But (x) is impossible. The new maximum (x) would be greater than the previous maximum (k), which is absurd—a maximum cannot be increased. Therefore, he concludes, the amount of contraries is limited by the absolute maximum degrees of the quality measured. Qualities and their contraries, consequently, cannot be intensified in the same object beyond this maximum limit. There are undeniable quantitative features to this argument, comparable to the geometrical intuitions that animated fourteenth-cen