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	Gottlob Frege - Wikipedia, the free encyclopedia
		Frege was a major advocate of the view that arithmetic is reducible to logic, a form of logicism.
		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.
		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:
	en.wikipedia.org /wiki/Frege (1043 words)

	Gottlob Frege (Site not responding. Last check: 2007-10-21)
		Frege is widely regarded as the greatest logician since Aristotle (One of the greatest of the ancient Athenian philosophers; pupil of Plato; teacher of Alexander the Great (384-322 BC)).
		Frege was the first major proponent of logicism ((philosophy) the philosophical theory that all of mathematics can be derived from formal logic) -- 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 (United States mathematician who contributed to the development of atom bombs and of stored-program digital computers (1903-1957)) showed how to resolve the problems.
	www.absoluteastronomy.com /encyclopedia/g/go/gottlob_frege.htm (562 words)

	Talk:Gottlob Frege - Wikipedia, the free encyclopedia
		Frege's contribution was the way he expressed quantification by means of variables; he did not invent quantification itself.
		Frege did not create a separate theory of propositional logic, as the above suggests, and actually it is an achievement of Frege's to combine propositional connectives and quantifiers in one calculus.
		Frege never did manage to amend his axioms to his satisfaction, however; and after Frege's death, Kurt Gödel's incompleteness theorems showed that Frege's logicist program was impossible.
	en.wikipedia.org /wiki/Talk:Gottlob_Frege (1628 words)

	Gottlob Frege [Internet Encyclopedia of Philosophy] (Site not responding. Last check: 2007-10-21)
		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.iep.utm.edu /f/frege.htm (9562 words)

	Gottlob Frege
		Frege took intransitive verb phrases such as ‘is happy’ to be functions of one variable (‘x is happy’), and resolved the sentence "John is happy" in terms of the application of the function denoted by ‘is happy’ to the argument denoted by ‘John’.
		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.
		To solve these puzzles, Frege suggested that the terms of a language have both a sense and a denotation (i.e., that at least two semantic relations are required to explain the significance or meaning of the terms of a language).
	www.seop.leeds.ac.uk /archives/fall2003/entries/frege (5231 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.
		Frege saw himself very much in the spirit of Bolzano (1817), who eliminated the appeal to intuition in the proof of the intermediate value theorem in the calculus by proving this theorem from the definition of continuity, which had recently been defined in terms of the definition of a limit (see Coffa 1991, 27).
	plato.stanford.edu /entries/frege (10319 words)

	AllRefer.com - Gottlob Frege (Philosophy, Biography) - Encyclopedia
		Gottlob Frege[gOt´lOp frA´gu] Pronunciation Key, 1848–1925, German philosopher and mathematician.
		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.
	reference.allrefer.com /encyclopedia/F/Frege-Go.html (229 words)

	Glossary of People: Fr (Site not responding. Last check: 2007-10-21)
		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 was a Lutheran and a political reactionary.
		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.
	www.marxists.org /glossary/people/f/r.htm (3090 words)

	Gottlob Frege on Being, Existence, and Truth
		Milton Fisk: A paradox in Frege's semantics 382; 24.
		According to Burge, Frege is committed to the doctrine that logic is primarily concerned with the normative notion of truth.
		Haaparanta focuses her attention on Frege's concept of existence, which receives special attention in Frege's thought in connection with the thesis concerning the ambiguity of such words for being as the English `is'.
	www.formalontology.it /fregeg.htm (5354 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)

	Philosophers : Gottlob Frege (Site not responding. Last check: 2007-10-21)
		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)

	MSN Encarta - Gottlob Frege
		Gottlob Frege (1848-1925), German mathematician and philosopher, the founder of modern mathematical logic.
		Frege sought to derive the principles of arithmetic from the principles of logic.
		Faced with the ambiguity of ordinary language and the inadequacy of available logical systems, he invented many symbolic notations, such as quantifiers and variables, thus providing the foundation for modern mathematical logic.
	encarta.msn.com /encnet/refpages/RefArticle.aspx?refid=761558232 (161 words)

	A Slice of Philosophy: Gottlob Frege (1848-1925) (Site not responding. Last check: 2007-10-21)
		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)

	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.
		Despite the fact that a contradiction invalidated his system, Frege validly derived the Peano Axioms governing the natural numbers from a powerful and consistent principle now known as Hume's Principle (some philosophers have proposed that the derivation of the Peano Axioms from Hume's Principle should be called `Frege's Theorem').
		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)

	Philosophical Dictionary: Four Terms-Fuzzy Logic
		Frege was an early exponent of the view that arithmetical truth could be established on purely logical grounds.
		In "Über Sinn und Bedeutung" ("On Sense and Reference") (1892), Frege proposed a strict distinction between the sense and the reference of terms as a way of avoiding difficult epistemological paradoxes about informative statements of identity.
		Also see SEP on Frege and the foundations of arithmetic, IEP, and Edward Zalta, MMT, ColE, Andy Blunden, DPM, ELC, and BIO.
	www.philosophypages.com /dy/f9.htm (869 words)

	Gottlob Frege -- Encyclopædia Britannica
		Working on the borderline between philosophy and mathematics—viz., in the philosophy of mathematics and mathematical logic (in which no intellectual precedents existed)—Frege discovered, on his own, the fundamental ideas that have made possible the whole modern development of logic and thereby...
		A German mathematician and philosopher, Gottlob Frege was the founder of modern mathematical logic.
		Considered the great Danish national poet, Adam Gottlob Oehlenschläger was a leader of the Romantic movement in 19th-century Denmark.
	www.britannica.com /eb/article-9035314 (694 words)

	NS: Gottlob Frege - Recreated LOGIC by constructing Predicate Calculus 2001-10-25 (Site not responding. Last check: 2007-10-21)
		Gottlob Frege (1848 - 1925) was a German mathematician, logician, and philosopher who worked at the University of Jena.
		One of the axioms that Frege later adopted for his system, in the attempt
		The external representations are readable by humans and may also be used in communications between humans or between humans and machines.
	www.hi.is /~joner/eaps/cs_frege.htm (375 words)

	Gottlob Frege at PhilosophyClassics.com -- essays, resources
		Stanford Encyclopedia of Philosophy - Gottlob Frege -- Outlines Frege's work in logic, ontology, and the philosophy of language.
		Frege: Two Theses, Two Senses -- Penco's thesis is that there is a tension in Frege's account of the interconnectedness of thoughts and sentences.
		Own thousands of works of classic literature for less than 3c a book: our Classics Digital Library CD is the intelligent way to read and interact with the classics.
	www.philosophyclassics.com /philosophers/Frege (342 words)

	Academic Directory on Frege, Friedrich Gottlob (Site not responding. Last check: 2007-10-21)
		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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