 Projective geometry also possessed one startling feature, called duality, which stimulated epistemological reflections on its possible source. In plane projective geometry it is possible to exchange the terms ‘point’ and ‘line’, ‘coincident’ and ‘concurrent’ and in this way obtain from a valid statement a new one. As a result all definitions, theorems, and proofs in projective geometry have a dual character. The dual of the statement of Desargues’ theorem and its proof, for example, is the converse of the theorem and its proof. In three dimensions, the terms ‘point’ and ‘plane’ can be exchanged in the same way, leaving ‘lines’ unchanged. This raises intriguing epistemological issues: duality was regarded by Cremona as a law of logic; also, it is easy to conceive of the plane as made up of points, but impossible to regard it intuitively as made up of lines. To make matters worse, space is three-dimensional when regarded as made up of points, but four-dimensional when made up of lines.