Russell, Gödel and logicism. (English) Zbl 0840.01023

Rodríguez-Consuegra, Francisco A.

Czermak, Johannes (ed.), Philosophy of mathematics. Proceedings of the 15th international Wittgenstein-Symposium, 16-23 August 1992, Kirchberg am Wechsel, Austria. Part I. Wien: Hölder-Pichler-Tempsky. Schriftenreihe der Wittgenstein-Gesellschaft. 20/I, 233-242 (1993).

By giving evidence from published and unpublished sources the author questions and partially refutes three standard assertions concerning Bertrand Russell’s relation to Gödel’s results: 1) Rusell did not understand Gödel’s results, which he interpreted as implying that arithmetic is inconsistent; 2) Russell was unable to handle the distinction between metatheory and theory; and 3) Russel’s logicism collapsed after Gödel’s incompleteness results. On certain “weaker” forms of logicism the author concludes that “as a whole they all are enough to show that some form of philosophical logicism, which was the only interesting one for Russell, can still be maintained, by simply accepting and incorporating Gödel’s results as mere mathematical limitative results” (p. 240).
For the entire collection see [Zbl 0836.00022].

Reviewer: V.Peckhaus (Erlangen)

MSC:

01A60	History of mathematics in the 20th century
03-03	History of mathematical logic and foundations

Keywords:

logicism; incompleteness; Russell; Gödel