Jena: Hermann Pohle, 1891.
First edition, very rare, of this important essay, in which Frege carried out a revision of his famous Begriffsschrift (1879), which was necessary in order to carry out his programme of reducing arithmetic to formal logic. Function und Begriff contains Frege’s two main innovations since the publication of Begriffsschrift, namely the notion of ‘sense’ and his ‘Basic Law V’ (see Alnes, p. 1). Function und Begriff also contains the earliest traceable germ of the ideas that lead to the modern formalism of functional grammars and to the Church-Kleene lambda calculus of the 1930s that was to play such an important role in the development of the theory of programming languages (see, for example, Klement). Together with his two subsequent papers, Über Sinn und Bedeutung (1892) and Über Begriff und Gegenstand (1892), Function und Begriff was incorporated into his magnum opus, Die Grundgesetze der Arithmetik (1893-1903). OCLC lists copies at Chicago, Harvard and Lehigh only in US.
“In the preface to Begriffsschrift, Frege announced his interest in determining whether the basic truths of arithmetic could be proven ‘by means of pure logic.’ Kant’s answer had been negative. According to Kant, the truths of arithmetic are synthetic a priori… One of Frege’s main goals in Die Grundlagen der Arithmetik was to refute this view by giving purely logical proofs of the basic laws of arithmetic, thereby showing that arithmetical truths can be known independently of any intuition” (Routledge Encyclopedia of Philosophy, Vol. 3, p. 772).
“In Die Grundlagen der Arithmetik he did not give a completely formal reduction of arithmetic to logic. Instead, and possibly at the instigation of Carl Stumpf, he offered a logicist reduction in informal language. Frege was conscious that [Die Grundlagen] had only made it plausible that arithmetic was a branch of pure logic and that a complete demonstration would demand carrying out the reduction in question within the formal Begriffsschrift, thereby ensuring the Luckenlosigkeit [rigour] of his derivations. In 1882 Frege had already indicated in correspondence that the formal execution of the logicist reduction was close to completion. Eventually this task turned out to be no routine matter and markedly more difficult than was expected at first. The 1879 Begriffsschrift proved insufficient for the work at hand: it had to be revised considerably...
“The three major philosophical essays that Frege published in the early 1890s provide an attempt at a philosophical underpinning of the revised Begriffsschrift. Of these essays, ‘Über Sinn und Bedeutung’ has acquired a special prominence, owing in large measure to the importance attached to the sense-reference distinction, and variants thereof, within current philosophy of language… The first appearance of the distinction in print, however, is in Function und Begriff” (Sundholm, pp. 57-8).
“During the years 1887-1890, [Frege] published nothing, but was engaged in thinking through afresh his system of philosophical logic and redesigning, in accordance with it, the formal system he had presented in Begriffsschrift. He announced his new ideas in the lecture Function und Begriff of 1891. The principal changes in his philosophical logic were the introduction of the far-reaching distinction between sense and reference, and the identification of truth-values as objects and as the references of sentences. The principal changes in his formal system were the introduction of value-ranges, and the obliteration of any formal distinction between sentences and singular terms; the addition of a description operator was an important secondary development. During the middle period, lasting from 1891 to 1906, his thought evolved little… The logical basis for all the work of the middle period was presented complete and entire in Function und Begriff; and it scarcely altered through throughout the whole period” (Dummett, p. 2).
Michael Dummett, Frege: Philosophy of Mathematics, 1992; Kevin C. Klement, Frege and the logic of sense and reference, 2002; Jan Harald Alnes, ‘Sense and Basic Law V in Frege’s logicism,’ Nordic Journal of Philosophical Logic, Vol. 4 (1999), pp. 1-30; Göran Sundholm, ‘Frege, August Bebel and the return of Alsace-Lorraine,’ History and Philosophy of Logic, Vol. 22 (2001), pp. 57-73.
8vo (233 x 149 mm), pp. [iv], 31, . Original printed wrappers, uncut and unopened. Wrappers with some wear, top margin with small loss.