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37. Frege and Russell

R. M. SAINSBURY


Subject Philosophy

People Frege, Gottlob , Russell, Bertrand

DOI: 10.1111/b.9780631219088.2002.00042.x


Extract

Frege was born in 1848, and spent most of his adult life in the mathematics department of the University of Jena. His first major work, the Begriffsschrift or ‘concept-script’, in which he set out his formal language, was published in 1879, when Russell was a child of seven. In his Grundlagen (Groundwork of Arithmetic) of 1884 he gave an informal exposition of his logicist position, defining numbers in terms of extensions of concepts, which he took to be a purely logical notion. The two works were brought together in his Grundgesetze (Basic Laws of Arithmetic, 1893), in which the formal devices of the Begriffsschrift were applied to the logicist programme set out in the Grundlagen. Close to this time, he wrote the two articles upon which this chapter focuses: ‘Function und Begriff of 1891 (‘Function and Concept’, 1984) and ‘ Uber Sinn und Bedeutung ’ (‘On Sense and Meaning’, 1892). Russell's first exposition of logicism, and one of his earliest works, was in his Principles of Mathematics (1903). At a late stage in its preparation, he discovered that apparently true assumptions led to a contradiction concerning classes, a discovery known as Russell's paradox. He wrote to Frege in 1903, showing that Frege's logical system in the Grundgesetze permitted a proof of the contradiction. The blow had a paralysing effect upon Frege. An appendix to volume 2 of the Grundgesetze ... log in or subscribe to read full text

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