The Structure of Discovery

Scientific discovery is no less logicalthan deduction.

Peter Caws

It has been widely held that, whilelogical analysis is appropriate to thejustification of claims to scientificknowledge, such knowledge being ex-pressed in hypotheses having empiricalconsequences, it is not appropriate toan inquiry into the way in which suchclaims originate. Questions about ori-gins are said to belong to the "contextof discovery" rather than to the "con-text of justification," and to require adifferent kind of logic. The devisingof hypotheses is ascribed to genius, in-tuition, imagination, chance, or anynumber of other extralogical processes;it comes to be regarded as a paradigmcase of science in its authentic naturalstate, inaccessible to logical reconstruc-tion by philosophers who do not reallyknow what it is like to be a scientist.One of the tactics most often used

by proponents of the mystique ofgenius, who are always bandying aboutterms like creativity, insight, ripeness,and so on, is the recounting of talesabout moments of enlightenment in thelives of the great scientists. Everybodyhas heard of Kekule's dream about thesnakes biting one another's tails, and ofPoincare's long bout with the Fuchsianfunctions on his geological bus tripthrough Normandy. Such stories nodoubt give an accurate account ofwhat "really happened"; they are suit-ably sensitive to the "actual develop-ment" of scientific theories. But todraw attention to them at all in con-nection with an analysis of the processof discovery seems to me a radical mis-take. The mistake involved shows upclearly in a passage from Popper's TheLogic of Scientific Discovery, where hesays (1, p. 31): "the initial stage, theact of conceiving or inventing a theory,seems to me neither to call for logicalanalysis nor to be susceptible of it. The12 DECEMBER 1969

question how it happens that a newidea occurs to a man-whether it isa musical theme, a dramatic conflict,or a scientific theory-may be of greatinterest to empirical psychology; but itis irrelevant to the logical analysis ofscientific knowledge."

Popper thus dismisses the possibilityof a logical analysis of the conceptionor invention of a theory because hethinks of these things in terms of "howit happens." But in the case of deduc-tive argument nobody would think ofasking how it happens; it would be thestructure of the process, not its particu-lar embodiment in a particular indi-vidual, that would be seen by every-body to be the crucial issue. In fact,in demonstrative argument just as inthe process of discovery, there wouldbe nothing strange in its not happen-ing at all-the actual movement fromthe premises to a conclusion is just asintuitive, creative, and so on as theactual having of a new idea, and verystupid or very stubborn people, likethe tortoise in Lewis Carroll's fable,may quite well decline, or be unable,to make it-but the fact that it failedto happen would not alter in any waythe logical structure of the relationshipbetween premises and conclusion. Evenif one wished to maintain that, in thecase of discovery, there are not anyidentifiable premises [or even any prem-ises at all-a strategy I have exploredelsewhere (2)] one could still choose toregard the process as in principle in-telligible rather than unintelligible;what is disturbing about the passagefrom Popper is that he seems to optfor the latter. In fact he says explicitly(1, p. 32): "My view may be expressedby saying that every discovery contains'an irrational element,' or a 'creativeintuition,' in Bergson's sense."

My point is that if this is to be saidof the process of discovery it may justas well be said of the process of strictlogical deduction, so we might add tothe canon exciting tales about that ac-tivity too. I hope I may be forgivenan autobiographical example to try outthis parallel. I remember very clearlythe moment when, as a schoolboy, Ifirst understood the principle of linearsimultaneous equations. The circum-stances are engraved in my memory justas clearly as Poincare's foot on the stepof the bus became engraved in his; itwas in the yard of my school, and Iremember the red brick wall, the bi-cycle racks, and so on, in properProustian fashion. I saw, in a flash ofintuition, why two equations wereneeded for two unknowns, and how thesubstitution from one equation into theother proceeded. Now, as I need hardlysay, there was no question of originalityhere; I had had all the information for anumber of weeks, during which mymathematics teacher had been trying topound the principle into my head. Asfar as that goes, it wasn't that Icouldn't do simultaneous equations-Icould follow all the rules and get theright answer; it was just that I hadn'tseen the underlying rationality of theprocess. When I finally saw it I got the"Eureka feeling," of which Koestlerspeaks (3), just as surely as if I hadinvented simultaneous equations my-self, but I didn't suppose that that hadanything to do with the logic of thesituation.The trouble with "Eureka!" is that

the temptation to shout it is a verypoor index of success in the enterpriseat hand. Such a feeling can only be aby-product of the process-a not un-important one, perhaps, from some evo-lutionary point of view, but certainly adispensable one. A discovery would stillbe a discovery if it were made in coldblood without any such affective con-comitant, and if it turned out to bemistaken it would still be mistakeneven though the heavens had openedupon the lucky discoverer at the mo-ment he thought he was making it. Itis perhaps conceivable that somebodymight become addicted to the Eurekafeeling and, in order to have it as oftenas possible, try very hard to make manydiscoveries, some of which might bevalid. But scientists have to learn to

The author is professor of philosophy at Hunt-cr College of the City University of New York,New York, N.Y. This article is adapted from anaddress delivered 30 December 1967 at the NewYork meeting of the AAAS.

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be wary of emotional commitments totheir hypotheses. Darwin says, "I havesteadily endeavored to keep my mindfree so as to give up any hypothesis,however much beloved (and I cannotresist forming one on every subject) assoon as facts are seen to be opposed toit. Indeed, I have had no choice but toact in this manner, for with the excep-tion of the Coral Reefs, I cannot re-member a single first-formed hypothesiswhich had not after a time to be givenup or greatly modified." And he con-tinues, "this has naturally led me todistrust greatly deductive reasoning inthe mixed sciences" (4, p. 83).Another distinction frequently drawn

between the logic of justification andthe logic of discovery is that in theformer case rules can be given. Thisis only apparently true; on the onehand, although in principle all deduc-tions can be carried out by a rule-fol-lowing technique, in practice good logi-cians and mathematicians are constantlymaking wild leaps only later justified byrules, if at all, while on the other handcertain workers-notably Polya (5)-have made significant steps in the di-rection of formulating rules for "plausi-ble inference." Frege was among thefirst to try to carry out logical deduc-tions strictly according to rule, and hefound it extraordinarily difficult, as hetestifies in the preface to the BegrifJ-schrift (6). If there were no rules ofplausible inference, nobody could learntechniques of research, nor could theagencies responsible for funding it haveany confidence whatever that the tasksundertaken by researchers would bearfruit. Yet people do learn, and suitablyfinanced campaigns of research (likethe Manhattan project) do regularlyproduce results. The task is then tofind out what is going on, not dismiss itall as ineffable or mysterious.

Scientists, as Norwood Russell Han-son points out, "do not start from hy-potheses; they start from data" (7). Thequestion, then, is what happens be-tween the data and the hypotheses,taken in that order-not whether adeductive rule can be written to getfrom the former to the latter, butwhether some intelligible structure canbe discerned in the transition. I take"intelligible" in this context to be equiv-alent to "logical"-a procedure whichcertainly has etymological sanction,even if it means abandoning the nar-rower sense of "logical," which requiresthe specification of rules. In fact itneed not mean this, if we remember

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that the use of "logic" in the expression"inductive logic" is a perfectly orthodoxone, and that it sanctions a use of"rule" in the expression "inductiverule" which differs considerably in itsconnotations from the correspondinguse in the deductive case. We havecome to think of deductive rules as ef-fective procedures, leading with cer-tainty to the right result. In the induc-tive case, however, we have to get ac-customed to rules which lead, withfinite probability, to the wrong result.When people say "there could be norule for making discoveries," they gen-erally have the first sense of the termin mind: there could be no way ofbeing sure of making discoveries. Butthere might still be sets of rules, which,if faithfully followed, would increasethe chances of making them. These, asinductive logicians have begun to real-ize, may include rules of acceptance aswell as rules of inference. The mannerof their implementation (their relationto rules of practice) needs further study,but it is not my purpose to pursue thequestion further here.

A Model for Discovery

How do hypotheses arise? The an-swer I wish to suggest is that, strictlyspeaking, they arise naturally; hypoth-eses are to be accounted for in the samemanner as the events they seek to ex-plain-indeed the hypothesis that thisis so has arisen in this way. The evi-dence for this hypothesis is of coursefar from conclusive; while I think itpreferable to any alternative which callsupon nonnatural occurrences, it wouldadmittedly be difficult to show that nosuch occurrences were involved in theprocess (just as it would be difficult toshow this for deductive arguments). Butif a model can be constructed withinwhich the emergence of hypotheses fol-lows obviously from other properties ofthe model, the nonnatural element willbe shown to be dispensable, just as itmight be shown to be dispensable indeductive arguments by remarking thatanybody can follow the rules.

Such a model can, I think, be puttogether from a number of disparatesources. It shows that, given certainfacts about human beings and humancultures, there is nothing odd about theemergence of science or about the rateof its development, or about the factthat some of the men who have contrib-uted to this development have been

geniuses. The model, it is true, givesthe main part of its account in col-lective rather than in individual terms-but that has now become commonplace,since the analysis of individual discov-eries has shown that, in practicallyevery case, the individual acted as thecatalyst for a complex process in whichmany other individuals played a role.This need not be taken to mean thatno credit is due the individual forhaving advanced his science in a par-ticular way at a particular time, butit does mean that (probably) no indi-vidual has been indispensable to theadvance of science in general. "Verysimple-minded people think that ifNewton had died prematurely we wouldstill be at our wits' end to account forthe fall of apples," says Medawar (8).We must be able to find a way of rec-onciling our admiration for Newtonwith the avoidance of this mistake.

I make no apology for beginning myexposition of this theory of discoverywith Bacon, whose method has, I be-lieve, been misunderstood in importantrespects. The feature of the methodwhich has always struck me most forc-ibly occurs in book II of the NovumOrganum (9), where, after the construc-tion of the inductive Tables, Bacon says(aphorism xx): "and yet since truth willsooner come from error than from con-fusion I think it expedient that the un-derstanding should have permission,after the three Tables of First Presenta-tion (such as I have exhibited) havebeen made and weighed, to make anessay of the Interpretation of Nature inthe affirmative way; on the strength bothof the instances given in the Tables, andof any others it may meet with else-where. Which kind of essay I call theIndulgence of the Understanding or theCommencement of Interpretation or theFirst Vintage." This is strikingly simi-lar to Darwin's remark in the introduc-tion to The Origin of Species, where hesays (10): "It occurred to me, in 1837,that something might perhaps be madeout on this question by patiently ac-cumulating and reflecting on all sortsof facts which could possibly have anybearing on it. After five years' work Iallowed myself to speculate on the sub-ject. . . ." He remarks elsewhere (4,p. 68) that he worked on "true Ba-conian principles," a claim which isdenied by a number of commentatorswho have not read Bacon as closely asDarwin himself evidently did. There isa hint of the same kind of thing inFrege's concern not to jump to con-

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clusions in the course of his logicalwork.The truth to which I think these and

other citations point is that the practi-cal problem is often one not so muchof finding hypotheses as of holdingthem in check. Bacon's use of a wordlike "indulgence," Darwin's of thephrase "I allowed myself," suggest that,once the evidence is in, there is simplyno need of a rule for getting the hy-pothesis-it has long since formed andis only waiting to be recognized. (Re-member Darwin's comment: "I cannotresist forming one on every subject.")But two questions immediately presentthemselves: By what mechanism ofthought did the hypothesis come intobeing? And, if it is a natural process,why isn't everybody a genius? (It wasBacon's failure to recognize that every-body is not a genius which constitutedthe chief weakness in his program formaking the methods of science avail-able to the population at large.)As for everybody's not being a ge-

nius, the answer may be that everybodyabove a certain level of natural intelli-gence in principle is, until inhibitingfactors supervene-which almost alwayshappens. It may be worth making amore general point here about a habit ofthought into which philosophers of sci-ence sometimes fall-a habit due large-ly, I suspect, to the influence of Hume'sanalysis of causality. We think of eventsas in general being made to happen (andask what antecedent events producedthem), rather than as just happening(in which case the relevant questionwould be what antecedent events, byfailing to happen, failed to preventthem). It is noticeable however that,when scientists perform delicate ex-periments, they expend their energy noton making sure that the desired out-come occurs but on trying to make surethat some undesirable outcome does notoccur; they take experimental precau-tions against Nature, rather than givingexperimental encouragement to Nature.Similarly, a man engaged in logicalargument doesn't really need a rule totell him how to proceed; what he chieflyneeds is a kind of single-minded con-centration that keeps out irrelevantthoughts, and a facility for spottingwrong moves. The motive power of theenterprise doesn't come from the rules-they just keep it on the rails. Rules, itis true, can play a leading rather than aguiding part when the motive power iscomparatively unintelligent, as in com-puters, but the critical thing seems to

12 DECEMBER 1969

be to let the machinery run. This viewis fully in keeping with the fact, fre-quently remarked upon, that the processof discovery may be unconscious: thescientist wakes up the next morning-or, in stubborn cases like Poincare's, aweek or so later-with the requiredsolution. Whether or not all the stepsare conscious is irrelevant to the ques-tion of whether or not they are logical.

If we are to admit biographical evi-dence, the point about inhibiting factors(and, on the other side of the coin,stimulating ones) may be illustrated bythe fact that many men of genius havebeen characterized by a strong re-sistance to authority (that is, resistanceto having their conclusions drawn forthem) and, at the same time, by anopenness to random suggestion amount-ing almost to credulity. Ernest Jones(11) observes this with respect to Freud,and Darwin (4, p. 82) observes it withrespect to himself. Ordinary social ex-perience, and especially education,work, of course, in precisely the oppo-site sense, imposing, even in the mostwell-meaning of democracies, an ex-traordinarily authoritarian view of theworld and, at the same time, encourag-ing the belief that a man should be selec-tive about what he takes in, and skepticalabout all evidence from nonauthori-tarian sources. These tendencies alonewould be enough to account for the in-hibition of discoyeries in all but a hand-ful of the population at any given time.The hypothesis emerges naturally only

when all the evidence is in-the con-clusion follows only from a complete oralmost complete set of premises. I add"almost complete" because there is apowerful Gestalt phenomenon to be ob-served here: closure is sometimes pro-cured by the addition of a premisewhich is the obviously missing one, theonly one which fits in with the rest ofthe pattern. Often, however, not eventhis much is required. All the premisesfor the hypothesis of the origin ofspecies through natural selection werepresent both for Darwin and for Wal-lace, and, once they had them all (in-cluding the indispensable contributionfrom Malthus), they both got the pointat once. Now there is of course no ef-fective way of ever being sure that onehas all the premises. But in this re-spect, also, the logic of discovery is inprecisely the same boat as deductivelogic: the rules there do not yield thepremises either, they only yield theconclusion once the premises have beenprovided.

What are the premises which lead toa scientific discovery? Where do theycome from? At this point, in the litera-ture, the search for a logic of discoveryfrequently gets thrown off the scent bythe insertion of a great deal of irrele-vant talk about motivation, perplexity,or crisis; it is thought necessary to pointout that discoveries do not happen ifthere is not some problem with thescience we already have. This kind ofthing is not only confusing but down-right misleading. It suggests, again, aspurious difference between deductivelogic and the logic of discovery. In fact,of course, nobody would carry out de-ductions either if there were not somereason to do so-and if that reasonoften amounts to nothing more than apassion for mathematics, having no di-rect relevance to the solution of anypractical problem, a similar passion forinvestigation into nature has accountedfor a great deal of inductive progresstoo.The premises in question are of two

principal kinds: on the one hand thereare theories and observations made andconfirmed by previous workers, and, onthe other, observations not adequatelycovered by earlier theories, made byor communicated to the discoverer. Thediscovery consists, of course, in the pro-vision of an adequate theory to coverthese new observations. Premises of theformer kind are part of the inheritanceof the scientist, although he may haveto search the literature for them. Thoseof the latter kind may come from plainobservation or from experiment; theymay come into the possession of the sci-entist quite by accident, in a disguisedform, and so on. It is at this stage-inthe provision of the premises, ratherthan in the structure of the argument-that the notorious uncertainty of theprocess of discovery arises, that seren-dipity plays a part, and so on.By far the most important contribu-

tion, however, is made by what I havespoken of as the scientist's "inheri-tance," although it might be better touse the genetic term rather than thelegal one and speak instead of "hered-ity." Newton's celebrated remark about"standing on the shoulders of giants"(12) reminds us that the development ofscience is a stepwise process; nobodystarts from scratch, and nobody getsvery far ahead of the rest. At any pointin history there is a range of possiblediscovery; the trailing edge of the rangeis defined by everything known at thetime (I overlook here the fact that peo-

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ple are constantly "discovering" whatis already known, which blurs this edgesomewhat), and the leading edge is afunction of what is already known, to-gether with variables representing avail-able instrumentation, the capacity ofhuman brains, and so on. But, withinthe range, all movement is not forward-quite the contrary. While the mindmoves with a kind of subjective con-viction and (as it persuades itself) un-erringly to its inductive conclusion,that conclusion is not always the discov-ery it is thought to be. There may beseveral reasons for this: the "discovery,"if it fits the facts, may have been madebefore; if it does not fit them, that maybe because there are still, without thescientist's knowing it, some missingpremises (some fact he does not know,some previously established theory hehas not taken into account), or just be-cause he has made a mistake. In orderto get a clear picture of scientific dis-covery the account has to be broadenedsomewhat to take into considerationthe population of scientific workers atthe time, together with the nature ofthe development of science. The bestanalogy for this development is againa genetic one: Just as mutations arisenaturally but are not all beneficial, sohypotheses emerge naturally but are notall correct. If progress is to occur,therefore, we require a superfluity ofhypotheses and also a mechanism ofselection. At any given epoch in the de-velopment of science-to deal with thefirst requirement first-hypotheses arein fact emerging at a much higher ratethan one might suspect from readingsubsequent historical accounts. We allknow about Darwin and Wallace, forexample; but how many of the hundredsof other well-meaning naturalists of themiddle 19th century, all tackling theproblem of the persistence or mutabil-ity of species, are now remembered?

It may be useful in this connectionto draw attention to a well-known phe-nomenon which is more relevant to thedevelopment of science than most of usperceive it to be-namely, the phe-nomenon of the crackpot. We are ac-customed to thinking of the advance-ment of science in terms of the halfdozen great names in a given field; onreflection we may see that these halfdozen are supplemented by a thousandor so working in more obscure labora-tonres. But we should also rememberthat there are myriads of people specu-lating, generally in a half-informed way,about the same topics from myriads of

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private vantage points; the occasionalwild manifestos we all receive, showinghow misguided Darwin and Einsteinwere, represent a mere fraction of theiroutput. In every epoch something likethis has gone on, and the unrecordedhistory of unsuccessful speculationwould swamp completely the history ofscience as we know it if it could everbe added to the literature. Unsuccessfulhypotheses are weeded out, of course,by their failure to square with the facts,or if they can be made to do that, bytheir failure to be predictive. But in thisconnection certain social factors tend toiilterfere with the evolutionary pattern,just as they do in the biological case.Just as the children of rich familiesmay, under a less than equitable socialsystem, be comparatively better pro-tected against the hostility of the en-vironment than the children of poorones, so some theories produced underpowerful sponsorship may have a longerrun than they deserve.

Despite the fact that parallels pre-sent themselves so readily, there are acouple of puzzling things about the de-velopment of science that make thisevolutionary analogy suspect. First of all,there is the fantastic rate of its growth inthe last three or four centuries, quiteunlike the leisurely pace at which bio-logical adaptation usually proceeds. Sec-ond, there is the remarkable fact, docu-mented in the work of Robert Mertonand others (13), that virtually all validdiscoveries (let alone incorrect hypothe-ses) have been made by more than oneworker, sometimes by many, while somegreat scientists appear to have madefar more than their fair share of suchdiscoveries. Clearly a random-mutation,Mendelian evolutionary model will notdo.

The Evolution of Science

At this point it would be convenientto introduce some statistical analysis(already hinted at by the reference toMerton's work on multiple discoveries)to show how a given frequency of theo-retical interest in a population, pre-sumed to yield a rather smaller fre-quency of correct conjectures-these tobe selected by the hostility of the experi-mental environment toward false theo-ries-would account for the develop-ment of science. Unfortunately the nec-essary statistical apparatus has not beenworked out, since statisticians have con-centrated their attention on Mendelian

genetics, whereas the form of genetictheory required for this purpose is clear-ly Lamarckian. The accumulated em-pirical and theoretical knowledge passedon from one generation of scientists toanother counts as an acquired charac-teristic, the fruit of direct adaptationrather than of mutation. To make mat-ters worse, the pattern of reproductionis quite evidently not sexual. I can offerone or two further genetic analogies-for example, it is easy to find parts oftheory behaving like dominant charac-teristics, in that they exclude or sub-sume- alternative views, and others be-having like recessive ones, in that theyare passed on with the rest of the in-herited material but do not become im-portant until they are conjoined withsome other factor-but I have not beenable to work out the details of the ap-propriate model.

Still I think the general evolutionarypoint holds. Discoveries represent akind of adaptation which is almostbound to occur in a number of indi-viduals if they are subjected to roughlysimilar environmental pressures, the en-vironment in this case being an intel-lectual one. Medawar, in an exchaiigewith Arthur Koestler about the latter'sbook The Act of Creation, remarks (8):"Scientists on the same road may beexpected to arrive at the same crestina-tion, often not far apart. Romanticslike Koestler don't like to admit this,because it seems to them to derogatefrom the authority of genius. Thus ofNewton and Leibniz, equal first withthe differential calculus, Koestler says'the greatness of this accomplishment-is hardly diminished by the fact thattwo among millions, instead of oneamong millions, had the exceptionalgenius to do it.' But millions weren'ttrying for the calculus. If they hadbeen, hundreds would have got it."That is as close to backing on the sta-tistical point as I am likely to come forthe moment. It is notoriously difficultto confirm counterfactuals of this sort,but there does seem to be a practicalsense in what Medawar says, borne outby the tendency of various agencies tobombard scientists with research grantsin an expectation of results at least com-parable to that of geneticists bombard-ing Drosophila with gamma rays.

I have now sketched the main out-lines of a possible model for scientificdiscovery. But there are two importantcomponents still missing-namely, someexplanation, on the one hand, of thetendency of the human mind to produce

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hypotheses at all and, on the other, ofthe tendency of some great minds toproduce many correct ones. Given thathypotheses are in fact produced, in asufficiently prodigal fashion to providethe grounds for natural selection andconsequently for the origin of new theo-ries, how are we to account for the phe-nomenon? It is not enlightening in thisconnection to talk about genius. To talkabout imagination is a little better, al-though, as Peirce remarks in an essayon Kepler (14), "'imagination' is anocean-broad term, almost meaningless,so many and so diverse are its species."I have already made reference tostresses from the intellectual environ-ment, suggesting a theory of "necessityas the mother of invention," but thatcertainly cannot be carried through fora large-perhaps the greater-propor-tion of scientific discoveries.

Let me deal first with the specialpoint about the disproportionate num-ber of discoveries made by great sci-entists, and then go on to the more gen-eral, and concluding, point about thebasic mechanism. Obviously no accountwhich ignored "the distinctive role ofscientific genius," as Merton calls it,can be considered satisfactory; but theterm genius, meaning originally thespirit assigned a man at birth to guidehis destiny, can now be admitted, if atall, only to describe the man who hasalready proved himself in the businessof making discoveries, not to describesome potentiality he had before hestarted. There are clearly genetic de-terminants involved, having to do withbrain capacity and other characteristicsnormally distributed in the population,with respoect to which the genius willbe found to lie under the right-handshoulder of the bell-shaped curve, butnone of them, nor any combination,can be equated with scientific genius,since a lot of similarly endowed peoplewill be found living normal lives asstockbrokers, lawyers, and so on.

Once again, what makes a man agenius has nothing whatever to do withthe logic he employs; and the point Iwish to stress is that he need have nospecial logical endowment, no bag ofcreative tricks, in order to rise to thelittle eminence which, in the long his-torical view, he occupies for such ashort time. I say "little eminence" notto minimize the respect we owe togenius-from close up, after all, we canproperly refer to Einstein as a "tower-ing genius"-but to reinforce the pointmade earlier about the comparatively12 DECEMBER 1969

narrow range within which at any timescientific discoveries can be made. Theformation of a scientific genius, in fact,is comparable to the formation of anOlympic runner, or a tennis or chesschampion. The chess analogy is a use-ful one; chess is, after all, a strictly de-ductive game, and all it takes to winevery time is the ability to do a fewbillion calculations in the head withinthe period legally allowed for a move.Imagine a chess game in which thereare some concealed pieces, moved by athird player, which influence the pos-sible moves of the pieces on the board,and imagine that, instead of 16 piecesto a side, there are several million, somegoverned by rules of play not yetknown to the players. In such a game aman who, after a long apprenticeshipwith the masters of his time, made threeor four good moves during his careerwould have gained a place in history.The kind of inference a great scien-

tist employs in his creative moments iscomparable to the kind of inference themaster at chess employs; it involves anability to keep a lot of variables in mindat once, to be sensitive to feedback fromtentative calculations (or experiments),to assess strategies for the deploymentof time and resources, to perceive therelevance of one fact to another, or ofa hypothesis to facts. The difference be-tween his logic and our logic is one ofdegree, not of kind; we employ pre-cisely the same methods, but moreclumsily and on more homely tasks. Iwish to conclude by considering somecrucial properties of the common logi-cal mechanism with which we are allequipped, which explain, I think, thenatural tendency for hypotheses toemerge, and in this connection to callon two diverse kinds of evidence, onefrom psychology and one from anthro-pology.

Psychology and Structuralism

On the psychological side, Berlynehas recently drawn attention to a formof behavior among higher animalswhich he calls "exploration." Under thisheading, he says, may be grouped ac-tivities describable as "curiosity" and"play," or, in a human setting, as "recre-ation," "entertainment," "art," or even"science." This kind of activity is notindulged in because of its utilitarianvalue, although it sometimes has usefulby-products. "An animal looking andsniffing around may stumble upon a clue

to the whereabouts of food. A scien-tist's discovery may contribute to publicamenity and to his own enrichment orfame. Much of the time, however, or-ganisms do nothing in particular aboutthe stimulus patterns that they pursuewith such avidity. They appear to seekthem 'for their own sake'" (15). Ber-lyne offers two lines of explanation forthis exploratory activity. One of themis the conventional one of response tonecessity, leading to "specific" explora-tion. The second, and more interesting,at least from the point of view of theproblem of discovery, deals with whatBerlyne calls "diversive" exploration."It seems that the central nervous sys-tem of a higher animal is designed tocope with environments that produce acertain rate of influx of stimulation, in-formation, and challenge to its capaci-ties. It will naturally not perform at itsbest in an environment that overstressesor overloads it, but we also have evi-dence that prolonged subjection to aninordinately monotonous or unstimu-lating environment is detrimental to avariety of psychological functions. Wecan understand why organisms mayseek out stimulation that taxes thenervous system to the right extent,when naturally occurring stimuli areeither too easy or too difficult to as-similate." It looks, therefore, as if acertain kind of nondirected exploratorybehavior is to be expected, both whenthe exterior world is too exciting (the in-tellectual withdraws into his ivorytower) and when it is not excitingenough (the explorer sets off to con-quer new territories).Now science is manifestly not the

only possible kind of human explora-tion, even on the intellectual level, andthis I think has to be recognized if sci-entific discovery is to be put in itsproper context. The notion that truehypotheses emerge from the welter ofspeculation by a process of natural se-lection (the condition of survival beingagreement with empirical evidence) canbe extended by analogy to the emer-gence of science itself from a welter ofnatural mental activity. The final com-ponent of my model owes its inspirationto the work of the structuralists, notablyClaude Levi-Strauss, although it is anextension rather than a simple invoca-tion of their views.

Levi-Strauss observes, from the an-thropologist's point of view, a phenom-enon exactly analogous to that observedby Berlyne from the psychologist's.Primitive people, along with their

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totems and their myths, turn out to havean extraordinarily rich lore of a kindthat can only be called scientific, sinceit represents a body of hypotheses aboutthe natural world linked in some primi-tively acceptable way to a body of ob-servations. This "science of -the con-crete," as L6vi-Strauss calls it, is not,in his words, "of much practical effect."But then "its main purpose is not apractical one. It meets intellectual re-quirements rather than or instead ofsatisfying needs. The real question isnot whether the touch of a wood-pecker's beak does in fact cure tooth-ache. It is rather whether there is apoint of view from which a woodpeck-er's beak and a man's tooth can be seenas 'going together'. . . and whether someinitial order can be introduced into theuniverse by means of these groupings"(16).

This line of work is one which Ithink is at the moment of great interestand promise. What emerges from it is aview of mind as a structuring agent,which puts together a world of thoughtcomparable in its complexity to theworld of experience, thus satisfying theoptimum conditions of mental activitydescribed by Berlyne. The chief agencyof structure is, of course, language. Ofthe various constructions made possi-ble by language, science counts as onlyone, and initially enjoys no special ad-vantage over myth. But sometimes whatit says turns out to be true (the herbreally does cure the disease), and al-though it is a long step from the truthof a report of practice to a genuinelytheoretical truth, this realization is thestarting point of the process of scien-tific development. A story told for noother initial purpose than to keep mindin a kind of dynamic balance with the

world, to assert it over against theworld, turns out to hold the clue tocontrol of the world. Other people con-tinue to tell stories for other purposes,and the accumulation of specializedlinguistic habits, specialized techniques,and so on, may soon persuade the sci-entist that he is no longer like the oth-ers 'but is engaged on a differentquest with its own creative character.It is true that scientists, on the whole,care more than other men do that thestories they tell should be true; but thentruth itself is a comparative latecomeron the linguistic scene, and it is cer-tainly a mistake to suppose that lan-guage was invented for the purpose oftelling it.

Scientific theories are na longer cre-ated ex nihilo; the stories scientists tellare not free inventions. If the creativeprocess starts from a very large set ofpremises already demonstrated to betrue, its conclusion has a greater chanceof being true than it would have if theprocess had started, like the conjectureof the primitive, from a random as-sortment of propositions indifferentlytrue and false. When the conclusion isshown to be true by comparison withthe evidence, we call the invention adiscovery. ["Formulas are invented," asBunge puts it, "but laws are discovered"(17).] The major point I have wished tomake can be summed up in this way:In the creative process, as in the processof demonstration, science has no speciallogic but shares the structure of humanthought in general, and thought pro-ceeds, in creation as in demonstration,according to perfectly intelligible prin-ciples. Formal logic, whose history as arigorous system started with Frege andended with Giodel, represents a refine-ment and specialization of the principles

of everyday argument; the logic of sci-entific discovery, whose rigorous formu-lation is yet to be achieved (not that itholds out the hope of completenessonce entertained by deductive logic),will similarly prove to be a refinementand specialization of the logic of every-day invention. The important thing torealize is that invention is, in its strictestsense, as familiar a process as argu-ment, no more and no less mysterious.Once we get this into our heads, scien-tific creativity will have been won backfrom the mystery-mongers.

References and Notes

1. K. Popper, The Logic of Scientific Discovery[Harper, New York, new ed., 1965 (originalGerman ed., 1934)].

2. P. Caws, Phil. Phenomenol. Res. 25, 522(1965).

3. A. Koestler, The Act of Creation (Hutchin-son, London, 1964), pt. 2.

4. C. Darwin, in The Life and Letters ofCharles Darwin, F. Darwin, Ed. [Basic Books,New York, new ed., 1959 (original ed., 1888)].

5. See, for example, G. Polya, Patterns ofPlausible Inference (vol. 2 of Mathematicsand Plausibk Reasoning) (Princeton Univ.Press, Princeton, N.J., 1954).

6. G. Frege, in From Frege to G8del, J. VanHeijenoort, Ed. (Harvard Univ. Press, Cam-bridge, Mass., 1950), p. 5.

7. N. R. Hanson, Patterns of Discovery(Cambridge Univ. Press, Cambridge, England,1958), p. 70.

8. P. B. Medawar, The Art of the Soluble(Methuen, London, 1967).

9. F. Bacon, The New Organon [Liberal ArtsPress, New York, new ed., 1960 (originaled., 1620)].

10. C. Darwin, The Origin of Species [ModemLibrary, New York, new ed. (original ed.,1859)].

11. E. Jones, Sci. Monthly 84, 75 (1957).12. Sir Isaac Newton, letter to Robert Hooke

(1676).13. R. K. Merton, New Sci. 12, 306 (1961).14. C. S. Peirce, Values in a Universe ot

Chance, P. P. Wiener, Ed. (Doubleday, Gar-den City, N.Y., 1958), p. 255.

15. D. E. Berlyne, Science 153, 25 (1966).16. C. Levi-Strauss, The Savage Mind [Univ. of

Chicago Press, Chicago, new ed., 1966, p. 9(original French ed., 1962)].

17. M. Bunge, The Search for System (vol. 1of Scientific Research) (Springer, New York,1967), p. 345.

18. This article is dedicated to the memory ofNorwood Russeli Hanson, vice president ofAAAS, Section L in 1961-62 and for manyyears secretary of the section.

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The Structure of DiscoveryPeter Caws

DOI: 10.1126/science.166.3911.1375 (3911), 1375-1380.166Science 

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