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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 mathematics, mathematical logic, Philosophy of language
Notable ideas Predicate calculus, Logicism, Sense and reference
Influenced Giuseppe Peano, Bertrand Russell, Rudolf Carnap, Ludwig Wittgenstein, Michael Dummett, Edmund Husserl, and most of the analytic tradition

Friedrich Ludwig Gottlob Frege (8 November 1848, Wismar, Grand Duchy of Mecklenburg-Schwerin – 26 July 1925, Bad Kleinen, Germany) (IPA: [ˈgɔtlop ˈfʁeːgə]) was a German mathematician who became a logician and philosopher. In the 18th century the philosophies of The Enlightenment began to have a dramatic effect the landmark works of philosophers such as Immanuel Kant and Jean-Jacques Events 1519 - Hernán Cortés enters Tenochtitlán and Aztec ruler Moctezuma welcomes him with great a Celebration Year 1848 ( MDCCCXLVIII) was a Leap year starting on Saturday (link will display the full calendar of the Gregorian Calendar (or a Leap Events 657 - Battle of Siffin. 811 - Battle of Pliska; Byzantine Emperor Nicephorus Year 1925 ( MCMXXV) was a Common year starting on Thursday (link will display the full calendar of the Gregorian calendar. Analytic philosophy (sometimes analytical philosophy) is a generic term for a style of Philosophy that came to dominate English-speaking countries in the 20th century The philosophy of mathematics is the branch of Philosophy that studies the philosophical assumptions foundations and implications of Mathematics. Mathematical logic is a subfield of Logic and Mathematics with close connections to Computer science and Philosophical logic. Philosophy of language is the reasoned inquiry into the nature origins and usage of Language. In Mathematical logic, predicate logic is the generic term for symbolic Formal systems like First-order logic, Second-order logic, Many-sorted 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 The distinction between Sinn and Bedeutung (usually but not always translated sense and reference, respectively was an innovation of the German philosopher Giuseppe Peano ( August 27, 1858 &ndash April 20, 1932) was an Italian Mathematician, whose work was of exceptional Bertrand Arthur William Russell 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970 was a British Philosopher, Historian Rudolf Carnap ( May 18, 1891 &ndash September 14, 1970) was an influential German -born philosopher who was active in Sir Michael Anthony Eardley Dummett FBA DLitt (born 1925 is a leading British Philosopher. Edmund Gustav Albrecht Husserl (ˈhʊsɛrl April 8 1859 – April 26 1938) was a philosopher, known as the father of Analytic philosophy (sometimes analytical philosophy) is a generic term for a style of Philosophy that came to dominate English-speaking countries in the 20th century Events 1519 - Hernán Cortés enters Tenochtitlán and Aztec ruler Moctezuma welcomes him with great a Celebration Year 1848 ( MDCCCXLVIII) was a Leap year starting on Saturday (link will display the full calendar of the Gregorian Calendar (or a Leap Wismar (ˈvɪsmaʁ is a small port and Hanseatic League town in northern Germany on the Baltic Sea, in the state of Mecklenburg-Vorpommern,about Mecklenburg-Schwerin was a Duchy (from 1815 a Grand duchy) in northern Germany, formed by a partition of the Duchy of Mecklenburg. Events 657 - Battle of Siffin. 811 - Battle of Pliska; Byzantine Emperor Nicephorus Year 1925 ( MCMXXV) was a Common year starting on Thursday (link will display the full calendar of the Gregorian calendar. Bad Kleinen is a municipality in the Nordwestmecklenburg district in Mecklenburg-Vorpommern, Germany. Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Logic is the study of the principles of valid demonstration and Inference. Philosophy is the study of general problems concerning matters such as existence knowledge truth beauty justice validity mind and language He helped found both modern mathematical logic and analytic philosophy. Mathematical logic is a subfield of Logic and Mathematics with close connections to Computer science and Philosophical logic. Analytic philosophy (sometimes analytical philosophy) is a generic term for a style of Philosophy that came to dominate English-speaking countries in the 20th century His work has exerted a fundamental and far-reaching influence on 20th-century philosophy. See also [[Analytic philosophy]] and [[Continental philosophy]] The 20th century brought with it upheavals that produced a series of conflicting developments within Philosophy

Contents

Life

Childhood (1848–1869)

Frege was born in 1848 in Wismar, in the state of Mecklenburg-Schwerin (the modern German federal state Mecklenburg-Vorpommern). Wismar (ˈvɪsmaʁ is a small port and Hanseatic League town in northern Germany on the Baltic Sea, in the state of Mecklenburg-Vorpommern,about Mecklenburg-Schwerin was a Duchy (from 1815 a Grand duchy) in northern Germany, formed by a partition of the Duchy of Mecklenburg. Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. Mecklenburg-Vorpommern, sometimes translated as Mecklenburg-Western Pomerania or Mecklenburg-West Pomerania, is a state in Northern Germany comprising His father, Karl Alexander Frege, was the founder of a girls' high school, of which he was the headmaster until his death in 1866. High school is the name used in some parts of the world (in particular Scotland, North America and Australia) to describe an institution Afterwards, the school was led by Frege's mother, Auguste Wilhelmine Sophie Frege (née Bialloblotzky, apparently of Polish extraction). The Polish people, or Poles, (Polacy) are a Western Slavic Ethnic group of Central Europe, living predominantly in Poland.

In childhood, Frege encountered philosophies that would guide his future scientific career. For example, his father wrote a textbook on the German language for children aged 9-13, the first section of which dealt with the structure and logic of language. A textbook is a manual of instruction or a standard book in any branch of study Logic is the study of the principles of valid demonstration and Inference. A language is a dynamic set of visual auditory or tactile Symbols of Communication and the elements used to manipulate them

Frege studied at a gymnasium in Wismar, and graduated at the age of 15. A gymnasium (pronounced with ɡ- in several languages is a type of school providing Secondary education in some parts of Europe, comparable to English grammar His teacher Leo Sachse (also a poet) played the most important role in determining Frege’s future scientific career, encouraging him to continue his studies at the University of Jena. A poet is a person who writes Poetry. Etymology From the Ancient greek: ποιέω, poieō: "I make or compose" Friedrich Schiller University of Jena (FSU is located in Jena, Thuringia in Germany and was renamed for the German writer Friedrich Schiller

Studies at University: Jena and Göttingen (1869 – 1874)

Frege matriculated at the University of Jena in the spring of 1869 as a citizen of the North German Federation. The North German Confederation (Norddeutscher Bund came into existence in August 1866 as a military alliance of 22 states of northern Germany with the Kingdom of In the four semesters of his studies there he attended approximately 20 courses of lectures, most of them on mathematics and physics. An academic term is a division of an academic year the time during which a School, College or University holds classes A lecture is an oral Presentation intended to present information or teach people about a particular subject for example by a University or College Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. The teacher most important to him was Ernst Abbe (physicist, mathematician, and inventor). Ernst Karl Abbe ( January 23, 1840 &ndash January 14, 1905) was a German Physicist and professor at the University A physicist is a Scientist who studies or practices Physics. Physicists study a wide range of physical phenomena in many branches of physics spanning A mathematician is a person whose primary area of study and research is the field of Mathematics. An inventor is a person who creates or discovers a new method form device or other useful means Abbe gave lectures on theory of gravity, galvanism and electrodynamics, theory of functions of a complex variable, applications of physics, selected divisions of mechanics, and mechanics of solids. Gravitation is a natural Phenomenon by which objects with Mass attract one another Biology, galvanism is the contraction of a Muscle that is stimulated by an electric current. Classical electromagnetism (or classical electrodynamics) is a theory of Electromagnetism that was developed over the course of the 19th century most prominently Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of Mathematics investigating functions of Complex Mechanics ( Greek) is the branch of Physics concerned with the behaviour of physical bodies when subjected to Forces or displacements A solid' object is in the States of matter characterized by resistance to Deformation and changes of Volume. Abbe was more than a teacher to Frege: he was a trusted friend, and, as director of the optical manufacturer Zeiss, he was in a position to advance Frege's career. After Frege's graduation, they came into closer correspondence.

His other notable university teachers were Karl Snell (subjects: use of infinitesimal analysis in geometry, analytical geometry of planes, analytical mechanics, optics, physical foundations of mechanics); Hermann Schäffer (analytical geometry, applied physics, algebraic analysis, on the telegraph and other electronic machines); and the famous philosopher, Kuno Fischer (history of Kantian and critical philosophy). Infinitesimals (from a 17th century Modern Latin coinage infinitesimus, originally referring to the " Infinite[[ th]]" member of a series have Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of Geometry Analytical mechanics is a term used for a refined highly mathematical form of Classical mechanics, constructed from the Eighteenth century onwards as a formulation Algebra is a branch of Mathematics concerning the study of structure, relation, and Quantity. Electronics refers to the flow of charge (moving Electrons through Nonmetal conductors (mainly Semiconductors, whereas electrical Kuno Fischer, born Ernst Kuno Berthold Fischer, ( July 23, 1824 in Sandewalde bei Guhrau - July 5, 1907 in Heidelberg Kantianism is the philosophy of Immanuel Kant, a German philosopher born in Königsberg, Germany (now Kaliningrad, Russia Attributed to Immanuel Kant, the critical philosophy movement sees the primary task of Philosophy as Criticism rather than justification of knowledge criticism

Starting in 1871, Frege continued his studies in Göttingen, the leading university in mathematics in German-speaking territories, where he attended the lectures of Alfred Clebsch (analytical geometry), Ernst Schering (function theory), Wilhelm Weber (physical studies, applied physics), Eduard Riecke (theory of electricity), and Rudolf Hermann Lotze (philosophy of religion). Göttingen ( ˈgœtɪŋən, Low German: Chöttingen is a College town in Lower Saxony, Germany. Rudolf Friedrich Alfred Clebsch ( 19 January 1833 – 7 November 1872) was a German Mathematician who made important contributions Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of Geometry Ernst Christian Friedrich Schering ( May 31, 1824 &ndash December 27, 1889) was a German apothecary and industrialist who created Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of Mathematics investigating functions of Complex Wilhelm Eduard Weber ( October 24, 1804 &ndash June 23, 1891) was a German Physicist. Rudolf Hermann Lotze ( 21 May, 1817 – 1 July, 1881) was a German Philosopher and Logician. Philosophy of religion is a branch of Philosophy that is concerned with the philosophical study of religion including arguments over the nature and existence of God religious (Many of the philosophical doctrines of the mature Frege have parallels in Lotze; it has been the subject of scholarly debate whether there was a direct influence arising from Frege's attending Lotze's lectures. )

In 1873, Frege attained his doctorate under Ernst Schering, with a dissertation under the title of "Über eine geometrische Darstellung der imaginären Gebilde in der Ebene" ("'On a Geometrical Representation of Imaginary Forms in a Plane"), in which he aimed to solve such fundamental problems in geometry as the mathematical interpretation of projective geometry's infinitely distant (imaginary) points. A doctorate is an Academic degree that indicates the highest level of academic achievement A dissertation (also called thesis or disquisition) is a document that presents the author's Research and findings and is submitted in support of candidature Projective geometry is a non- metrical form of Geometry, notable for its principle of duality.

Work as a logician

Main article: Begriffsschrift
Gottlob Frege
Gottlob Frege

Though his education and early work were mathematical, and especially geometrical, Frege's thought soon turned to logic. 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 His 1879 Begriffsschrift (Concept Script) marked a turning point in the history of logic. 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 The Begriffsschrift broke new ground, including a rigorous treatment of the ideas of functions and variables. The Mathematical concept of a function expresses dependence between two quantities one of which is given (the independent variable, argument of the function A variable (ˈvɛərɪəbl is an Attribute of a physical or an abstract System which may change its Value while it is under Observation. Frege wanted to show that mathematics grew out of logic, but in so doing devised techniques that took him far beyond the Aristotelian syllogistic and Stoic propositional logic that had come down to him in the logical tradition. Logic is the study of the principles of valid demonstration and Inference.

Title page to Begriffsschrift (1879)
Title page to Begriffsschrift (1879)

In effect, he invented axiomatic predicate logic, in large part thanks to his invention of quantified variables, which eventually became ubiquitous in mathematics and logic, and solved the problem of multiple generality. In Mathematics, an axiomatic system is any set of Axioms from which some or all axioms can be used in conjunction to logically derive Theorems In Mathematical logic, predicate logic is the generic term for symbolic Formal systems like First-order logic, Second-order logic, Many-sorted Quantification has two distinct meanings In Mathematics and Empirical science, it refers to human acts known as Counting and Measuring Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and The problem of multiple generality names a failure in Traditional logic to describe certain intuitively valid inferences Previous logic had dealt with the logical constants and, or, if. In Symbolic logic, a logical constant of a language L is a Symbol that has the same semantic value in all models of (the expressions . . then. . . , not, and some and all. But iterations of these operations, especially "some" and "all", were little understood: even the distinction between a pair of sentences like "every boy loves some girl" and "some girl is loved by every boy" could only be represented very artificially, whereas Frege's formalism would have no difficulty expressing the different readings of "every boy loves some girl who loves some boy who loves some girl" and similar sentences, in complete parallel with his treatment of, say, "every boy is foolish". It is frequently noted that Aristotle's logic would not be able to represent even the most elementary inferences in Euclid's geometry, but Frege's "conceptual notation" could represent inferences involving indefinitely complex mathematical statements. The analysis of logical concepts and the machinery of formalization that is essential to Bertrand Russell's theory of descriptions and Principia Mathematica (with Alfred North Whitehead), and to Gödel's incompleteness theorems, and to Alfred Tarski's theory of truth, is ultimately due to Frege. Bertrand Arthur William Russell 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970 was a British Philosopher, Historian The theory of descriptions is one of the philosopher Bertrand Russell 's most significant contributions to the Philosophy of language. The Principia Mathematica is a 3-volume work on the Foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell Alfred North Whitehead, OM ( February 15 1861, Ramsgate, Kent, England &ndash December 30 1947, Kurt Gödel (kʊɐ̯t ˈgøːdl̩ (April 28 1906 – January 14 1978 was an Austrian American Logician, Mathematician and Philosopher In Mathematical logic, Gödel's incompleteness theorems, proved by Kurt Gödel in 1931 are two Theorems stating inherent limitations of all but the most Alfred Tarski ( January 14, 1901, Warsaw, Russian ruled Poland – October 26, 1983, Berkeley California

One of Frege's stated purposes was to isolate genuinely logical principles of inference, so that in the proper representation of mathematical proof, one would at no point appeal to "intuition". If there was an intuitive element it was to be isolated and represented separately as an axiom: from there on the proof was to be purely logical and without gaps. Having exhibited this possibility, Frege's more ultimate purpose was to defend the view that arithmetic is a branch of logic, a view known as logicism: unlike geometry it was to be shown to have no basis in "intuition," and no need on non-logical axioms. Arithmetic or arithmetics (from the Greek word αριθμός = number is the oldest and most elementary branch of mathematics used by almost everyone 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 Already in the 1879 Begriffsschrift important preliminary theorems, for example a generalized form of mathematical induction, were derived within what he understood to be pure logic. Mathematical induction is a method of Mathematical proof typically used to establish that a given statement is true of all Natural numbers It is done by proving that

This idea was formulated in non-symbolic terms in his "Foundations of Arithmetic" of 1884. Later, in the "Basic Laws of Arithmetic" (Grundgesetze der Arithmetik (1893, 1903)), published at its author's expense, he attempted to derive all of the laws of arithmetic by use of his symbolism from axioms he asserted as logical. Most of these axioms were carried over from his Begriffsschrift, though not without some significant changes. 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 The one truly new principle was one he called the Basic Law V: the "value-range" of the function f(x) is the same as the "value-range" of the function g(x) if and only if ∀x[f(x) = g(x)]. The crucial case of the law may be formulated in modern notation as follows. Let {x|Fx} denote the extension of the predicate Fx, i. The extension of a predicate a Truth-valued function is the set of Tuples of values that used as arguments satisfy the predicate Sometimes it is inconvenient or impossible to describe a set by listing all of its elements e. , the set of all Fs, and similarly for Gx. Then Basic Law V says that the predicates Fx and Gx have the same extension iff ∀x[Fx ↔ Gx]. ↔ The set of Fs is the same as the set of Gs just in case every F is a G and every G is an F. (The case is special because what is here being called the extension of a predicate, or a set, is only one type of "value-range" of a function. )

In a famous episode, Bertrand Russell wrote to Frege, just as Vol. 2 of the Grundgesetze was about to go to press in 1903, showing that Russell's paradox could be derived from Frege's Basic Law V. Part of the Foundations of mathematics, Russell's paradox (also known as Russell's antinomy) discovered by Bertrand Russell in 1901 showed that the It is easy to define the relation of membership of a set or extension in Frege's system; Russell then drew attention to the set of things x that are such that x is not a member of x. The system of the Grundgesetze entails both that it is and that it was not a member of itself, and was thus inconsistent. Frege wrote a hasty last-minute appendix to vol. 2, deriving the contradiction and proposing to eliminate it by modifying Basic Law V. (This letter and Frege's reply are translated in Jean van Heijenoort 1967. Jean Louis Maxime Van Heijenoort (pronounced highenort) ( July 23 1912, Creil France - March 29 1986, Mexico City )

Frege's proposed remedy was subsequently shown to imply that there is but one object in the universe of discourse, and hence is worthless (indeed this would make for a contradiction in Frege's system if he had axiomatized the idea, fundamental to his discussion, that the True and the False are distinct objects; see e. The domain of discourse, sometimes called the universe of discourse, logical discourse, or simply discourse, is an analytic tool used in Deductive g. Dummett 1973). Sir Michael Anthony Eardley Dummett FBA DLitt (born 1925 is a leading British Philosopher. But recent work has shown that much of the program of the Grundgesetze might be salvaged in other ways:

Frege's work in logic was little recognized in his day, in considerable part because his peculiar diagrammatic notation had no antecedents; it has since had no imitators. Moreover, until Principia Mathematica appeared, 1910-13, the dominant approach to mathematical logic was still that of George Boole and his descendants, especially Ernst Schroeder. The Principia Mathematica is a 3-volume work on the Foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell 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. For the actor see Ernst Schröder (actor. Ernst Schröder ( 25 November, 1841 Mannheim Germany – Frege's logical ideas nevertheless spread through the writings of his student Rudolf Carnap and other admirers, particularly Bertrand Russell and Ludwig Wittgenstein. Rudolf Carnap ( May 18, 1891 &ndash September 14, 1970) was an influential German -born philosopher who was active in

Philosopher

Main article: On Sense and Reference

Frege is one of the founders of analytic philosophy, mainly because of his contributions to the philosophy of language, including the:

As a philosopher of mathematics, Frege attacked the psychologistic appeal to mental explanations of the content of judgment of the meaning of sentences. Psychologism is a generic type of position in Philosophy according to which Psychology plays a central role in grounding or explaining some other non-psychological His original purpose was very far from answering general questions about meaning; instead, he devised his logic to explore the foundations of arithmetic, undertaking to answer questions such as "What is a number?" or "What objects do number-words ("one", "two", etc. ) refer to?" But in pursuing these matters, he eventually found himself analysing and explaining what meaning is, and thus came to several conclusions that proved highly consequential for the subsequent course of analytic philosophy and the philosophy of language. Analytic philosophy (sometimes analytical philosophy) is a generic term for a style of Philosophy that came to dominate English-speaking countries in the 20th century Philosophy of language is the reasoned inquiry into the nature origins and usage of Language.

It should be kept in mind that Frege was employed as a mathematician, not a philosopher, and published his philosophical papers in scholarly journals that often were hard to access outside of the German speaking world. He never published a philosophical monograph other than The Foundations of Arithmetic, much of which was mathematical in content, and the first collections of his writings appeared only after World War II. A volume of English translations of Frege's philosophical essays first appeared in 1952, edited by students of Wittgenstein, Peter Geach and Max Black, with the bibliographic assistance of Wittgenstein (see Geach, ed. Peter Thomas Geach (giːtʃ born 29 March 1916) is a British philosopher Max Black ( 24 February 1909, Baku, Russian Empire [[Azerbaijan]] – 27 August 1988, 1975, introduction). Hence despite the generous praise of Russell and Wittgenstein, Frege was little known as a philosopher during his lifetime. His ideas spread chiefly through those he influenced, such as Russell, Wittgenstein, and Carnap, and through Polish work on logic and semantics.

"Sinn" and "Bedeutung"

The distinction between Sinn and Bedeutung (usually translated "Sense and Reference", but also as "Sense and Meaning" or "Sense and Denotation") was an innovation of Frege in his 1892 paper Über Sinn und Bedeutung ("On Sense and Reference"). The distinction between Sinn and Bedeutung (usually but not always translated sense and reference, respectively was an innovation of the German philosopher According to Frege, sense and reference are two different aspects of the significance of an expression. Frege applied "Bedeutung" in the first instance to proper names, where it means the bearer of the name, the object in question, but then also to other expressions, including complete sentences, which bedeuten the two "truth values", the true and the false; by contrast, the sense or Sinn associated with a complete sentence is the thought it expresses. The sense of an expression is said to be the "mode of presentation" of the item referred to. The distinction can be illustrated thus: In their ordinary uses, the name "Charles Philip Arthur George Mountbatten-Windsor," which for logical purposes is an unanalyzable whole, and the functional expression "the Prince of Wales," which contains the significant parts "the prince of ξ" and "Wales", have the same reference, namely the person best known as Prince Charles. But the sense of the word "Wales" is a part of the sense of the latter expression, but no part of the sense of the "full name" of Prince Charles. These distinctions were disputed by Bertrand Russell, especially in his paper "On Denoting"; the controversy has continued into the present, fueled especially by the famous lectures on "Naming and Necessity" of Saul Kripke. " On Denoting " written by Bertrand Russell, is one of the most significant and influential philosophical essays of the 20th century Naming and Necessity is a book by the philosopher Saul Kripke that was first published in 1980 Saul Aaron Kripke (born on November 13, 1940 in Bay Shore New York) is an American philosopher and Logician now Emeritus

Important dates

Important works

Logic; foundation of arithmetic

Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens (1879). 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 Halle a. S.

Die Grundlagen der Arithmetik: eine logisch-mathematische Untersuchung über den Begriff der Zahl (1884). Breslau.

Grundgesetze der Arithmetik, Band I (1893); Band II (1903). Jena: Verlag Hermann Pohle.

Philosophical studies

Function and Concept (1891)

On Sense and Reference (1892)

Concept and Object (1892)

What is a Function? (1904)

Logical Investigations (1918–1923) Frege intended that the following three papers be published together in a book titled Logische Untersuchungen (Logical Investigations). Though the German book never appeared, English translations did appear together in Logical Investigations, ed. Peter Geach, Blackwells, 1975.

Articles on geometry

References

Primary

Secondary

Philosophy:

Logic and mathematics:

External links


Persondata
NAME Frege, Friedrich Ludwig Gottlob
ALTERNATIVE NAMES Frege, Gottlob
SHORT DESCRIPTION Important German logician and philosopher
DATE OF BIRTH November 8, 1848
PLACE OF BIRTH Wismar
DATE OF DEATH July 26, 1925
PLACE OF DEATH Bad Kleinen

Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. Logic is the study of the principles of valid demonstration and Inference. Philosophy is the study of general problems concerning matters such as existence knowledge truth beauty justice validity mind and language Events 1519 - Hernán Cortés enters Tenochtitlán and Aztec ruler Moctezuma welcomes him with great a Celebration Year 1848 ( MDCCCXLVIII) was a Leap year starting on Saturday (link will display the full calendar of the Gregorian Calendar (or a Leap Wismar (ˈvɪsmaʁ is a small port and Hanseatic League town in northern Germany on the Baltic Sea, in the state of Mecklenburg-Vorpommern,about Events 657 - Battle of Siffin. 811 - Battle of Pliska; Byzantine Emperor Nicephorus Year 1925 ( MCMXXV) was a Common year starting on Thursday (link will display the full calendar of the Gregorian calendar. Bad Kleinen is a municipality in the Nordwestmecklenburg district in Mecklenburg-Vorpommern, Germany.
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