unanswerable questions

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Symposium: Unanswerable Questions

Author(s): Renford Bambrough and Rush RheesReviewed work(s):Source: Proceedings of the Aristotelian Society, Supplementary Volumes, Vol. 40 (1966), pp.151-186Published by: Wiley on behalf of The Aristotelian SocietyStable URL: http://www.jstor.org/stable/4106729 .

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UNANSWERABLEQUESTIONSBy RENFORDAMBROUGHnd RUSHRHEES

I-RENFORDBAMBROUGHIt is tooeasilyassumedhatanyquestion as ananswer.SirHarold effreys, cientificnference.Theres,then, oeveryquestion trueanswer, final onclusion,o whichtheopinion f everyman s constantlyravitating.

C. S. Peirce,CriticalReviewof Berkeley's dealism.There are no unanswerablequestions.There are no unanswerablequestions.Every question has a right answer.That is my thesis. It would be convenient if I could now go onto offer my defence of it. But there are two obstacles. The firstobstacle is that there are several natural ways of taking my thesisin which it is not only false but obviouslyfalse. If my thesis istaken to mean that we know the answer to every question, then itis false. It is also false if it is taken to mean that we, or ourdescendants, shall ever know the answer to every question. It isprobably false (though I am not so clear about this) that it wouldeven make sense to suppose that any person, or group of people,could know the right answer to every question.But when I suggest that every question has a rightanswer,I amnot making any of these false or problematicalsuggestions. It is asobvious to me as to everybody else that there are some questionsto which we do not know the answers, and some to which neitherwe nor our descendantsshall ever know the answers. And I find itas problematicalas anybody else does to suppose that there couldever be a man or a people who knew the right answers to allquestions at once.What I am maintainingis that to everyquestion thereis a rightanswer, and not that I or you or anybody knows, or ever hasknown, or ever will know the right answer to every question, orindeed to any question. It is also obvious to me, as to Mooreand many others, that there are many questions to which we doknow or have known or shall know the right answers. But mythesis is not an historical thesis about the contingent fact that weor others have such-and-suchknowledge: it is a philosophical ormetaphysical or conceptual thesis about the nature of knowledge,

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about the concepts of knowledge, question, answer, reason,truth and justification.These points may all seem obvious, but I have found that tomany people they are not obvious, and that discussion of mythesis can proceed satisfactorily only when these points havebeen made over-abundantly clear. One way of making themover-abundantlyclear is to limit our attention for a moment toone definite class or kind of question, say historical questions.We know that Julius Caesar was assassinated on the Ides ofMarch, 44 B.C. We do not know, but may know in the future,whether there was collusion between Britain and Israel in theSuez Crisis of 1956. We do not know, and we shall probablynever know, in what year the last pterodactyl died. But it is clearthat all these questions are of the same logical character,and thatto each of them there is a right answer, independentlyof whetheranybody knew, knows or everwill know, what that rightansweris.Neither the logical character nor the truth-value of a historicalproposition is logically affected by any facts about who knows ordoes not know the proposition to be true or to be false.I am now in a stronger position to make clear what my thesis is.It is that every question is answerable in the sense in which allthree of my examples of historical questions are answerable.Every question is logically capable of being correctly answered,although it is obvious that some questions cannot in fact beanswered by us, and that some questions will never in fact beansweredby us. (Even if we cannot say of anyparticularquestionthat it will never be answered,we can still say that there are somequestions which will never be answered by us or by our succes-sors; just as we can say that there are some numbers that willnever be thought of, even if we are not able to say of any partic-ular number that it will never be thought of.)When I say that all questions are answerable I am not sayingthat there are no practical obstacles in the way of our answeringcertain questions. I am not denying that we are beset by practicaldifficulties. Nor am I saying that our capacity for answeringquestions is not regrettably meagre. I am not denying that thepower of the human understanding is regrettably feeble. Butthese obstacles and these limitations keep us from finding outhow things are; and how they are is independent of our beingheld back by these barriers and burdens from finding out howthey are.



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If I claimthatscienceor mathematicss a branchof knowledgeI do not claim that I or anyonecan answerall (or even any)scientificor mathematical uestions.Scientific ndmathematicaltruthdoes not dependon beingknown orbeingtrue. Manywhowillrecognise hispointwhen t is made about scienceor mathe-matics will denyit whenit is made aboutethicsoraestheticsortheology or philosophy. My thesis is that this point applieswithoutexception o all enquiries:hat all enquirys objective.Thisleadsto the secondandgreaterof my two obstacles: herangeandscopeof mythesis. Theobjectivity f ethicsor aesthe-tics, or philosophy(or even of logic)-each one of these is animportantand difficultand controversialphilosophical opic inits own right. To defendthe objectivityof any one of thesebranchesof knowledge its claim to be a branchof knowledge)needsa book initself. Indefendingmypresent hesisI amarguingthatall theseare branches f knowledge.Whatmakes t possibleto engage n thislarge-scalewholesaleoperations that,althougheveryoneof theseproblemshasits ownspecial eatures,here s arecurrentatterno befound n the variousdoctrines thevariousscepticisms)that consist in denying the objectivityof thesevariousbranchesof knowledge. Some of the reasonsthat aremost usuallyofferedagainstthe objectivityof ethics are closelysimilar o some of those most usuallyofferedagainstthe objec-tivityof theology,aesthetics,philosophyand evenlogic. What smore,theyarecloselysimilaragain o someof thereasonsofferedby scepticsagainst heobjectivity f matterandmind;against heclaim thatphysicsandpsychologyarebranchesof knowledge.The link between all these scepticisms-what makes it notimpossible(however oolhardy) o try to deal with them all atonce-is thattheyareallconcernedwiththeconcept f knowledgeand the related concepts of verification,reason, justification,truth and so on. In spite of the enormousvarietyof kinds ofknowledgeagainstwhichscepticalattacks have been mounted,there is a single patternwhich,with appropriate ariations, svisible n all thesescepticalattacks.

The pattern s fully and instructively xemplifiedby Sartre'sdiscussion, in Existentialismand Humanism,"of the predicamentof his young pupil:

xTranslated by Philip Mairet. (Methuen, 1948.)



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As an example by which you may the better understandthis state of abandonment, I will refer to the case of a pupil ofmine, who sought me out in the following circumstances. Hisfather was quarrellingwith his mother and was also inclined tobe a " collaborator "; his elder brother had been killed in theGerman offensive of 1940 and this young man, with a senti-ment somewhat primitivebut generous, burned to avenge him.His mother was living alone with him, deeply afflictedby thesemi-treason of his father and by the death of her eldest son,and her one consolation was in this young man. But he, at thismoment, had the choice between going to England to join theFree French Forces or of staying near his mother and helpingher to live. He fully realisedthat this woman lived only for himand that his disappearance-or perhaps his death-wouldplunge her into despair. He also realised that, concretely andin fact, every action he performed on his mother's behalfwould be sure of effect in the sense of aiding her to live, where-as anything he did in order to go and fight would be an ambi-guous action which might vanish like water into sand andserve no purpose. For instance, to set out for England hewould have to wait indefinitelyin a Spanish camp on the waythrough Spain; or, on arriving in England or in Algiers hemight be put into an office to fill up forms. Consequently, hefound himself confronted by two very different modes ofaction; the one concrete, immediate, but directed towardsonly one individual; and the other an action addressed to anend infinitely greater, a national collectivity, but for that veryreason ambiguous-and it might be frustratedon the way. Atthe same time, he was hesitating between two kinds of mora-lity; on the one side the morality of sympathy, of personaldevotion and, on the other side, a morality of wider scope butof more debatable validity. He had to choose between thosetwo. What could help him to choose ? Could the Christiandoctrine ? No. Christian doctrine says: Act with charity,love your neighbour, deny yourself for others, choose the waywhich is hardest, and so forth. But which is the harderroad ?To whom does one owe the more brotherlylove, the patriot orthe mother ? Which is the more useful aim, the generalone offighting in and for the whole community, or the precise aim ofhelping one particular person to live ? Who can give an



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answer to that a priori? No one. Nor is it given in any ethicalscripture. The Kantian ethic says, Never regard another as ameans, but always as an end. Very well; if I remain with mymother, I shall be regardingher as the end and not as a means:but by the same token I am in danger of treating as meansthose who are fighting on my behalf; and the converse is alsotrue, that if I go to the aid of the combatants I shall be treatingthem as the end at the risk of treating my mother as a means(pp. 35-6).It is by presenting and discussing this example that Sartreseeks to show that " every man, without any support or helpwhatever,is condemned at everyinstant to invent man." No signsare vouchsafed on earthfor man's orientation: " for a man himselfinterpretsthe signs as he chooses." The young man's dilemma isoffered as an example of an unanswerable question, a questionthat has no objectively right answer.This case is typical of the cases that can be plausibly offered ascounter-examplesto my thesis, and Sartre introduces and relies onall the main elements in the recurrentpattern of sceptical argu-ment that I wish to criticise. In the first place, he is at pains toemphasise the difficulty and the complexity of the young man'spredicament. There are indefinitely many separate items andfactors to be isolated and weighed, and they are of several diff-erent kinds. He has to estimate the causal consequences of thevarious courses of action that areopen to him. If he does decide tojoin the Free French Forces, he may find that he will spend thewhole war isolated in Algiers or England filling up forms. He alsohas to calculate the moral (or logical) consequences of the variouscourses of action; to be clear about what he is committed to if hepursues this or that line of conduct.Like other moral sceptics, Sartre also lays great stress on thedisagreement that is so usual a consequence of the difficultyandthe complexity of moral choice. The young man cannot solve hisproblem by turningto other people for advice, even if only becausethe available advice is so varied, so conflicting, and so predictablethat to choose an adviser would in effect be to choose a course ofaction; or, to put the same point in another way, because thedifficultyof selectingan adviseris itself a difficultyof thesame kindand degree as the difficulty on which he needs advice, evenperhaps another form of the same difficulty.



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He may think of turning to a priest. But there are collabora-tionist priests, priests of the resistance, and Cures-of-Bray. Heis inescapably alone. Nobody can ever show him or assure himthat he would be right to choose or to reject any particularcourse of action. If he tries to find an answer, the answer, heis (and, according to Sartre, must be) in a state of agonisinguncertainty:If values are uncertain, if they are still too abstract to

determine the particular, concrete case under consideration,nothing remainsbut to trust in our instincts. That is what thisyoung man tried to do; and when I saw him he said, " In theend, it is feeling that counts; the direction in which it is reallypushingme is the one I ought to choose. If I feel that I love mymother enough to sacrificeeverythingelse for her-my will tobe avenged, all my longings for action and adventure-then Istay with her. If, on the contrary, I feel that my love for her isnot enough, I go." But how does one estimatethe strengthof afeeling ? The value of his feeling for his mother was deter-mined preciselyby the fact that he was standingby her. I maysay that I love a certain friend enough to sacrifice such or sucha sum of money for him, but I cannot prove that unless I havedone it. I may say, " I love my mother enough to remain withher," if actually I have remainedwith her. I can only estimatethe strength of this affection if I have performed an action bywhich it is defined and ratified. But if I then appeal to thisaffection to justify my action, I find myself drawn into avicious circle (pp. 36-7).Here we find a third important source of moral and otherscepticism: the " craving for generality" that was rebuked byWittgenstein. Sartre thinks of value-judgments as being neces-sarily general. Values are " too abstract" to be of direct assist-ance to his puzzled pupil, whom he describes as "hesitatingbetween two kinds of morality ". He emphasises again on p. 38the useless generality of moral reasoning and moral principles ashe understandsthem:

In coming to me, he knew what advice I should give him,and I had but one reply to make. You are free, thereforechoose-that is to say, invent. No rule of generalmorality canshow you what you ought to do: no signs are vouchsafed inthis world. The Catholics will reply, " Oh, but they are! "



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Verywell; still it is I myself, n everycase,whohave to inter-pretthe signs.Another source of puzzlementand scepticism hat is wellillustratedby Sartre'sexampleis the familiardifficultyaboutborderline ases;a difficultyhat so often findsexpressionn thechallenge:" But wheredo you drawthe line ? " Thisfeatureofdifficultmoraldilemmas s connectedwiththe earlierpointsaboutcomplexityanddisagreement. f the case were somewhatalteredin one directione.g.,by restoringhe mother'sdeadson)it wouldbe clearthat theyoungmanoughtto go to fightfor France. Butif it were somewhatalteredn anotherdirection saybyremovingthesurvivingon'srightarm) t wouldthen be clearthathe oughtto stayat homeandsupporthis mother.Thecaseis so classicallyborderlinehatwe maywell wonder,withSartre,how we couldeversettle such a question. How canwe fix the exactpositionofthis case in thebewilderingmanifoldof relatedcases? It is smallwonder hat Sartre houldgo on to speak(38-9)of abandonmentanddespairandanguish.I have triedto conveythe senseof agoniseduncertainty, fmoralperplexityo the pointof scepticism,hat is presented ndevokedby Sartre. But I have done this becauseI now wish tosuggestthat it is completelyunjustified, nd that all the reasonsthat Sartrehas offered n its defencewhollyfail to support t.Thecomplexity nddifficulty f moralchoice,of whichSartreand other moralscepticsmake so much,is no greater han thecomplexity and difficultythat we face in many non-moralenquiries. History, sociology, textual criticism,meteorology,cosmology,andmolecularbiologyareonlythe firstexampleshatcome to mindof an enormous angeof non-moral ields n whichthere s complexity hat can at leastmatchthe complexityof themoralproblem hat Sartrehas set beforeus.But for my purpose t is not important o settle this disputeabout the degreeof difficultyor complexityof moralchoice ascomparedwith thedifficulty ndcomplexity f historyor science.Thatsomethings difficult or a particularman,orforallmen, s amatteroffact. It has no bearingon the logicalcharacter f thequestion hatpresentshedifficulty.We mustnot confuse he actthat our powersand capacitiesare so regrettablyimitedwith asupposed intrinsicor logical difficultyor impossibility n thesettlingof moralquestionsand dilemmas. It is now a common-place that automaticcomputingmachineshave vastlyextended



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our power to perform mathematical calculations and computa-tions. The machines have actualised for us what were at one timemere possibilities. But that is just the point: the possibilities werealways possibilities. The limitations of our powers are contingentlimitations, and with good fortune and strenuous effort we canhope to extend our powers. There is no a priori reason (thoughthere may be many reasons of other kinds) why we should not,with similar effort and pertinacity, extend our power to deal withmoral, political, philosophical and religious perplexities.The greater the difficultyand the greater the importance of aproblem, the more inappropriateand the more irresponsible it isto suggest that, instead of persistingwith as strenuous and as well-directed an effort as we can make in the search for the rightanswer to that problem, we should more or less arbitrarilyanddogmaticallymake a choice, or enter into a gratuitous commit-ment. Cosmologists are at present engaged in disputes whichcan, for difficulty and complexity (even if not for practicalimportance) match any moral problem that Sartre or any otherphilosopher could find or devise. But they recognise that noamount of difficultyor complexity couldjustify them in arbitrarilyor gratuitously taking sides. Ministers and civil servants arefaced every day with questions of home or foreign policy ascomplex and intractable as the dilemma of Sartre's young man.But we are rightly unwilling to dispense then from the duty ofstriving to achieve a more complete and accurate and consistentview of the manifold and multifarious facts and events, featuresand factors, that are relevant to the solution of their problems.Similarpoints apply again to the use that sceptics make of theextent, or the alleged extent, of our disagreementabout ethics andpolitics and philosophy and religion. That men should agree ordisagreeto this or that extent is afact and not a logical necessity.It is therefore irrelevant to questions about the logical characterof the questions concerning which the disagreementarises.Sceptics are in any case inclined to exaggerate the extent ofactual disagreementabout morality, and to make the exaggerationplausible by a biased selection of examples; by comparing casesthat are not comparable. We are invited to contrast our impres-sive and immediate agreementthat there is a glass of water on thetable with the depth and tenacity of our disagreements aboutcapital punishmentor the Bomb. It would be a sufficientreply tocontrast the disagreementsof cosmologists or theoreticalphysicists



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with our general agreement hat this child, who is about toundergoa surgicaloperation, hould be anaesthetised.It is truethat thereare someminorities, uch as Jehovah'sWitnesses,whoareopposed o theadministrationf anaestheticsvento children.But it is also true that thereis a smallbut vigorousFlat EarthSociety,anda legionof believersn astrology. For everycaseofextrememoraldisagreementt is possible o quotea parallelcaseof extremedisagreementbouta non-moralquestion. For everysimpleand uncontroversial on-moralquestion t is possibletoquotea parallelcase of a moralpropositionwith whichnobodybut a madmanor a philosopherwould disagreeor pretendtodisagree.The most influential ourceof moralscepticism,as of otherkindsof scepticism,s thecraving or generality:he idea thatwecannot establisha particular pecificmoraljudgmentwithoutfirst(oripso acto)establishing moralgeneralisationrprinciplefromwhichthe particular udgmentcan be derivedas a logicalconsequence.Sartredescribes isyoungpupilasbeingfacedwitha choicebetweentwomoralities.But all that is justifiedby theinformationhatSartreprovidess the claim hathe is facedwithachoice between two courses of action in thisparticularsituation.Themakingof a particularhoicein thisparticularituationwillnot commithimto making hecorrespondinghoice n anyotherparticularituation.(Wemay gnore hedegeneratease in whichthe " other" situation s identicalwith the presentone.) If hemakesa particularhoice n thisparticularituationhe willat themost(andI shouldsayalso at theleast)commithimself o dealingwith a similarsituation n the future eitherby makingthe cor-respondingchoice or by showingthat the second situationisrelevantlydifferentromthe first. The so-calledrequirement f"universalisabilityis a fancy-dressersionof therequirementfconsistencywhichall reasoning,n all fields,mustsatisfy. When-ever I make two differentudgments,of whateverkind, I mustalwaysbe preparedo dischargehe onus of showingthat thereare differences etween he casesthatjustifythe differencen myjudgmentof them.Thetroubleaboutborderline asesalso arises roma cravingforgenerality nda misunderstandingf the natureof generality.It is alsocloselyconnectedwith,sometimes rises rom,andeasilygivesriseto, amisunderstandingbout he natureof questions ndanswers.For ourpresentpurpose t willbe most convenientand



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most useful to approach this cluster of difficulties through aconsideration of the natureof the process of asking and answeringquestions.

A borderline question is one to which it seems clear that theanswer " definitely yes " and the answer " definitely no " areequally inappropriate. For example, if we are asked " Is this manbald ? " and the man in question has too much hair to justify us incalling him definitelybald, and too little hair to justify us in callinghim definitely not-bald, he is a borderline case between baldnessand not-baldness. It is then tempting to say that the question " Ishe bald ?" has no answer. But this involves assuming that aquestion has no answer unless it has either the answer" definitelyyes " or the answer " definitely no ", and this assumption isclearly mistaken. If I say " He is rather thin on top ", or " He israpidlygoing bald ", or even " Well, Yes and No ", I am answer-ing the question " Is he bald ? " And each of these possibleanswers, like the answer " Yes " or the answer " No ", will beeither right or wrong. A question to which " Yes " is a wronganswer, and to which " No " is also a wrong answer, is not aquestion to which there is no answer, but one to which someanswer other than " Yes " or " No " is the right answer.It here becomes apparenthow unsatisfactoryit is to say that inanswer to a borderline question we can " say which we like ".Since a borderline question is one to which the answer is neither" Yes " nor " No ", if we give the answer " Yes " or the answer

" No "we are giving a wronganswer to the question. And to sucha question, just as much as to any other question, we must strivealways to find and give the right answer, whether it is an answerthat we like or not.The inadequacy of the injunction " Say which you like ", andof any account of any type of question which suggeststhat we havea choice of answers, can be brought out more fully and moreclearly by asking, " Have we any choice as to whether a given

question is a borderline question or not ? " That the case aboutwhich we ask a question is a borderlinecase is itself an objectivematter. The question is borderline because the case about whichwe ask it falls, as a matter of objective act, neither among thecases of which the answer " Yes " would be definitely right noramong the cases of which the answer " No " would be definitely



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UNANSWERABLEUESTIONS 161

right. But it has its own placein the manifoldof cases,andtoanswera questionaboutit is to saythat thatplaceis.A simplediagrammaybeusefulhere:S? xThe left handextremity f the linerepresents casein whichtherightanswer o the question,"Is this man bald ?" is "definitelyYes ". Therighthandextremity epresents case in whichtherightanswer s "definitelyNo ". The line itself representshecontinuum fpossiblentermediateases.Themid-pointof thelinewill then clearly representa borderlinecase, a case where" definitelyYes" and" definitelyNo " are bothdefinitelywrong.The rightanswer n this case (as in any othercase)will be theanswer hatcorrectlyocates hecase n itsplaceon thecontinuum.That t hasthatplaceonthe continuumather hananotherplace sobjectivelyrue, s independent f the wishes, nterests, inguisticconventions, eliefsandattitudesof those whoaskandanswer hequestion,and is also independentof whetheranybodyasks oranswershequestion. In theserespectst does not differ romthecases at the extremeendsof theline.Of coursethe diagramwouldhaveto be morecomplicated-would have to be suppliedwith furtherdimensions-before tcouldrepresenthelogicalcharacter f anyof thereallyplausiblecounter-exampleso my thesis, such as the dilemmaposed bySartre.Butthis increasencomplexitywouldnot alter hepositionin anywaythatwouldcountagainstmythesis;and that thisis somaybe sufficientlyndicatedbya case whichwillservenot onlyasanexamplebutalso as ananalogy ormanyotherexamplesmorecomplexand more importantthan itself, includingthe Sartreexample.If I place a ball or a box or some other objectof regulargeometrical hapebetweena white screenanda single,powerfulsourceof light, I may succeed n so arranging hingsthat theshadowon thescreens of aregular eometricalhape:circular, rsquare, or triangular,with such-and-suchexact angles anddimensions. In sucha case it will be possibleand easyto givethe rightanswer o the question," What s the size andshapeofthe shadow on the screen?" The answer will be simple,obvious,clearanddefinite.If I now fix up severaldistinctand variedsourcesof diffusedlight, of different ntensitiesand in widelydifferentpartsof theroom; and if, instead of having one regularlyshaped object

M



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castinga uniformshadowon the screen,I have a complicatedarrangementof complicatedobjects (lace curtains,ferns andfoliage, spiders'webs) between the sources of light and thescreen, shallprobably ucceed n so arranginghingsthat it willbe extremelydifficultandperhaps mpossible o givea completeand accuratedescriptionof the complexand variedpatternofshadowson the screen.But thepatternof shadows nthescreenwillbewhat t is, inde-pendently f oureffortsor ailuresto describet. And we shallbeable to assess,by referenceo thepattern tself,the adequacyorinadequacy f the effortsof ourselvesand othersto describe hepattern. It may be that even the most successfulattemptwillmanifestlyall shortof givinga completeandaccurate ccountofthe pattern. But it will only be becausewe can see what thepatterns likethatwe shallbe able to see andsaythat thisor thatdescriptions inadequateo this or that extent or in this or thatrespect. And to recognise hat nobodywill evergive the com-pletelyauthoritative escriptionof the patterndoes not provideany reason to say that there is any intrinsic ndeterminacyasopposedto indefiniteness)n the pattern tself.Everyquestionaboutthe patternwill have a rightanswer.Therewillbe manyquestionsaboutthe pattern o whichtheright answerwill be neithera straight"Yes" nor a straight" No ".Nobodywillbe ableto givetherightanswer o everyquestionaboutthe pattern.

Nobody will ever knowthe right answerto everyquestionaboutthe pattern.Theinvestigation nd discussionof the patternmaycontinueindefinitely.The topic is inexhaustible,ven if it is not of inex-haustible nteresto anybody.I have tried o makethecase of thecomplexshadowas like aspossible o the casesin which t is most usual andmostplausibleto speakof questions hat haveno answers. Evenif I have suc-ceeded n doingthis, it will require urtherdiscussion o indicatethat the case of the complexshadowhas importanteatures hatbelong o all questions,andwhicharejust the features hat leadphilosophersnto scepticalarguments ndtheories,and also intotranscendentalistrgumentsand theories. (Transcendentalismand scepticism lwaysgo handin hand,because heyboth insistthat what areordinarilyakento be thegroundsof a certain ype



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of conclusion are insufficientto support conclusions of that type.They agree that something else is necessaryif the conclusions areto be adequately supported, but of course they disagree aboutwhether there is anything else that is capable of providing therequiredsupport.)The language of spatial location, which I have alreadyused inspeaking of theplace of a particularcase in a continuum or mani-fold of cases, may be extended in such a way as to provide auseful analogy for logical space, and hence for the whole natureof reasoning and classification, and to provide also a means ofdiagnosing the misunderstandingsof the nature of universalsandgenerality that are among the prime sources of scepticism andtherefore of opposition to the thesis that I am defending.Propositions about the locations of physical objects in space,and the procedures for determining the locations of objects inspace, are not only themselvesexamples of verifiablepropositionsand rational procedures: they are also well fitted to illustratepoints about the nature of rational enquiryin generaland as such.For these examples can clearly be shown to have just the charac-teristics which, when they occur in other kinds of propositionsand procedures, provide what can be made to appear plausiblegrounds for scepticism about such propositions and procedures,and groundsfor transcendentalistanti-scepticalviews about them.And yet few philosopherswould be preparedto acceptthe scepticalor transcendentalistview about enquiry into spatial location thatconsistencywould requireof them if they were to persistwith theirscepticism or transcendentalismabout other forms of knowledgeand investigation.Before making any further philosophical comment I willsimply make some very obvious remarks about spatial location.1. If I ask where something is in space, you can answer myquestion only by referring to the position of something else inspace. This means that in order to understand and to benefitfrom your answerto my question about the location of a particularobject, I must alreadyknow where in space some other particularobject or objects can be found.2. An enquiryinto the spatial position of an object need nevercome to an end, and in one sense cannot come to an end. Ofcourse, if I ask you where Peterhouse is, and you tell me that it isopposite to Pembroke, and I already know where Pembroke is,then we need not discuss any further the spatial location of

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Peterhouse.Butneitherat this nor at anyotherstagecouldweeversucceed n sayingeverythinghat is bothtrueandrelevant o myquestionaboutthe locationof Peterhouse. Thereare infinitelymany true propositionsexpressingspatial relations betweenPeterhouse nd otherobjectsandpositions n space.3. An object nto whose ocationweenquireon oneparticularoccasionmayon anotheroccasionserveas a landmarkby refer-ence to whichwe specifythe locationof some otherobject. Aman who asks wherePembrokes maybe told that it is oppositeto Peterhouse, ndthismaybe all thathe needsto know.4. There are no objectsor positionsin spacewhichhave aspecialorprivilegedtatusas paradigms, r baselines,or ultimatelandmarksor the locationof all otherobjects. Wemayenquireinto the positionof any object,and referin our enquiry o thepositionof anyotherobjectorobjects.Thetheoreticallyomplete(and also theoretically mpossible)specificationof the locationof any particularobjectwould involvereference o everyotherparticularobject. That is why it is theoreticallympossibletocomplete t.Considernow some of the waysin whichphilosophersmightendeavoureither to support sceptical conclusionsabout thelocation of objectsin space,or to persuadeus that some veryspecialconditionsmust be satisfied,or very specialproceduresmust be adopted,or very special insightor intuitionmust beavailableo us,in order o guarantee runderwrite urknowledgeof thelocationof objectsn space,and theprocedures ywhichweordinarily cquireandextendsuchknowledge.1. It mightbe suggested hat we can never know whereanyobject is in space, simplybecause,in order to say and knowwherean object s, we mustrelate t to otherobjectswhoseposi-tions arealreadyknown. It mightbe suggested,n fact,that thejustification f any propositionaboutthe locationof an object nspaceinvolvesthe fallacyof petitioprincipii, ince we can neverjustifyany propositionof this kind exceptby relyingon someotherpropositionor propositionsof the samekind.

2. A similarpointmightbeputbyaccusing urproceduresorlocatingobjects n spaceof involvinga viciously nfiniteregress.We locate one objectby relating ts positionto that of anotherobject,andthatobject n turnby relatingt to stillotherobjects,and so ad infinitum.3. It mightbe suggested hat we can and must, in order to



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escape these difficulties, suppose that there are some objects orpositions which are the ultimate bases to which we must referanyquestion about the location of any other object. (It is veryunclearwhat these paradigm objects or positions could be, and it is partic-ularly difficult to see how they could themselves be objects orpositions in space if they had the exemption from enquiry intotheir location that this sort of theory would require themto have.)There is a close parallelismof structurebetween my imaginarydispute about the objectivity of spatial location and the familiartraditional disputes about the objectivity of reasoning, classifica-tion, justification, valuation. In all these actual disputes, as in myimaginary dispute, it is the infinityof the process of enquiry thatis the prime source of misunderstanding,and therefore of falsetheories. The imaginary sceptic about spatial location relied onthe infinity of the process of justifying a proposition about thelocation of an object as an indication that the process does notdeserve to be called a process of justification. The imaginarytranscendentalist about spatial location arguedthat there must beinitial landmarks or baselines, themselves exempt from enquiryinto their ocation, because he thought that therewas no other wayof escape from the argument of the sceptic.The sceptic and the transcendentalist share the mistakenassumption that a process cannot be a process of justification if itis potentially infinite. Here as often in philosophy there is scopefor the application of Ramsey's Maxim, the principlethat chronicphilosophical disputes commonly rest on mistaken assumptionsthat are shared by the conflicting parties.At least since the time of Aristotle's Metaphysics F, philo-sophershave perplexedthemselveswith what Mr. W. W. Bartley2has recently called " the dilemma of ultimate commitment ".It seems obvious that every conclusion needs to be supportedby a reason, and hence that every premissmust be supportedby afurtherreason, so that the process of justifying any conclusion willbe infinite and impossible. But the equally unpalatablealternativeis to suppose that our knowledge rests on fundamental premissesfor which no reason or justification can be offered. The moststubborn rationalist seems to be forced in the end to irrational

2TheRetreatto CommitmentChattoand Windus,1964). Mythanksaredue to the Editor of the NewStatesmanandNationfor allowingme to reprintpartof my review of Mr.Bartley'sbook.



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166 J. R. BAMBROUGH

commitment, even if only to his reliance on the power of reasonitself. Tillich and other Protestanttheologians have exploited thisdilemma in order to present rationalist critics of religion with aresounding tu quoque.Mr. Bartley's answer is a doctrine of " comprehensivelycritical rationalism ". He holds that the dilemma presents itselfonly to those who have a false picture of rationality. Sir KarlPopper has suggested that scientific propositions are falsifiablebut not verifiable: Bartley invites us to widen the scope of thissuggestion and to recognise that propositions and theories anddoctrines, of whatever kind, are capable only of being criticisedand not of being justified. Mr. Bartley's " non-justificationist"theory of rationalityis safe from Tillich's tu quoquebecause it canconsistently admit that it is itself as open to criticismas any othertheory on this or any other topic.Mr. Bartley's radicalism will startle philosophers of manyschools, but he has still not been radicalenough. He still preservesat least half of the traditional picture of reasoning that he isstriving to erase. He accepts the consequence that we can neverjustify any of our beliefs instead of rejecting the picture becauseit has this consequence.Like most of the philosophershe is most concernedto criticise,he clings to the delusion thatjustificationis always and necessarilya deductive process of deriving the particular from the general;that in the search for foundations we need a ladder and not aspade. He sees, as many have failed to see, that foundationscannot be up there, but he thinks that they must be up there ifthey exist at all, and so he fails to notice them beneath his feet.The elementary is the fundamental. Sir Harold Jeffreys hasremarkedthat the scientist is tempted to " spurn the base degreesby which he did ascend " and Professor Bondi has pointed outthat everychild of three has alreadylearned more physics than hewill ever learn again.The traditional blue-print of justification fails to fit the justi-fications that are offered, and rightly offered, in science, philo-sophy, mathematics,moralsand criticism. Philosophers,including



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Mr. Bartley,draw the wrong conclusionat this point becausethey treat the blue-printas thoughit were an architect'splanratherthan a geographer'smap. Whatevermay happenon abuildingsite,a mapcanneverprovea landscape o be wrong.Sartre'smaltreatment f the dilemmaof hispupilarises romasimilarlydogmaticattachment o a similarly nadequateblue-print.He,too, assumeshat ustificationlimbso itsfoundations,

and that it consequentlynvolves eitheran infiniteregressor aviciouscircle. He recogniseshatknowledgehas no foundationsbuilt to this design,and he thinks that knowledge equires uchfoundations.He showsallthe standardymptoms f the standardmisunderstanding.He asksforsigns,buthe looksforthem n thewrongquarter,and no signis vouchsafed.His own treatmentof his own examplebelies his assump-tions. He can defendhisscepticism, isaccusation hathe andallof us are deeplyand incurablygnorant,andcan defend t withsuch treacherousplausibility,only because we know so much.Hechooseshisconundrumromamonga manifold fsurroundingcasesthat we do know how to settle. Onlybecause t is so like somanythat areclearly o beanswered n oneway,and alsolikesomanyothersthat areclearly o be answeredn the oppositeway,is it so well fittedfor its r81eof scepticalconundrum.We may go further. Sartreclearlyknowswhatare the con-siderations hat are relevantto the solution even of his ownchosenconundrum.It is as plainto him as it is to us thatloyaltyto parentsand resistance o tyrannyare bothgood: the dilemmaarisesbecause hese twogoodthingsconflict. It is asplainto himas it is to us that theyoungmanwould be doingwrongf he wentto SouthAmerica o escapebothhisconflicting bligations.Thisanda hundredotherpossibleanswersare so clearlyruledoutthat

theyare not so much as mentioned.To mention hemis at onceto see howpartialandhowinadequates Sartre's iscussion f hisown example,and hence how inaccurateand inadequates theepistemologyof morals that he baseson that exampleand thatdiscussion.



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We maygo furtherstill. Sartrenot only fails to supporthisscepticism. Like othersceptics,he is himselfdogmatic,and hisdogmatismdevourshis scepticism. For his examplecan onlyappear to serve his sceptical purpose because Sartre himselfimplicitlyclaims to knowthe rightanswerto the young man'sdilemma.He claimsto have shownthat the considerationsn favourof

each of the two possible answers-Mother or France-areexactlyequal n weight. And thatis to claimto have shownthatthe rightanswerto the dilemma s that it is a matterof moralindifference hichof the two choicesthe youngman makes. Ifthisis so (and t is importanto notice thatSartredoes not supplyus with sufficient atato know whetherornot it is so) thenindeedtheyoungmanmayfreelyand evenarbitrarilyhoosebetween hetwo alternativeso which Sartrehas rightlyrestrictedhim. Butthis freedomarisesnot fromtherenot beinga rightanswer o theboy'sdilemma,butfromthenatureof therightanswer hatthereis. He is free only becausethe rightanswer s neither hat hisobligation o his motheroutweighshis obligation o his countrynorthat his obligation o his countryoutweighshis obligation ohismother,butthat the two obligationsare of equalweight. Andto knowin such a complexcasethattwoobligationsare of equalweightis to have a veryfull understandingf the case, to havebetterand fullerknowledgehanis usually nvolved n seeing hatone obligationmanifestly utweighs nother:ustas to know thatthe rightanswer o the question"Is it raining?" is " Yes andNo " is to have moreprecise nformationabout the state of theweather than is usually expressedor summedup by a plain" Yes " or a plain " No ".

To know that the two obligationsare of equalweightis toknow wherethe case lies on the manifoldof actual andpossiblecases. And to knowthat is to know therightanswer o theyoungman'sagonisedquestion.And yet enquiryis endless. Thereis alwaysmore to learnaboutthe relationsof the givencase to otherrelevant ases. But



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we do not have to knowtheinfiniteall beforewe knowanyof it.We may know where Peterhouseand Pembrokeare withoutknowing everything boutthespatial ocationof Peterhouse ndPembroke. And whatgoes for spacegoes for logical spaceandfor moralandphilosophical ndtheological pace.Thepatternsof shadowandlightcannotbe fullyknown,butthey can be known:and everythinghat lies betweenour finite

knowledge nd theinfinite otalityof knowledges something lsethat we can know.Logicalspaceis relative,as spaceis relative:but as spaceisobjective,ogicalspace s objective.Scepticism boutmoralityandphilosophyandtheologyarisesfromthe confusionof the absolutewith the objectiveand of therelativewiththe subjective.My thesis thateveryquestionhas a rightanswer s offered noppositionto an over-simpleblue-print hat philosophershavetriedto imposeon thevarietyandcomplexityof questionsandofanswers.Wittgensteinndsomeof hisfollowers,who havestrivenso hard and so effectively o liberate us from so many of thepicturesthat hold us captive,have themselvessometimessuc-cumbed o a too limitedandcrampeddeaof what t is to answer

question.ProfessorWisdomhasinveighedagainst hemistakeof" treatinga questionwhichbecauseof thevaguenessof languagehas no definiteansweras if it had one, or insisting hat it is adifferentquestion,one which has a definiteanswer,or insistingbecauseit hasn't a definite answerthat it isn't a question"(PhilosophyndPsycho-analysis,. 280). ButWisdomhimselfhasspokenin similarconnexionsof " questionswithout answers",and this way of speaking nvolvessuggesting hat an indefiniteanswer sn'tan answer.

WhenWisdom peaksof " questionswithoutanswers"hehasin mindquestionswhich have no straightforward,efinite,Yes-or-Noanswers.But ustasa reasoncan bea reasonwithoutbeing



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170 J. R. BAMBROUGH

either a deductivereason or an inductivereason, and just asknowledge an be knowledgewithoutbeingeither ogicalknow-ledge or empiricalknowledge,andjust as a questioncan be aquestionwithoutbeinga question hat has a definiteanswer,socan an answerbe a rightanswerwithoutbeinga straightforward,definite,Yes-or-No answer, and hence a question can be aquestion hat hasa rightanswerwithoutbeinga question hathasa straightforward,efinite,Yes-or-Noanswer.At other imesWisdomhasspokenof a questionas expressinga need,and has suggestedhat the needthat a questionexpressesis always uch hatit couldconceivably emet,even f it cannot nfact be met. Now theneedthat a questioner xpressess a needforunderstanding, nowledge, xplanation,apprehension,nsight;aneed for release romignoranceor puzzlement r perplexity; ndto meet his need, to providethe knowledgeor insightthat helacks,is to answerhis question.Sometimes childwill ask a question hat evincesa misunder-standingor confusionof whichhe is unaware:" What do cloudseat?" " Is thetreeproudof beinga tree ?" " Is Jesus he samesize as God, or slightlysmaller?" Such a questionhas to bedealtwithin a waythatthequestionerdoesnot expect. But evenwhenthe questioner'sneed is not what he thinksit is, thereisalwaysa need when there is a question,and alwayssomethingthat one coulddo to meetthatneed.And of course it is not only children,but also grown-up

children,who ask suchquestions:scientists,philosophers, oets,theologians.

It is in cases where he answer o a question akesa differentform from what the questioner xpects,andfrom whatthe formof his questionseemsto require, hat it becomes empting o saythat the questionhas no answer. But an unexpected orm ofanswers stillananswer;and one thatis calculatedo remove ust



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the perplexity that the question expresses or evinces is a rightanswer.

There will always be something available (even if it is notavailable to us) that is calculatedto remove the perplexity: and Ido not mean drugs or hypnosis or a big stick.

Finally I should like to point to a peculiar and peculiarlyinteresting difficulty that faces any philosopher who denies thethesis of this paper. It can be most sharply presented by askingthe question, " Does the question, ' Does every question have aright answer ?' have a right answer ? "

We have alreadyseen instances of the way in which scepticismdefeats itself by offering arguments and reasons for scepticalconclusions. The sceptic'svery persistencein enquiryand disputeis at odds with his suggestion that no progress can be made inenquiry and dispute. This point is especially sharp in the caseof somebody who vigorously and intelligently opposes mythesis that every question has a right answer. For he is main-taining that to the question " Does every question have a rightanswer ? " I am giving the wronganswer and he is giving therightanswer.

Now the question "Does every question have a rightanswer ? " is itself typical of the questions that can most plausiblybe offered as counter-examples to the thesis that every questionhas a right answer. Yet it would clearly be inconsistent to offerthis question itself as a counter-exampleto my thesis: for to do sowould be to claim to be giving the right answer to a question thathas no right answer. I suggest that the same inconsistency lurksnot far behind the position of anybody who produces any allegedcounter-example to my thesis. For a question is a plausiblecandidate for the r6le of counter-example only if it has theproperties of difficulty, complexity and contentiousness thatbelong also to the question " Does every question have a rightanswer ? "



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172 J. R. BAMBROUGH

At present I am content to claim that my answer to thisquestion is eitherright or wrong. But I believe that anybody whoaccepts this very modest claim will be driven to inconsistencyunless he also accepts the strongerclaim that I have been makingin this paper.



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II-RUSH RHEESAlthough Bambrough discusses only three or four sorts ofquestion, he thinks these are typical, so that what he says of themcan be extended to all questions. But I do not understand thissense of " all ".If he had taken two or three typical questions in kinetics inorder to bringout some generalfeatureof questions in this field-

or perhaps some illustrations of the kind of questions that belongto the study of history, or some typical questions in medicaldiagnosis-I could see the sense of speakingof all or most ques-tions in this particular field. But would it have sense to say"These are typical of all questions"? I do not see what" typical " would mean.There are questions or problems in mathematics, but what Imight call typical of these would not be typical of questionsoutside mathematics. And what might be typical of questionsasked in the course of preparingthe annual accounts of a businesswould not be typical of questions asked in interviewinga candi-date for a teaching post, nor of the questions a curious neighbourmay ask the housewifewho hasjust moved in, nor of the questionsof a disappointed child.Asking a question in one connexion may not be what it is inanother. I do not mean, for instance, that you have to knowsomething about a subject before you can know what questionsto ask in it. (I cannot ask questions about football if I knownothing about the game and never follow it.) I mean that askinga question-as opposed to asserting or explaining or contra-dicting, etc.-is different in mathematics and in medicine; anddifferent again in a family quarrel or in examining one'sconscience.If asking is different,answeringwill be; and also the sense of" are there unanswerable questions?" In certain cases it mayhave none. If we call problems questions (not always the otherway round, for plenty of questions are not problems) then" decision problems " in mathematicallogic might be an example.If anyone said " there are no unsolvable decision problems " noone would know what he meant. That there is sometimes aproof that the problem is unsolvable, belongs with the meaningof " decision problem ". Bambrough might say these are



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174 RUSHRHEES

technical senses of " problem " and of " solving ", outside thelimits of his thesis. But there are examples which are nottechnical and do not fall within his thesis either, as far as 1can see.

Sartre'spupil will solve his moral problem if he can come to adecision. This is why no one can solve his problem for him.If I have got lost in a problem of statistics I may ask an expertto do it for me. He may explain the reasons for the way he goesabout it, and why what I did was wrong. Sartre's pupilmay be trying to find some reasons that will make it clearwhat he must do. But whatever the role of reasons here, theyare never conclusive in the way the steps of a mathematical proofare, nor in the way in which material evidence of guilt may be,And further: what makes any circumstance or consideration a" reason " for a decision? what makes it something that weighsin favour or weighs against deciding this way? What counts asa reason in my decision, might not have weighed with you in myposition. So that the problemis generally not the same for oneperson and another.But moral problems are a mixed bag. (People are vagueabout what it includes, and some can only stare in wonder at theexamples others call typical.) In some of them reasons arerecognized in other ways and have other functions than they had,I imagine, for the man Sartre tells of.I might be wondering whether I ought to join the army, orwhether I ought to join the Communist Party, or whetherI oughtto join the Church. These are serious steps, and I may askanother's advice-especially if I keep wondering whether " inconsistency " or " if I am to be true to the principlesI recognize "I ought to act in this way or in that. He may discuss with mewhat it is that such principles require, and whether they reallyrequirethe actions I imagined they did.It is different when a woman is wondering whether to leaveher lover and return to her husband whom she does not love



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(like Sue in Hardy'sJudethe Obscure); r a man mustdecidebetweenstayingwithhiswife andgoingto pieces,or leavingherand bringingdisasterthat way. Here it is not a questionofwhatyou ought n consistencyo do.I maybe makinga mistake n decidingojoin theCommunistParty,or in decidingnot to. Butwe cannotspeakof mistakeslike this in the othercase. I mayfeel it was a terrible hingforSue to havetakenthe courseshe did (though f I do I havenotunderstoodmuch). But I could not say she missedthe rightdecisionand took thewrongone. If I tellyouI amin agreementwithall themaintenetsof communismndI do notseehowI canwithany honestystandbackand refuseto join the Party-thenyou may questionmy conclusion. But there is nothingof thisin Sue'sproblem. Her lovermightsay to her whatJudesaid;that is all. It wouldmakeno sense to ask which of themwasright.Herproblem s not of seeingwhat it is she wants,but whatshecando. Justwhat thisperplexitys, is nothinganotherper-son cangraspor do muchto imagine. It is withher thatthingsweigh as they do; and howeverdeeplyyou respectand try tounderstand erdifficulty,t is nevera difficulty ouhave. She isnot trying o findthe rightanswer. If you supposeshe is . ..youcannotsee the importance f theproblemn herlife, or howit canbring ragedy.

II

If Sartreclaimsthat it wouldhaveno senseto say the manmustindtherightanswero hismoralproblems,emakeshisplausible,Bambroughhinks,becausehe has taken a borderlinecase or a borderlinequestion--comparableo the question" Isthis man bald?" He thinks "the difficultyabout borderlinecases " is " a feature of difficult moral dilemmas ". But I donot see the analogybetween"Whatought I to do here?" and" Is this manbald?" If the questionaboutbaldness s border-line, I do not thinkthe other is.



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In this example " Is he bald?" is not a question of fact. Ofcourse I might have asked it about someone I had never seen,and then it would be. But here I am not asking you to tell meanything about him; I am asking whether " bald " is the wordyou would use here. And if you feel like shrugging your shoul-ders, this is not because you would have to examine the manmore carefully before you could say. As far as that goes I cansee him as plain as you can.But in " What ought I to do here?" the man is not undecidedabout the use of a word-as though he were not asking what todo but what to call the action before and after performing it.Bambroughthinks the trouble is in knowing where to place thisproblem among others which resemble it in different ways, andwhich are clearly not unanswerable. The man does not see inwhat respects his problem is like that other case, and where it isno longer like that and looks like this other case which he wouldanswer in the opposite way. So the problem seems to have twofaces-or ratherto fluctuate from this face to that without show-ing any of its own. But if this is a difficulty,it is not what Sartrewas talking about. As though the man were saying: " When Isee how much this is like a question of that sort, I say' yes, I mustgo '; but when I see how much it is like a question of this othersort, I say 'no, I must not go'. But . . it is not definitely ofthe one sort or of the other, so I cannot say either' yes ' or' no '."That would not be a moral difficulty-a difficult choice-at all.What makes a moral decision difficult is not that I am be-wildered by the rules or uncertainwhich rule applies here. It isthat what I have to do goes against what I feel to be deeplyimportant; I shall be doing what I feel I would give my life toavoid doing-harming those I least want to harm. The problemis difficultbecause whichevercourse I take I shall be doing some-thing for which I can never forgive myself.In any case, when I notice a resemblance between this prob-lem and those others, and when I judge the degree and the im-portance of this resemblance,I am making judgments of value-choosing a frame of reference-whose character will depend onthe moral convictions and moral feelings I have developed.Bambrough speaks of " similarity" in this connexion almost asthough it were like matching colours. He speaks of knowing"where the case lies on the manifold of actual and possiblecases ", but he says nothing of how we decide on the order of



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cases in this manifold. If I say the resemblanceto that problemis more important than the resemblance to this one-what sortof measure is this? If Bambrough says people never disagreein such judgments unless they are madmen or philosophers, heis making the circle of the brethrenvery wide.When " Is he bald?" is a borderline question I have noanswer: but not because I waver between thinking how like heis to someone obviously bald, and how like someone who isnot. Here Bambrough would agree. But why does he saythat " the case about which we ask . . . has its own place in themanifold of cases . . . the continuumof possible intermediatecases"? (" Case " is confusing here. Is it the state of theman's scalp? Or is it the grammatical form of question andanswer?)The point in speaking of a continuum of cases is to suggestthat the " cases " do not overlap: for if they did we could notsay " this case has just that place on the continuum,while thiscase has just that place " etc. And Bambrough does want tospeak in this way.I mightmake a film, or perhapsan animatedcartoon, showingsomeone gradually growing bald: a thick head of hair growingsteadily thinner on top, gradually leaving a bald spot and thebald area steadily spreading. We could draw sharp lines atvarious points in this film, but these would not correspond toour use of " thick hair", " slightly bald ", " quite bald ", etc.For these are not expressions which vaguely indicate areas thatfit end to end in a continuous transition. There could be noexperiment to find just where the condition of not being baldends and the condition of beginning to grow bald begins; wherebeginningto grow bald ends and " being somewhat bald " begins,etc. What we speak of as " beginning to grow bald " does nothave an end, in that sense, nor a beginningeither.When Bambrough speaks, for instance, of " the midpointofthe line " representing " the continuumof possible intermediatecases ", he seems to be thinking of a definite boundary distin-guishing what is borderline from what is not. But this wouldmean nothing. No more than it would if we were using anexpression such as " roughly ", " somewhere about ", "nearenough "-e.g., " This stick isn't exactly three feet long." " Well,it's near enough "-and you wanted to determine the point

N



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178 RUSH RHEES

where near-enough ends, and not-near-enough begins. (Witt-genstein would have said " we are not speaking in that geo-metry". Cf. PhilosophischeBemerkungen,pp. 263 ff.)Suppose I show the film to someone slowly and stoppingfrequently to ask " Is that beginning to go bald?", " Is thatpartly bald?" and so on. When I have stopped I sometimesstart again from a point a little further back. At one point thesubject says, " No, he is not yet beginningto go bald ", and thenwhen I show him what is in fact an earlier stage he says " Yes,now he is ". There would be no reason to say either answerwaswrong. Still less, as Bambrough suggests, that both were" definitely wrong ". (I might have said "as you like "-i.e.,there is no objection to either, and no reason to prefer either.Of course, this does not mean " it depends on whether you likeit or not ".)Obviously it would be nonsense to say that the top of his headis in an indeterminate state. And if we are puzzled by our useof the word " bald ", this is because we mix up describing thegrammar of the word with what we describe when we use theword.There is no definite answer to " How much sand does therehave to be to make a heap?" (Cf. Wittgenstein, loc. cit.). Butwe cannot say " a heap of sand is something indeterminate".It is just as determinate as a mountain is. If the question " Isit a heap now?" leads sometimes to apparently contradictoryanswers although we would not say either was wrong, we do notconclude that we are dealing with a physical object which mayhave contradictoryproperties.We do not use the word" heap " or the expression " heap ofsand " as we use " cord of wood " for instance. But this doesnot mean that a heap of sand is " something of a different cate-gory " from a cord of wood.It is important to emphasize that there are expressions ofthis sort-for which sometimes the question " Is this one?" isundecided; and emphasize that this is a property of theexpressions we are using. We may imagine a use of the ex-pression " number " with similar properties. If we say that inthis use of " number" there is no law of excluded middle, weare not calling attention to a special property of certainnumbers-understanding the word now in the sense or sensesgenerally recognized.



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III

In somewaystheproblemof the heap s likeproblemsaboutcontinuousmotion, such as " Can we say that a movingbodyoccupiesa definiteplaceat anytimeduringtsmotion?"," Whena billiardball rolls acrossthe table, is its motion one or many(simple or composite)?","Is everythingwe call continuousmotionreallydiscontinuous?".The difficulties boutcontinuity omewhen we tryto explainit by some form of discontinuity;when we may want to ask" How many?" " Continuity" is used differently n mathe-maticsand outsidemathematics. I do not meanthatthere aretwo kinds of continuity-mathematical continuity and non-mathematicalontinuity. Butif there s a propositionn mathe-maticsthat such-and-such curve s continuous, hen in mathe-maticsthis is eitherpostulatedorproved. Outsidemathematics,in experience,we never prove that somethingis continuous,althoughwe have ways of findingout whetherit is or not.Whereasin mathematicswe never find out that something scontinuous. The aim of the mathematicalheory is to con-struct a conceptof continuity. And this does not presentdiffi-culties of the sort I mentioned. These come when we try tounderstand the use of the word " continuity ", and especiallywhen we try to understandhow it is connectedwith " discon-tinuity ".

(What I say about continuityin these twelve paragraphscomes from conversationswith Wittgenstein-and may welldistort deaswhichwenttogetherwithothers.)Anythingonemightcall a theoryof continuousmotionwouldtryto explain t by a formof discontinuity. Butthiscould meantwo entirelydifferenthings.We could imaginea theoryin physics, explainingwhat wenow call continuousmotion by means of discontinuouspro-cesses. This might be somethingroughly analogous to theinvestigationof eventson a cinema screenby peoplewho didnot know theircauses:theydiscover he filmandthe projector,andtheyfindthat whattheyhadsupposedo bemovingshadowsis in fact a rapid successionof discretestationaryshadows.Imaginethat the physicalinvestigationenabledus to observediscontinuoushappeningswhich showedthat what appearsto

N2



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180 RUSHRHEES

be a continuous movement in 3-dimensional space is really asuccession of discrete positions.This might be a working hypothesis which we do not extendbeyond special cases. Or on the other hand we might decide toextend the theory to apply not only to those forms of continuousmotion for which it had been clearly established, and say that allmotion is really discontinuous.Now obviously the results of our experiments would notshow that we were making a mistake if we went on distinguishingbetween a continuous change of place and a discontinuouschange of place as we always had done. If I have been followingthe experiments and if I think them very important I may saythat the older way of speaking was inexact, and that it would bemore accurate to distinguish between the type of discontinuityin the one case and in the other. Or I may not say this. Theexperiments have established a connexion between certaincontinuous movements and certain discontinuous processes;and under the special conditions of the experiments, the con-tinuous motion may appear as discontinuous. But theexperiments do not show that any of these happenings is what" really " happens.So if we have wondered whether perhaps all change of placeis really discontinuous, no physical investigation could showwhat the right answer is. This does not mean I am sceptical-that I doubt, say, whether experimental methods can yield anyconclusions.

On the other hand, we might want to give a theory of con-tinuous motion in a different sense, and say that all continuityis a form of discontinuity. This would not be like a physicaltheory or hypothesis of a discontinuity behind the phenomenon.It would be saying that in its essence the continuity of motionmust be a form of discontinuity-" as it were, continuousdiscontinuity ".We may put the question in the form: " Is continuous motionone or many?" And this is like asking, " Is a curve, say a circle,one or does it have parts? " I might say, " Tell me firstwhat youwould call a ' part ' here?" (as in other connexions " Well, whatwould be needed to show you that it was composite?" Investi-gations, ?47.) If we do not know what would distinguish onepart from another, how should we know what anyone was



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saying if he said that it has parts or that it has none? But some-times people will answeras if this made no difference-as thoughit were not that kind of question--and say " Obviously the circleconsists of parts ", or " Obviously the circle is one, there are noparts." If we asked the first man what the parts of the circleare, he might point to certain sectors; and when we asked himwhy just those sectors, since the circle could be divided in otherways, he might say finally that it consists of points. And if weasked the other man why he said there are no parts, he might saysomething like " Well, there are no sides to a circle." But thesewould be after-thoughts,and not what led them to say what theydid.Neither answer is an empirical statement-the two partiesmay agree on all questions of experience. " There are no partsto a circle " is not a statement describing something called a" circle ". We might say ratherthat it describes our idea of theword, or that it describes the image which at the moment sumsup for us the use of the word " circle ". It is not exactly agrammatical rule. But it is the sort of expression which Witt-genstein called " pre-lingual" or " a preparationfor language ".It is what I might say if I asked myself " Now how do I meanthat?" And if I said, " for us the circle is one ", " The circle isa unity shape, namely this: O ", " Circularity has no parts "," It cannot have sense to speak of parts of a circle, only of partsof a circular object ", " the circle is always undivided"-innone of these sentences should I be usingthe word " circle ".I might also have said " It is the essence of the circularshapethat it is one and undivided." Which amounts to: " This ishow we must imagine it."In the same way we might answer " Clearly a continuousmotion consists of parts ". And if someone asked what theparts of a continuous motion are, we might refer to earlier andlater parts; and then, to make sure of having parts that do notoverlap,wemightsaythatmotionconsists of points orpositions.Or we might have said, " Clearly it is all one motion ". Theanswer we give will depend on the connexions in which motioninterests us: the circumstances in which we most commonly askabout and speak about the motions of bodies. When a physicistdetermines the velocity of a motion, he depends on measurementsof distances and times. He must know where the body is at aparticular moment. He might say all that interests him (or all



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that matters)in the motion of a body is that it is in those positionsat those times. The motion must include a number of positionsanyway. And it would probably seem stupid to say that themotion was partly positions and partly something else. So he isinclined to say that the continuous motion from A to B is thebody's passing through all the positions betweenA and B. Thisis not a proposition of which he makes any use in physics. Butin spite of its obscurities-the use of " all" in " all the posi-tions ", for instance-it may provide a picture which sums upthe way he looks at motion; and this may influence the notationin which he writes and speaks of it.There are other considerations inside and outside physicswhich make people inclined to say motion consists of positions.But you would not be inclined to say this if you were watchingthe movements of a ballet dancer or studying the movements ofanimals. When you admire a particularlywonderful movementby the dancer . . . " being in those places at those times: is thatwhat makes it that movement?" It is only by recognizing it asa single movement-as one-that you can see what it is. Icould never tell you what movement she had made, by speakingof component parts and their relations to one another.

I suggested that " In essence the continuity of a motion isthat of a sequence of positions " is a way of saying: " This is howwe must imagine it ". We might call this an expression ofprejudice,and so a mistake. A curious kind of mistake, in someways: about what is " possible" or "thinkable ". And suchmistakes do not show that " the right answer to the question"would mean anything.(" Prejudice" fits ill, since it suggests " superficial" or"without much thought behind it ". And the statement givingthe essence of something may be anything but that. Perhapsthis is plainer when we reflect that what begins as a scientifichypothesis or scientific law may come to be regardedmore and more as an expression of essence: almost as definingwhat it appliesto. The history of laws of motion might illustratethis; or laws in the theory of gases. Or we might say now thatgeneral principles of scientific investigation form the conceptsof our thinking-or of the way we think-about the world:determining,for us, what can be imagined or what no one could



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seriously imagine. " Stating the essence of so-and-so " mayshow or express ways of speaking that have taken deep hold onus-i.e., that go through almost everythingwe do in our lives.)

IV

Bambrough says that " the language of spatial location . . .may be extended in such a way as to provide a useful analogy forlogical space, and hence for the whole nature of reasoning andclassification."But he has made the extension the opposite way. He thinksof spatial location in analogy with position in logical space; andhe has little to say about the kinds of reasoning that go withlocating bodies in space.I suppose he takes " logical space " as the expression is usedin the Tractatus-where a place in logical space is like a placein a system of co-ordinates, i.e., a geometricalplace. This is thesense of Tractatus 3.4 and the three remarks which follow it.In 3.0321 Wittgenstein had emphasized the distinction betweenwhat is geometrically possible and what is physically possible.An occurrenceis physically possible if, according to the observa-tions we have made, its occurrence would be consistent withestablished laws of physics. The question " Where is that bodynow?" would generally mean " Which among the positions itmight be in now . . .?", i.e., positions physically possible for it,not just geometrically possible. Obviously the "now" isimportant, but so are other physical data.In geometry the question "where?" is like other questionsin mathematics. " Where is the highest point in this curve?"asks you to calculate or construct the highest point in the curve.(Cf. PhilosophischeBemerkungen,p. 209.) There would be nodifference between explaining or describingthe construction andcarrying it out. Or we might say roughly that in geometry thereis no difference between explaining how to find the point andfinding it. To ask " Where is the highest point of the arch ofthis doorway?" would be another sort of question, and theanswer would not make sense in geometry.



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I should think it nonsense to say that " something can existin " a geometrical place-I should wonder what sort of " can "that is, for one thing-although of course co-ordinate geometryis an important part of the phraseologyin which we speak of theplace of a physical body.In most physics, I should have thought, the question " Whereis such-and-sucha body?" would have no sense unless we knewthe methods of measurement assumed by the person who askedit. These go with the meaning of " the place where the bodyis ". We may say if we like that to understand the question wemust know the methods to be used in finding an answer. Buthere of course explainingin detail how to carry out the measure-ments would not be the same as carryingthem out.

Bambrough seems to confuse two questions:(1) What do we regardas the markswhich define a particularplace?(2) How do we decide whether a body is in that place or insome other?He says that " if I ask you where something is in space, youcan answer my question only by referring to the position ofsomething else in space ". This suggests that " where is it?"can be answered always in the same way: that " giving theplace or the position " has always the same sense. But think ofthe phrase " the position of a moving body at a particulartime ",for instance. If you ask me whetherthe billiard ball now moving

across the table is in any position while it is moving, I could sayyes, because it is roughly there now, and roughly there now.And if it is roughly somewhere now, it must also be exactlysomewhere now. But the trouble is that I could have said thesame thing, apparently,-" it is roughly there now "-if I hadbeen referringto a body at rest in this area. And if it does meanthe same, then when I pass from " it is roughly there" to " it isthere" I give it a place which it cannot have and still be moving.A physicist does not want to know when the body is roughlytherebut when it is exactly there in the course of its motion. So hedoes not mean by " the positions of the moving body " what Imeant when I first spoke of the positions of the moving billiardball. He means something new, which he expresses by " it ispassing through this position ". And this does not fit Bam-brough's formulation.



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Bambrough says nothing about alternative frames of refer-ence in describing the positions and movements of bodies. Butneither does he speak of the " procedures for determining thelocation of an object " when we have conflictinganswers to thequestion " where?" I give a statement of where Land's End isthat conflicts with your statement. Or you say the train is atthat point now, and I say it is somewhere else. If we try todecide this, then part of what we do will probably be to look andsee where certain things are (perhaps not the object in question,but others whose positions we must know if we are to say wherethat is). And here " where they are" does not refer to theposition of something else in space.Suppose you are pointing to the ash tree because you want totell me where you left the mower: " A little to the right of thattree and 10 yards further on." I am looking at the tree to whichyou are pointing and I say " But where is that tree?" Why isthis nonsensical?You might say " Why it's right there where you see it." Butthen you are not saying where it is in relation to anything else.When I go to work some men from the Gas Board are tryingto find where the leak in the gas main is. I come back duringtheir dinner hour and I ask "Well, where was it?" They takeme along to show me. " It was just there." Is there anythingrelativeabout this?I know what it means for a tree or a rock to be "there" or" here ". These are primitive starting points for our ideas of" being somewhere "-the differencebetween being in one placeand being in another-making it possible for concepts of locationto come into what we say and ask about things.I should think it obvious that they are prior to saying wheresomething is by referringto the position of something else. IfBambrough wants to say that I am introducing a different senseof " where "-he will have gone far to agreewith me.When Bambroughspeaks of positions, he is generallythinking

of maps and geography: what we might call " the relations ofdifferent places to one another ". But this leaves out a greatdeal. I may ask whether a particularroad or river is where thismap says it is-whether it is further from the coast than thatpond is, etc. But this is not like trying to determine theposition of a body which is sometimes in one place, sometimes



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in another. If I were misled about this, it would not be amistake in geography." I know the river runs near to the north side of the churc

unanswerable questions

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