Functions in Begriffsschrift. (English) Zbl 1030.03005

Baker, G. P.; Hacker, P. M. S.

Synthese 135, No. 3, 273-297 (2003).

The authors argue against the assertion promoted by M. Dummett, A. Kenny, P. T. Geach, and others that G. Frege’s concepts of function developed in “Begriffsschrift” (1879) and in “Grundlagen der Arithmetik” (Vol. I, 1893) were radically different. Contrary to the later concept, functions in “Begriffsschrift” were linguistic functions, i.e. Frege identified logical functions with linguistic expressions.
With the help of a close reading of §§9 and 10 of “Begriffsschrift”, the authors criticize this interpretation. They stress that the basic objects of Frege’s early logical system are judgeable contents, thus no linguistic expressions. They furthermore hint at the fact that Frege applied the term “function” to symbols in concept-script. They can show that with this interpretation one can get rid of some obstacles in the text entailed by the alternative interpretation. In concluding, they remark: “The upshot [of the opinion of the opponents] is an ‘interpretation’ which projects modern ideas onto a very recalcitrant text and which, incidentally, completely undermines the logico-mathematical achievement of Begriffsschrift” (p. 291).

Reviewer: Volker Peckhaus (Paderborn)

MSC:

03A05	Philosophical and critical aspects of logic and foundations
01A55	History of mathematics in the 19th century
01A60	History of mathematics in the 20th century
03-03	History of mathematical logic and foundations

Keywords:

concept of function; linguistic functions; conceptual content; context principle; symbols