Danny & the Ducks

About two months ago, my son Daniel (aged 20 months) was given a kite that is shaped like an eagle and has an eagle imprinted on it. After flying it, Danny and his father tacked the kite up on the wall. Danny pulled me into the room, pointed at the kite, and said, "Mama, Duck!" I picked Danny up and tried to explain to him that, in fact, the picture was of an eagle. I started to point out the talons and the hooked beak. Danny, however, was having none of it. He grabbed me by the chin, pulled me to face him, and said, "No! Mama! Duck! Quack-quack-quack-quack!" He was, in fact, so insistent that I ended up agreeing it must be a duck.

Now it has to be noted here that Danny is no novice when it comes to ducks. His crib-guard, comforter and pillow all have little puffy characterizations of ducks on them. He has fed live ducks in the water, and he has watched them fly overhead from the hills across the street. He has a little yellow rubber ducky with a hole in its tummy to hold soap for his bath. And he was even kissed by a 5-foot Donald Duck when he went to Disneyland . In fact, Danny is probably quite an expert when it comes to ducks.

There are two immediate questions, then, that must be answered in considering Danny's classification of his kite as a duck. The first is, quite simply, why is it a duck? The second question, decidedly more difficult than the first, is when and how will he learn that it is not a duck?

It is not enough to simply attribute Danny's classification of the kite as a duck to an overextention based on perceptual similarity, (Whitehurst ,1987). It is true that the eagle looks a great deal like a real duck - but the fact is that someday it will become an eagle and Donald and the rubber ducky will remain ducks. If they did not, Whitehurst would attribute that to under extention. We must, therefore, find a way to explain why an eagle will become differentiated without relying on perceptual similarity alone.

Similarly, Smith and Medin (1981) describe the holistic view of concept formation. In this view, the individual forms a "template" of a concept, based on an average of all past exemplars of the concept and to which all future instances are compared. This holistic view is logically inconsistent in itself, because the template must be constructed through the averaging of individual features, and cannot therefore be truly holistic in the first place. But aside from that, we can see that Danny would find such a template completely useless. I cannot imagine what a template that included Donald, the ducky, real ducks, and Danny's pillow-ducks would look like, but I think it is fair to say that it would probably be more perceptually similar to the eagle than, say, to Daisy Duck. 1

The classical view of concept formation would state that the concept "duck" has a number of features that are singly necessary and jointly sufficient to classify an instance as a duck. Problems with the classical view abound, however. First, it is virtually impossible to list the necessary and sufficient features for a concept. (The current debates in the courts serve as evidence that we cannot seem to agree on the necessary and sufficient features of even so broad a concept as "life".) Second, according to the classical view, all instances of a concept are equal - and yet, empirical findings are that some instances are more "typical" of a concept than others: they are classified faster and with less error. For example, both an apple and a fig are instances of the concept “fruit.” Both have all the necessary and sufficient features of fruit. Nonetheless, when people are asked if an apple is a fruit, they are able to answer quickly and they rarely make a mistake. When asked about a fig, there is a longer time to response and less accuracy. Third, Rosch and Mervis (1975) found that the degree of typicality of an instance is correlated with its "family resemblance", that is, with the weighted number of features shared with other members of the concept, even if those features are wholly unnecessary in defining the concept. Fourth, because concepts may be nested one within the other (subordinate concepts being more detailed than superordinate concepts), the classical view would predict that subordinate concepts would be more slowly classified in the immediate superordinate concept than in a distant one (because there would be more features to compare) - and this is rarely the case. And finally, from a developmental point of view the classical position seems completely untenable. In order to correctly classify an eagle or anything else, Danny would have to separate the necessary and only the necessary features from the instances presented to him - which in the case of Danny's ducks would be an extremely difficult task! Not all of the ducks breathe, not all of them are small or large. They are not the same color. They don't all have feathers. An adult might be able to come up with some necessary features, but I don't think they would relate to Danny's ducks: we might state that a reasonable requirement for “duckness” is the ability for the female to lay eggs, for example,. Yet, three nephews notwithstanding, I have never heard it said that Daisy lays any eggs and I'm absolutely positive that the rubber ducky doesn't. (Of course, it could be male.)

The probabilistic view of concept formation seems to hold more promise. In this view, features need be neither necessary nor sufficient in order to be part of a summary description of a concept. Thus, Danny could decide that the eagle is a duck because it is about the same size as many (but not all) of the other ducks he has seen, because it shares some coloring characteristics with some (but not all) other ducks, and so on. There are two divisions of the probabilistic approach described by Smith and Medin: it is possible to view the summary statement as one composed of features or as one composed of dimensions. In the former, the instance would be categorized according to a series of all-or-none attributes (e.g., has feathers or doesn't), while the latter would entail gradients (e.g., size). Critics of the first point out that the list of features can become exceedingly long and can change depending upon the contrast category. Critics of the latter challenge the dimensional position that concepts can be represented in metric space (with dimensions along the axes).

The representation of a concept in metric space is convenient and very descriptive. Unfortunately, it also has some major problems. The use of metric space involves three assumptions: 1) minimality - one point is the same distance from itself as any other point is from itself; 2) symmetry - point A is the same distance from point B as point B is from point A; and 3) triangular inequality - the distance from point A to point C is smaller than the distance from point A to point B plus the distance from point B to point C. The transference of this into psychological space is difficult, as is exemplified by three types of empirical results:. 1) the distance from typical items to themselves is less than the distance from atypical items to themselves; 2) North Korea is rated as more similar to China than China is to North Korea ; and 3) Jamaica is like Cuba , and Cuba is like Russia , but Russia is not at all like Jamaica !

If we accept that Danny has classified the eagle as a duck because it shares many features with many other ducks (although not necessarily all of them and not necessarily "defining" features), we have come halfway toward answering our two questions. The more difficult question, however, concerning how Danny will learn that the eagle is NOT a duck, is more problematic. Rosch and Mervis (1977) have posited that the way we can tell something is NOT an instance of a category is on the basis of cue validity. Cue validity is measured in terms of the probability that a specific cue will occur in another contrasting category. Thus, having wings is not a very good cue for ducks because many other birds also have wings. Each feature may then be weighted in terms of its cue validity (defined as the probability that it will occur in that category divided by the probability that it will occur in that and any other contrasting category). If a feature occurs only in that category, the cue validity is one. The problem, of course, is that Danny has no contrasting category. He cannot assess the cue validity of various features (i.e., that which could be either "duck" or "eagle") because he has no category for eagle.

A third type of concept formation described by Smith and Medin may help us to overcome this problem. In the exemplar view, category formation is based not on some summary statement about the category, but rather on a number of examples of the category, which are stored separately. Categorization of a new instance is then based on similarity to one of the stored instances. (Daisy is a duck because she is like Donald, the kite is a duck because it looks like a real duck.) This helps us out of our bind somewhat, because as Danny is presented with an example of an eagle, the eagle kite will look more like the eagle than like a duck.

The exemplar view can be supported with a couple of pieces of evidence. First, empirical research with first and sixth graders has shown that first graders remembered lists better when given memorization instructions that emphasized specific instances, while sixth graders remembered better when summary statements were emphasized. (Thus, the first graders seem to be using exemplars to categorize, while the older children summarized.) The second piece of evidence is in the formation of what I call "verbal graphic collections". Children in Brown's stage I of language development (mean length of utterance between 1 and 2 words) often form collections of objects that have no logical or "summary" connection. For example, Danny calls both popcorn and cheerios "bamba" because on the television there was a commercial in which a kernel of popcorn that had a face and arms and legs turned into a piece of popped popcorn to the tune of "La Bamba". On the back of the cheerios box there was once a picture of an M & M's candy that also had arms and legs and looked somewhat similar to the kernel. Because the cheerios were inside the box and the popped popcorn was next to the kernel, both are now in the same category. The category "bamba" has been formed based on contiguity and salience of a number of different characteristics, not on the basis of a summary statement.

The very rarity of verbal graphic collections, however, also argues against the exemplar view of category formation - because indeed if we had no summary statements and categories were formed only by the memorization of exemplars we would see far more verbal graphic collections than we do. Besides, it is difficult to see why Danny would so vehemently deny that the eagle was an eagle if he had not classified it based on a summary representation of some kind. Lots of things are similar to the rubber ducky (in color, size and use) and none of them are ducks, or so classified by Danny.

Perhaps a combination of views is appropriate here. In first formation, it is possible that exemplars are used. As two or more exemplars are found for a category, a preliminary summary statement based on shared features can be formed. As additional exemplars are found, the summary statement can be updated and so on. Verbal graphic collections, for which no summary statement can be found, will be (and are) dropped. In memory, then, we would find both exemplars and summary statements.

When I was explaining my problem with concept formation to a colleague, he suggested that I look up an article by a fellow at Penn State comparing the problem of language development to Plato's paradox as presented in the Meno. While I didn't have time to look up the fellow at Penn State , I always have Plato. I looked up the Meno, and the essence of Plato's paradox is this: how can a man learn something (e.g., virtue, of course) if he does not already know it? In other words, how can Danny ascertain the cue validity of any cue if he does not already have a concept for eagle? That the problem I have been pondering in my car for the past two months was being pondered 2,500 years ago in the agora by Socrates is discouraging. It seems evident that Danny is going to have to figure out that an eagle is not a duck without the definitive aid of modern (or even ancient) psychology.

Notes

  1. Of course, we could make things a lot easier here if we simply said that Donald and the ducky and so forth were not ducks at all. But this is simply begging the question. The argument would go something like this: "Those are not ducks, they are simply characterizations." "Of what?" "Well, of ducks." "How do you know?" And we would be back to start. Besides, since I am the one who ended up conceding that an eagle is a duck, I gladly leave to someone else the task of convincing Danny that Donald is not a duck!

Note from the Author: Those of you who have indulged this little trip down memory lane will be pleased to know that Danny is now working in Hong Kong, and he is able to distinguish an eagle from a duck most of the time.