 Hilbert had been introduced to a number of controversies about elementary projective geometry that concerned what results in what settings implied what other results. The most notable concerned Desargues’s theorem (see Arana and Mancosu 2012). In 3-dimensional projective geometry, Desargues’s theorem is a consequence of the incidence axioms alone, but it is a theorem about points and lines in a projective plane (and so in 2-dimensional geometry) yet no-one had been able to derive it from the incidence axioms of 2-dimensional projective geometry. It had come to be suspected that it might not be deducible from those axioms alone, and Giuseppe Peano was able to show that indeed it could not be deduced without some extra assumptions. Independently, Hilbert also gave an example of a geometry meeting all the incidence axioms of 2-dimensional projective geometry but in which Desargues’s theorem was false. It was replaced by the simpler example found by the American mathematician and astronomer F.R. Moulton in all later editions of Hilbert’s Grundlagen der Geometrie (1899).