Formalism II: Gödel's Results

How destructive are Gödel's theorems for Hilbert's Program?

Your answer may include discussion of the following questions:

• What is the content of the First and Second Incompleteness Theorems?
• Which of them is more important for Hilbert's Program?
• How crucial is the finitary consistency proof for the formalist conception of mathematics?
• Should the collapse of Hilbert's Program have wider philosophical significance?

Readings

For a general overview see (Nagel and Newman, 1959, chs. II, III, VII). For a very perceptive elementary exposition of Gödel's results consult (Weyl, 1946, Appendix A). A more advanced treatment of Gödel's theorems is in (George and Velleman, 2002, ch. 7). Those particularly intrigued should go to (Boolos and Jeffrey, 1989, chs. 12, 14-16).

(George and Velleman, 2002, ch. 6, pp. 156-71);

(Kreisel, 1958, §§1-7, 18), until the sentence `It is to be emphasized...'.

Resnik (1974)

Detlefsen (1986b);

Further readings

(Lavine, 1994, 197-203);

Dummett (1978)