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# Topic: Frege

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 Gottlob Frege - Wikipedia, the free encyclopedia Frege was the first to devise an axiomatization of propositional logic and of predicate logic, the latter of which was his own invention. Frege was a major proponent of logicism about arithmetic (the view that arithmetic is reducible to logic). Frege never did manage to amend his axioms to his satisfaction, although later work by Russell and by John Von Neumann suggested ways to resolve the problem. en.wikipedia.org /wiki/Gottlob_Frege   (744 words)

 Gottlob Frege - Encyclopedia.WorldSearch   (Site not responding. Last check: 2007-11-07) Friedrich Ludwig Gottlob Frege (November 8, 1848 – July 26, 1925) was a German mathematician, logician, and philosopher who is regarded as a founder of both modern mathematical logic and analytic philosophy. Frege was the first major proponent of logicism -- the view that mathematics is reducible to logic. Frege never did manage to amend his axioms to his satisfaction, although later work by Russell and by John Von Neumann showed how to resolve the problems. encyclopedia.worldsearch.com /gottlob_frege.htm   (686 words)

 Gottlob Frege [Internet Encyclopedia of Philosophy] Frege suggests also that this confusion would have the absurd result that numbers simply are the numerals, the signs on the page, and that we should be able to study their properties with a microscope. Frege suggests that rival views are often the result of attempting to understand the meaning of number terms in the wrong way, for example, in attempting to understand their meaning independently of the contexts in which they appear in sentences. Frege was then able to use this definition of the natural numbers to provide a logical analysis of mathematical induction, and prove that mathematical induction can be used validly to demonstrate the properties of the natural numbers, an extremely important result for making good on his logicist ambitions. www.utm.edu /research/iep/f/frege.htm   (9562 words)

 Frege   (Site not responding. Last check: 2007-11-07) Alexander Frege was the head of a girls' high school in Wismar and it was in that town that Gottlob was born. Frege was proud to live in the state of Mecklenburg, he loved the ducal house of Mecklenburg, and certainly believed in this form of government rather than a democratically elected one. Frege, who had not allowed the previous lack of reaction to divert him from the tasks that he had set himself, decided to delay publication of the second of his three proposed volumes. www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Frege.html   (2794 words)

 Gottlob Frege: Tutte le informazioni su Gottlob Frege su Encyclopedia.it   (Site not responding. Last check: 2007-11-07) Frege è uno dei più grandi logici dopo Aristotele ed è il padre del pensiero formale del '900. Frege è stato il primo propugnatore del logicismo -- la prospettiva secondo la quale la matematica è riducibile alla logica. In realtà, Frege non riuscì però mai ad emendare i suoi assiomi in modo soddisfacente e dopo la sua morte i teoremi di incompletezza di Gödel dimostrarono formalmente che lo scopo perseguito da Frege non era raggiungibile. www.encyclopedia.it /g/go/gottlob_frege.html   (231 words)

 Frege's New Science, Aldo Antonelli, Robert May We propose that Frege's critique rests on his view that language is a set of propositions, each immutably equipped with a truth value (as determined by the thought it expresses), so to Frege it was inconceivable that axioms could even be considered to be other than true. Because of his adherence to this view, Frege was precluded from the sort of metatheoretical considerations that were available to Hilbert; but from this, we shall argue, it does not follow that Frege was blocked from metatheory in toto. Frege had reservations about the method, however, primarily because of the apparent need to stipulate the logical terms, those terms that must be held invariant to obtain such proofs. projecteuclid.org /getRecord?id=euclid.ndjfl/1038336844   (1036 words)

 Gottlob Frege Info - Encyclopedia WikiWhat.com Friedrich Ludwig Gottlob Frege (born November 8 1848 in Wismar, died July 26 1925 in Bad Kleinen), was a German mathematician, logician, and philosopher who founded modern mathematical logic and analytic philosophy. Frege is arguably the greatest logician since Aristotle. Frege was also an important philosopher of language. www.wikiwhat.com /encyclopedia/g/go/gottlob_frege.html   (633 words)

 Gottlob Frege Frege's functional analysis of predication coupled with his understanding of generality freed him from the limitations of the ‘subject-predicate’ analysis of ordinary language sentences that formed the basis of Aristotelian logic and it made it possible for him to develop a more general treatment of inferences involving ‘every’ and ‘some’. Frege made a point of showing how every step in a proof of a proposition was justified either in terms of one of the axioms or in terms of one of the rules of inference or justified by a theorem or derived rule that had already been proved. Then Frege's definition of ‘x is an ancestor of y in the fatherhood-series’ ensured that a is an ancestor of b, c, and d, that b is an ancestor of c and d, and that c is an ancestor of d. plato.stanford.edu /entries/frege   (10319 words)

 Gottlob Frege Frege's second-order predicate calculus was based on the `function-argument' analysis of propositions and it freed logicians from the limitations of the `subject-predicate' analysis of Aristotelian logic. Frege's formal system made it possible for logicians to develop a strict definition of a proof. Frege is most well-known among philosophers, however, for suggesting that the expressions of language have both a sense and a denotation (i.e., that at least two semantic relations are required to explain the significance of linguistic expressions). mally.stanford.edu /frege.html   (610 words)

 Frege's Logic, Theorem, and Foundations for Arithmetic Thus, Frege's second-order logic and theory of extensions together required the impossible situation in which the domain of concepts has to be strictly larger than the domain of extensions while at the same time the domain of extensions has to be as large as the domain of concepts. Frege then moves from this realization, in which statements of numbers are analyzed as predicating second-level numerical concepts of first-level concepts, to develop an account of the cardinal and natural numbers as ‘self-subsistent’ objects. Frege's goal then stands in contrast to the Kantian view of the exact mathematical sciences, according to which general principles of reasoning must be supplemented by a faculty of intuition if we are to achieve mathematical knowledge. plato.stanford.edu /entries/frege-logic   (15095 words)

 Glossary of People: Fr   (Site not responding. Last check: 2007-11-07) Frege entered the University of Jena in 1869 and then went to the University of Göttingen to study mathematics, physics, chemistry, and philosophy, subsequently spending the remainder of his working life teaching all branches of mathematics at Jena. Frege devoted the next decade to a series of articles elaborating the philosophy of Logicism, but his work continued to be largely ignored and occasionally belittled. Frege's philosophy, known as Logicism, asserts all of mathematics to be derivable from logic without the use of any specifically mathematical concepts. www.marxists.org /glossary/people/f/r.htm   (3090 words)

 Philosophers : Gottlob Frege   (Site not responding. Last check: 2007-11-07) Frege was the father of modern mathematical logic. In "On Sense and Meaning" Frege grapples with the problems of the difference between meaning and reference, and between proper name and its sense. He opened up new areas in the study of sense and meaning that were widely written on for the next 5 decades. www.trincoll.edu /depts/phil/philo/phils/frege.html   (118 words)

 Concept Script: Frege Frege's attempt to set up the natural numbers in logic is based on what he calls his definition of a sequence -- this is his main application of his logic to mathematics. Frege does not specify a particular relation r which will lead to a sequence like the natural numbers -- this will first appear in Dedekind, 1888, where r is selected to be one-one, not onto, function from a domain to itself. Frege lack of serious study of his foundations of numbers, but this was to change. www.math.uwaterloo.ca /~snburris/htdocs/scav/frege/frege.html   (1883 words)

 A Slice of Philosophy: Gottlob Frege (1848-1925)   (Site not responding. Last check: 2007-11-07) Frege was born in Wismar, a German port town. Frege's main goal was to improve the foundations of mathematics and scientific work in general. Frege intended to solve the problem, but later had to resign in his efforts when he got time towork on the problems. www.findlink.dk /frege/frege.htm   (852 words)

 Björn's Guide To Philosophy - Frege   (Site not responding. Last check: 2007-11-07) Frege, son of Alexander Frege, a principal of a girls' high school, entered the University of Jena in 1869, where he studied for two years. Frege became bitter by the lack of understanding from his colleagues in his own lifetime. Frege was married but his wife died during World War I, and did not have any children of his own. www.student.liu.se /~bjoch509/philosophers/fre.html   (336 words)

 Amazon.com: Books: The Frege Reader (Blackwell Readers)   (Site not responding. Last check: 2007-11-07) This is the first single-volume edition and translation of Frege's philosophical writings to include all of his seminal papers as well as substantial selections from all three of his major works. It contains in particular Frege's four papers "Function and Concept", "On Concept and Object", "On Sense and Reference", and "Thought", and new translations of key parts of the Begriffsschrift, The Foundations of Arithmetic, and the Basic Laws of Arithmetic. The excerpts from many of Frege's letters are a great addition as these shed light on the development of his project. www.amazon.com /exec/obidos/tg/detail/-/0631194452?v=glance   (1340 words)

 AllRefer.com - Gottlob Frege (Philosophy, Biography) - Encyclopedia   (Site not responding. Last check: 2007-11-07) Frege was one of the founders of modern symbolic logic, and his work profoundly influenced Bertrand Russell. He claimed that all mathematics could be derived from purely logical principles and definitions. See P. Geach and M. Black, ed., Philosophical Writings of Gottlob Frege (1952); M. Resnik, Frege and the Philosophy of Mathematics (1980); M. Dummett, The Interpretation of Frege's Philosophy (repr. reference.allrefer.com /encyclopedia/F/Frege-Go.html   (229 words)

 Gottlob Frege Frege was one of the founders of modern Frege and the Surprising History of Logic: Introduction to Claude Imbert, "Gottlob Frege, One More Time".(Critical Essay) (Hypatia) Frege, Friedrich Ludwig Gottlob (1848-1925) (The Hutchinson Dictionary of Scientific Biography) www.infoplease.com /ce6/people/A0819624.html   (156 words)

 FREGE Alliance   (Site not responding. Last check: 2007-11-07) The FREGE mission is to secure space for free travel in commerce and trade for honorable (non-pirate) corporations. By securing trade routes for these corporations we will insure that selected regions maintain a reasonable market value for market traded commodities and maintain lower regional prices for our allies. FREGE will eventually expand and start securing further regions classified as 0.0 space. www.frege-online.com   (221 words)

 Academic Directory on Frege, Friedrich Gottlob   (Site not responding. Last check: 2007-11-07) In this essay, Kent Bach of San Francisco State University compares the theories of reference put forward by Frege and Russell, with a special focus on proper names. Edward N. Zalta of Stanford University wrote this somewhat technical entry on Frege's logic and philosophy of mathematics for the Stanford Encyclopedia of Philosophy. This paper by William W. Tait of the University of Chicago compares Frege's views on the concept of number with those of Cantor and Dedekind. www.alllearn.org /er/tree.jsp?c=40178   (362 words)

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