15 December 1993
In "Toward a Cognitive Theory of Pictorial Representation", Jesse Prinz proposes an initial formulation of a cognitivist theory of pictorial representation. Prinz offers his theory as an alternative to both conventionalist accounts, which he sees as incapable of explaining recent anthropological data, and naive resemblance theories, whose credibility has been seriously compromised by attacks from conventionalist quarters.
The majority of Prinz's paper is devoted to an attack from empirical data on the conventionalist account of pictorial representation. Toward the end of the paper, Prinz turns to his own positive account, which might be called a non-naive resemblance theory of pictorial recognition. While I am enthusiastic about the theory Prinz endorses, I think his arguments remain incomplete in two significant ways. First, I think Prinz's preliminary statement of his own theory fails to spell out clearly enough the conditions under which a viewer s recognizes p as an O. Second, although Prinz's theory successfully answers important conventionalist objections leveled against the naive resemblance theory, the infinite regress it generates makes it, like its naive predecessors, open to the charge of vagueness.
In what follows, I shall first consider Prinz's negative case against the conventionalist and then provide some objections against his positive account.
Prinz recognizes the limited utility of the argument from intuition, and therefore proceeds by adducing empirical evidence which he claims is incompatible with the conventionalist account. Prinz tells us that the success of the pictorially innocent Me'en at recognizing the content of certain simple pictures threatens conventionalist (and especially strong conventionalist) theories of pictorial representation. According to these theories, a viewer associates a picture p with a depictum O just in case there is a conventionally prevalent code known to that viewer according to which p depicts O. This code specifies which qualities of the picture p are relevant and which are not in recognizing that it depicts O. Because the Me'en neither make nor have been exposed to depictions, it is difficult to imagine that they would be skilled at the application of any code of depiction. Therefore, the conventionalist should expect that the Me'en would be incapable of associating a picture p with its depictum O. The empirical result that the Me'en are in fact quite adept at making certain of these associations seems to disconfirm the conventionalist picture.
What is most conspicuously absent from this discussion is an explanation of the notion of "preponderance" as it occurs in (ii) above. Prinz tells us that s is O-competent if she is o-competent for every property o in O. But we are also told that s is o-competent just in case she "internalize[s] a group of properties [O'] which typifies things with the property [o], and so on." If I understand him here, Prinz thinks that s's O-competence actually involves an infinite regress through finer and finer levels of competence.{1} That the O-competence required by Prinz's condition (i) involves an infinite capacity is not problematic in itself --- human linguistic competence involves a similar facility to understand any of potentially infinitely many strings.{2}
But Prinz's recursive characterization of the O-set is more troublesome. According to Prinz, each element of the O-set is, like the O-set itself, a non-empty set, each of whose elements is a non-empty set, each of whose elements is a non-empty set, and so on. Thus, on pain of circularity, we must conclude that the O-set is infinite. Because this is so, it is unclear what Prinz means by his requirements (ii) and (iii).
In view of the infinite cardinality of the O-set, we wonder what it would mean for an object p to have a preponderance of properties of the O-set. Because the O-set is infinite, preponderance cannot be understood as a simple numerical majority. Perhaps Prinz might elucidate his notion of preponderance through some sort of statistical measure, in terms of a weighting scheme, or by specifying some finite subset of the O-set possession of all of whose members would constitute O-preponderance. Whatever he has in mind here, he owes us more explanation than he gives us if we are to understand his condition (ii).
On the other hand, even if p has every property in the O-set (and therefore, presumably has a preponderance of those properties) it is not clear that s could recognize this preponderance as is required by Prinz's condition (iii) in view of the finite cognitive capacities of human beings.{3}
I emphasize that the problems connected with Prinz's conditions for recognition are of two kinds. The infinite regress generated by these conditions led to no difficulty with condition (i), but gave rise to a logical problem with condition (ii) and an epistemological problem with condition (iii). Because the O-set has infinite cardinality, we found ourselves unable to understand condition (ii) as it is presented by Prinz. This logical problem can be solved by a more explicit formulation of the preponderance required by condition (ii). In contrast to this purely logical difficulty, condition (iii) raises an epistemological challenge. Whatever the preponderance in condition (ii) is taken to mean, the recognition of this preponderance required by condition (iii) would seem (at least in some cases) to make exorbitant epistemological demands on the agent s. It seems to me that this latter, epistemological objection can be met most effectively by reducing the requirements made on s: perhaps s's awareness of finitely many particular properties of the O-set is sufficient for s's perception of p as an O.{4} Whatever course he may choose to meet this criticism, I find myself unable to make sense of Prinz's present formulation of the conditions for recognition.
Conventionalists have attacked naive resemblance as a theory of recognition on the grounds that if p and p' are both recognized as O because they both resemble O (or some prototype of O), then p and p' must share the properties in virtue of which they are said to resemble O. Therefore, it is tempting to say that p should be recognized as a p', or vice versa. But the claim that an apple should be recognized as an orange merely because apples and oranges are both recognized as fruits is implausible at best.{6}
Is Prinz's theory of recognition vulnerable to this objection? I think not. According to Prinz, it is enough that the apple and the orange possess distinct (though most likely not disjoint) properties of the fruit-set for them to recognized as fruits. Even though they share some properties in virtue of which they are both recognized as fruits, there are other properties relevant to these recognitions held by one but not both of them. Although they share some qualities relevant to their classifications as fruits, this partial overlap is, by itself, insufficient to permit recognition of an apple as an orange.
But conventionalism poses another, more serious objection against the naive realist---one which, I think, also applies to Prinz's account in its current formulation. The conventionalist admonishes the resemblance theorist for her excessive vagueness. Any object x is like any other object y in some way. And yet, although x is like y in many ways, it is unlike y in many others. Resemblance theories are explanatorily insufficient because they fail to specify which of the many ways in which x is like y are relevant to the determination of whether x is recognized as a y. In this respect, conventionalists complain that the resemblance view "suffers from a vagueness bordering on vacuity."{7} Conventionalism is offered as a means of explaining why certain of the properties of x, and not others, are relevant to the determination of whether x is a y. Conventionalists suggest that convention tells an agent which of x's many similarities and dissimilarities with y to heed in making her decision.
While Prinz's empirical case that convention is insufficient for this task is compelling, he does not offer any suggestion of what might take its place. Yet, in view of Prinz's explicit reliance on an infinite set of properties (the O-set), it is critical that he provide some means of determining which members of that set are relevant to the recognition that p is an O. I expect that Prinz intends to fill this role by his notion of preponderance. But until this notion is spelled out more fully, his account is unable to defend itself from the conventionalist charge of vagueness.