Lectures on Begriffsschrift. (Vorlesungen über Begriffsschrift. (Nach der Mitschrift von Rudolf Carnap. Unter Mitwirkung von Christopher von Bülow und Brigitte Uhlemann, mit Einleitung und Anmerkungen herausgegeben von Gottfried Gabriel).) (German) Zbl 0860.01036

Frege, Gottlob

Hist. Philos. Log. 17, No. 1, iii-xvi, 1-48 (1996).

The long awaited edition of the notes which Rudolf Carnap took in Frege’s lectures on Begriffsschrift has now been published as an issue of the journal “Hist. Philos. Log.”. Gottfried Gabriel and his team of specialists provide a scholarly edition of the lecture courses “Begriffsschrift I” from the winter term 1910/11 and “Begriffsschrift II” from the summer term 1913. The lecture courses deserve a special interest because they give evidence for Frege’s revisions in his presentation of logic, of his concept of number and of other mathematical concepts which were caused by Bertrand Russell’s discovery of the paradoxes in Frege’s system of “Grundgesetze der Arithmetik” (1893, 1903). This edition gives furthermore evidence for Carnaps thorough reception of Frege’s philosophy and logic, and may help to uncover the “continental” roots of an “analytical” philosopher (cf. IV). In his helpful introduction the editor gives a first analysis of the material presented, discussing the context of the lectures within the development of Frege’s philosophy of mathematics and logic. He deals with Carnap as a “student” of Frege, and he describes, in a detailed way, the manuscripts, which were written almost completely in the shorthand of Stolze-Schrey. Frege does not even mention Russell’s paradox. He presents those parts of his logical system which were not affected. He consequently avoids speaking of extensions of concepts and of value ranges. He keeps the basic laws I–IV, eliminating basic laws V and VI. He furthermore eliminates those rules which depend on value ranges. The editor discusses in length (vii–x) Frege’s various attempts in his later writings to determine the concept of number and their consequences for his logicistic position in the philosophy of mathematics. The Nachgelassene Schriften und wissenschaftlicher Briefwechsel. Herausgegeben von Hans Hermes, Friedrich Kambartel und Friedrich Kaulbach (Meiner, Hamburg, 1969; Zbl 0185.00503) prove Frege’s abandonment of logicism in his last writings. The lectures show his problems to fix his position between the alternatives (1) to propose a modified logicism, taking number statements as propositions about second level concepts without using value ranges as presented in “Begriffsschrift I”, and (2) to advocate the ontological opinion that numbers refer to special nonlogical objects as in “Begriffsschrift II”. One can expect that this edition gives fresh impulses for future research on Frege.

Reviewer: V.Peckhaus (Erlangen)

MSC:

01A75	Collected or selected works; reprintings or translations of classics
03-03	History of mathematical logic and foundations

Keywords:

Begriffsschrift; logicism; value ranges; concept of number

Citations:

Zbl 0185.00503