Edgerton proceeds to show how Panofsky's notion of symbolic form is inspired by Ernst Cassirer's Kantian philosophy, which he capsulates as follows:
The symbols man uses to communicate ideas about the objective world have an autonomy all their own. Indeed, the human mind systematizes these symbols into structures that develop quite independently of whatever order might exist in the natural world to begin with...
The real thrust of [Panofsky's] essay was not to prove that the ancients believed the visual world was curved or that Renaissance perspective was a mere artistic convention, but that each historical period in Western civilization had its own special "perspective," a particular symbolic form reflecting a particular Weltanschauung. Thus linear perspective was the peculiar answer of the Renaissance period to the problem of representing space...
In the 15th century, there emerged mathematically ordered "systematic space," infinite, homogeneous, and isotropic, making possible the advent of linear perspective... Linear perspective, whether "truth" or not, thus became the symbolic form of the Italian Renaissance because it reflected the general world view of the Italian people at this particular moment in history. (1975, pp. 156, 157-8)
As Edgerton so well explains, Panofsky's position was not blithely relativistic: It is more important to understand why the artists of the Renaissance were interested in perspective than to determine whether it is the "correct" method of representation. In this book, I have attempted to convey the variety as well as subtlety of the reasons why Renaissance artists were interested in perspective. I hope I have persuaded the reader that "truth" was not at stake here. To be sure, perspective was a system that enabled artists to represent space according to geometric rules. Mainly, however, it was a framework within which originality without arbitrariness2 could be achieved.
Nelson Goodman took the issue a step further by marshaling all his philosophical arguments in support of the relativistic conception of perspective. Goodman's sustained analysis of the notions of representation, realism, and resemblance is also an impassioned defense of the argument that perspective is not an absolute standard of fidelity, that it is but one of many methods of representation. According to Goodman, depictions are analogous to descriptions, and descriptions need not resemble the things they describe. Indeed, sometimes they cannot resemble the thing they are describing because that thing simply doesn't exist (e.g., a unicorn). Why then do we think that a picture should resemble the thing it represents? Goodman answers that conventions of representation are responsible for this misapprehension. From the correct observation that a picture usually resembles other pictures of the same kind of thing, we tend to infer that a picture resembles the kind of thing it represents. The key argument is here: Goodman asks himself whether
the most realistic picture is the one that provides the greatest amount of pertinent information. But this hypothesis can be quickly and completely refuted. Consider a realistic picture, painted in ordinary perspective and normal color, and a second picture just like the first except that the perspective is reversed and each color is replaced by its complementary. The second picture, appropriately interpreted, yields exactly the same information as the first... . The alert absolutist will argue that for the second picture but not the first we need a key. Rather, the difference is that for the first the key is already at hand. For proper reading of the second picture, we have to discover rules of interpretation and apply them deliberately. Reading of the first is by virtually automatic habit; practice has rendered the symbols so transparent that we arc not aware of any effort, of any alternatives, or of making any interpretation or all. (1976, pp. 35-6) .
I believe that I have provided us with the tools to refute Goodman's radical relativism3. I have shown that perspective is not a thoroughgoing, arbitrary application of the geometric system of central projection. Rather, it is a geometric system tempered by what perception can or cannot do. It has evolved into a system adapted to the capabilities of our perceptual system. To respond, Goodman would have to claim that what perception can do depends on what it learned to do, and that there is no limit to what perception can learn. But that argument is false. There are clear limits to the extent of perceptual rearrangement (induced by wearing prisms, mirrors, and other devices that modify the form of the optical information reaching our eyes) to which human beings can adapt. We cannot arbitrarily change the way we perceive optical information, nor can we arbitrarily change our motor responses to it, regardless of the amount of time or effort we might invest in doing so (Welch, 1978, pp. 277-9).
We have seen that Panofsky's view on the conventionality of perspective may not have been as extreme as some have interpreted it to be because it does not exaggerate the importance of the role played by the "correct" representation of space in Renaissance art. We ham also seen that Goodman's view, on the other hand, is the most radical position on this matter that one can take precisely because it makes the "correctness" of perspective into a central issue, thereby impoverishing our understanding of perspective in Renaissance art rather than enriching it. We turn now to a third view, which shares some of the features of Goodman's approach. Suzi Gablik, in her book Progress in Art, has presented a cultural analog of the classical embryological law, "ontogeny recapitulates phylogeny," according to which an embryo, in the course of its maturation, goes through stages during which it takes on the appearances of its evolutionary ancestors. Gablik has proposed a similar law for the evolution of art, which I call "sophogeny recapitulates ontogeny," namely, that the evolution of cultural wisdom parallels the development of the individual. I will argue that Gablik, to make her point, emphasizes only one of the goals of Renaissance perspective - the representation of objects in space - and that she implies that art cannot achieve this goal without being rigid and inflexible, rule-bound and lacking in true conceptual autonomy.
Gablik's point of departure is the theory of cognitive development of Jean Piaget, the celebrated Swiss psychologist. Piaget proposed that it is possible to discover milestones in the development of thinking, perception, problem solving, and all the other cognitive abilities. He distinguished three major stages in cognitive development. In the preoperational stage (which ends at about 5 years of age), children have a very poor grasp of causality and reversibility. For instance, if you pour a liquid from a tall, narrow glass to fill a squat, short one of equal capacity, refill the tall glass with liquid, and then ask a preoperational child which glass contains more liquid, the child will say that the taller glass contains more. The child does not understand the concepts of conservation (the amount of fluid) and of compensation (the trade-off of height for area of the cross section), which are physical expressions of the formal concept of reversibility. In the concrete-operational stage (which runs to about the age of 10), children understand the reversibility underlying certain physical operations but are unable to deal with the logical concepts that are their abstract representation. Finally, in the formal-operational stage, children can understand abstract logical and mathematical structures that underly reality.