From draft of a letter by Franz Brentano of 30 April 1905 to Edmund Husserl
But the most ingenious of mathematicians, such as Euler and Descartes, never considered mathematics as being an end in itself. It is not surprising, therefore, that your Felix Klein, weary of excursions into metamathematics, should turn to the technological applications of mathematics.
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.
From FRANZ BRENTANO, 2002 by Wolfgang Huemer
Brentano has often been described as an extraordinarily charismatic teacher. Throughout his life he influenced a great number of students, many of who became important philosophers and psychologists in their own rights, such as Edmund Husserl, Alexius Meinong, Christian von Ehrenfels, Anton Marty, Carl Stumpf, Kasimir Twardowski, as well as Sigmund Freud. Many of his students became professors all over the Austro-Hungarian Empire, Marty in Prague, Meinong in Graz, and Twardowski in Lvov, and so spread Brentanianism over the whole Austro-Hungarian Empire. Another of Brentano's students, Tomas Masaryk, was to become founder and first President (from 1918 to 1935) of the Republic of Czechoslovakia, where he created ideal conditions for the study of Brentano's philosophy. These factors explain the central role of Brentano in the philosophical development in Middle-Europe, especially in what was later called the Austrian Tradition in philosophy.
Page created 31 August 2003
Last updated 15 September 2003