Conventionalism in geometry

Either:

How do we decide between alternative geometries, according to Poincaré?

or:

1. According to Kant, geometrical truths are known via a peculiar capacity of the human mind (intuition);
2. Everything that is dependent on the capacities of the human mind is empirical'
3. Therefore, geometry is empirical, according to Kant.

Your answer may include discussion of the following questions:

• Is there geometrical truth?
• What is the rôle of intuition in geometry? How is it related to the notion of pure intuition in Kant?
• What is the basis of rigour in geometry?

Readings

(Torretti, 1978, 320-40 (esp. 328-35));

(Poincaré, 1978a, chs. 3, 5);

(Poincaré, 1978c, chs. III, IV(§§1-6 only));

(Poincaré, 1963, ch. III, §§1,4-6);

(Kant, 1997a, A19/B33-A30/B45)

Further readings

(Poincaré, 1978a, ch. 4);

(Poincaré, 1963, ch. II);

Stump (1991)