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Philosophie der Arithmetik. Psychologische und logische Untersuchungen. Erster Band (alles).


Halle-Saale, C.E.M. Pfeffer (Robert Stricker), 1891. 8vo. Nice contemporary red half cloth with gilt title and gilt lines to spine. A very nice, clean, and fresh copy. XVI, 324 (last p. errata) pp. ¶ The very rare first edition of Husserl's first major work, "The Philosophy of Arithmetic".

Initially a student of mathematics, Husserl began attending Brentano's lectures on psychology and philosophy in Vienna and decided to devote himself primarily to philosophy. In 1887 he wrote "Über den Begriff der Zahl", on which his first proper scientific work which appeared four years later is based. In his "Philosophy of Arithmetic" he wishes to provide a sound foundation for mathematics by combining it with philosophy and psychology, here analyzing the psychological processes necessary for the concept of number, -a variant of the psychologism, he later came to criticize so severely.

The book was met with instant positivity and received much warm praise, though one person criticized it to bits: Gottlob Frege.
Frege who was one of the sharpest and most important logicians of the 19th century had shown that the sentences of arithmetic were analytical, and that arithmetic could be regarded as a branch of logic. He thus built the foundation of mathematical logistics. In spite of him being the chief logician of the 19th century, Frege was barely recognized in his lifetime, and he was barely read by his contemporaries. Husserl, however, did study him intensively, and we know for a fact that he knew all of Frege's works (at least until the year 1893), and it is likely that it was Frege who had inspired his interest in the relationship between the formalities of arithmetic and of logic.

In this early work Husserl sharply attacks Frege and his anti-psychologism, and he sets out to define the natural numbers by counting with the methods of descriptive psychology (primarily Brentano's). It is to be noted, however, that the form of psychologism of logic and mathematics which he so sharply attacks in his logical investigations differs somewhat from the sort presented in his early work.

The "Philosophy of Arithmetic" is also hugely interesting in the attempt to determine the philosophical development of the greatest philosopher of the very late 19th-20th century. He himself states that already before the work was published, he had changed his mind, and he had actually been in doubt as to psychologism from the very beginning. As opposed to what is frequently stated, Frege's attacks on Husserl's work is not fully justified, which Frege probably also recognized himself. Husserl actually does distinguish between subjective representation and objective representation, and objectivism is clearly stated in the "Philosophy of Arithmetic". Thus Husserl here actually, independent of Frege, reaches the same theory of sense and reference as him, and Frege also recognized this.

Frege's attacks were probably to a large extent aimed at the current ideas of the foundations of arithmetics at the Berlin School of Weierstrass, but these differed from Husserl's point of view in a number of ways.
Still, Husserl's notion of logic and mathematics must not be confused with Frege's; -for Frege Arithmetic can be derived from logic; for Husserl mathematics is the ontological correlate of logic, but the two cannot be reduced to one another.

Husserl is now famous as the father of phenomenology, and he decisively influenced the likes of Heidegger, Sertre, Carnap, Merleau-Ponty, Levinas, Ricoeur, Derrida etc. etc.

24 277 SEK

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