  All this follows, of course, from the very nature of axiomatics, as explained in the passage quoted from Pasch. Indeed, such truth-preserving semantic permutations were no news in geometry after Gergonne (1771–1859) drew attention in 1825 to the following principle of duality: Any true statement of projective plane geometry gives rise to another, equally true, dual statement obtained by substituting ‘point’ for ‘line’, ‘collinear’ for ‘concurrent’, ‘meet’ for ‘join’, and vice versa, wherever these words occur in the former. (In projective space geometry, duality holds for points and planes.) The same result is secured, of course, by exchanging not the words, but their meanings. 