Rand and Empirical Responsibility 11

“Definitions preserve ... the logical order of their hierarchical interdependence.” This touches on the Objectivist contention that knowledge is hierarchical. The concept animal is a step higher in the conceptual hierarchy than mammal, for example. Is it true, as Rand asserts, that definitions "preserve" the "logical order" of this hierarchy?

Rand derived her doctrine of definitions from Aristotle. It is not however clear what she means by "logical order," or how definitions go about preserving it. What Rand seems to have in mind (although she's none too clear about it) is the ideal of knowledge as a complete "logical" structure (logical in this sense meaning: integrated without contradiction). In this, Rand is mirroring Aristotle's ideal of knowledge as (in the words of Karl Popper) "an encyclopaedia containing the intuitive definitions of all essences, that is to say, their names together with their defining formulae."

For better or worse, there exists no compelling evidence that knowledge works this way; nor does Rand (or her disciples) provide any evidence, or seem in the least interested in the empirical side of this issue. Yet there is a great deal of evidence that formal definitions are of little importance to understanding the meaning of words. Most words are learned unconsciously, without the aid of formal definitions or dictionaries. Moreover, it can easily be observed that many people understand the meaning of words without being able to provide formal definitions for them. Just ask anyone (besides a linguist or a grammarian) to define the word the and you'll see what I mean.

Now it could be argued that Rand's theory of definitions is not confined to mere formal definitions, but applies to "tacit" or "implicit" definitions as well (whatever those might be), and that when she declares that definitions preserve the logical order of conceptual hierarchies, she is not distinguishing whether those definitions are consciously formalized or are merely implicit and tacit. Yet if this is so, Rand needs to explain (1) how she knows this to be true; and (2) provide compelling evidence for her view.


“Words without definitions are not language but inarticulate sounds.” If by definitions, Rand means consciously formalized definitions (after Aristotle methods of essentialist definitions), this is a grossly implausible position, for the reasons provided above. If Rand means merely "tacit" or "implicit" definitions, in the absence of any evidence (none of which is provided by Rand), it is not clear that this is true (or if it is true, whether it has any significance). What would make a lot more sense would be Words without meanings are not language but inarticulate sounds. This suggests that Rand has confused the concept meanings with that of definitions. Definitions are explanations of what a word means; but this does not mean that a definition is identical with the meaning. The meaning of a term can be understood without defining it, because knowledge is largely tacit and intuitive, rather than formalized and logical, as Rand seems to assume.

“The process of forming, integrating and using concepts is not an automatic, but a volitional process.” Given how important this assertion is to some of Rand's claims about history and morality, Rand's unwillingness to provide any evidence for it is most unfortunate. I suspect it never occured to her that she needed to provide evidence, because empirical responsibility was not part of her basic MO. In any case, had she tried to find evidence for it, she almost certaintly would have realized that the statement is not true. Many concepts, perhaps even most concepts, are formed unconsciusly, without anything remotely describable as volition having anything at all to do with the process. Indeed, this is an obvious fact that can be gleaned merely by observing young children learning to speak. How Rand could have ignored and/or evaded these obvious facts is difficult to comprehend.

An animal cannot perform a process of abstraction. Really? How on earth did Rand know this? For it's not clear at all that this is true. Consider the testimony of two neuroscientists, Jorge Martins de Oliveira and Julio Rocha do Amaral:

Although there is no general agreement, we believe that other species are also capable to develop abstractions. Some primates and cetaceans, without any doubt, have abstract conceptions, but these must be very tenuous and, certainly, they never develop, as humans do, to a point of giving rise to high creativity. And, even if it so happened, it would be an innocuous creativity, since they lack the physical attributes to allow them to build up something that could be considered significant and concrete. In spite of these handicaps, the exercise of conscious and abstract thoughts, among dolphins and superior simians, has been widely evidenced.

Objectivism & History, Part 9

The force of logic Sometimes the most curious doctrines in Objectivism are not those that are explicitly formulated but rather those that are merely hinted at or presupposed by explicit convictions. One such presupposition is the very odd view that neither people nor societies can long hold contradictory beliefs. Consider this passage from Rand’s “For the New Intellectual”:

From her start, America was torn by the clash of her political system with the altruist morality. Capitalism and altruism are incompatible; they are philosophical opposites; they cannot co-exist in the same man or in the same society.

Rand believed that people cannot long hold beliefs that contradict their fundamental premises. Such contradictions will eventually be resolved in favor of the more “fundamental” belief. So if an individual believes in altruism and capitalism, his belief in altruism will undermine his belief in capitalism because (1) altruism and capitalism contradict each other and (2) altruism is more “fundamental” than capitalism.

Here we find Rand once again misrepresenting human nature. There is no evidence that the majority of human beings have any great concern for whether they hold contradictory beliefs. As human experience repeatedly testifies, most human beings have a weak grasp of logic and are blissfully ignorant of the many contradictions floating about in their brains. The sociologist Vilfredo Pareto dedicated a 250,000 word volume to analyzing what he called “non-logical” action, which is to say, action based on contradictory or non-logical notions. “Pareto not only shows that non-logical conduct is predominant,” noted James Burnham; “his crucial point is that the conduct which has a bearing on social and political structure, on what he calls the ‘social equilibrium,’ is above all non-logical. What happens to society, whether it progresses or decays, is free or despotic, happy or miserable, poor or prosperous, is only to the slightest degree influenced by the deliberate, rational purposes held by human beings.” Pareto, therefore, comes to almost the exact opposite conclusion from Rand. Human beings, he notes, are frequently destitute of logic. And he gives hundreds of examples of non-logical actions in his treatise Mind and Society.

But even if Pareto turned out to be wrong on this issue, Rand and her disciples would still not be in the clear; for they would still have to reckon with the evidence of cognitive science, which pretty much settles the issue. Cognitive scientists have conducted a great many experiments examining the degree to which human beings are logical, and they have found that nearly all human beings not only lack any natural facility for logic, but that, in the normal business of life, they make frequent use of illogical inferences to get things done. As Morton Hunt puts it:

[F]ormal logic is not a good description of how our minds usually work. Logic tells us how we should reason when we are trying to reason logically, but it does not tell us how to think about reality as we encounter it most of the time.…

Logic enables us to judge the validity of our own deductive reasoning, but much of the time we need to reason non-deductively — either inductively, or in terms of likelihoods, or of causes and effects, none of which fits within the rules of formal logic. The archetype of everyday realistic reasoning might be something like this: This object (or situation) reminds me a lot of another that I experienced before, so probably I can expect much to be true of this one that was true of that one. Such reasoning is natural and utilitarian — but logically invalid....

If there still remain doubts on this score, simply attend more closely to the beliefs of other human beings. If one observes the human animal, one will find an astonishing mixture of contradictory notions and clashing ideas. I have recently been listening David McCullough’s The Great Bridge, in which one finds a biographical portrait John Augustus Roebling, the engineer who designed and built the Brooklyn Bridge. Although Roebling was a man of science and a great engineer, this did not prevent him from wallowing in non-logical and empirically dubious activities. In his youth, he studied philosophy under the exquisitely preposterous Hegel. In later years, he dabbled in spiritualism and hydropathy. Hegel’s arch-enemy, the philosopher Arthur Schopenhauer advocated quietism and asceticism, but he didn’t practice what he preached. He declared he was incapable of practicing his philosophy, even though he insisted that his philosophy was right. I’ve talked to several Obama supporters in the last few months who don’t seem to agree with many of Obama’s positions. Yet when this is pointed out to them, they are unphazed. They simply don’t care whether a contradiction exists between the policies the favor and the candidate they support.

Examples of this sort could be multiplied many many times. Some people—perhaps even most people—don’t really care too much about either logic or consistency, particularly about matters that are remote to their particular sphere of practical action. Rand and her disciples seem to admit of this non-logical aspect of human belief when they talk of people with “mixed” premises. But they don’t seem to realize that the very fact that people can hold mixed premises contradicts Rand’s conviction that capitalism and altruism cannot exist the same person because the two are contradictory.

Yet this is not the only contradiction involved in insisting that contradictions in the human psyche will tend to be resolved in favor of the more “fundamental” belief. Rand and Peikoff both contend that epistemological ideas are more fundamental than ethical and political ideas. This, however, is a problematic position. What if an individual were to embrace epistemological convictions that deny the importance or “validity” of logic? If an individual doesn’t believe in logic, wouldn’t this mean that there would exist no force or tendency in his mind to resolve contradictions between his ethical and political beliefs? After all, why should such contradictions matter to someone who doesn’t give a fig for logic? Moreover, since Rand did not belief that people had innate tendencies, she can hardly presuppose the existence of an innate tendency to resolve contradictions in favor of the more fundamental view. Since people have free will, they should be able to hold as many contradictory beliefs as they damn please? The Objectivist supposition that contradictory beliefs tend toward a resolution in favor of the more fundamental premise can therefore be dismissed as a mere prejudice, without basis in either logic or fact.

Van Damme Replies (Sort of)

While cleaning up some comments spam I came across this brief note that may have been lost in the flurry. In this post Greg criticised a passage from Lisa Van Damme's essay "The False Promise of Classical Education."

In a kind of proxy comment, an anonymous contributor passed this reply on, allegedly from Van Damme:

From Lisa VanDamme:

What defines the hierarchical order of concepts is distance from the perceptual level, not "wideness." "Doberman" is, unquestionably, more abstract than "dog": Ayn Rand addresses this issue in ITOE, and nothing I have ever said contradicts it.

Leaving aside the oddness of replying by anonymous proxy - surely it would be easier just to reply directly - this also seems to not answer the issue. Here's what Greg quoted from Van Damme's original essay:

Van Damme: "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."

Greg's point in the post was that if this was true, one would start with "Doberman", go up to "dog", then to "organism" etc. Yet this seems unlikely.

Van Damme and other commenters do not seem to have a direct response to this, and merely reply to the effect that Greg's demonstration is a "straw man" because Rand said otherwise in the ITOE. But if Rand's theory (or Van Damme's expression of it) does not stand up to its own derivable consequences, this is hardly Greg's problem! Rather it speaks to the basic wooliness and what I regard as the outright emptiness of most of the speculations expressed in the ITOE.

At any rate, it would be interesting if Van Damme wished to reply in a bit more detail - even by proxy - to Greg's original post, and we cordially invite her to do so.

Anon: "As for your point about the rationalization of philosophic speculation, I don't know where it's coming from. Objectivism views philosophic reasoning and scientific reasoning as of a piece."

Perhaps Anon and I have very different ways of making truth judgments, and that's getting in the way. Or maybe Anon is focussing exclusively on the intention of the Objectivist theory, rather than on its practical results. My tendency is to judge from the outside, not the inside. I'm not greatly interested in the so-called inner logic of theories and doctrines, but in their practical effect. What is the practical effect of Rand's epistemological convictions? How do they effect the cognitive behavior of those who think they are true? To answer these questions, I examine Rand's actual knowledge claims. Are her knowledge claims better, more true, more plausible, as a result of her epistemological theories? Or are they less so?

Now I realize that this is a somewhat conjectural proceeding. It's quite possible that Rand's epistemological theories have nothing to do with her knowledge claims, that the Objectivist epistemology is just window dressing. But in that case, I would seriously question the practical relevance of her epistemology. In any case, it's hard to square the window dressing view with textual references in Rand's own works, where the practicality of her theories is stressed.

"If Rand made assertions that you take to be contrary to what some scientists say, then either she was simply mistaken in her reasoning or the scientists are. The problem has nothing to do with her theory of concepts."

Not necessarily. If her theory of concepts gave in her unjustified confidence in her abstract reasonings (which I suspect is the case), then it would simply be naive to suggest there's no connection. Anon appears to think that it is only a problem of logic. But I believe — and findings in cognitive science support this — that this view of the matter is naive. Psychology also plays an important role in thinking. It particularly influences those who don't realize this, because they don't think to take counter measures against it.

"Next you say that Rand does not accept that some sciences may involve degrees of uncertainty. I don't know where you're getting that from or why, once again, it relates to the epistemological relevance of a theory of concepts."
Well, actually what I said is "Rand does not appear to have accepted the notion" that some sciences may involve degrees of uncertainty—a subtle but important difference. Where did I get the notion? Why, from Rand's own practice: from the fact that her statements about economics and politics are made as if she knew them to be certain. My contention is they can't be, and one of the reasons why this is so is because of that problem of oversimplified premises I noted in the earlier post. Take the issue of free trade, for example. Does anyone seriously believe that Rand did not regard the economic arguments for free trade as not being certain? But given the fact that they're based on over-simplified premises, that's problematic. There are, in fact, compelling arguments, ignored by most economists, that, under specialized conditions, some kinds of tariffs may increase output — a view, moreover, that's actually more consistent with the (admittedly not entirely conclusive) empirical evidence.

But what does all this talk about theories have to do with the theory of concepts? Well, it partly goes back to Anon's statement that the point of the hierarchy was "to show how abstract reasoning connects to perceptual evidence." I wanted to provide a relatively simple argument showing why I don't believe the Randian theory succeeds in achieving this goal. But there is another consideration which I have been hesitant to introduce because of the added complexity, and it is this: I regard concepts as theory-laden. To my mind, it is the theoretical content of concepts which makes them interesting and important. The emphasis in Objectivism on "validation of conceptual knowledge" is misplaced. As Karl Popper (who helped clarify this issue for me) puts it:

If so many philosophers and scientists still think that concepts and conceptual systems (and problems of their meaning, or the meanings of words) are comparable in importance to theories and theoretical systems (and problems of their truth, or the truth of statements), then they are still suffering from Plato's main error, ... which is [a] traditional [error], ... known as "the problem of universals." This should be replaced by "the problem of theories," or "the problem of the theoretical content of all human language."

What Rand would have said about the notion of concepts as theory-laden I don't know. Since it is a position that, at least in some respects, challenges the Aristotlean tradition (see Open Society and Its Enemies, vol 2, p. 9-21), I wouldn't expect Rand, who admired Aristotle immensely, to react all that favorably toward it.

Isn't it important to know whether the concepts we use in our theories our "valid"? No, not in practice. In fact, it's not helpful in the least — quite the contrary. After all, what does it mean to say that a concept is valid? Any arguments about "valid" or "invalid" concepts will often, in practice, reduce themselves to mere wranglings about the meaning of words. That is why scientists don't get their fur ruffled over the definitions of terms. That way madness lies! Indeed, there is no compelling evidence, either from science or from common life, that errors in cognition are caused by "inappropriate" or "invalid" concept formation. (And what is an "invalid" concept, anyway?) In successful sciences, like physics and chemistry, people argue, not about concepts or words, but about theories and assertions about facts. Those philosophers who, following in the tradition of Aristotle and Plato, were obsessed with concepts and conceptual systems, wound up becoming inextricably tangled in futile arguments about the meanings of words (e.g., medieval scholasticism). If the history of philosophy can be our guide in this manner, obsession with concepts and theories about the "justification" of concept-formation, must, because of the very futility of it (concepts being formed largely unconsciously) must lead, in practical terms, to what Popper calls "verbalism" — i.e., useless argumentation attempting to determine the "proper" definition, or the proper "validation," of this or that concept.

I regard the phrase "Galileo had to justify the concept of inertia as a rather inapt way of describing the fact that Galileo had to corroborate the theory of inertia. Even worse is the phrase "Both inertia and value are abstract and need to be abstracted in the proper order, connected to the proper evidence," because it suggests that the critical aspect of any knowledge-claim involves the formation of the concept in which that claim is expressed, and not the development of a theory about concept's referents. The phrase "abstracted in the proper order," is particularly mischievous, because it suggests that a concept's theory can be tested by examining the place of that concept in the hierarchy, all the way down to the so-called perceptual level. In practice, this would appear to be mean examining a concept in the light of other concepts. In short, it means what Popper calls "verbalism" and others call rationalism.

Having spent years studying the rationalizations of ideologues, I have found that one very important aspect of verbalism involves taking advantage of the ambiguity of "wider" concepts to carry forth points that are contrary to logic and fact. This is why Rand's defense of such high-level abstractions arouses my suspicions. "When concepts are integrated into a wider one, the new concept includes all the characteristics of its constituent units," she insists in IOTE. But this is psychologically misleading. Wider concepts generally have more varied referents. And some of those referents may have important differences that are ignored when one simply refers to them under the wider concept. Anon unwittingly provides an illustrative example in his post, where he writes "the cognitive view of emotions is hardly distinctive to Objectivism. It has been held by Aristotelians for decades (see Magda Arnold), and more recently by the highly successful discipline of cognitive-behavioral therapy." At first glance, this seems like a respectable argument. Since both Rand and cognitive-behavioral therapy share a "cognitive view of emotions," Anon can use the success of CBT as evidence for the Randian theory of emotions. But what is not noticed is the critical details that have been ignored under the concept cognitive view of emotions. The fact of the matter is, that Rand's particularly version of the theory has not been accepted by the CBT community. We know this because one of the most important figures in CBT, Albert Ellis, who wrote for the first critical book about Objectivism (i.e., Is Objectivism a Religion?), declared that the relationship Rand posits between thought and emotions is "nonexistent." So the fact that Rand's theory can be classified under the wider category of cognitive view of emotions along with CBT does not mean that evidence for CBT can also be regarded as possible evidence for Rand's theory!

Now I realize it could be argued that Anon's error is a logical fallacy (namely, the fallacy of equivocation). While this is true, it misses the larger point. In abstract reasonings, there can be scores of wide level concepts that could all be positively drenched in the logical sin of equivocation. It is a thankless task, and utterly futile, for the intrepid critic to comb over some particularly abstruse piece of abstract reasoning and try to pick out all the equivocation fallacies embedded, like so many land mines, within it. Much more easier simply to examine the conclusions of those reasonings and subject them to as rigorous empirical criticism as the circumstances allow.

Anon's post is so rich in many of the issues it raises that there still remains a great deal more to be covered. But that will have to wait for other posts.

The Failure of the Hierarchy to Justify Abstract Reasoning

In Anon's most recent reply, he focuses largely on the issue of explaining why "the concepts we need to learn first are just the ones whose referents have the most obvious perceptual similarities." I'll leave it to cognitive scientists (including those mentioned by Anon, along with others) to determine the degree to which this part of the theory accords with reality. In the meantime, I want to focus at what I consider the chief point at issue: the hierarchy as a theory of justification. As Anon admits, the theory attempts "to show how abstract reasoning connects to perceptual evidence." Does it really? But how can that possibly be? At the very most, it only shows how the concepts in use among propositions relate to perceptual evidence. However, abstract reasonings are used to formulate theories; and under no circumstances is it plausible to conclude that a theory can be justified merely by showing "how one's higher-level concepts (and associated propositions) derive from lower-level concepts." Knowledge about very complex aspects of reality — knowledge of economics or politics, for instance — is expressed in theories, and theories are more than the sum of their concepts or the logic of their propositions. It is entirely possible that a theory could be made up of valid concepts and pristinely logical reasoning yet still fail to accord with important facts. The reason for this is quite simple: social theories are (and must be because of the complexity of the subject matter) based on simplified premises. Economics, for instance, seeks to understand what would happen under simplified conditions never realized, but often closely approached in practice. Knowledge of reality involves achieving human scale, and that will sometimes involve a certain degree, hopefully within tolerable limits, of cognitive inadequacy. Sometimes the best we can hope for in a given branch of knowledge is merely to achieve a tolerable degree of plausibility.

Rand does not appear to have accepted the notion that theoretical knowledge of subjects like economics and politics might be characterized by a unspecifiable degree of uncertainty. She presented her own notions on these matters as if they were quite obviously the certain conclusions of reason, which any rational and moral person would accept as a matter of course. And she appears to have believed that her validation of concepts, of which the hierarchy theory (along with measurement omission) is a critical part, removed any problems related to the possible distorting effects of condensation. Nor, sad to say, does she appear to have confronted the problems of the actual simplification that takes place in the process of devising the premises of theories. The hierarchy of knowledge does not, and cannot, address this issue, since the problem has nothing to do with whether the concepts (or even the propositions) are "connected" to reality, since the way in which any really sophisticated theory "connects" to reality is far too complicated to be tested by tracing its concepts back to their perceptual concretes. Theories "model," in greatly compressed form, certain aspects of reality. When we talk about theories or concepts or propositions being "connected" to reality, we are speaking metaphorically, not precisely or literally. Theories don't mirror reality; they reduce an immense complexity to human scale, so that the mind can get some inkling of that complexity. Theories of complex phenomena are not proved or corroborated or justified by tracing their concepts back through a hierarchy to their "perceptual base." Perhaps that would be possible with something really simple, like a theory of furniture. But it's not in the least possible if we are talking about the theory of the fall of the Roman Empire, or an economic theory of tariffs, or a theory of the circulation of elites within a socio-political system.

So how do we know if these theories are true if you can't connect them back through the "hierarchy" to the perceptual base? Science uses rigorous empirical testing to corroborate the conclusions of a theory. No need to trace anything back to the perceptual base from which reasoning proceeds; no, simply test the conclusions! Much simpler, and far more convincing. But there are situations when, because of the inability to run experiments and isolate variables, such empirical tests can hardly be considered conclusive. In economics, for instance, one can't provide entirely convincing empirical tests "proving" that, under all conditions, tariffs will reduce the total output of an economy. The most you can hope for in fields of study where empirical tests yield ambiguous results is to attempt to determine, on the basis of abstract reasoning from simplified premises, what is likely to be true or plausible. Certainty (or near certainty), whether of a contextual variety or otherwise, does not appear possible in such disciplines.

Now, the belief in an epistemological theory that promises what it can't deliver will likely lead to cognitive mischief. The danger is that the theory will give its proponents an unjustified confidence in "abstract reasoning." Even if the intention of the hierarchy is merely to justify so-called "justified" speculation, if the theory does not deliver on its justificationist promises, it will likely lead its proponents unwittingly down the primrose path of rationalist speculation. Isn't this what we find in Objectivist thought — unjustified speculation run rampant, yet all done with the most naive sort of cognitive innocence? Rand herself made any number of assertions about matters of fact that are grossly implausible, and yet she seems to have made them with an entirely serene and untroubled epistemological conscience. For example: "Man is born with an emotional mechanism, just as he is born with a cognitive mechanism; but, at birth, both are 'tabula rasa.'" "Emotions are the automatic results of man’s value judgments integrated by the subconscious." "Emotions are not tools of cognition." “[A man’s] body will always follow the ultimate logic of his deepest convictions.” "A man is a ... being of self-made soul." These statements are not presented as possible conjectures or yet-to-be-proved hypotheses, but as veritable certainties. Some of the statements are very likely false. You would be hard pressed to find any scientist acquainted with the relevant evidence who believes in the blank slate model of human nature advocated by Rand. Nor are Rand's views of emotions any better supported by scientific evidence, as Damasio, among others, has discovered. Her statements relating to human nature are, in the light of evidence compiled in genetics and cognitive science, immensely implausible. Her justificationist epistemological theories have here let her down! Instead of leading her to truth and enlightenment, they have mislead her into error and delusion!

I don't see among Rand or her followers any appreciation for how difficult it is to determine the veracity of certain types of truth claims. Too much confidence is placed in reasonings based on vague generalities or insufficiently detailed understanding of the subject at issue. The consequence is a philosophy characterized by an overabundance of implausible and semi-plausible assertions. My suspicion is that Rand's justificationist theories, including her hierarchy theory, by giving her an unwarranted confidence in her own reasoning abilities, served merely to fortify her rationalistic and dogmatic tendencies.

Van Damme's "The False Promise of Classical Education"

The Objectivist theory of education, as I have noted before, is one of the least objectionable theories in all of Randian inspired philosophy. But this doesn't mean there aren't some serious things wrong with it. Consider, as an example, Lisa Van Damme's essay "The False Promise of Classical Education." Van Damme is at her best when she writes from her own experience as an instructor. When, however, she tries to write as Objectivist, she immediately gets in trouble. What she calls "secular classical education" is seriously flawed because it is too rationalistic. It thinks it can teach children by ramming "floating abstractions" down their throat. It fails because it doesn't take account of the "hierarchy of knowledge," which, or so Van Damme insists, is "absolutely vital to a proper education."

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.