The Objectivist view of the hiearchy of knowledge is one of those theories that attempts to use a commonplace to mask a fallacy. Certain forms of knowledge are "hierachical" in the sense that, before one can understand them, one needs to grasp that knowledge in its simpler form. Hence, one needs to know arithmetic and algebra before one is going to have much of a chance to grasp calculus. Yet this sort of hierarchy is not quite what Objectivist have in mind when they babble on about it. Here's how Van Damme herself puts it:
There is a necessary order to the formation of concepts and generalizations. A child cannot form the concept of “organism” until he has first formed the concepts of “plant” and “animal”; he cannot grasp the concept of “animal” until he has first formed concepts such as “dog” and “cat”; and so on. The pedagogical implication of the fact that there is a necessary order to the formation of abstract knowledge is that you must teach concepts and generalizations in their proper order. An abstract idea—whether a concept, generalization, principle, or theory—should never be taught to a child unless he has already grasped those ideas that necessarily precede it in the hierarchy, all the way down to the perceptual level.
This theory assumes that knowledge is build from narrower concepts, narrower generalizations, on up. Note that Van Damme presents no scientific evidence for her theory. There is a good reason for this. No such evidence exists. Human knowledge is not built up from narrower to wider concepts. Calculus is not a wider concept than arithmetic. It simply describes a more complicated subject matter. It's the sophistication and complexity of the subject matter, not the width of the concepts, that's hierarchical.
We can easily refute the Objectivist theory of the hiearchy of knowledge with the following cognitive experiment. Let's create an Objectivist hierarchy of concepts, going from higher to lower, starting with a breed of dog (which we will assume, for argument's sake, to be the narrowest concept possible), and going up the hierarchy all the way to the concept animal. The hierarchy is as follows: doberman, dog, wolf, Canidae, Carnivora, mammal, Vertebrata, Chordata, Animalia. This is, of course, not a complete hierarchy, but it's close enough for our purposes. If the Objectivist theory is correct, a child should learn the concept doberman before he learns the concept dog, and the concept Canidae before he learns the concept animal. As a matter of fact, as a little empirical work would soon demonstrate, a child is more likely to begin forming concepts of animal and dog long before he forms concepts of doberman and Canidae. The initial conceptions of infants and toddlers, as far as we can tell, are not necessarily "low level," "concrete bound," or "perceptual," as Objectivist theory posits, but tend to be on a fairly general level from the very start. There's every reason to believe, as Hayek argued in his essay "The Primacy of the Abstract," that very young children (and animals as well) think largely in terms of broad generalizations, and that maturation of thought in the human species involves the ability to make very fine distinctions so that our conceptions become much richer and cognitively powerful over time.
