John Stuart Mill
From Sun Wen Hsueh Shu by Sun Yat-sen, 1919
The science of naming is nominalism and is not logic at all. The former represented one of the two great schools of thought in the medieval age. The other opposing school was represented by realism. Followers of the rival camps waged bitter struggles during the 11th century which continued until the middle of the 12th century. Thenceforth the study of nominalism steadily declined.
From THE PROBLEM OF KNOWLEDGE, 1940 by Ernst Cassirer
The first prominent mathematician to restore this dignity [“of the human spirit”] by a strictly logical deduction of the theory of numbers was Frege, and his Elements of Arithmetic grew out of this endeavor. The pitiless acidity with which it exposed the psychological bias in Mill’s theory of mathematics paved the way for Husserl’s criticism in his Logische Untersuchungen (1900). According to Frege if the cooperation between philosophy and mathematics had led so far to no real result despite numerous attempts on the part of both it was because philosophy was still entangled in a prejudice of psychologism which it must lay aside if it was ever to recognize the true nature of mathematics.6 An interpretation like that of Mill, which regarded number not as a definite concept but only as an idea “in the mind,” consequently reducing it to the rank of the merely subjective, could never lead to any real development of the theory of numbers ; it must always remain “an arithmetic of cookies or pebbles.” The essential insight that Frege’s book means to vindicate against such an interpretation was that the actual truth value of the science of numbers as well as its strictly objective character can be established only when we sharply distinguish it from anything having to do with “things.” Statements about number and statements about objects are quite distinct in meaning, and whoever confuses the one with the other has not laid a foundation for arithmetic but rather has misunderstood and falsified its substance.
Author Mill, John Stuart, 1806-1873. Uniform Title [ Correspondence. English. Selections] Title The correspondence of John Stuart Mill and Auguste Comte / translated from the French and edited by Oscar A. Haac, with a foreword by Oscar A. Haac and an introduction by Angèle Kremer-Marietti. Publisher New Brunswick, U.S.A. : Transaction Publishers, c1995. Description xxvi, 403 p. : ports. ; 24 cm. Note Includes bibliographical references (p. 27-32) and index. ISBN 1560001488 Language English
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Last updated 22 November 2004