 Where there is a choice between different possibilities, conventions only become involved at a further step of the mathematical construction where the properties of the transformation group are studied and choices are made concerning distance (a metric). It follows that the Euclidean axiom of distance is not exclusively the result of a conventional (decisional) choice in the linguistic sense, rather, it is a “disguised definition” or an “apparent hypothesis.” Poincaré uses the term “disguised definition” before 1899, the year of Hilbert’s famous Foundations of Geometry, to express the fact that language apparently used descriptively is not descriptive in actuality. Certain axioms appear descriptive, but instead define the objectivity of a fact (Poincaré 1899: 274). Such a fact is found to be defined only up to structure, although it clearly reflects the truth of certain relations between sensations whose qualities remain unknowable, as shown by Helmholtz and others (Poincaré 1905b: 174.