Depiction

3. Goodman’s radical alternative

The most radical reaction to these difficulties would be to abandon not merely the idea of resemblance, but also the strong contrast between depiction and linguistic representation, and the idea that the former is peculiarly visual. The key exponent of such an approach, and indeed of the criticisms of resemblance that motivate it, is Nelson Goodman (1969; Goodman and Elgin 1988).

Goodman locates the difference between the ways in which pictures and words represent things in formal features of the representational systems in question. To do this, he develops a set of theoretical tools. Marks on surfaces are grouped as inscriptions of different characters. For example, you are currently looking at marks, each of which is an inscription of a character in the Roman alphabet. Characters are grouped so as to form symbol schemes - the Roman alphabet is one such scheme, while the first eigh t characters in it form another. If the characters are correlated with a field of reference (a range of things to which they refer), the result is a symbol system. Examples include the system for naming the eight notes in a musical octave, and, at a higher level of complexity, written English.

What is special about symbol systems that are pictorial? Goodman identifies three important features. First, such systems are ‘syntactically dense’. That is, they involve infinitely many characters, and are so ordered that between any two characters lies a third. (Curves on a graph can be so ordered, the first eight letters of the Roman alphabet cannot.) Second, they are ‘semantically dense’. The field of reference of the characters is so ordered that between any two referents there is a third. (The range of possible pitches of a sound meets this condition, the whole notes making up a scale do not.) Finally, they are ‘relatively replete’ - a relatively wide range of properties of the mark determines which character it inscribes. Roughly, this amounts to the following. Pictorial systems are ones in which, for a wide range of properties of the mark on the surface, the tiniest differences in that property affect what is represented. This is not so for linguistic systems - consider, for instance, the English names for the constellations. Whatever the colour or font or style of handwriting in which we write the name ‘Orion’, provided we have indeed written the right characters in the right order, we have written down a word that refers to that set of stars. More generally, Goodman claims that all three of his features are exhibited by pictorial systems, and that they are not all exhibited by those which represent linguistically. Beyond this simple claim to differentiate the two he is reluctant to tread.

Many of Goodman’s critics have sought to attack his position by counterexample. A graph might be used to track the various properties of a colourless gas over time. With time represented by distance along the x -axis and temperature along the y -axis, thickness of the plotted line might represent the density of the gas, colour might represent its radioactivity, and so on. Such a graph could be a symbol in a system that is both syntactically and semantically dense, and relatively replete. No difference in the graph is in principle too small to affect the precise state of the gas represented. Despite this, the graph would not depict anything (see Peacocke 1987).

It has not always been recognized that these examples prove little as they stand, save that Goodman was right not to claim to provide conditions sufficient for depiction. Nonetheless, there are the seeds here of a stronger case against him. They lie in the question why it is so plausible that, in this example, the graph does not depict the gas.

One answer is that the graph lacks certain features common to all depictions. For one thing, it does not represent the gas from any particular point of view. Pictures, by contrast, always represent what they depict from some perspective - sometimes several. Further, the graph does not represent any properties of the gas that are properties of its visual appearance. The gas has no visual appearance, and is not represented as having one. Again, depiction is always the representation of things as having an appearance. Finally, although the graph has a comparatively complex content, it might easily not have done. Had every one of the above features fed in some weighted manner into the representation of the temperature of the gas, the graph would still have met Goodman’s conditions for belonging to a pictorial symbol system, but would have represented nothing more than temperature. Yet pictures always have comparatively detailed contents, even when relatively schematic. This is the truth in the old saw that a picture paints a thousand words.

The force of the example can now be made clear. It not only shows that the account is incomplete, but also indicates how seriously it is so. The graph, at least in the revised form just described, meets Goodman’s differentiation conditions without having any of the three features characteristic of depiction. An adequate theory of depiction must be a theory of a form of representation with those features, and should ideally explain why they hold. As it stands Goodman’s account plainly does not meet either of these requirements. Moreover, it does not seem that it could readily be developed to meet them. For what might be added to the specification of formal features of the symbol system so as to obtain this result? It seems that the only emendations to suffice would amount to gerrymandering. Thus the only course, if these features are to be accommodated, seems to be to return from Goodman’s radicalism towards views which bind depiction more closely to the visual. (Though see Kulvicki 2006 for a sophisticated attempt to improve on Goodman’s theory, and to address the worry just stated.)