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Euclidean and non-Euclidean geometries

`It is necessary and a priori that only one straight line lies between two points' (Kant);

`In fact we know nothing in nature but movement, without which sense impressions are impossible. Consequently all other concepts, e.g. geometrical concepts, are generated artificially by our understanding, which derives them from the properties of movement' (Lobachevsky).

What is the conflict, if any, between these claims?

Readings

(Torretti, 1978, 1-10, 29-33, 53-67);

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

(Kant, 1997b, First Part, Note I (follows after §13));

(Barker, 1964, chs. 2,3)

Further readings

the rest of Torretti (1978) through p. 67.

Hempel (1945)



Sandy Berkovski