The assertion that the Cubist depiction of space, mass, time, and volume supports (rather than contradicts) the flatness of the canvas was made by Daniel-Henry Kahnweiler as early as 1920, but it was subject to criticism in the 1950s and 1960s, especially by Clement Greenberg. Contemporary views of Cubism are complex, formed to some extent in response to the "Salle 41" Cubists, whose methods were too distinct from those of Picasso and Braque to be considered merely secondary to them. Alternative interpretations of Cubism have therefore developed. Wider views of Cubism include artists who were later associated with the "Salle 41" artists, e.g., Francis Picabia; the brothers Jacques Villon, Raymond Duchamp-Villon and Marcel Duchamp, who beginning in late 1911 formed the core of the Section d'Or (or the Puteaux Group); the sculptors Alexander Archipenko, Joseph Csaky and Ossip Zadkine as well as Jacques Lipchitz and Henri Laurens; and painters such as Louis Marcoussis, Roger de La Fresnaye, František Kupka, Diego Rivera, Léopold Survage, Auguste Herbin, André Lhote, Gino Severini (after 1916), María Blanchard (after 1916) and Georges Valmier (after 1918). More fundamentally, Christopher Green argues that Douglas Cooper's terms were "later undermined by interpretations of the work of Picasso, Braque, Gris and Léger that stress iconographic and ideological questions rather than methods of representation."

Who asserted that the flat canvas supported Cubism?