Questions & answers

Inexperience talks into empty space, having yet to learn `the discipline' -- i. e. how to interpret the sonar echoes, how to backplot the intersections of sufficiently different answers to sufficiently similar questions.

Your contribution: to find an answer which in its turn is sufficiently different, to a question which is sufficiently similar.

Any answer you find won't quite be an answer to the question you started with. Any question you find won't quite match the answer you started back from. Part of the gap will be invisible to you. Of the rest, part can be met by massaging the question, or the answer, or both. The remaining bits of mismatch are best confessed, wrily and without defeatism -- i. e. in a style at which none of us gets enough practice.

Paul Feyerabend: "We shall have to give up either questions of the form `What is X?' or the demand that X possess the same meaning in the question and in the answer."

Paul A. Freund: "When a judicial nominee is cross-examined by a senator on whether he believes that the meaning of the Constitution changes, the question is an invitation to a discussion of linguistic, quite as much as constitutional, philosophy, although the nominee would doubtless be thought rude and evasive in suggesting this -- just as a schoolboy who, when asked what caused the Civil War, gives the only sensible answer, `Why do you want to know?' would no doubt be sent to the headmaster for disciplinary action."

Does `the meaning of the Constitution' in the above include meanings strictly implied but not as yet expressed? But such entities are at best atolls in a sea of commentary where more will drown than find landfall. We desperately need people who can talk themselves, and us, out of such painful dilemmas. One selection-test is whether they can tell the difference between Question-&-Answer and the deceptively similar Dilemma-&-Parry.

Anthony Kenny: "Wittgenstein's Investigations contains 784 questions, only 110 of these are answered and 70 of the answers are meant to be wrong."

Dorfmann: "Thorstein Veblen frequently used in the classroom those excellent strategic devices -- `in the light of modern science,' and `but with that we are not concerned'. When a student asked ingenuous questions Veblen would simply answer: `I don't know, I'm not bothered that way myself.'"


Diderot: "Le maître. -- Ne sois ni fade ni panégyriste, ni censeur amer; dis la chose comme elle est.

Jacques. -- Cela n'est pas aisé. n'a-t-on pas son caractère, son intérêt, son goût, ses passions, d'après quoi l'on exagère ou l'on atténue? Dis la chose comme elle est! Cela n'arrive peut-être pas deux fois en un jour dans toute une grande ville. Et celui qui vous écoute est-il mieux disposé que celui qui parle? Non. D'où il doit arriver que deux fois à peine en un jour, dans toute une grande ville, on soit entendu comme on dit.

Le maître. -- Que diable, Jacques, voilà des maximes à proscrire l'usage de la langue et des oreilles, à ne rien dire, à ne rien écouter, et à ne rien croire! Cependant, dis comme toi; je t'écouterai comme moi, et je t'en croirai comme je pourrai.

Jacques. -- Mon cher maître, la vie se passe en quiproquos. Il y a les quiproquos d'amour, les quiproquos d'amitié, les quiproquos de politique, de finance, d'église, de magistrature, de commerce, de femmes, de maris..."


We can't say much about how we understand a sentence; even if we understood it last time there will still be a problem about replicating that understanding next time. In evidence I call Emerson: "It is curious what new interest an old sentence or poem acquires in quotation". When a critic quotes, their mere isolation on the page invites closer attention than the lines got in the original text. It seems to give some undertaking that, if I am prepared to consider the possibility of a change of mind, it will be worth the effort, even without the critic's gloss.

Or at least that might be so, if `mere isolation' were the only factor -- which it can never be. Even critics we've never heard of are evidently eminent enough to get paid for quoting. And invariably they do so not just to invite our re-interpretation, but to sell their own. If their reputation is too light, we don't accept the invitation to reconsider; if too heavy, we cannot separate the invitation from the sales-talk. Which is the lesser risk ?

A source-citation means, at best: `My case rests on a non-obvious result the evidence for which is given there but is too long to repeat, and which is not so well-known that I can assume familiarity with it. You can check my accuracy in quoting and the solidity of the supporting evidence there is no room for here, if you think what I build on it justifies the effort.

But sometimes citation means no more than: `This phrase I take from A. Greatman. In quoting it I make no claim to have mastered his theories, nor (therefore) the part this phrase played in them; but I have no compunction in placing upon his words an interpretation favourable to my argument. This is a double whammy: Not only can I enlist the apparent approval of A. Greatman, but I have done my bit to reinforce a meccano-type epistemology, in which interpretation-problems are rare and arguments are assembled from tight-fitting parts.'

The conventions allow useful ambiguity, as between phrase-scrumping at the lower end and full-scale theory-splicing (if such a thing is possible) at the upper end.

Joseph Needham put an asterisk on biblio-items he quoted but hadn't read...

Emerson: "A writer appears ever to much more advantage in the pages of another man's book than in his own. Coleridge, Wordsworth, Schelling are conclusive when Channing or Carlyle or Everett quote them, but if you take up their own books then instantly they become not lawgivers but modest peccable candidates for your approbation."


Irving E. Fang: "Of all readability formulas the best known, and probably the most widely used, is: R.E. = 206.835 - .846wl - 1.015sl where R.E. means reading ease, wl the number of syllables per 100 words, and sl the average sentence length in words."


B relies (not explicitly or consciously) on a a solar-system model of meaning. In this, one great central Sol-like entity is the source of all life, i.e. of certified top-quality reliable meaning. B's interest in the lower-quality entities, of at best only possible meaning, which orbit this central body falls off very sharply as their iffiness (or distance from the centre) increases. With inferences whose probability is Plutonically or even Saturninely remote, his interest is barely detectable. In any case a sort of Bode's law limits the number of such relatively insignificant bodies to about half-a-dozen. B's meaning-space is hardly more than two-dimensional, and its mathematics is well understood; that is, he refuses to allow the dimensionality of his space to exceed what his mathematics well understands.

For C, meaning-space or inference-space has many more dimensions, filled with all too many bodies acting on each other by forces not all of one kind. This untidiness, unbearable to B, is for C what makes everything worthwhile. He may only understand occasional fragments, and then only via processes which he cannot often retrace and only rarely replicate; but the satisfaction they give him is all the intenser. Part of this satisfaction comes from putting one across the Laws of Probability; and part from intuiting an elegance which a later Newton -- guided by the isolated results of C and those like him -- will one day discover how to express in some superdifferential calculus.

It follows that for C there is hardly any possible meaning so remote as to be declared not worth inspection -- not of course routine inspection, for very little in C's universe is amenable to routine -- but worth a second glance if his apparently mapless rambles take him that way. But B would never dream of rambling, and is agoraphobic without a map, and has already made up his mind that finding a meaning for `apparently mapless' is going to be more trouble than it's worth. Problem: How can B and C talk to each other? And how can we manage if they don't?

Reading, scenario 1

Teacher tells you what to read, and takes you through part of it to indicate what he means by `read'. He tells you what he thinks part of it means, and then asks direct questions of two kinds: (a) What did I say this bit meant? and (b) What does a bit from the unexplained part mean? You can get a pass by remembering (a), and a II/i by practising answers to (b) and remembering them (if they turn up). With most such teachers the (b)-part is smaller than the (a)-part.

Reading, scenario 2

Teacher doesn't tell you what to read: he recommends some texts, and shows you how to find others. Nor does he tell you what the recommended texts `really' mean. He doesn't deal in such goods. Even if there were such a thing as `what it really means,' and he had worked it out for himself, he wouldn't be so inconsiderate as to deprive you of the pleasure of doing likewise, by telling you prematurely. He doesn't recommend a text unless its meaning is in dispute and its commentators in evenly-matched disagreement. He doesn't even tell you which of two (or n) meanings has his vote. He cares less about what it means than about whether you can learn, by contact with such texts:

All these things take time. Just how much time is one of the presumptions most likely to need adjustment.

Recommended reading

I commend certain texts, but do not specify what for, because:

So texts read in the prior conviction that they are sacred will yield a sense that reinforces -- and seems to have created -- that conviction.

Representative fragments

What we need is practice at pursuing the tireless devious demon of self-kidology, tackling not simplifications but fragments of the real thing. The necessary attitudes could be illustrated from any fragment. Teachers earn their keep by their skill in choosing representative fragments, small enough to be bitten off and big enough to stretch the jaws.

Equally instructive are the merits and demerits of the chosen passage. On the negative side the give-aways -- over-protestings, shiftiness, signs of self-deception; the acceleration past the tricky bit, the uncalled-for waspishness, the martyred tone. On the positive side, the creative flash, the home-thrust, the true ring of the double-edged.

It takes concentration to detect these under-messages -- not because their signals are feeble, but because we listen too little on that wavelength. On second thoughts, that puts it too politely. The signals would be clear enough, had we not somehow used up all our energies scouring every part of the spectrum except the Home Service.

I do not know whether the ability to tune in to those signals is common or rare, compared with other abilities we pretend to measure; but it is one which a familiar kind of collusion between teacher and learner can most easily wither.

Take the phrase "I was always taught that Š". Those who use it have evidently blanked out the deafening signals of complacency they are emitting: "It is for me a matter of special pride that on this point I have never, but never, thought for myself." There may indeed be some small grounds for pride, in a child, at fathoming what Teacher wanted. It may even be desirable, at some stage, to take Teacher's word for it. But between learning to take Teacher's word for it, and learning to take Teacher's word for the time being, there's a transition, from one view of Education to a rather different one. Perhaps it goes with a shift from Pupilhood to Learnerhood. Apparently many pupils feel too comfortable in Pupilhood ever to leave it; or perhaps their teachers, for whatever reason, missed too many of the critical opportunities for abdicating Teacherhood.


Can a teacher who has never made a discovery convey anything of what it is like to do so ? The same (going down the scale) goes for one who has never confirmed (but from another direction) someone else's discovery; and one (further still) who has never even had the good fortune to find a good problem and be defeated by it.

Nowhere was there a higher correlation between research and teaching than in 18th-century Oxbridge -- zero in both departments.

What makes a research area exciting is the sense of powerful new generalisations on the edge of over-extension. One step more, and we're flying, or is it falling? -- not long to the impact which will tell us which.


C. S. Peirce: "Good instruction in reasoning is exceedingly rare. How few teachers understand the logic of mathematics! and how few understand the psychology of the puzzled pupil! The pupil meets with a difficulty in Euclid. Two to one the reason is that there is a logical flaw. The boy, however, is conscious only of a mysterious hindrance. What his difficulty is he cannot tell the teacher; the teacher must teach him. Now the teacher probably never really saw the true logic of the passage. But he thinks he does because, owing to long familiarity, he has lost that sense of coming up against an invisible barrier that the boy feels. He simply cannot understand why the boy should feel any difficulty; and all he can do is to exclaim `Oh, these stupid, stupid boys!'

But suppose, by some extraordinary conjunction of the planets, a really good teacher of reasoning were to be appointed, what would be his first care? It would be to guard his scholars from that malady with which logic is usually infested, so that unless it runs off them like water from a duck, it is sure to make them the very worst of reasoners, namely, unfair reasoners, and what is worse unconsciously unfair, for the rest of their lives.

The good teacher will therefore take the utmost pains to prevent the scholars getting puffed up with their own logical acquirements. He will wish to impregnate them with the right way of looking at reasoning before they shall be aware that they have learned anything; and he will not mind giving considerable time to that, for it is worth a great deal. But now come the examiner and the pupil himself. They want results, tangible to them. The teacher is dismissed as a failure, or, if he is allowed another chance, he will take good care to reverse the method of his teaching and give them results -- especially, as that is the lazy way."

Kierkegaard: "For if inwardness is the truth, results are only rubbish with which we should not trouble each other. The communication of results is an unnatural form of intercourse between man and man, in so far as every man is a spiritual being, for whom the truth consists in nothing else than the self-activity of personal appropriation, which the communication of results tends to prevent."

Reviving the meaning

J. S. Mill: "Many doctrines of religion, ethics, and even politics, so full of meaning and reality to first converts, have manifested (after the association of that meaning with the verbal formulas has ceased to be kept up by the controversies which accompanied their first introduction) a tendency to degenerate into lifeless dogmas; which tendency, all the efforts of an education expressly and skilfully directed to keeping the meaning alive, are barely found sufficient to counteract.

It is natural and inevitable that in every age a certain portion of our recorded and traditional knowledge, not being continually suggested by the pursuits and inquiries with which mankind are at that time engrossed, should fall asleep, as it were, and fade from the memory. It would be in danger of being totally lost, if the propositions or formulas, the results of the previous experience, did not remain, as forms of words it may be, but of words that once really conveyed, and are still supposed to convey, a meaning. While the formulas remain, the meaning may at any time revive.

Thus there is a perpetual oscillation in spiritual (I do not mean religious) truths, and in spiritual doctrines of any significance, even when not truths. Their meaning is almost always in a process either of being lost or of being recovered. Even when recognising verbally the same doctrines, they attach to them at different periods a greater or a less quantity, and even a different kind, of meaning. But the words and propositions lie ready, to suggest to any mind duly prepared the remainder of the meaning. Such individual minds are almost always to be found; and the lost meaning, revived by them, again by degrees works its way into the general mind.

The arrival of this salutary reaction may however be materially retarded, by the shallow conceptions and incautious proceedings of mere logicians. It sometimes happens that towards the close of the downward period, when the words have lost part of their significance, and have not yet begun to recover it, persons arise whose leading and favourite idea is the importance of clear conceptions and precise thought, and the necessity, therefore, of definite language. These persons, in examining the old formulas, easily perceive that words are used in them without a meaning; and if they are not the sort of persons who are capable of rediscovering the lost signification, they naturally enough dismiss the formula, and define the name without reference to it. In so doing they fasten down the name to what it connotes in common use at the time when it conveys the smallest quantity of meaning. Of the propositions in which it was formerly used, those which were true in virtue of the forgotten part of its meaning are now seen not to be true according to the definition. The ancient formulas are accordingly treated as prejudices; and people are no longer taught, as before, though not to understand them, yet to believe that there is truth in them. They no longer remain in the general mind surrounded by respect, and ready at any time to suggest their original meaning."


To engage in face-to-face argument is to run two serious risks: not only that of hearing something new, but also that of outwitting one's censor. For amid the flying dust we let cats out of bags, into the open where it is harder not to see them.

Of course it is only some time later -- back home, alone, in a darkened room -- that we realize what we did. Realizations of this kind need to be checked out where there are no witnesses, circumspectly, in case they turn out to be too hot to be realized after all.

If it seems safe, we can then switch on the light and start hunting the quarry with the only weapon that works: a pen. `Reconstruire la fuite, le glissement et le ressort, c'est un travail difficile, qu'il faut faire à loisir, souvent par retouches, toujours en reprenant de loin. Travail de plume, la parole n'y peut rien' (Alain).

What is exposed in the flash of talk is developed and fixed in a solution of ink. Speech is sometimes corrigible in time, before its wounds have time to bleed. But writing is corrigible and re-corrigible in rehearsal -- slowly, item by item, safely.

In the corresponding passives, listening (in public) may feel safer than reading (in one's study); for to be alone is to reduce the number of possible scapegoats in the room to a dangerously low level. But writing is always re-writing, and so not solitary: it is an argument between myselves, and shares the power of conversation to produce what was not planned, or even known, by either participant. The correcting persona shares the burden of his twin's embarrassment; and this may help them both to see that the process of amelioration may be more instructive than the individual result. But the starting-point (as Paley recommended to his pupils) is `the courage to be alone'.

Good-ideas-captured-in-fitting-words come through inspiration, when they will. Or, less rarely, in the thrust-and-parry of a good conversation. Or, most painfully, by repeated rewrites, removing layers of not-quite-truth to the worthwhile kernel which may or may not lie beneath. Whichever way they come, one is grateful, but silently, lest a spell be broken. One hardly dares wonder if each route has its own kind of good idea.

To demonstrate the art of rewriting one looks, to start one off, for some text about equidistant from the flawless and the hopeless, by some naive but forgivable author whose heart [if not much else] was more or less in the right place. A likely candidate is one's own draft of the other week. There at least one is on reasonably good terms with the author, and may have some idea of what he was trying so clumsily to convey. Moreover if one can find the form of correction which will avoid hurting his feelings, there should be no problem about doing the same for ordinary, less sensitive mortals.

Seeing one's own words as if with another's eyes is easier than hearing them as if with another's ears. Cold storage or a switch in time-scale can help us to see with new eyes -- even the mechanical task of copying a corrected draft au net can make some of its unintended implications more visible. It then turns out that some of them are undesirable (and getting rid of these is hard work); the rest, if we let them, can astonish us. Some of our best ideas started life as unintended side-effects. The trick is to filter out the undesirables while treating the welcome gate-crasher as guest of honour, never to be captured by anything so crude as direct invitation.

If at first you don't succeed, try the run-up from further back. You may miss the ruts of your previous tries.

T. H. Huxley: "My own way is to write and re-write things, until by some sort of instinctive process they acquire the condensation and symmetry which satisfies me. And I really could not say how my original drafts are improved until they somehow impress themselves."

Edmond Jabès: "Se relire: se retrouver seul, dans la salle décorée, au lendemain de la fête."


Reaching the current truth has required much wrestling which the much-amended `conclusion' can neither fully report nor entirely eliminate. It will baffle some, if it is conscientious about the painful parts; and sound misleadingly simple to others, if it isn't. Lines to avoid, unless you want success at any price, include:

`The right path is obvious, except to our born enemies.'

`The right path is obvious, trust me.'

`I give you a few reasons, which should suffice -- not as a logical basis for deciding the substantive issue but as an emotional basis for accepting my trustworthiness.'

Writer's rhetoric exploiting reader's courtesy, teacher's rhetoric exploiting student's insecurities.

All this stressing, emphasizing, insisting -- mere elegant variations of "said", which moreover present as clear something at best inherently difficult, and do so in a faintly minatory tone. Far from bringing light, I take them to mark (as papering-over marks a crack) places where the writer is actually rather worried but not quite ready to admit it.

To earn a reputation as a person of principle, the first step is to let it be known that you have an Ideal, a desideratum that overrides all others. In more advanced rhetorics one can be the proud defender of more than one desideratum that overrides all others. One can then switch from one Ultimate Value to another just often enough to disconcert. You want the opponent to lose the argument, but it's just as effective if he can't find it.


E. Chargaff: "Definite procedures presuppose highly limited objects."

René Thom: "Tout ce qui est rigoureux est insignifiant."

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