×

Gödel’s theorem in focus. Reprint of the 1988 orig. (English) Zbl 0763.03002

Philosophers in Focus Series. London: Routledge,. x, 261 p. (1991).
The book, a collection of (mostly) previously published papers, is intended to serve mainly philosophically interested readers as a survey of essential aspects connected with Gödel’s incompleteness theorems.
After a short biographical sketch by J. W. Dawson jun. (pp. 1-16) [Math. Intell. 6, No. 4, 9-17 (1984; Zbl 0575.01009)] and an English translation (by J. van Heijenoort) of K. Gödel’s original paper (pp. 17-47) [Monatsh. Math. 38, 173-198 (1931; Zbl 0002.00101)], one finds a survey of Gödel’s work by S. C. Kleene (pp. 48-73) [J. Symb. Logic 41, 761-778 (1976; Zbl 0366.02001)], an overview of the reception of the incompleteness results by J. W. Dawson jun. (pp. 74-95) [Philos. Sci. Assoc., Vol. 2 (1984)], and an essay by S. Feferman (“Kurt Gödel: Conviction and caution”, pp. 96-114) [Philos. Natur. 21, 546-562 (1984)] on some of Gödel’s philosophical positions.
In the three final papers philosophical aspects of Gödel’s incompleteness results are discussed: the seriousness of the sceptical problem by M. D. Resnik (pp. 115-130) [J. Philos. Logic 3, 133-147 (1974; Zbl 0278.02008)], relations to Hilbert’s Programme by M. Detlefsen (pp. 131-154) [J. Philos. Logic 8, 297-313 (1979; Zbl 0405.03003)], an Wittgenstein’s way of resolving by dissolving a claimed crisis by S. G. Shanker (“Wittgenstein’s remarks on the significance of Gödel’s theorem”, pp. 155-256) [previously unpublished].

MSC:

03-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations
00B60 Collections of reprinted articles
03A05 Philosophical and critical aspects of logic and foundations
00A30 Philosophy of mathematics
01A60 History of mathematics in the 20th century
01A70 Biographies, obituaries, personalia, bibliographies
03-03 History of mathematical logic and foundations
PDFBibTeX XMLCite