Gottlob Frege
>From Wikipedia, the free encyclopedia Western Philosophy 19th-century philosophy, Friedrich Ludwig Gottlob Frege <http://upload.wikimedia.org/wikipedia/en/thumb/3/34/Frege.jpg/200px-Frege.j pg> 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, Wismar 26 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. Contents * 1 Life * 2 Logician * 3 Philosopher * 4 References * 5 External links [edit] 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. 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. [edit] Logician Main article: Begriffsschrift Frege is widely regarded 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. 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). 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. [edit] Philosopher Main article: On Sense and Reference 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: * Function-argument analysis of the proposition; * Distinction between the sense and reference (Sinn und Bedeutung) of a proper name (Eigenname); * Advocacy of a mediated reference theory; * Distinction between concept and object (Begriff und Gegenstand); * Advancement of the context principle. * Formulation of the principle of compositionality. 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. 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. [edit] References Primary * Online bibliography of Frege's works and their English translations. <http://www.ocf.berkeley.edu/~brianwc/frege/fenglish.html> * 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. * 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. [edit] External links * A comprehensive guide to Fregean material available on the web; by Brian Carver. <http://www.ocf.berkeley.edu/~brianwc/frege/> * Stanford Encyclopedia of Philosophy: Gottlob Frege. <http://plato.stanford.edu/entries/frege/> * Stanford Encyclopedia of Philosophy: Frege's Logic. <http://plato.stanford.edu/entries/frege-logic/> * Internet Encyclopedia of Philosophy: Gottlob Frege. <http://www.utm.edu/research/iep/f/frege.htm> * Internet Encyclopedia of Philosophy: Frege and Language. <http://www.utm.edu/research/iep/f/freg-lan.htm> * Frege on Being, Existence and Truth. <http://www.formalontology.it/fregeg.htm> Retrieved from "http://en.wikipedia.org/wiki/Gottlob_Frege"; _______________________________________________ Marxism-Thaxis mailing list [email protected] To change your options or unsubscribe go to: http://lists.econ.utah.edu/mailman/listinfo/marxism-thaxis
