Ps and Qs

The cunning writer addresses those who understand p, but himself talks only in terms of (p + q). Some readers will catch the habit, and learn to raise the complexity stakes.

To understand (p + q), each in the light of the other, is to understand p better than before, satisfactory though that earlier understanding may have seemed at the time. Does the mere juxtaposition suggest that our earlier pre-qunderstanding of pwas perhaps in something of a hurry to conclude? Whether or no, these readers also learn something about the limitations of `satisfactoriness' which may be of more value than the parochialities of any particular (p + q).

Still, the reader who now understands a little better finds it hard not to look down upon that only-just-younger self who didn't. The trick is to combine justifiable gratification at our present smartness with affection for the earlier struggler. One reason is that it won't be long before our present smartness will itself need all the sympathy it can get. A second and better reason is that rejection of earlier obtuseness diminishes present understanding. The wit -- which is the truth -- of (p + q) lies in the disproportion between the two values of p -- before and after it came into the same eye-span as q. To read it juxtaposed is to read it with an eye and a half; leaving half an eye for the instructively different sense it had in isolation. This was the collusion the writer set out to provoke -- the shared recognition of the tension between two readings: the first, in a routine context, the second in the context he has set up.

We need such little victories to keep language in its place.

Problem: How to express `p, at the same time q' in such a way that when we get to q we have retained most of the p it was at-the-same-time-as ?

Parallel processing

Oliver Wendell Holmes sr: "My thoughts flow in layers or strata, at least three deep. I follow a slow person's talk, and keep a perfectly clear under-current of my own beneath it. Under both runs obscurely a consciousness belonging to a third train of reflections, independent of the two others. I will try to write out a mental movement in three parts.

A. -- first voice, or Mental Soprano, -- thought follows a woman talking.

B. -- Second voice, or Mental Baritone, -- my running accompaniment.

C. -- Third voice, or Mental Basso, -- low grumble of an importunate, self-repeating idea.

A. -- White lace, three skirts, looped with flowers, wreath of apple-blossoms, gold bracelets, diamond pin and ear-rings, the most delicate berthe you ever saw, white satin slippers --

B. -- Deuce take her! What a fool she is! Hear her chatter! (Look out of window just here. -- Two pages and a half of description, if it were all written down, in one tenth of a second.) -- Go ahead, old lady! (Eye catches picture over fire-place.) There's that infernal family nose! Came over in the `Mayflower,' on the first old fool's face. Why don't they wear a ring in it?

C. -- You'll be late at lecture -- late at lecture -- late -- late -- late."


J. S. Mill: "We may ask, whether the plan of nineteen-twentieths of our unendowed schools be not an organized system of charlatanerie for imposing upon the ignorance of parents? Whether parents do, in point of fact, prove themselves as solicitous, and as well qualified, to judge rightly of the merits of places of education, as the theory of Adam Smith supposes? Whether the truth be not, that, for the most part, they bestow very little thought upon the matter; or, if they do, show themselves in general the ready dupes of the very shallowest artifices? Whether the necessity of keeping parents in good humour does not too often, instead of rendering the education better, render it worse; the real ends of instruction being sacrificed, not solely (as would otherwise be the case) to the ease of the teacher, but to that, and also to the additional positive vices of clap-trap and lip-proficiency? We may ask, whether it is not a matter of experience, that a schoolmaster who endeavours really to educate, instead of endeavouring only to seem to educate, and laying himself out for the suffrages of those who never look below the surface, and only for an instant at that, is almost sure, unless he have the genius and the ardour of a Pestalozzi, to make a losing speculation? Let us do what we may, it will be the study of the merely trading schoolmaster to teach down to the level of the parents, be that level high or low; as it is of the trading author to write down to the level of his readers."


Locke: "The words whereby it [the mind] signifies what connexion it gives to the several affirmations and negations that it unites in one continuing reasoning or narration are generally called particles; and it is in the right use of these that more particularly consists the clearness and beauty of a good style. To think well, it is not enough that a man has ideas clear and distinct in his thoughts, nor that he observes the agreement and disagreement of some of them; but he must think in train and observe the dependence of his thoughts and reasonings one upon another; and to express well such methodical and rational thoughts, he must have words to show what connexion, restriction, distinction, opposition, emphasis, etc., he gives to each respective part of his discourse.

[These words] are all marks of some action or intimation of the mind; and therefore to understand them rightly, the several views, postures, stands, turns, limitations, and exceptions, and several other thoughts of the mind, for which we have either none or very deficient names, are diligently to be studied. Of these, there are a great variety, much exceeding the number of particles that most languages have to express them by; and therefore it is not to be wondered at that most of these particles have divers and sometimes almost opposite significations. In the Hebrew tongue there is a particle consisting but of one single letter, of which there are reckoned up, as I remember, seventy, I am sure above fifty several significations."


We argue about A, workloads, assessment-formulas, componency, rarely about B, pedagogical attitudes, of which (one might suppose) A are derivatives (though not mere derivatives). Does this mean we should argue about B first, or instead? But we have forgotten how to, and must first recover the sense of Paths-leading-back-from-A, and then find which of them leads to some candidate for B-ness. Meanwhile, the decisions are reached by taking the average of as many incompatibles as possible.

To say this is not to be optimistic about B-level arguments getting anywhere. The total area of disagreement would remain the same, but the number of sub-areas would be smaller (where A-level discussion makes them increase without limit).

In all this the self-exculpations of Left and Right share an elegant symmetry. The incompetences of Them are widespread, disgraceful, but curable by Education, if We run it. The incompetences of Us are less serious though still quite widespread (present company excepted, of course), entirely attributable to Them, but curable by self-education. Each side is determined to teach the other whole-hearted co-operation -- if necessary by diktat. That must be the formula they remember as having worked best when they were themselves being taught.


The problems that matter are perennial and protean. Some formulation of them captured the energies of a past generation; didn't give the results it seemed to promise; was reacted against as a sign and proof of the wrong-headedness de papa; leaving the next generation to get excited over a new-model problematic and to bend their energies, first to what mattered most: establishing their independence and modernity; next, to establishing their ancestry, i. e. dependence; and finally coming to recognize what perennial problematic theirs was a deceptively dissimilar paraphrase of.

It's not so much that the `same' issue can be expressed in an inexhaustible variety of ways; rather that it has to be.


There are many perplexing things you wish to `understand', many that you wish to have `explained'. Among them, should we not include the meaning of `understand' and `explain'? Of the few who think that question worth asking, some answer No, on the grounds either that everyone already shares the same meaning of those words (but, unlike those who think the question not worth asking, these do not add the word `obviously'), or that, if they don't, nothing more can be said. I hope the proponents of the `No'-view will not object if I call it the Standard Answer. But not everyone gives that answer; which is to say, not everyone shares the same meaning of the words.

The strength of the Standard Answer is that we have all had the aha!-experience: `Now I see!' Its weakness is to assume perplexical atomicity: when I am perplexed, my perplexity is supposed to be well defined, and perfectly congruent with the explanation.

It seems more plausible to suppose that part of my perplexity is its lack of well-definedness. Typically, your explanation works by replacing one of my unstated auxiliary assumptions with a `better' but not-necessarily-stated one of your own. In offering to dispel not the original but a better perplexity, it teaches me something about the inappropriateness of the term Explanation as applied to the perplexity as originally worded.

The residue of my perplexity is presumably made up, in unknown proportions, of further hidden assumptions, plain wrong-headedness, and stuff we just don't know; but your explanation doesn't go into all that.

It may seem that the progress of the sciences is to be measured by the reduction in the number of perplexities. But a shortage of perplexities would be worse by far than a shortage of solutions. Happily humankind has an aptitude for finding new perplexities, or reincarnating old ones.

Just because I've had a generation's start (or two) I mustn't forget that the many ways in which your perplexities differ from mine are all legitimate. Indeed, your perplexities are of more concern, for they are moving towards the light, still learning to speak for themselves. To help me only I have only two resources: Patience, and the mysterious ability to tell which wail means colic.


Depending on your personality-type, ideas are either believed (one at a time), or entertained (never less than two alternative versions at a time).

Personality!-- the discovery, defence, renewal of the self! Just to pronounce the word is to invoke powers far beyond our puny control: the Board of Studies feels the whisper of a cosmic draught. Someone somewhere is keeping a rather different version of the minutes, in another language altogether:

`First to you, kindred spirits, who understand what I say. I cannot do much to help you; but if I can avoid hampering you I am happy to settle for that. Later, you may come to think I taught you something, though you will be unable to convey what it was. I judge you by serious standards -- the same, I hope, as those by which I would wish to be judged myself. That judgment is of course qualitative. It is more often reached quickly than late, but in any case not to timetable. It can be written alongside a quantitative judgment, but no power can add the two together. The decisive experiences are few, and lasting.'

But to the others: `I cannot reach you, nor you me. Recognizing that is all I can do for you. I avoid judging your work by the standards I know as serious, for we do not use the same language. Instead I manipulate some ersatz evidence which enables me after all to award most of you the Order of Chastity, Second Class.'

When evidence is ersatz there is nothing to be done but manipulation, which might as well be expeditious and cheerful. But some of us feel guilty about not having better evidence, and think the guilt can be assuaged if the procedure by which the ersatz evidence is manipulated can be given a sufficiently tedious complexity.

What keeps me cheerful under a simpler system is a low estimate of the difference it makes. The role of most of us is to be the roughage in some Higher Peristalsis, keeping the channels open against the day they may carry nutriment. So the system is made to work, at the usual cost of double standards. Who suffers by this duplicity? Not you, mon dissemblable. Only Mr Guest, and Mr Keen, and Mr Nettlefold; and me, if I allow the serious standard to be blurred by compromise; and the kindred spirits, hampered in consequence; and the body waiting for that nutriment.

Everyone needs at least two personalities, or one of them has got away with murder.

Emerson: "Every body has two or three lives, two or three consciousnesses which he nimbly alternates."

P. F. Strawson: "Deadlock is reached by each party refusing to count as understanding, a condition which is not reached by the method he advocates. There may be something final about this deadlock. For there may be here something which is in part a matter merely of preference, of choice."

L. H. Myers: "It is chiefly a sense of precedence which hampers us in our manifestations. Each one of us has a fixed, unconscious notion of what constitutes his character, and is prevented from carrying into effect the behests of his imagination, by an irrational, but compelling instinct to conform with that accepted idea of himself. This compulsion is greatest when initiates are present. The unfortunate ego, partly in deference to the suggestion of others, and partly in self-protection against them, has encrusted itself in a hard shell. It has made public profession of a certain `character', which its manner and behaviour are constrained to `illustrate'. This is its response to the need to exhibit a definite outline, by which its fellow-creatures shall recognise it; but it is also -- and, alas, more urgently still! -- a response to its own need to possess a form by which it shall recognise itself.

In the conduct of everyday life each one of us likes to refer to some fairly well-defined conception of his own character in order to decide without trouble what to do, what to say, and even what to think. We require some rule of thumb in our current self-manifestations; for a perpetual effort of choice would be an intolerable burden. Do we not all habitually repose with a sense of satisfaction upon what we take to be our fixed characteristics -- upon the supposedly fatal element within us? And of those given characteristics are not even the most trifling our pride? `Yes,' we reflect with complacency, `I'm like that. It is strange, but that's what I always am.' What pride in discovering in the malleable substance of ourselves something demonic, something which the reason cannot coerce, nor the consciousness incorporate, something genuine, in fact -- in the sense of being spontaneous, self-existent, and inevitable -- when all the rest of the poor little personality is a make-up, in which the only inevitabilities are those imposed by helplessness."

G. P. Meredith: "It is possible for an educational institution to adopt a purely technical and scholastic view of its functions -- to give instructions, to conduct examinations and to be entirely indifferent to the personal development of its alumni. But it is impossible to enforce this policy. For when you have human beings gathered together there you have human relations. A spontaneous system of influence will inevitably spring up, with unpredictable and uncontrollable characteristics. This may, of course, be perfectly healthy. But given the inevitable sprinkling of psychopathic characters in any community, whose incompleteness as persons drives them towards the assumption of leadership, these will find a following."

Persuasive anecdotes

Persuasion via an anecdote, or via a representative example, is an appeal to some shared experience, as to a higher court, seeking to reverse the verdict `Guilty of Disagreement' reached on the evidence of our differing theoretical clichés. For the appeal to be effective I must choose an experience we can both imagine having had, and find, for a part of that experience, the words which will evoke the rest of it for you. The example I thus present is to remind you not only of the fuller experience but also of the whole class of such experiences. The second jump is the riskier. I give you a piece of something representative of what you are to be reminded of, but the respects in which it is representative you must manage to find by yourself.

I also need the example myself, relying on its recalcitrant authenticity to save me from over-generalization. That is, I rely on finding more than I knew in my own evocation.

Whole cultures can be reconstructed (like dinosaurs from toe-bones) from what they take to be an Example-for-purposes-of-persuasion; for it reveals how the culture-sellers regard their prey. The key question isn't whether the example is simple enough. An Example must of course give the customers what they'll go for, but also more than they bargained for. Juicy bait is no good unless it hides a hook.


James Sledd: "The number of phonologists among the recognised critics of English poetry is zero."

D. G. Brinton: "The third point in the phonology of these tongues to which I alluded is the frequency with which the phonetic elements, as graphically expressed, are inadequate to convey the idea.

With difficulties of this nature to encounter, a person accustomed to the definite phonology of European tongues is naturally at a loss. The Spanish scholar Uricoechea expresses this in relating his efforts to learn the Chibeha of New Granada, a tongue also characterised by these fluctuating phonetics. He visited the region where it is still spoken with a grammar and phrase book in his hand, and found to his disappointment that they could not understand one word he said. He then employed a native who spoke Spanish, and with him practised some phrases until he believed he had them perfect. Another disappointment -- not one of them was understood. He returned to his teacher and again repeated them; but what was his dismay when not even his teacher recognised a single word! After that, Uricoechea gave up the attempt."


It goes without saying that the arguments presented in exam-papers and assignments can never be 100% original. In all of them you will have to use some ideas of other people, and sometimes their very words. No-one expects you to give the source of every borrowed idea; and even some direct quotations can be assumed to be too familiar to need attribution. But you must give the source of every borrowing which constitutes an important link in your argument, and of every verbatim non-cliché quotation even if not important to your argument.

It also goes without saying that borrowed ideas are not sufficient; though an arrangement of borrowed ideas can constitute originality. What counts is your two-penn'orth: a properly modest contribution, but a contribution. Non-trite borrowed ideas plus an interesting commentary earn credit on both grounds. Not much credit is deserved for borrowing bad ideas, or ideas once good but now trite, or by adding too little commentary to borrowed ideas however excellent.

If you think that none of the above is yet very specific, you're quite right. Only reading, practice and helpful comment by the marker can give a sense of the right proportions of quotation and commentary.

C. S. Lewis: " I only once detected a pupil offering me some one else (Elton) as his own work. I told him I was not a detective nor even a schoolmaster, nor a nurse, and that I absolutely refused to take any precaution against this puerile trick; that I'd as soon think it my business to see that he washed behind his ears or wiped his bottom. He went down of his own accord and I never saw him again. I think you ought to make a general announcement of that sort. You must not waste your time constantly reading me and Dowden and Churton Collins as a sort of police measure. It is bad for them to think this is `up to you'. Flay them alive if you happen to detect them; but don't let them feel that you are a safeguard against the effects of their own idleness. What staggers me is how any man can prefer the galley-slave labour of transcription to the freeman's work of attempting an essay on his own."

Poisson distribution

"In 1798 Poisson entered the Ecole Polytechnique, and immediately began to attract the notice of the professors of the school, who left him free to follow the studies of his predilection." Encyc. Brit.

"... Il devient alors royaliste et reçoit plus souvent que ne le voudrait le calcul des probabilités les fonctions de juré dans les principaux procès politiques." Larousse du XIXe siècle


The damage done across the board by a crudification of disputational style must far outweigh the (in any case dubious) benefit in any one area from victories made more triumphant by such means.

I speak here autobiographically, and assume we all could: remembering occasions when the balance of our assent, in our own learning and teaching, was tipped by something other than the rational or the legitimately rhetorical parts of the case; and coming, though slowly, to understand that every illegitimate ploy, once acknowedged, is invaluable as marking the site of a crux or cusp.

What makes it crucial or cusp-like is that here the opposing arguments come closest together. This was the Tempter's best shot. The path not chosen comes nearest to being the path that might have been chosen, was and still is the defining alternative which must constantly be borne in mind -- together with its co-definer. This is where the frontiers were hardest fought and are still most likely to call for local adjustment. Those who picture the adversarial undialectically find these metaphors hard to take; just how hard, we can detect by any rise in stridency.

In controversy at its rare best, interest and duty on both sides lie in maximizing the number of items not in present dispute. On these points we are agreed; on those, nothing much hangs; each side getting an allowance of gut-feelings confessedly stronger than the arguments used to support them.

The residue will be quite tough enough by itself.

Priests & Pedagogues

Orestes Brownson, 1840: "We look not for the regeneration of the race from priests and pedagogues. They have had a fair trial. They cannot construct the temple of God. They always league with the people's masters, and seek to reform without disturbing the social arrangements which render reform necessary. They merely cry peace, peace, and that too when there is no peace, and can be none."


Print protects and distances, where the live teacher is the focus of affect, equally disturbing whether we are talking of love or hate, and whether of defect or excess.

Behind the printed word, to reconstruct as much of the individual intonation as is needed to find the sense, or one of them. Within the spoken word, to discount as much of the individual intonation as is needed to find the truth, or one of them.

With printing, literacy was secularized. That is, the texts remained at first largely sacred, but the readers were no longer consecrated. When confined to a priestly class, the mystery had no doubt been exaggerated, for syndical reasons; becoming accessible to all, and then the entitlement of all, the mystery was understated, to about the same degree. Equal privilege for all was demanded, and seemed to be won -- an inevitably dusty victory.

These matters are too profound for most classrooms. For the others one can only aim at providing a baggage whose richness will be unpacked (if at all) slowly, long after the students have gone `down'. This has some chance of working with literary classics, which are memorable first and understandable later -- a claim which became harder to make for the philosophical classics when these stopped being in verse or dialogue. As for the classics of modern linguistics, one can only echo Emerson: `The annals of Poland would be as good to a philosopher as those of Greece, but these last are well composed.'

What Mill says of ancient formulas [we were `taught though not to understand them, yet to believe that there is truth in them'] could be said of all classic texts, whose perenniality mocks any pretence by the teacher to have extracted their `essential' meaning.

Charles Lamb: "There is something to me repugnant, at any time, in written hand. The text never seems determinate. Print settles it. I had thought of Lycidas as of a full-grown beauty -- as springing up with all its parts absolute -- till, in evil hour, I was shown the original written copy of it in the Library of Trinity, kept like some treasure to be proud of. How it staggered me to see the fine things in their ore! interlined, corrected! as if their words were mortal, alterable, displaceable at pleasure! as if they might have been otherwise, and just as good! as if inspirations were made up of parts, and those fluctuating, successive, indifferent! I will never go into the work-shop of any great artist again, nor desire a sight of his picture, till it is fairly off the easel; no, not if Raphael were to be alive again, and painting another Galatea."

Benjamin Franklin: "I imagin'd it might be well to publish the Articles of their Belief and the Rules of their [the Dunkers'] Discipline. He said that it had been propos'd among them, but not agreed to, for this Reason; "When we were first drawn together as a Society, says he, it had pleased God to inlighten our Minds so far, as to see that some Doctrines which we once esteemed Truths were Errors, and that others which we had esteemed Errors were real Truths. From time to time he has been pleased to afford us farther Light, and our Principles have been improving, and our Errors diminishing. Now we are not sure we are arriv'd at the End of this Progression, and at the Perfection of Spiritual or Theological Knowledge; and we fear that if we should once print our Confession of Faith, we should feel ourselves as if bound and confin'd by it, and perhaps be unwilling to receive farther Improvement; and our Successors still more so, as conceiving what we their Elders and Founders had done, to be something sacred, never to be departed from.'"


Seeds can be true, for a while, as can friends. As to propositions, even when not exactly false, the word `true' is wasted on them. You can detect this waste by the vestiges of the full sense, the warming of the heart inseparable from even low-grade uses of the word, as when it is wasted on `2x2=4'. That small excitement comes from finding, at last, a specimen of the truly True, a guarantee that there is something for the word to mean; but also from a back-of-the-mind feeling that this declarative is not without a trace of the optative: `Let it be that way for ever, don't even think of the little flaws in the truest seed, the truest friend, the most truth-preserving transformation.' There might be some therapeutic gain in using a word with fewer of those golden overtones: say, `eslaf'; or F. M. Akeroyd's 'tralse', i. e. true before time t and false thereafter.

George Eliot: "So long as a belief in propositions is regarded as indispensable to salvation, the pursuit of truth as such is not possible."

Emerson: "In the progress of the character there is an increasing faith in the moral sentiment, and a decreasing faith in propositions."

A psycholinguistic experiment

Sterne: "And how did Garrick speak the soliloquy last night? -- Oh, against all rule, my lord, -- most ungrammatically! betwixt the substantive and the adjective, which should agree together in number, case and gender, he made a breach thus, -- stopping, as if the point wanted settling; -- and betwixt the nominative case, which your lordship knows should govern the verb, he suspended his voice in the epilogue a dozen times three seconds and three-fifths by a stop-watch, my lord, each time, -- Admirable grammarian! -- But in suspending his voice -- was the sense suspended likewise? Did no expression of attitude or countenance fill up the chasm? -- Was the eye silent? Did you narrowly look? -- I look'd only at the stop-watch, my lord. -- Excellent observer!"

Public service

We try to maintain a bearable mix of altruism and proper reward, juggling with assorted carrots (chauffeurs, K's, comparability) and sticks (black-balls, Bastilles, bullets). The balance is extremely delicate: if one factor is even slightly over-weighted, the signs of dysfunction quickly become scandalous.

Perhaps that is why we adopted St George as patron saint -- to persuade ourselves (and it would take a myth as strong as that one to do so) that dragon-disposers work on a results-only basis, and would never dream of asking for more than out-of-pocket expenses. The power of the myth matches the power of the guilt it was devised to overcome -- I mean our guilt at ducking responsibility for the disposal of our own dragons. As if the price of liberty were hiring the services of Eternal Vigilance Inc., on as short a contract as possible.

More familiar is the hero who Saves the Country, and then divides it among his in-laws. One wonders why in warmer climates they still go in for armies, when the odds on a military takeover every few years are so high. Do our generals know what it is that protects us from that? And is anyone monitoring the condition of that protection?

Of course the same holds for other kinds of Leader, other institutions -- Soul-savers, Supreme Soviet, Serious Crime Squad. One of the factors gets over-weighted, and boom!

Given that the founding fathers had a higher than average proportion of saints among the ordinary Joes and psychotics, what brings the latter to the top, and so quickly too ?


When publishing replaced letter-writing, as lecturing replaced teaching, they tried to persuade us that nothing qualitative had changed. From the start the implicit slogan was: `Designed with you in mind, whoever you are'. But it's only by a kind of optical illusion that a published text, or a talk to an unknown audience, seem to be addressed to Anybody. Anybody would love to believe this, but knows there must be a catch -- the little clause: `The editor's decision is final,' or 'No goods exchanged.' So the book-buyer who placed too much trust in the blurb learned to hope at best for 20% on the secondhand market. Doubtless some new Education Act will allow the sophomore who finds he has placed too much trust in the prospectus to flog his university place for what it will fetch.

It isn't only blurb-writers who `assume no previous knowledge,' not only blurb-readers who in their innocence take the phrase to be reassuring. What is `assumed' in all cases is something rather harder to come by than previous knowledge. Printed or spoken, exposition is addressed only to the prepared, to kindred spirits; not to all the invited, nor all the purchasers.


On every propitious day we set out to hunt for the soluble aspects of some puzzle and/or the puzzling aspects of some solution, without (as far as possible) having decided which of these two it is to be. The quarry (I wish I could say) is the puzzolution.

Reaction to a text isn't -- it seems absurd that one has to spell it out -- a provision of conclusions, but a noticing of some -- it doesn't matter how few or which, for a start -- of the puzzolutions.

The first qualification isn't to be capable of puzzlement (there is no shortage of people who have more puzzlements than they can handle). The difficulty is to acknowledge one's puzzlement -- the first step towards this being to value it. If no puzzlement occurs, I throw in my hand, for the time being. But once a puzzle has been located you may take all the time you need to stalk it. I don't say that everybody is actually or potentially equally good at that, or equally amenable to guidance. But helping learners to characterize what they have themselves located is a more attractive pedagogic role.

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