Alfred North Whitehead on “inert ideas”

One of the most remarkable essays I have read on education is “The Aims of Education” by Alfred North Whitehead. First published in 1917, it calls some of our current “wars” into question, particularly the apparent battles between progressives and traditionalists. When Whitehead argues against the danger of “inert ideas,” he seems both progressive and traditional at once.

Whitehead (1861-1947) was a mathematician and philosopher. He co-authored the Principia Mathematica with Bertrand Russell. He is the founder (to some degree) of “process philosophy,” which he explains in Process and Reality: An Essay in Cosmology.

Already, I am bristling, because the very idea of “process philosophy” sounds like so much nonsense. But when Whitehead says something, he makes you think–in a way that differs from what you might expect. His points don’t fall in the usual classifications.

The second paragraph of “The Aims of Education” reads:

In training a child to activity of thought, above all things we must beware of what I will call “inert ideas”–that is to say, ideas that are merely received into the mind without being utilised, or tested, or thrown into fresh combinations.

Now, this is interesting, because such “inert ideas” could consist of disjointed facts and big, vague concepts. In other words, schools that emphasize isolated bits of information and schools that emphasize ungrounded “critical thinking and problem-solving” are committing a similar error. They are giving students material out of context. As commenters on Michael’s most recent post have suggested, it is the motion of a topic that makes it interesting and memorable. Daniel T. Willingham has made similar points in his book, Why Don’t Students Like School?

But am I reading things into Whitehead? Not at all; here’s more:

Furthermore, we should not endeavour to use propositions in isolation. Emphatically I do not mean, a neat little set of experiments to illustrate Proposition I and then the proof of Proposition I, a neat little set of experiments to illustrate Proposition II and then the proof of Proposition II, and so on to the end of the book. Nothing could be more boring. Interrelated truths are utilised en bloc, and the various propositions are employed in any order, and with any reiteration. Choose some important applications of your theoretical subject; and study them concurrently with the systematic theoretical exposition. … Also the theory should not be muddled up with the practice. The child should have no doubt when it is proving and when it is utilising. My point is that what is proved should be utilised, and that what is utilised should–so far, as is practicable–be proved. I am far from asserting that proof and utilisation are the same thing.

Very interesting. So there should be “theoretical exposition,” short and thorough, alongside (and clearly distinct from) practical application. The theory should be presented in a systematic manner, but “interrelated truths” should be utilized “en bloc.”

In none of this can the details of the subject or the hard work of practice be avoided:

All practical teachers know that education is a patient process of the mastery of details, minute by minute, hour by hour, day by day. There is no royal road to learning through an airy path of brilliant generalisations. There is a proverb about the difficulty of seeing the wood because of the trees. That difficulty is exactly the point which I am enforcing. The problem of education is to make the pupil see the wood by means of the trees.

But what of the aims of education? What are they? Whitehead writes:

What education has to impart is an intimate sense for the power of ideas, for the beauty of ideas, and for the structure of ideas, together with a particular body of knowledge which has peculiar reference to the life of the being possessing it.

Here’s where things get a little shaky for me. What does he mean by “peculiar reference”? Does he mean that studies should be of personal relevance to each student? Or does he mean that a subject taught in motion is a subject made relevant–that the very motion, the procession from one idea to another, consitutes the relevance, as it helps us see where a particular idea comes from and where it is going? I believe he means the latter. He continues:

The appreciation of the structure of ideas is that side of a cultured mind which can only grow under the influence of a special study. I mean that eye for the whole chess-board, for the bearing of one set of ideas on another. Nothing but a special study can give any appreciation for the exact formulation of general ideas, for their relations when formulated, for their service in the comprehension of life. A mind so disciplined should be
both more abstract and more concrete. It has been trained in the comprehension of abstract thought and in the analysis of facts.

There is much more to the essay than I am conveying here. What’s tantalizing is that some of his ideas are so good and can be misunderstood so easily. They resemble, at first glance, some of the education jargon out there (regarding the “joy of discovery,” for instance) but mean something quite different. One need not agree with all of his points, but they raise the possibility that there is something beyond the oppositions familiar to us today.

I bring up Whitehead in my forthcoming book, Republic of Noise: The Loss of Solitude in Schools and Culture. I am grateful to the mathematician who brought Whitehead’s essay to my attention.


  1. tim-10-ber says:

    Thanks for the link to the article.

    Aren’t government schools doing today exactly what he warned against? Taking snippets, inert ideas, and teaching just the snippet without the full underlying foundation because…because only that snippet will be taught?

    I swear if we use a solid, well rounded, deep and broad curriculum taught by strong teachers in every subject that figure out a way to “hook” the student into how what is being taught is relevant even today, the kids will do fine on the standardized tests. Why? Because the curriculum, coupled with the teachers skills, would cover in more depth than done today, the standards the government says kids need to master.

    Is anyone even attempting this? I really want to know what schools and more importantly what districts are doing this…

    thank you —

  2. Michael E. Lopez says:

    I’m quite fond of this essay myself. I was just going over some of my notes on it a few days ago. (It’s part of the “main” pile of stuff I have for my dissertation.)

    Meaning absolutely no disrespect — this is just something of an area of expertise for me so I feel compelled to say something — I think you’re letting your reading of some of his passages get a little lax, or a little “Englishy” as we say in philosophy.

    Many humanities authors from other disciplines — and some philosophers — accomplish their writing goals by way of sort of vague hand-waving at an idea. (This is not meant as an insult: there are many forms of writing other than exacting prose that are marvelous ways to communicate ideas.) Most philosophers, and most here includes Whitehead, don’t traffic in vague, beautiful, efficacious ideas. They traffic in very specific arguments and assertions. The passage about “peculiar reference” that you’re talking about is part of a very discrete, very particular argument that he’s making.

    I’m pretty sure that by “peculiar reference” he’s talking about the interests of the student, for whatever reasons, in a specialist field of study. Recall that he just got finished talking about how special(ist) courses of study were, essentially, easier to teach for two reasons: first, that the student is more fully-formed and so you’ve got a better base for developing new learning, and second, that “the specialist study is normally a study of peculiar interest to the student. He is studying it because, for some reason, he wants to know it.”

    But it’s not as if you can just simply pull specialist education away from general education: “You may not divide the seamless coat of learning,” after all. So in obtaining a (seamless) education, you get two things:

    1) A general education: “an intimate sense for the power of ideas… together with…”

    2) A specialist education: “a particular body of knowledge which has peculiar reference to the life of the being possessing it.”

    There’s still a more general point to be made about relevance, of course. It’s in the subtext of the bit about specialist education certainly — and I’m actually working on a post right now that talks about the necessity of desire for learning. It’s also discussed, explicitly it seems, much earlier in the essay:

    “Let the main ideas which are introduced into a child’s education be few and important, and let them be thrown into every combination possible. The child should make them his own, and should understand their application here and now in the circumstances of his actual life. From the very beginning, the child should experience the joy of discovery. The discovery which he has to make, is that general ideas give an understanding of that stream of events which pours through his life, which is his life.”

    It does seem, though, as if Whitehead has in mind something like *demonstrating* the relevance of the general body of knowledge to allow for the experience of power-through-understanding, or perhaps in a more Deweyan-frame, power-through-deployed-understanding. But that’s another issue entirely.

  3. Michael,

    I am sorry if my points came across as “English-y”–I agree with you that he was arguing for both general and special study. I agree, likewise, that the “peculiar reference” has to do with a student’s interest. But where does that interest come from? It seems that, according to Whitehead, it comes, at least in part, from a grasp of the motion and combinations of ideas. True, different students will take interest in different subjects, but instruction that brings out the motion and combinations is more likely to arouse interest (and bring forth competence) than instruction that does not. Wouldn’t you say that’s a big part of his point? He illustrates it with specific examples, which I did not bring up.

    I agree, also, that he does not “traffic in vague, beautiful, efficacious ideas.” In fact, I find that his essay clears up much of the confusion in education discussion about “big ideas.”

    I was trying to convey some of his intriguing points in a short space; this was not meant as a detailed analysis. But if I unwittingly committed the very error that he warns against, then I will take that into consideration.

  4. I would argue, moreover, that Whitehead argues not only through specific assertions, but through contradictions intended to give readers a wider or deeper view.

    That is, he doesn’t let the reader easily settle on some conclusion about what he is trying to say. He sets forth a number of seeming oppositions: systematic and spontaneous study; specialized and general study; the joy of discovery and the hard work required for mastery of a subject; the need to teach in the present (the “holy ground” of learning) and the conception of the present as past, present, and future; and more.

    But instead of arguing for a “balance” or saying that it isn’t an “either-or proposition,” he shows how these oppositions might in fact be reconciled. At the same time, he doesn’t resolve every single one, and this, I believe, is intentional.

    If you disagree with me here, I would love to hear your views. And if you agree with me, I’d likewise be interested. So I do hope you say more about this.

  5. Process and Reality is the most challenging book I ever read.

  6. Michael E. Lopez says:

    So there’s two things to respond to here… I hope that others don’t grow bored as we discuss with each other, and I hope above hope that everyone else will feel free to comment on your VERY interesting thread.

    (1) About the passage: I was initially confused by your claim that the “motion… constitutes the relevance.” That’s the sentence that made me frown slightly. Now that I see what you’re up to, I think there’s really only a minor quibble to be had.

    I certainly think that Whitehead believes that a properly structured general course of study will give rise, naturally, to the “foci of special interest” through its presentation of ideas not inertly, but in terms of their involvement in activity. This active presentation of ideas will lead somewhere, namely to aspects of life (goals, problems, etc.) which require more specialized study.

    (I prefer “activity” to “motion” because I suspect Whitehead means to invoke the action-passion distinction, not the motion-stasis distinction; but we’re talking about the same thing.)

    So you’re probably right as an empirical matter that thinking actively about ideas and such will lead one to these opportunities for special interest, and that this makes the arousal of interest “more likely” across a given population. More opportunities, more interest, we should think.

    Now the very minor quibble: I’d venture to guess that Whitehead wouldn’t care to comment on the likelihood of the arousal of interest of any particular student. The interest itself I think he pretty clearly is cashing out as to be “peculiar” to each student, a sort of black box, if you will. In “The Rhythmic Claims of Freedom and Discipline”, he says, “But for all your stimulation and guidance the creative impulse towards growth comes from within, and is intensely characteristic of the individual.” We can provide opportunities, but little else.

    So that’s the first issue. The second is about whether he attempts to make points through contradictions, pushing his readers into difficult positions where easy conclusions are evasive. Here I think we disagree. I think he goes to great pains to avoid doing exactly what you’re attributing to him. The “oppositions” you’re describing I don’t read as oppositions at all, at least not as he presents them.

    The systematic study of a subject is about methodology, a method that values rigor and sparseness and activity; the spontaneity (he doesn’t use that word, but I think I understand what you mean) is about the motivation and impulse to learn: the timing and picking of subject matter as it is linked to the active life. They aren’t in opposition, because they’re about completely different aspects of the learning process.

    By contrast, specialized and general study are really just two aspects of the same thing: a learning to be active in life through a development of basic powers on the one hand, and the addressing of particular interest-based tasks through more focused study on the other. So they aren’t in opposition, either.

    I will confess that his talk about the present being past and future is a bit on the cryptic “made-you-think” side of things to the modern reader, but I also strongly suspect he’s just making a metaphysical point about being: to the extent that anything exists it must exist in the present. The past doesn’t exist, as such, it “existed”. To the extent it is talked of “existing” at all, it exists in how we treat with it here and now. Likewise the future, which “will exist” but does not exist, as such.

    He doesn’t resolve this, true — which is to say he doesn’t explain it — but I also think he expects that his audience (the Mathematical Association of England in 1916) to be able to understand the underlying point about existence. (It was common at the time to think of things in the past and the future as “nonexistent objects”, and much of the discussion was actually about how to refer to them.) And I don’t really see anything else that he leaves unresolved, either, at least not as an intentional matter of style.

    I’m fairly certain that any other seeming contradictions or oppositions are as easily explained. There are people who write like that (I write like that sometimes), but I’m going to go on record as saying Whitehead wasn’t one of them — at least not here.

    Again, I can’t stress enough that I hope that Diana and I aren’t discouraging lively engagement through our somewhat involved discussion.

    (Because it risks undermining my point if I don’t, I want to add the probably unnecessary caveat that when I say “metaphysics” I’m not talking about the metaphysics section at the local Barnes and Noble, which is so much new age spirituality. I’m talking about philosophical metaphysics.)

  7. This has turned into a very interesting discussion. I, too, hope that others will not hesitate to jump in. I am delighted to be discussing Whitehead on this grey day.

    First, I agree that Whitehead would say that interest comes from within the individual. Yet it seems that one of his chief complaints about “inert ideas” is that they are dull. External examinations, because they are not intimately related to the instruction, take part in this dullness (this is a long quote, too good to shorten):

    “The best procedure will depend on several factors, none of which can be neglected, namely, the genius of the teacher, the intellectual type of the pupils, their prospects in life, the opportunities offered by the immediate surroundings of the school and allied factors of this sort. It is for this reason that the uniform external examination is so deadly. We do not denounce it because we are cranks, and like denouncing established things. We are not so childish. Also, of course, such examinations have their use in testing slackness. Our reason
    of dislike is very definite and very practical. It kills the best part of culture. When you analyse in the light of experience the central task of education, you find that its successful accomplishment depends on a delicate adjustment of many variable factors. The reason is that we are dealing with human minds, and not with dead matter. The evocation of curiosity, of judgment, of the power of mastering a complicated tangle of circumstances, the use of theory in giving foresight in special cases all these powers are not to be imparted by a set rule embodied in one schedule of examination subjects.”

    So, although a teacher cannot control or guarantee the students’ interest, certain forms of curriculum, teaching, and examination can do a pretty good job of deadening it, wouldn’t you say?

    Now, as for the oppositions, you argue that he didn’t see them as oppositions at all, and that he leaves none of them unresolved (or if any of them are, he assumes his audience understands their resolution). I am partly convinced, but not entirely. He writes, for instance:”I know that it seems contradictory to allow for specialism in a curriculum especially designed for a broad culture. Without contradictions the world would be simpler, and perhaps duller. But I am certain that in education wherever you exclude specialism you destroy life.” So, here he is acknowledging the existence of a contradiction but resolving it at the same time.

    There’s also a slight hint of mischief in his argument now and then. At one point he makes a suggestion (regarding the connections between subjects, or the applicability of algebra to history) and then makes clear that he himself is not claiming to be able to pull it off:

    “If this course be followed. the route from Chaucer to the Black Death, from the Black Death to modern Labour troubles, will connect the tales of the mediaeval pilgrims with the abstract science of algebra, both yielding diverse aspects of that single theme, Life. I know what most of you are thinking at this point. It is that the exact course which I have sketched out is not the particular one which you would have chosen, or even see how to work. I quite agree. I am not claiming that I could do it myself. But your objection is the precise reason why a common external examination system is fatal to education. The process of exhibiting the applications of knowledge must, for its success, essentially depend on the character of the pupils and the genius of the teacher. Of course I have left out the
    easiest applications with which most of us are more at home. I mean the quantitative sides of sciences, such as mechanics and physics.”

    So, here he suggests a certain opposition (I’m already getting a little tired of calling it that) between subjects as they are known and subjects as they could come to life under the right kind of instruction. But this “education as Life” is nowhere near as vague and sweeping as a reader might assume at first. It involves and requires the details of the subjects. There is a discipline involved, but it is a discipline with expanse, a discipline that allows for “the idiosyncrasy of the workman.”

    As for the discussion of the “present,” much does depend on what understanding he assumed of his audience, as you point out. What strikes me is that he is not undercutting the study of the past or the structured study of any subject. At the time of this essay’s publication, quite a few educators and schools (at least in the U.S.) were trying to emphasize “real-life” learning as opposed to book-learning. It is possible that he was not addressing this audience at all, not even in his mind.