical logician. ... Sir Michael Anthony Eardley Dummett (born 1925) is a leading British philosopher. ... Ivor Grattan-Guiness is a prolific contemporary historian of mathematics and logic. ... Hans Sluga is Professor of Philosophy at the University of California, Berkeley. ...

External links


  Results from FactBites:
 
Gottlob Frege (907 words)
Gottlob Frege began his studies with logic, which he thought to be the simplest rules of deduction, on the basis that if the foundations of all mathematics are in arithmetic, then the foundations of arithmetic must be in logic.
Friedrich Ludwig Gottlob Frege was born on November 8, 1848, in Wismar, Germany to Karl Alexander Frege and Auguste Bialloblotzky.
Frege was one of the founders of modern symbolic logic pioneering the view that mathematics is reducible to logic.
  More results at FactBites »

 
 

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