Frege, (Friedrich Ludwig) Gottlob
Frege, (Friedrich Ludwig) Gottlob
1848-1925, German mathematician and logician. Professor of mathematics at the University of Jena, 1879-1918. Largely unknown to, or misunderstood by, his contemporaries, he is now regarded by many as “beyond question the greatest logician of the Nineteenth Century” (quotation from Tarski). He must be regarded — after Boole (q. v.) — as the second founder of symbolic logic, the essential steps in the passage from the algebra of logic to the logistic method (see the article Logistic system) having been taken in his Begriffsschrift of 1879. In this work there appear tor the first time the propositional calculus in substantially its modern form, the notion of propositional function, the use of quantifiers, the explicit statement of primitive rules of inference, the notion of an hereditary property and the logical analysis of proof by mathematical induction or recursion (q. v.). This last is perhaps the most important element in the definition of an inductive cardinal number (q.v.) and provided the basis for Frege’s derivation of arithmetic from logic in his Grundlagen der Anthmetik (1884) and Grundgesetze der Arithmetik, vol. 1 (1893), and vol. 2 (1903). The first volume of Grundgesetze der Arithmetik is the culmination of Frege’s work, and we find here many important further ideas. In particular, there is a careful distinction between using a formula to express something else and naming a formula in order to make a syntactical statement about it, quotation marks being used in order to distinguish the name of a formula from the formula itself. In an appendix to the second volume of Grundgesetze , Frege acknowledges the presence of an inconsistency in his system through what is now known as the Russel paradox (see Paradoxes , logical), as had been called to his attention by Russell when the book was nearly through the press. — A.C.
P.E.B. Jourdain,
Gottlob Frege, The Quarterly Journal of Pure and Applied Mathematics, vol. 43 (1912), pp. 237-269.
H Scholz,
Was ist ein Kalkul und was hat Frege fur eine punktliche Beantwortung dieser Frage geleistet?, Semester-Berichte (Mnster i. W.), summer 1935, pp. 16-47.
Scholz and Bachmann,
Der wissenschaftliche Nachlass von Gottlob Frege, Actes du Congres International de Philosophie Scientifique (Pans, 1936), section VIII, pp. 24-30.