I hear talk about the hierarchy of knowledge all the time and what it means about this education program or the other. It is often used to stress the necessity of certain curricula or the wrongness of child-led learning. So, I want to explore this idea a little.
First, I went to the Lexicon to see what Ayn Rand had to say about the hierarchy of knowledge. These quotes are all from the Introduction to Objectivist Epistemology.
"Since the definition of a concept is formulated in terms of other concepts, it enables man, not only to identify and retain a concept, but also to establish the relationships, the hierarchy, the integration of all his concepts and thus the integration of his knowledge. Definitions preserve, not the chronological order in which a given man may have learned concepts, but the logical order of their hierarchical interdependence."
"To know the exact meaning of the concepts one is using, one must know their correct definitions, one must be able to retrace the specific (logical, not chronological) steps by which they were formed, and one must be able to demonstrate their connection to their base in perceptual reality."
"Concepts have a hierarchical structure, i.e., . . . the higher, more complex abstractions are derived from the simpler, basic ones (starting with the concepts of perceptually given concretes)."
So, in light of that bit of explanation, I want to ask a few clarifying (at least to me) questions.
1. Where does this hierarchy exist?
It lives in our brains. It is in that amazingly cool realm of mental constructs created using real world data. This is what it means for concepts to be objective. They are based on real facts, on things that really exist. And they are made using human mental processes. Not subjective (can't be based on any crazy thing a person might dream up), not intrinsic (the concepts and the order don't exist in nature independent of a human brain).
2. If the hierarchy is created and integrated in our own heads, why would we have to enter data in any particular order?
I don't think we do have to. In fact, I think people often learn based on the kinds of facts and experiences they encounter in their households and lives. They do not learn "out of order," as long as they integrate their knowledge logically. As Ayn Rand says, a person "must be able to retrace the specific (logical, not chronological) steps by which [their concepts] were formed, and one must be able to demonstrate [the concepts'] connection to their base in perceptual reality." It is the logical connections we make between our concepts that must be in a certain order, not their chronology. We can introduce any kind of knowledge that interests us into our heads; we just have to be aware of what we are introducing and conscious about integrating it with other things we know.
Rand's description of Gail Wynand's childhood and adolescence in The Fountainhead includes his reading habits. "Without advice, assistance or plan, he began reading an incongruous assortment of books; he would find some passage which he could not understand in one book, and he would get another on that subject. He branched out erratically in all directions; he read volumes of specialized erudition first, and high-school primers afterward. There was no order in his reading; but there was order in what remained in his mind."
What Ayn Rand describes is Wynand forming his hierarchy of knowledge. The disorder of his pursuit of facts did not negatively affect the order in which he held the fact in his mind because we must each create a logical hierarchy, no matter what facts we get or in what order we get them.
3. Wouldn't learning sometimes be more time-efficient if we go in the order another person has already figured out?
Certainly. But that isn't essential to correct understanding. A person might choose to save time and effort by using someone else's work as a way to study a subject. Another person might get joy out of figuring some part of it out by himself. Time efficiency and minimizing the effort required is only one way (though often a convenient way). If the goal is to get the info in order to do another value, the quickest and easiest seems best. But if the goal is different (not a specific value but enjoyment of the experience or honing one's skills), it might be better to tackle it in a different order.
History is a wonderful example. If the goal is to get a broad overview of history quickly in order to understand modern politics, it seems logical to learn the facts chronologically. But if the purpose is to deepen your enjoyment of traveling to American Revolution sights, it makes sense to begin where your interest lies. Your desire to learn about the Founding Fathers may take you back to Ancient Greece and Rome eventually, but it would be silly to start there, when you really want to know about Jefferson. There is no violation of the hierarchy of knowledge in this example. As long as you integrate your concepts logically, it doesn't matter the order in which you gather your info.
4. If people are exposed to ideas before they understand the underlying facts and concepts, won't that cause them to hold floating abstractions?
Hearing something that you don't have the facts to support is okay, as long as you say, "Well, I don't really understand that" or at least accept a tentative kind of knowledge about a subject. Tentative knowledge and unexplored concepts are not wrong. Floating abstractions (in the negative sense Objectivists speak of) are disconnected pieces of knowledge that a person pretends are grounded and certain. A floating abstraction requires evasion of the fact that the connection of the concept to reality are not known.
5. Should children be exposed to ideas that they don't have the facts to ground?
I don't think there is any way to avoid it. Does the infant understand the language you are speaking to him? No, but he will one day. Unless you are willing to lock children in a closet and then pass him facts through a cat door one at a time and in order, there is no way to keep children from hearing and absorbing words and ideas that they don't completely understand.
Not only is it impossible to prevent children from hearing things they don't understand, I think it beneficial for them to be exposed to them. I think the best way to learn Objectivism, for instance, is at the feet of adult Objectivists. There is no reason to protect children from hearing you and your partner and friends talking about politics, ethics, epistemology, and metaphysics. If they ask questions, answer them at a level the child can understand. One day, they will have an adult's understanding, and how much easier it will have been to learn a little at a time as a part of daily life than to try to integrate it whole into already arranged minds, as most of us did.
Of course, there is no point in purposely presenting ideas to children that they are incapable of understanding. There is nothing wrong with a baby watching and listening to his sister working on phonics. But sitting the baby down to learn phonics is ridiculous. Why not choose something he can grasp, if you are choosing a topic of conversation with him? I wouldn't choose to bring up the Ground Zero Mosque with Livy, but if she hears Aaron and I talking about it, I will certainly answer her questions.
So how do we prevent them from settling for floating abstractions instead of real knowledge? Ask them questions. "How do you know that?" "What made you think that?" "Where's your evidence?" Explain things by linking to reality; giving reasons for your own actions, for your requests, for your ideas, for your choices, for the limits you set with them teaches children that human understanding requires concrete data and a logical progression from that data to the conclusion. Give examples of your own floating abstractions and how you have fixed them. "I used to believe in a god, but then I realized that there was no god I could see, touch, taste, hear, or smell in the world. I had been believing it all along without having any evidence! I'm glad I looked for evidence finally."
And finally, when a child says something he doesn't fully grasp, it isn't necessarily a floating abstraction. "When I grow up I am going to marry Daddy" is not floating; the child's understanding of marriage is very limited (people who live together and love each other), but it is grounded in reality (examples of mom and dad and others). It isn't floating at all, just immature. As the child grows, she will understand marriage more fully. No reason to keep that concept from her until she understands sex, legal contracts, child-raising, and monogamy.
There are plenty of other arguments about life-learning and child-led learning (which you can feel free to ask me about - formspring might be a good way), but I don't buy this one. The logical formation of a child's hierarchy of knowledge doesn't require encountering ideas in a pre-formed logical order.
First, I went to the Lexicon to see what Ayn Rand had to say about the hierarchy of knowledge. These quotes are all from the Introduction to Objectivist Epistemology.
"Since the definition of a concept is formulated in terms of other concepts, it enables man, not only to identify and retain a concept, but also to establish the relationships, the hierarchy, the integration of all his concepts and thus the integration of his knowledge. Definitions preserve, not the chronological order in which a given man may have learned concepts, but the logical order of their hierarchical interdependence."
"To know the exact meaning of the concepts one is using, one must know their correct definitions, one must be able to retrace the specific (logical, not chronological) steps by which they were formed, and one must be able to demonstrate their connection to their base in perceptual reality."
"Concepts have a hierarchical structure, i.e., . . . the higher, more complex abstractions are derived from the simpler, basic ones (starting with the concepts of perceptually given concretes)."
So, in light of that bit of explanation, I want to ask a few clarifying (at least to me) questions.
1. Where does this hierarchy exist?
It lives in our brains. It is in that amazingly cool realm of mental constructs created using real world data. This is what it means for concepts to be objective. They are based on real facts, on things that really exist. And they are made using human mental processes. Not subjective (can't be based on any crazy thing a person might dream up), not intrinsic (the concepts and the order don't exist in nature independent of a human brain).
2. If the hierarchy is created and integrated in our own heads, why would we have to enter data in any particular order?
I don't think we do have to. In fact, I think people often learn based on the kinds of facts and experiences they encounter in their households and lives. They do not learn "out of order," as long as they integrate their knowledge logically. As Ayn Rand says, a person "must be able to retrace the specific (logical, not chronological) steps by which [their concepts] were formed, and one must be able to demonstrate [the concepts'] connection to their base in perceptual reality." It is the logical connections we make between our concepts that must be in a certain order, not their chronology. We can introduce any kind of knowledge that interests us into our heads; we just have to be aware of what we are introducing and conscious about integrating it with other things we know.
Rand's description of Gail Wynand's childhood and adolescence in The Fountainhead includes his reading habits. "Without advice, assistance or plan, he began reading an incongruous assortment of books; he would find some passage which he could not understand in one book, and he would get another on that subject. He branched out erratically in all directions; he read volumes of specialized erudition first, and high-school primers afterward. There was no order in his reading; but there was order in what remained in his mind."
What Ayn Rand describes is Wynand forming his hierarchy of knowledge. The disorder of his pursuit of facts did not negatively affect the order in which he held the fact in his mind because we must each create a logical hierarchy, no matter what facts we get or in what order we get them.
3. Wouldn't learning sometimes be more time-efficient if we go in the order another person has already figured out?
Certainly. But that isn't essential to correct understanding. A person might choose to save time and effort by using someone else's work as a way to study a subject. Another person might get joy out of figuring some part of it out by himself. Time efficiency and minimizing the effort required is only one way (though often a convenient way). If the goal is to get the info in order to do another value, the quickest and easiest seems best. But if the goal is different (not a specific value but enjoyment of the experience or honing one's skills), it might be better to tackle it in a different order.
History is a wonderful example. If the goal is to get a broad overview of history quickly in order to understand modern politics, it seems logical to learn the facts chronologically. But if the purpose is to deepen your enjoyment of traveling to American Revolution sights, it makes sense to begin where your interest lies. Your desire to learn about the Founding Fathers may take you back to Ancient Greece and Rome eventually, but it would be silly to start there, when you really want to know about Jefferson. There is no violation of the hierarchy of knowledge in this example. As long as you integrate your concepts logically, it doesn't matter the order in which you gather your info.
4. If people are exposed to ideas before they understand the underlying facts and concepts, won't that cause them to hold floating abstractions?
Hearing something that you don't have the facts to support is okay, as long as you say, "Well, I don't really understand that" or at least accept a tentative kind of knowledge about a subject. Tentative knowledge and unexplored concepts are not wrong. Floating abstractions (in the negative sense Objectivists speak of) are disconnected pieces of knowledge that a person pretends are grounded and certain. A floating abstraction requires evasion of the fact that the connection of the concept to reality are not known.
5. Should children be exposed to ideas that they don't have the facts to ground?
I don't think there is any way to avoid it. Does the infant understand the language you are speaking to him? No, but he will one day. Unless you are willing to lock children in a closet and then pass him facts through a cat door one at a time and in order, there is no way to keep children from hearing and absorbing words and ideas that they don't completely understand.
Not only is it impossible to prevent children from hearing things they don't understand, I think it beneficial for them to be exposed to them. I think the best way to learn Objectivism, for instance, is at the feet of adult Objectivists. There is no reason to protect children from hearing you and your partner and friends talking about politics, ethics, epistemology, and metaphysics. If they ask questions, answer them at a level the child can understand. One day, they will have an adult's understanding, and how much easier it will have been to learn a little at a time as a part of daily life than to try to integrate it whole into already arranged minds, as most of us did.
Of course, there is no point in purposely presenting ideas to children that they are incapable of understanding. There is nothing wrong with a baby watching and listening to his sister working on phonics. But sitting the baby down to learn phonics is ridiculous. Why not choose something he can grasp, if you are choosing a topic of conversation with him? I wouldn't choose to bring up the Ground Zero Mosque with Livy, but if she hears Aaron and I talking about it, I will certainly answer her questions.
So how do we prevent them from settling for floating abstractions instead of real knowledge? Ask them questions. "How do you know that?" "What made you think that?" "Where's your evidence?" Explain things by linking to reality; giving reasons for your own actions, for your requests, for your ideas, for your choices, for the limits you set with them teaches children that human understanding requires concrete data and a logical progression from that data to the conclusion. Give examples of your own floating abstractions and how you have fixed them. "I used to believe in a god, but then I realized that there was no god I could see, touch, taste, hear, or smell in the world. I had been believing it all along without having any evidence! I'm glad I looked for evidence finally."
And finally, when a child says something he doesn't fully grasp, it isn't necessarily a floating abstraction. "When I grow up I am going to marry Daddy" is not floating; the child's understanding of marriage is very limited (people who live together and love each other), but it is grounded in reality (examples of mom and dad and others). It isn't floating at all, just immature. As the child grows, she will understand marriage more fully. No reason to keep that concept from her until she understands sex, legal contracts, child-raising, and monogamy.
There are plenty of other arguments about life-learning and child-led learning (which you can feel free to ask me about - formspring might be a good way), but I don't buy this one. The logical formation of a child's hierarchy of knowledge doesn't require encountering ideas in a pre-formed logical order.
5 comments:
Loved especially the examples of starting anywhere in history, about possibly choosing a 'suboptimal' path when having values other than efficiency, and the Wynand quote. Great post!
Thanks for posting this, Kelly. I always appreciate the thought you put into your posts. I don't think you've got the concept of hierarchy in education quite correct, though. It's not about learning in some specific order based on chronology or someone else's breakdown of the facts. It's about organizing all of your knowledge on the basis of your own observations, as the "foundation" of the hierarchy. It's not that there's a certain order in which you have to enter information--it's that if you enter higher-level information without grasping that perceptual base, you don't have knowledge. You have information that you can use as a starting point, or that you can "hold" until you do have the hierarchy of knowledge to support it, but you don't have knowledge in a full, useful sense. I think that does describe what Gail Wynand was doing--if he read something he didn't understand, he went and "filled in" what he needed. Despite that description of his learning methods, I have a hard time imagining him starting math with a book on advanced calculus--he'd be reading whole other books in between sentences! At some point he would still have to sit down and learn addition before any of his other "knowledge" would make sense--that's an obvious example, but it works the same way in every subject a child needs to learn.
For example, in history, hierarchy does not equal chronology. You said it yourself--the place to start learning history is at the perceptual level, with objects and events that are meaningful to you and that you can grasp on a first-hand level. What you describe in learning history *is* exactly what is meant by hierarchy. How can a child understand strange customs and events of a culture removed from her by thousands of years and miles? The "base" of hierarchy is perception, not whatever came first.
In science, on the other hand, it's reasonable to teach concepts in historical order because people did, in fact, begin with observation and proceed to higher abstractions.
It's an interesting and very important topic and I appreciate this post. But please don't dismiss the entire concept out of hand based on a misunderstanding that hierarchy simply means chronology.
Heather, thank you for this thoughtful comment. I wouldn't disagree with much of what you said. In fact, I would say we see hierarchy in the same way. I don't want to dismiss it at all; I just want to dismiss it as a reason that children must be presented information in a certain order.
I agree completely with everything that you said except for the teaching of science. I think one very efficient way to understand the progression of science would be to learn the discoveries chronologically. However, I think you could have an equally good grasp of science by doing what Gail Wynand did, by starting with a subject that interests you, say weather, and learning the concepts that underlie that subject. Learning about weather first might lead to electricity (lightning), physics (tsunamis and tornadoes), chemistry (the composition of water and how it changes from gas to liquid to solid), biology (the way climate affects ecosystems).
My point was that it doesn't matter how you encounter information, as long as you are willing to do the hard work that Wynand did - make the logical connections and find the underlying concepts.
I would certainly never dismiss the hierarchy of knowledge; it is too important an epistemological discovery. I only wanted to clarify it (and it seems like we agree) and point out how I think it has been used wrongly as a justification for the need for certain curricula.
Great article. Thanks for writing this.
Kelly,
I'm a science educator, and here's how I currently conceptualize this issue. I think it's very similar, if not identical, to what you're saying:
In order for a concept to be fully understood, a learner must follow the logical hierarchy of a given concept. (And I emphasize, as you did, that aspect of Rand's definition: that the logical hierarchy does not necessarily match the chronological development of the concept).
However, this does not mean that *partial* knowledge is somehow an inherently bad thing, or even something that can or should be avoided. (I don't think it can or should.)
I think what's more important in this context is whether a person knows the difference in his own mind between the floating, partial knowledge, and the better- or fully-grounded knowledge.
As for how a student ultimately comes to acquire the skill of detecting that difference, is another question. It would make sense that it requires that plenty of knowledge be taught hierarchically, i.e. the overall emphasis in science education should be on teaching things for *full* understanding.
(I'm not surprised, for example, that the most rationalistic people I've met very rarely have a personal, concrete-rich understanding of much of anything.)
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