## Quick Reference

(1848–1925)

German mathematician, logician, and philosopher who laid the foundations for modern investigations into the philosophy of logic and language.

Born in Wismar (now East Germany), the son of a clergyman, he spent his entire career at the University of Jena, being appointed professor of mathematics in 1896. His first important book, Die Grundlagen der Arithmetik (1884; translated as The Foundations of Arithmetic, 1950), was little noticed. In it he argued that number could be defined in terms of the more fundamental notion of a class and went on to argue that mathematics could be derived from logic. For the next twenty years Frege sought to develop such a derivation and to present it in a completely formal manner. The task seemed to have been triumphantly completed in 1903, when he prepared for publication of the second volume of his Grundgesetze der Arithmetik (translated as The Basic Laws of Arithmetic, 1964). But before the work could appear Frege received a letter from Bertrand Russell informing him that a contradiction had been found in his system. All he could do was to add a postscript lamenting: ‘Hardly anything more unfortunate can befall a scientific writer than to have one of the foundations of his edifice shaken after the work is finished.’ Yet what was at stake, he could justifiably point out, was ‘not just my particular way of establishing arithmetic, but whether arithmetic can possibly be given a logical foundation at all’.

If Frege did not succeed in reducing mathematics to logic he had at least managed to identify the problem. He had earlier, in his Begriffsschrift (1879; translated as Conceptual Notation, 1972) developed a workable logical notation and shown in some detail the kind of logic that mathematics would have to be derived from. It was one in which, for the first time, predicates and quantifiers could be handled as readily as propositions. Frege also, in such classic papers as Über Sinn und Bedeutung (1892; translated as Sense and Reference, 1940) and Begriff und Gegenstand (1892; translated as Concept and Object, 1952), began to explore the interrelations between such important concepts as meaning, reference, truth, negation, thought, and function. The exploration has continued uninterrupted ever since.

It would be difficult to overestimate the influence of Frege on modern logic and philosophy. Since his introduction by Russell (in 1903) to a wider public his work has come to be more and more discussed by each succeeding generation.

*Subjects:*
philosophy.