Formalism I: Meaning, Truth, Existence

`Mathematics has become a court of arbitration, a supreme tribunal to decide fundamental questions -- on a concrete basis on which everyone can agree and where every statement can be controlled' (Hilbert).

Discuss.

Your answer may include discussion of the following questions:

• What is the nature of mathematical truth, according to formalism?
• What are the ideal elements?
• Does intuition play any rôle in mathematics?
• What is the source of mathematical certainty?

Readings

Hilbert (1900);

Hilbert (1918);

Hilbert (1922);

Hilbert (1926);

Hilbert (1931);

Frege (1900);.

(Resnik, 1980, 54-76);

(George and Velleman, 2002, ch. 6), until the sentence `There is a second hesitation...';

(Poincaré, 1978b, Book II, ch. 2, 4 (§§6-12))

Further readings

Hilbert (1930);

Hallett (1994);

Hallett (1990);

(Lavine, 1994, 182-97);

(Detlefsen, 1986a, chs. 1-2);

von Neumann (1931)