This article describes the relationship between Art, as painting or sculpture, and a new theory of perceptual meaning, which builds on and now further develops the Gestalt principles. A key new idea in the theory is that higher-order groupings principles exist which, like the spatial grouping articulated by the principle of Prägnanz, helps to associate and combine stimuli, but which, unlike the Gestalt laws, can explain combinations of dissimilar as well as similar forms of visual information in a lawful manner. Similarities and dissimilarities are put together again by virtue of another and more global grouping factor that overcomes the dissimilarities of the components: it is some kind of meaning principle that perceptually solves the differences among whole and elements at a higher level, making them appear strongly linked just by virtue of the differences. In this way, similarities and dissimilarities complement and do not exclude each other. Such higher-order principles of grouping-by-meaning are articulated and illustrated using Art, from prehistoric to modern.