Completeness has to be restricted: Gödel’s interpretation of the parameter \(t\). (English) Zbl 0856.01020

Hon, Giora

Hájek, Petr (ed.), Gödel ’96. Logical foundations of mathematics, computer science and physics – Kurt Gödel’s legacy. Proceedings of a conference, Brno, Czech Republic, August 1996. Berlin: Springer-Verlag. Lect. Notes Log. 6, 214-223 (1996).

The paper discusses some effects of Kurt Gödel’s new solution of the field equations in Einstein’s general theory of relativity, especially his considerations concerning the relativity of simultaneity which implies to a large extent the relativity of succession and leads to Gödel’s idea of rotating universes. The author concludes that Gödel succeeded in disturbing Einstein’s original relativistic cosmology from within. He did not claim new principles, but undermined the central Mach principle. The author relates Gödel’s interest in relativity theory to his contribution to logic and mathematics. In both fields Gödel sought to determine the limits of knowledge in broad conceptual issues: “With the derivation of the Gödel Universe as a solution to the field equations of general relativity, Gödel constructed a limiting case for the relativistic geometrization of time” (p. 220). Physics and mathematics are connected in Gödel’s Platonism which gave the reason for his objectivist conception of mathematics. To illustrate this, the author compares Bertrand Russell’s formulation of the vicious circle principle with Gödel’s.
For the entire collection see [Zbl 0844.00017].

Reviewer: V.Peckhaus (Erlangen)

MSC:

01A60	History of mathematics in the 20th century
83-03	History of relativity and gravitational theory
03-03	History of mathematical logic and foundations

Keywords:

general theory of relativity; field equations; rotating universes; succession of time; Platonism; vicious circle principle