fullerton - kantian doctrine of space i

7/28/2019 Fullerton - Kantian Doctrine of Space I

1/12

Philosophical Review

The Doctrine of Space and Time: I. The Kantian Doctrine of SpaceAuthor(s): George Stuart FullertonSource: The Philosophical Review, Vol. 10, No. 2 (Mar., 1901), pp. 113-123Published by: Duke University Press on behalf of Philosophical ReviewStable URL: http://www.jstor.org/stable/2176506

Accessed: 17/12/2010 05:56

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless

you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you

may use content in the JSTOR archive only for your personal, non-commercial use.

Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at

http://www.jstor.org/action/showPublisher?publisherCode=duke.

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed

page of such transmission.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

Duke University Press and Philosophical Review are collaborating with JSTOR to digitize, preserve and extend

access to The Philosophical Review.

http://www.jstor.org
http://www.jstor.org/action/showPublisher?publisherCode=dukehttp://www.jstor.org/action/showPublisher?publisherCode=philreviewhttp://www.jstor.org/stable/2176506?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/action/showPublisher?publisherCode=dukehttp://www.jstor.org/action/showPublisher?publisherCode=dukehttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/2176506?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=philreviewhttp://www.jstor.org/action/showPublisher?publisherCode=duke


2/12

VolumeX. March, 1901. WholeNumber . Number 6.

THEPHILOSOPHICAL REVIEW.

THE DOCTRINE OF SPACE AND TIME.I. THE KANTIAN DOCTRINE OF SPACE.1

THE plainman s apt to think f space as a real somethingbeyondconsciousness, n which the material thingswhichhe sees and feels exist and move. A littlequestioningrevealsclearlythat,concerning he natureof thissomething, e has thevaguest deas. It is not matter, nd it is not like matter; but itundoubtedlyxists,and it is plainly ndispensable o the existenceof material hings. He hesitatesto affirm hat it mayproperlybe called a ' thing' at all; but, thing' or not,he is sure that texists,and believesthat t would continue o exist even if everymaterial hingwereannihilated.Touchingsome oftheproperties fthisperplexing omething,however,he regards himself s having verydefinite its of in-formation. Space is three-dimensional; t ishomogeneous n allitsparts; it is infiniten extent; everyportion of it is infinitelydivisible. It is, in otherwords, n infiniteontinuum,hichmustbe grantedreal existence f theworld of matter s to be allowedany reality t all, and is not to be reduced to a mere semblanceof a world,an unrealdream.We shall see later that there s muchtruth, s well as somemisconception,n theplain man's views touching the nature ofspace. One thingwe may object to at theoutset, nd thatis the

' A portionf thispaperwas read atthemeetingf theAmerican sychological s-sociation eld in BaltimorenDecember, 9oo.


3/12

114 T HE PHILOSOPHICAL REVIEW. [VOL. X.assumption hat pace is a something uite beyondconsciousness,and, hence,quitecut off, s reflectionhowsthatall such thingsmustbe, from hesphereof ourknowledge. We would do thegeometer ittlegood bygranting im,as thesphere in which heis to exercisehis activity, n unknowable,unredeemedby eventhe gleams of meaning whichare usuallyinvoluntarilyllottedto unknowables. The plain man stands, as I have in earlierpaperspointedout, upon thepsychologicalstandpoint,ssumingan externalworld whollycut offfromhis knowledge, nd yetsomehowknownto him. He has graspeddimly he distinctionof subjective nd objective, nd he expresses himself nconsist-ently. He mustnotbe takenwholly t his word. But so muchhas been said ontheabsurdity fassuminga worldwhollybeyondconsciousnessand not madeof ' consciousness-stuff,'hat shallassume thatthere re a considerablenumberof those interestedin philosophywho are agreed upon thispointat least. It is tothesethat I shall speak in this series of paperson space andtime.I propose to examine as brieflys I may,the two leadingformsof doctrinewhich have been advanced in moderntimestouchingthe natureofspace and time, nd which o thisdaydis-pute thefieldbetween hem. These I shall call the Kantian andthe Berkeleian,using these appellationsin rather broad senseto indicate ypesofdoctrine, nd withoutmeaning o makeeitherphilosopher esponsible or ater dditions o,or alterationsn thestructurewhichhe reareduponthefoundationshathehimselfaiddown. Neitherdoctrine uitefalls ntothevulgarerrorofmak-ing space and time 'things,' and neither egards themas 'ex-ternal' in thepeculiarsense of thewordto which have alludedabove. In both doctrines pace and timeare treated s 'form'and not as ' matter,' . e., as the arrangement,he systemof re-lations,whichobtainsbetween ertain ontents f consciousness,and not as those contents hemselves. The two doctrineshavea good deal in common,but theyare, nevertheless,marked bydifferencesf no small importance;and the one whichhas hadthemoregeneral acceptanceprecipitates ts adherents ntodiffi-culties o greatand so hopelessthat tseemssurprising hatthey


4/12

No. 2.] THE DOCTRINE OF SPACE AND TIME. II5have not incited o a morewide-spread isaffectionnd a finalre-volt. This doctrine s the Kantian,and to it we will now turnour attention.We will first ake up Space. According to theKantian doc-trine, ur knowledgeof space is not a something t which we ar-rive as the resultof an elaborationof our experiences. Space isnot a construct orwhich our original xperiencesmerely urnishthe data. It is thenecessary 'form' of the intuitionsf theex-ternal ense, nd is givencomplete nevery uch intuition. Kantheld that: (I) Space is a necessaryform' of thought,and,hence,we cannotconceivethe possibility f the non-existence fspace, although we can easily conceive of the non-existenceofobjects n space; (2) we can represento ourselves but one space,of which all spaces are parts; fromwhich it followsthat spacecannot be conceived as limited; (3) all space is composed ofspaces, that is, space is infinitelyivisible,and that which fillsspace, the ' thing' given n sense-intuition, ust be infinitelyi-visibletoo.'In criticisinghe Kantiandoctrine,t snecessary o distinguishclearlybetweenwhatmaybe implied n regarding pace simplyas the 'form' of certain intuitivexperiences-as the 'formal'elementwhich,n unionwith the ' material' element, onstitutestheseexperiences-and whatmaybe supposed to followfrom heassumptionthatspace is a necessaryform'of thought, f sucha nature hat we are compelledtothink pace as infinite,nfinitelydivisible, nd incapable of being thoughtas non-existent. Tomake this distinctionlear, will take a concrete nstance. Inlookingat the tablebeforeme, I am conscious of a complex ofcolor-sensations. This Kant would have called a 'manifoldofsense.' In this complex I can distinguish etween form' and'matter,' . e., between sensational elementsand theirarrange-ment. I may regard the 'form' in my complex as somethingequally originalwiththe ' matter,' nd, if choose,mayattemptto account for it by saying that it is due to the nature of themind-that in thiswayand in no othermustthemind rrange ts

1Critique f Pure Reason,Transcendental sthetic, 2, 3, and 4; AntinomiesI and II, andObservations.


5/12

I6 THE PHILOSOPHICAL REVIEW. [VOL. X.sensationsof color. Bearing nmind what psychologiststell usabout the importance f sensationsof touch and movement, ndthe way n whichother ensations ome to stand as signsof these,we mayamendthe above by remarking hat we are reallycon-cerned with tactual thingforwhichthe visual complex underdiscussion tands s a sign; butthatwill not affect hedistinctionwhich has been drawn between form'and ' matter.' We stillhave to do with complex in which the two elements are dis-tinguishable, nd we should not forget ust what we mean by'form' when we are drawing the distinction. It is nothingoccult or mysterious. It is a certain lement n a given experi-enced content, nd nothing lse. In thegiven nstance, t is thearrangement f the tactual sensations which we have in mindwhen we say thatwe see the table.'But thespace givenus in such an intuition s limited. It iscoextensivewith the ' matter' of which t is the form,'and isnot a somethingwhich extendsbeyond t. It is limited becausethewhole complex is limited, nd, udging from this experiencealone, there appears to be no more reason forassumingtheformal lementto be infinitelyxtended than for assuming thematerial o be so. If I were intuitivelyonsciousof an infiniteextentof color (or tactual) sensation, should have an intuitionof infinitepace (theformal lement n thisexperience), orboth'form' and 'matter would be limitless. Or if, failingthis,were consciousofa certain imited mountofcolor sensation, ndwere,further,mmediatelyonsciousof a boundlessspace extend-ing from helimitsof thebitof space filledby the sensation as-suming that one maybe conscious of pure space), then, too, Ishould have an intuition f infinitepace. But to extract n in-tuition f infinitepace from hepatchof sensationwithwhichstarted ut is an impossibility. I can succeed indoingso onlyby

1It will be seen that treat form and ' matter as irreducible lements, sdoes theKantian. The bestargumentor heopposite iewthat know s containedin Professor ames's PsychologyChap. XX, pp. i49-i52), but I do not find twholly onvincing. I wish,however, o pointout thatthe argument ontained nthesepapers n no wisehingesupon the decisiongivento this question. Whether' form'be ultimatelyistinct rom,r identicalwith ensation,s somethingne mayleave undecidedwhile followingmy rgument.


6/12

No. 2.] iHE DOCTRINE OF SPACE AND TIME. II7juggling with the word ' intuition.' The statement that infinitespace is given in intuition is palpably absurd, when the word in-tuition is taken in its strict sense. It does not mean that we havereason to believe that space is infinite, nor that we are forced tothink that space is infinite. It means that we are immediatelyconscious of every part of space, as I am conscious of the bit ofspace within the limits of this patch of sensation. Can anyoneseriously maintain so absurd a doctrine ?

It may, however, be maintained that we have an intuitiveknowledge of infinite space in a somewhat different sense of theword 'intuitive.' That is, it may be held that we know in-tuitivelythat space is infinite. This does notmean that we areimmediatelyonsciousof nfinitepace, butmerely hat we knowspace to be infinite,nd know it withoutbeing compelled toprove it in any way. It is a ' necessity f thought.' An inter-estingchaptermightbe written n what have commendedthem-selves to thephilosophersofpast ages as necessities of thought,revelations f the inner ight, tc., etc. But I leave thistempt-ing subject,and content myselfwith pointing out that it is acounsel of prudence to be oracular regardingnecessities ofthought, nd to advance themwithoutattempting o provethatthey mustbe acceptedas such. Those who have attemptedtoprove thatwe mustaccepttheinfinityf space as a necessityofthought, r as an intuitionn the second sense of theword,haveoffered ighlydefective vidence of the fact. "We are," saysHamilton, "altogether unable to conceive space as bounded-as finite: that is, as a whole beyond which there is nofurther pace." ' "We find ourselves," echoes Mr. HerbertSpencer, "totally unableto imaginebounds beyondwhich thereis no space." 2 It is inferredromhis hatwe must hink fspaceas infinite.But what is it that these philosophershave invitedus to at-tempt? When scrutinized, amilton's argument s seen to benothingmorenor less thanthis: We are altogetherunable toconceivespace as bounded-as finite;that s, as a whole in the

I ectures nMetaphysics,XXVIII.2First Principles, III, Z 15


7/12

II8 THE PHILOSOPHICAL REVIEW. [VOL. X.space beyondwhich here s no further pace The word beyondin his argumenthas no meaningwhatever xcept as it refers ospace beyond,and Hamilton has simplyset up a contradictionforus to tilt t. He asks us to imaginea limit,with a space be-yond it,and at the same time no space beyond it. When wehave had a 'go' at this, nd feel ow-spirited ver the result,hetells us with n air of mystery hat we are in the clutches of a'necessity of thought.' Whatever may be said for or againstthe necessityof thinking pace as infinite,t is clear that thisdemonstrations a merequibble. It has been, however, verypopular quibble.The doctrinethat space is a necessity f thought in such asense that, lthoughwe can annihilaten thought all objects inspace, we cannot conceivethenon-existence f space itself-thisdoctrinerests upon a similarmisconception. There seems noreasonat all why, f by space given in intuitionwe mean onlythe formal lement n a givensensationalexperience,we shouldnot be able to think away the space withthe 'matter'of whichit is the ' form.' But we mustnot set ourselvesa contradictorytask, and erecta theory verour failure o accomplish t. " Wecan never represent o ourselves the non-existenceof space,"says Kant, " althoughwe can easily conceive that there are noobjects in space."' But what does one do when one triesto im-agine thenon-existence f space ? One first lears space of ob-jects, and thenone tries o clearspace of space in somewhatthesame way. We try to ' thinkspace away' as we express it,which does not mean thatwe turn ll thoughtof space out ofour mind,but that we try o think t away as we have thoughtobjects away, by clearingit away fromsomething, nd havingthatsomething eft. The attemptmust,ofcourse,fail; but thenit is foolish o make theattempt. That this swhat s commonlyattempted thinkcertain. It is whatI did,with good deal ofsatisfaction o myself,duringthe years when Kant's positionseemed to me well taken,and it is whatI have an impulseto do

1Critip~eof Pure Reason, TranscendentalEsthetic, 2: "Man kann sichniemals ineVorstellungavonmachen,dasskein Raumsei, ob man ich gleichganzwohldenkenkann,dasskeine Gegenstinde arin ngetroffenerden."


8/12

No. 2.] TSEE DOCTRINE OF SPACE AND TIME. lignow when I read the above-cited sentence from the Critique.So far s I can learnfrom heir wn accountsoftheir xperience,it is what otherstryto do when they find t impossible to thinkspace as non-existent. They tryto annihilate space, and yetkeep inmind, o to speak, the place where t was. They trytomake a Vorstellungf the non-existence f space, i. e., to keepbefore he mind ome intuition f the external ense, and yet an-nihilate ts 'form,' which is manifestlyelf-contradictory.Wehave here one of the countless instances f what may be called' the philosophic fallacy' par excellence. It is the especialweakness of the philosopherto say " I go," and then not go;to set about abstractingfrom omething, nd then not abstractfrom t; to offer o clearthe ground, nd then to leave an arrayof stumpswhich musttripup the feetof the unwary.The deductionswhich have been made from hesesupposednecessities f thoughtare rather startling, nd should in them-selves, I think, e sufficiento arouse a suspicionof thefounda-tionsupon which they rest. In the proofof the Antithesis fhis famousFirstAntinomy, antoffersn a priori demonstrationthat the sensibleworld mustbe conceivedof as unlimitedn ex-tent. To be sure,he also offerswhat he regardsas an equallysatisfactory roof f the contradictory roposition;but as readersof Kant know,this does not mean that he believeshis argumentto be defective. The argumentfor the infinitudef the sensibleworld,whichhe bringsforward s logically unexceptionable,sas follows:Space is infinite; ence the sensibleworld, f t be limited,mustlie in theinfiniteoid. But space is not an object; it is only the'form' of possible objects. Hence space may be limitedbyphenomena,but phenomena can not be limitedby an emptyspace beyondthem. It is, therefore,mpossible hata void spaceshould projectbeyondthe limits fa finiteworldof sense. Thespace beyond any given limitmust, hen,befilled space, and wemust conceiveofthe sensible worldas infiniten extent.It is clear that n this rgumentKant playsfast nd loose withthe reality fspace. He seems to make it a thing, r somethinglike a thing, nd yet not precisely thing. We have seen that


9/12

120 THE PHILOSOPHICAL REVIEW. [VOL. X.he regards t as real enough to persist in remainingwhen wethink way all objects n it. Here we see that he regards t asreal enough to be limited by phenomena, f it be a space withinthe worldof sense, but not as real enoughto limit henomenabyextending beyond. His argument s, in effect: Space is infinite(assumed as an intuitionn thesecond sense of the word); it isnot enoughofa thingto existby itself; t must, hen,be filled nwith something; this something must be infinite s space is;ergo, he world s unlimited. These are scholastic subtleties, ndit seems odd to me, at least, hatthey hould havebeenadvancedby so acute a thinker s Kant; and yet these reasonings eem toappeal to some vigorous mindseven in our day.It is always safe to be on one's guard against so-called ne-cessitiesof thoughtand the deductions which are drawnfromthem. Those who have electedto regard space as a ' necessaryform' of external intuition, r as a ' necessity f thought,'mayeasily be misled by these phrases into accepting s self-evidentwhat is not merely not self-evident,ut is even founded uponvery questionable reasonings. There is, to be sure, no doubtthat the statement hatspace is infiniteeems to be a reasonableone even to themanwho regards it as by no means certain hatthe universe f matter s infinite. What we mean by the state-ment that space is infinite,nd why it commends itself as areasonable one, I shall tryto make clear later. We shall seethat,to explain this general readiness o regard space as infinite,we are not forced o fall back upon such quibbles as the impos-sibility f thinking space beyond whichthere is no space, orthe impossibilityf magining henon-existence fspace.So much forour intuitiveknowledgeof space as infinitendindestructible.' Intuitions f this kind are no better thanthefateful orse whichbroughtruinto Troy. They maybe had asa gift, nd theyare big with disaster to those who receivethem.But if we confine urselvesto intuitionsn the first ense of theword, maywe notescape such difficulties? In the table whichI perceive beforeme, I distinguishmatter' and 'form.' The'form -the systemof relations-is as immediately ivenas theMatterr' In holding thatsome space, at least, s directly iven


10/12

No. 2.] THE DOCTRINE 0F SPACE AND TIME. 121in intuitionwe do not,hence,seem to be jugglingwiththewordor using it in an ambiguoussense.

But when we examinemorenarrowlywhat s implied n suchan intuition fspace,we are at once confronted ith ertain ener-able difficultieshat have exercised the ingenuity f mankindalmostfrom hebeginning f reflectivehought. Space we re-gard as infinitelyivisible. Everyspace, howeversmall,must,then,be madeup ofspaces,neverofpoints. It follows hat whatfills pace mustalso be infinitelyivisible. Thus every intuitionof the external ense' mustbe infinitelyivisible. It cannot bedenied thatwhen we divide up into its parts any given sense-experience,we speedily come to what appears to be no longercomposite. A line perceived by sight,forexample, does notappear to be composed of an infinite umber of line-portions.Subdivision eems o result n visualpointsnotcomposedofparts.The minimumensible, s it has been called, is not directly er-ceived to have partout ofpart.So much is admitted venbythose who maintain hatwe havean intuition f space as infinitelyivisible. The minimumensi-bledoes not present tself n consciousness s "' a manifoldwithits parts externalto each other." But, says Kant, "since wecannot reasonfrom he non-consciousness f such a manifold othe absolute impossibilityf its existencein any intuition f anobject, and since it is the latter hat s necessary o absolute sim-plicity, tfollows hatthiscannot be inferredrom nyperceptionwhatever." Here Kant has evidently allenback upon the sec-ond sense ofthewordintuition,venwhilediscussing ntuitionnthe first ense. We are not directly onscious of an experienceas infinitelyivisible, ut it is assumedthatwe have an intuitionof the fact hat it is so. As in the case of the infinitextent ofspace, so in the case of its infiniteivisibility,he statementhatsomething s given in intuition mountsonly to saying that weknowthisor that about something. We may well pause beforeacceptingas an indubitable eliverance f consciousness such asupposedbit ofknowledge; we certainlyeem justifiedn askinghowwe knowthatour experiencesofextension re thus infinitely

1 Qpcit.,SecondAntinomy,ntithesis.


11/12

122 THE PHILOSOPHICAL REVIEW. [VOL. X.divisible. If we do not immediately erceive hem o be infinitelydivisible,does not our conviction estupon an inference f somesort? How shall such an inference e justifiedOf course, somethingmaybe said forKant's statement hatwe cannotreasonfrom henon-consciousness f a ' manifold' tothe impossibilityf its existence in a given intuition, rovidedthat his words be understoodwith certain imitation. Somethings xist in consciousness clearlyand definitely,nd of somewe are very ndefinitelyonscious. It is quite conceivablethat agiven content of consciousnessmay be composite, nd yet maynot be recognized s such. But it is one thing o affirmhat anexperience n whichwe do not seem to be able to perceivepartout of part may reallyconsist of parts; and it is quite anotherthing to affirmhat it must consist of such parts, nd that theparts of which t consistsmust n their urnbe composite, nd soon, ad infinitum. The last statements an exceedingly old one,and should not be allowed to pass without demand forproofofsome sort. Shall we accept it as true merelybecause we aretold that t is a ' necessity fthought'?That Kant didnotappeal to intuition,n the first ense of theword,he has himselfmade evident. "' Against the principle fthe infiniteivisibilityf matter,"he writes, "whose groundofproof s purely mathematical, he monadists bring objections,which ay themselves pen to suspicionfromthe mere factthattheydo notadmit theclearestmathematical roofs s giving ninsight ntothe constitutionfspace, in so far s this s really heformal ondition f thepossibility fall matter. . . Ifwe listento them we shall have to conceive,not merely he mathematicalpoint-which, though imple, s not a partbut onlythe limit f aspace-but also physical points,which are likewisesimple,buthave the advantage, s parts of space, of filling pace by theirmereaggregation. I shall nothererepeat he common and clearrefutationsfthis bsurdity, hich xist nplenty; for t is whollyin vain to tryto quibble away the evidenceof mathematicsbymeans of merelydiscursiveconceptions. I will only remark,that fphilosophyhere falls ntochicaneryn dealingwithmathe-

1 Op cit.,SecondAntinomy,bservationsn the Antithesis.


12/12

No. 2.] THE DlOC TRINE OF SPACE AND TIME. I23matics, t is because it forgets hat in this questionone is con-cerned only with phenomena nd their conditions. It is notenough to find or he pureconceptionf the composite he con-ceptionofthesimple; forthe intuitionf the composite matter)one must find heintuition f the simple. This is by the laws ofour sensibility,nd, hence, n the case of objectsof our senses,wholly mpossible."Here Kant takes a double position, f may so express t. Inthe closingwordsof the extracthe falls back upon the assertionthat the " laws of our sensibility make it impossible that theabsolutely simple should be given in intuition. That is, hesimply nvokesthe magic of an ' intuition' in the second senseof the word. But he has admitted, s we have seen, that thesimple may apparently e given in intuition. He accepts theminimumensible ecognizedby Berkeleyand Hume beforehim,merelyarguingthat mathematics urnishes roof that this s afalseand deceitfulminimum, compositemasquerading in theattire fsimplicity. Kant thus maintains: (i) That what s givenin intuitionmustbe composite,for,by the law of our sensibility,nothing an be given n intuition hat is not composite-whichstatement,f we accept it as true,oughtto close the whole ques-tion; and (2) he argues that it is subversive f mathematics odenytheinfiniteivisibilityf what s given n intuition. Thesepositionsmaybe met by maintaining: (i) That the statementthat t is a law of our sensibilityhat thesimplecannot be givenin intuitions either baseless assumption,r it is based'upon themathematical easonings o whichKant refers; and (2) that theopposingdoctrines seen to be byno means subversive f mathe-maticalreasonings,whentheir ignificances clearlyunderstood.What maybe said upon these points will be considered later.Beforepassingon to this I wish to make clear the difficultiesabove alluded to,which ttachto theKantiandoctrine,ndwhichshould be honestly aced by thosewho elect to become its ad-herents. It willnot do to give them a perfunctorylance, callthem ogical puzzles, and straightwayorget hem. As we shallsee, theyare deserving fmost serious consideration.

GEORGE STUART FULLERTON.UNIVERSITY OF PENNSYLVANIA.

fullerton - kantian doctrine of space i

Documents