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Helmholtz's Zeichentheorie and Schlick's Allgemeine Erkenntnislehre: Early Logical Empiricism and Its Nineteenth-Century Background Author(s): Michael Friedman Source: Philosophical Topics, Vol. 25, No. 2, Analytic Philosophy (FALL 1997), pp. 19-50 Published by: University of Arkansas Press Stable URL: http://www.jstor.org/stable/43154262 Accessed: 16-11-2015 10:35 UTC

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This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions PHILOSOPHICALTOPICS VOL.25, NO. 2 FALL1997

Helmholtz' s Zeichentheorie and

Schlick's Allgemeine Erkenntnislehre:

Early Logical Empiricism and Its

Nineteenth-Century Background1

Michael Friedman IndianaUniversity

Theyear 1921 marked the one-hundredth anniversary ofthe birth of Hermann vonHelmholtz, one of the most remarkable minds of his era, who made fun- damentalcontributions toenergetics, physiological psychology, the founda- tionsof geometry,electrodynamics, and epistemology.In philosophy,in particular,he becameidentified as a leaderof the scientifically oriented "back to Kant!" movementand, as such,has a claimto be one of theprincipal foundersof the discipline we nowcall philosophyof science.2 When he died in 1894 Helmholtzwas universallyrecognized as thegreatest German sci- entificthinker of the nineteenth century. It is no wonder,then, that the cen- tenaryyear 1921 was distinguishedby a varietyof memorial lectures, journal issues,monographs, and thelike,3 including a collectionof Helmholtz's EpistemologicalWritings edited by MoritzSchlick and thephysicist Paul Hertz.4Schlick himself was thenidentified as perhapsthe most important of thesmall group of scientificallyminded philosophers inspired by the revo- lutionaryimport of Einstein'stheory of relativity.He hadpublished a sub- 5 stantialpaper on thespecial theory of relativityin 1915, followedby an

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions extremelyinfluential exposition of thegeneral theory, Space and Timein ContemporaryPhysics, first appearing in 1917 andgoing through four edi- tionsby 1922.6And his full-scale treatise on scientificepistemology, General 7 Theoryof Knowledge, had meanwhile appeared in 1918. On thestrength of theseachievements, especially his work on thephilosophical significance of thetheory of relativity,Schlick was namedin 1922 to theChair for the Philosophyof theInductive Sciences previously occupied by ErnstMach and LudwigBoltzmann at theUniversity of Vienna,where he becamethe leaderand guiding spirit of what we nowknow as theVienna Circle.8 In thecentenary collection of Helmholtz'sEpistemological Writings, Schlickcontributed extensive explanatory notes to the more explicitly philo- sophicalpieces, where, among other things, he attemptedto appropriate Helmholtz'sideas on behalfof his own developingversion of scientific empiricism- in explicitopposition, for example, to parallelattempts at appropriationby neo-Kantianphilosophers.9 Of particularimportance here is Schlick'sattempt to assimilateHelmholtz's celebrated Zeichentheorie of perception,according to whichour sensationsmust be viewed as signs [Zeichen],rather than pictures or images[Bilder] of external objects, to his owncharacteristic conception, developed at greatlength in GeneralTheory ofKnowledge, of the essence of knowledge and truth as consistingsolely in a relationof coordination [Zuordnung] or designation [Bezeichnung] between oursystem of concepts and judgments and its objects. In GeneralTheory of Knowledge itself, Helmholtz is notexplicitly invoked inthis context, but we do finda parallelrejection of the "popular" or "naive" conceptionof knowledge as somekind of picturing or imaging of reality: Thusthe concept of agreement [Übereinstimmung] melts awayunder the rays of analysis, insofar as itis supposedto mean samenessor similarity, and what remains is onlythe univocal coordination.In this consists the relation of true judgments to reality,and all those naive theories, according towhich our judg- mentsand concepts could somehow "picture [abbilden]" reality, arein principle destroyed. There remains no other meaning for theword agreement than that of univocal coordination. Univocality[Eindeutigkeit] is the sole essential virtue of a coordination,and, since truth isthe sole virtue of judgment, truth mustconsist in the univocality ofthe designation for which the judgmentis supposed to serve.10 AndSchlick makes it amply clear, moreover, that concepts so conceivedin theirpurely designative function operate merely as signs[Zeichen] and not as pictorialimages [Vorstellungen] (§§ 5, 8). Thesepassages from General Theory of Knowledge parallel Helmholtz's classicstatement of his Zeichentheorie in themost extensive presentation of hisepistemological position, "The Factsin Perception,"in 1878:

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions Insofaras thequality of our sensation gives us a reportof the characterofthe external influence through which it is excited,it maycount as a sign[Zeichen] of the latter but not as animage [Abbild].For of an imageone requires some kind of sameness withthe pictured [abgebildeten] object, of a statuesameness of form,of a delineationsameness of perspective projection inthe visualfield, of a paintingalso sameness of color. But a signneeds tohave no kind of similarity atall with that of which it is a sign. Therelation between the two is limitedto the fact that the same object,exerting an influencein the same circumstances, calls forththe same sign, and thus that different signs always correspondto different influences. Tothe popular opinion, which accepts in good faith the full truthof images [Bilder], this remainder ofsimilarity, which we do recognize,may appear very insignificant. In reality it is not so; forwith it a matterof the very greatest importance can still be achieved,namely, the picturing [Abbildung] ofthe lawlike- nessin the processes of the actual world.11 In hisexplanatory notes of 1921,Schlick then comments on thisfamous passage as follows: Anattempt ismade to show that such a picturing[Abbildung] ofthe lawlikeness of the actual with the help of a signsystem constitutes,ingeneral, the essence of all knowledge, so that our knowingcan fulfill its task in no other way, and needs no other methodfor this purpose, inSchlick, General Theory ofKnowledge, PartI.12

In thisway, the assimilation of Helmholtz's Zeichentheorie of perception to themost characteristic doctrines of GeneralTheory of Knowledge is made perfectlyexplicit and complete.13 I will hereexplore the relations between Helmholtz's Zeichentheorie and Schlick'sconception of coordinationor designationin some detail. We will see that,although it is certainlylegitimate to view Helmholtz's Zeichentheorieas a philosophicalprecursor of Schlick'sconception, there remaindeep and fundamentaldifferences between the two - differences directlyconnected with the very substantial changes in both the relevant sciences and in scientificepistemology that have since takenplace in the interim.Indeed, radically new developmentsin thefoundations of geometry,in particular,make it entirelyimpossible for Schlick to embrace Helmholtz'sZeichentheorie in itsoriginal form, and themost that we can say,in theend, is thatSchlick's conception constitutes a radical transforma- tionor transmutation ofthe former theory.14 By thustracing out some of the fundamentaldivergences between the two theories, we willgain additional insight,more specifically, into the intimaterelationship between early- twentieth-centuryscientific epistemology and its contemporaryscientific

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions context.We willalso increaseour appreciation, more generally, of the sub- tleand imaginative strategies - which,nonetheless, are oftenextraordinar- ilymisleading from a historicalpoint of view- employedby philosophers in appropriatingtheir philosophical past.

Atthe center of Schlick'sepistemological conception is a sharpand perva- sive distinctionbetween conceptual knowledge, on theone side,and intuitiveacquaintance, on theother. Indeed, the failure sharply to distinguish knowledge[Erkennen] from acquaintance [Kennen] constitutes, for Schlick, theroot of all philosophicalevil andleads, for example, to suchimpossible notionsas "intuitiveknowledge," "knowledge by acquaintance,"and so on (§ 12).To knowan objectis tosucceed in (univocally) designating itvia concepts,and knowledgeis thereforeessentially mediated by conceptual thought.To be acquaintedwith an object,by contrast,is simplyto experi- enceit [Erleben],as we experiencethe immediately given data of ourcon- sciousnessindependently ofall conceptualthought: "[i]n intuitive experiences [anschaulichenErlebnissen ], the immediate data of consciousness, e.g., pure sensations,we findpure facts that are independentof all thinking."15Such immediatedata thus constitute the objects of intuition; they are directly given realitiesthat are simply "there" present to consciousness; but they are not in thefirst instances objects of knowledge: "sensation gives us no knowledge, butonly an acquaintancewith things."16 This sharpdistinction between knowledge and acquaintanceis associ- atedwith a paralleldistinction between concepts [Begriffe] and ideas or images[Vorstellungen] (§§ 4, 5). Ideas or imagesare elementsof ourcon- sciousmental life (e.g., memory images). They belong to theimmediately givendata constituting the stream of ourconsciousness and, as such,share inthe privacy, subjectivity, fleeting and transitory character, and lack of pre- ciselydefined boundaries peculiar to all suchimmediate data. Concepts, by contrast,are supposed to be publicor objective representations with perfectly preciseboundaries. Concepts and conceptualthought make possible gen- uinelyscientific knowledge, a knowledgewhich is bothobjective and perfectlyexact. But how are such representations themselves possible, and how do theyacquire their exact and objectivemeaning? Concrete or ostensive definitionswould be quiteinadequate for this purpose, for such definitions inevitablylead backto theimmediately given data of consciousnesschar- acterizedprecisely by their inexactness and subjectivity (§ 6). Followingthe traditionof Moritz Pasch and David Hilbertin thefoundations of geometry, however,we see thatthere is an essentiallydifferent species of definition,

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions so-calledimplicit definition , whereby concepts are fully and precisely spec- ifiedthrough their mutual relationships with one anotherin a rigorous axiomaticsystem, without ever being related to intuitivelygiven objects existingoutside the system (§ 7). Hilbert-styleaxiomatic systems are thus paradigmatic of objective sci- entificconceptualization and objectivescientific knowledge. And the sharp distinction,pertaining to suchsystems, between the formal-logical structure expressedin theaxioms and their manifold possible interpretations (spatial, numerical,and so on) is mirroredin Schlick's centraldistinction between conceptualknowledge and intuitive acquaintance. Just as theHilbertian focus on formal-logicalstructure is intended to purge geometrical deduction from possiblymisleading reliance on spatialintuition - so as,in particular, toallow thelogical relations of dependence between geometrical propositions tostand outmore clearly - Schlick'stheory of scientific conceptualization is intended to freeit once and forall fromall vagariesof intuitiverepresentation by allowingus to characterizescientific concepts in generalsolely in termsof theirformal-logical relations to one another.In thisway, the Pasch-Hilbert distinctionbetween a formalaxiom system for geometry (what we would now call an uninterpretedformal system), on theone side,and a possible interpretationforsuch a systemvia intuitivespatial forms, on theother, pro- videsSchlick with the primary model for his own distinction between knowledge [Erkennen ] and experience or acquaintance[Erleben , Kennen ]. The modelof a Hilbert-styleaxiomatic system also leadsSchlick to the centralproblem of his early epistemology: elucidating the relation of such a systemto the objects or realities that are now supposed to be knownthereby. The problemis thata Hilbert-styleaxiomatic system, precisely in itspurely formal-logical,essentially uninterpreted character, is deliberatelyand self- consciouslydivorced from all contactwith reality: Implicitdefinition, bycontrast [with concrete or ostensive definition],never stands in community orconnection with reality, it deniesthis intentionally andin principle, itremains in the realm ofconcepts. A frameworkoftruths constructed with the help of implicitdefinition never rests on the ground of reality, but, as it were,floats free, bearing, like the solar system, the guarantee of itsstability within itself. None of the concepts appearing therein designate,inthe theory, a real thing | ein Wirkliches ]; rather, they mutuallydesignate one another in such a waythat the meaning ofone concept consists in a determinateconstellation ofa num- berof the others.17

To nowexplain how knowledge of reality is possible- thatis, in his own terms, how we can neverthelessset up a relationof designationor coordination betweena Hilbert-styleuninterpreted axiom system and some domain of real objects- is thusthe sine qua nonof Schlick'searly scientific epistemology.

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions His explanation,appropriately enough, is inspiredby the second great advancein thefoundations of geometry of his time, the application of non- Euclideangeometry to natureeffected by Einstein's general theory of relativity. Reality,for Schlick, includes, paradigmatically, the domain of ourpri- vate,immediately given data of consciousness, which constitute the totality of intuitiveobjects of acquaintance.These data are characterizedby both intuitivetemporality and intuitivespatiality, in thatthere are immediately giventemporal relations between them, and some of them (visual fields, for example)exhibit intuitive spatial extendedness as well.Such intuitivespa- tialityand temporality are just as subjectiveas theimmediately given data ofconsciousness themselves, and, in thissense, it is perfectlycorrect to say that(intuitive) space and time are subjective (§§ 27-29 [§§ 28-29]). Butthis realmof intuitively given data is notthe only reality, and the domain of intuitivespatiality and temporality, in particular, is notthe only spatiotemporal reality.On thecontrary, there is also an objectivespatiotemporal reality, described,paradigmatically, by modernmathematical physics, which includesa greatwealth of "transcendent" objects that are not intuitively given (electromagneticfields and the like) and thatextend far (in objectivespace andtime) beyond the meager domain of realities immediately present to our consciousness.In thissense, the domain of immediate acquaintance is only a smallfraction of existing reality. Moreover,in thisconnection, especially, the failure sharply to distin- guishbetween conceptual knowledge and intuitiveacquaintance has pro- duced seriousphilosophical confusion and has led to the temptation, specifically,to restrictthe domain of realityto theimmediately given data ofconsciousness. Once we see,however, that knowledge means designation by concepts,and thusin no wayrequires intuitive acquaintance, we are in thebest possible position definitively to resistthis temptation: Theintuition [Schauen] of things is notknowing and also not a preconditionofknowing. The objects of knowledge must be thinkablewithout contradiction, thatis, allow of a univocaldes- ignationvia concepts, but they do not need to be intuitively rep- resentable[anschaulich vorstellbar'}% So theway is nowopen, in particular,to rejectthe subjective idealist "philosophyof immanence"on behalfof a fullyrobust scientific realism (§§ 24-25 [§§ 25-26]). Indeed,Schlick's conception of knowledge as designationvia concepts actuallyleads to an evenstronger result, for it turnsout that those objects that,in thefirst instance, are capableof suchdesignation are notthe intu- itivelyspatial and temporal realities of immediate acquaintance, but are rather preciselythe objective "transcendent" realities described by modernmath-

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions ematicalphysics as existingin objective,mathematical-physical space and timeoutside of ourconsciousness. It is preciselythe latter realities, rather thanthe former, which constitute the proper objects of knowledge. This result alreadyfollows from Schlick's model of objectiveconceptual thought as givenby mathematicallyprecise axiomatic systems in whichconcepts are exactlyspecified, by meansof implicitdefinitions, through their formal- logicalrelations to one another.(No suchsystem is available,for example, forthe domain of introspectivepsychology.) But it followsequally from Schlick'sdetailed explanation of how an abstractlyspecified system of implicitdefinitions acquires a relationof designation or coordination to the realitiesthat are supposed to be knownthereby, for this explanation yields a paralleland complementaryemphasis on quantitativeas opposedto qualitativeknowledge. Schlickexplains how we set up thecrucial relation of designationor coordinationbetween our system of concepts and reality in section30 [31], entitled"Quantitative and QualitativeKnowledge." We begin,to be sure, withthe intuitive spatiotemporal ordering of the immediately given data of consciousness,since our constructionof theobjective or "transcendent" spatiotemporalordering is basedupon this subjective ordering: Theordering ofour contents ofconsciousness inspace and timeis likewisethe means by which we learn to determine the transcendentordering of things outside our consciousness, and thelatter ordering is the most important step towards their cog- nition. Theproblem now is to becomeclear how one proceeds fromthe intuitive spatiotemporal ordering tothe construction of thetranscendent ordering. This always occurs by thesame method,which we can designate as themethod of coincidences. Itis epistemologicallyofthe very highest importance.19 It turnsout, however, that what is primarilyknowable by this process is the quantitativestructure of the"transcendent" ordering thereby effected. The qualitativestructure of theimmediately given data of consciousnesswith whichwe begincan itselfonly become known after we have fullyarticu- latedthe objective ordering. We constructthe "transcendent" ordering, more specifically, on the basis ofsingularities orcoincidences in our various intuitively given sensory fields. For example,I see thetip of mypencil touch my finger in myvisual field and,at the same time, feel its touch on myfinger in my tactile field. The intuitivespatiality of these two sensory fields is entirelydifferent inthe two cases, and theyhave, as such,no intuitivespatial relations to one another.I then bringthem into relation by constructing a single, nonintuitive spatial order- ingcontaining both the pencil and my finger, where a singlepoint in objectivespace (thecoincidence of my finger with the pencil tip) corresponds to

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions bothsingular points in the two previously independent sensory fields. In this procedureI abstract completely from the qualitative peculiarities of my sensoryfields (color, tactile quality, and so on) andconcentrate solely on their purelytopological properties - the presence or absence of a singularity.And thisfocus on singularitiesor coincidencesis also crucialfrom a scientific pointof view,for it is preciselyon thebasis of suchcoincidences that the techniqueof numerical measurement now proceeds. We measureobjective spatialintervals by observingthe coincidences of theendpoints of a mea- suringrod with points on a measuredobject; we measureobjective temporal intervalsby observingcoincidences between events in a givennatural processand pointer positions on a clock;and so on: "all measurement,from themost primitive to the most sophisticated, rests on theobservation of spa- tiotemporalcoincidences."20 In themethod of coincidences, then, I constructa numerical model, as itwere, for an abstractlyspecified axiom system for mathematical physics21 by carryingout measurements (of objectivespatial and temporal intervals, butalso of variousobjective physical magnitudes, such as theelectromag- neticfield) based on myperceptions of measuringinstruments and thus, in theend, on immediatelygiven coincidences or singularitiesin myintuitive sensoryfields. In thisway, an abstractlyspecified axiom system acquires a relationof designation to quantitativelystructured objective reality by way ofthe immediate data of consciousness, and the objective or "transcendent" spatiotemporalordering of realitiesdescribed by modernmathematical physicsthereby becomes a genuineobject of knowledge. It does notfollow, however,that the purely qualitative data immediately present to conscious- nessthemselves become objects of knowledge as well.On thecontrary, pre- ciselybecause they are not yet describable in truly quantitative fashion, such purelyqualitative intuitive data are not yet objects of knowledge. They will onlyacquire this status, in fact, when they, too, are described in exactmath- ematical-physicalfashion: "[t]he life of consciousnessis thusonly com- pletelyknowable insofar as we succeed in transformingintrospective psychologyinto a physiological,natural-scientific psychology, ultimately intoa physicsof brain processes."22 We havenot yet drawn a connectionbetween the objective spatiotemporalordering known via themethod of coincidences and the new concep- tionsof space and timedue to thegeneral theory of relativity.Nor does Schlickhimself make this connectionexplicit in the relevantparts of General Theoryof Knowledge.Rather, it is in Space and Time in ContemporaryPhysics, written virtually simultaneously, that this crucial stepin Schlick'sreasoning is explained.The mostimportant chapter of the latterwork, in this connection,is entitled"The General Postulateof Relativityand the Metrical Determination of the Space-Time Continuum,"

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions whereSchlick draws a fundamentalcontrast between general relativity and bothNewtonian physics and specialrelativity. In bothof the latter two theories,he explains, [space]still preserved a certain objectivity, solong as itwas still tacitlythought as equippedwith completely determined metri- calproperties. Inthe older physics one based every measurement procedure,without hesitation, onthe idea of a rigidrod, which possessedthe same length at all times, no matter atwhich place andin which situation and environment itmay be found, and, on thebasis of this thought, all measurementswere determined in accordancewith the precepts of Euclidean geometry. ... Inthis way,space was still left with a "Euclideanstructure," as a sepa- rateand independent [selbständig] property, as it were, for the resultof these metrical determinations wasthought tobe entirely independentofthe physical conditions prevailing inspace, e.g., ofthe distribution ofbodies and their gravitational fields.23 Butthis is emphaticallynot the case in Einstein'snew theory: Ifwe want, therefore, tomaintain the general postulate of relativityin physics, we must refrain from describing measurements andsituational relations in the physical world with the help of Euclideanmethods. However, itis not that, in place of Euclidean geometry,a determinate other geometry - e.g., Lobachevskian orRiemannian - would now have to be usedfor the whole of space,so thatour space would be treatedas pseudosphericalor spherical,as mathematiciansandphilosophers are accustomed toimagine this. Rather, the most various kinds of metrical deter- minationsare to be employed,ingeneral, different ones at each position,and what they are now depends on thegravitational fieldat each place.24 Space-timein generalrelativity now has no backgroundgeometry at all- neitherEuclidean nor non-Euclidean - thatwould be determinedindepen- dentlyof thedistribution of mattertherein; and, according to thegeneral postulateof relativity(the principle of generalcovariance), the only back- groundthat remains is the topologicalor manifoldstructure of number quadruples,that is, the space-time coincidences, so that"the whole of physics can be conceivedas a totalityof laws in accordancewith which the occur- renceof these space-time coincidences takes place."25 In thefinal chapter, entitled "Relations to Philosophy,"Schlick then explainsthe significance of Einstein's new view of space and time for episte- mologaHe pointsout that the objective spatial structure employed by physics " " is notintuitively given, but is rathera conceptualconstruction , that is, a "nonintuitiveordering, which we thencall objectivespace and conceptually graspthrough a manifold of numbers (coordinates)."26 Yet this objective conceptualconstruction proceeds, just as inGeneral Theory of Knowledge, on the

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions basisof the subjective spatiotemporal coincidences present in various sensory fieldsof various individuals: In orderto fix a pointin space, one must somehow, directly or indirectly,point to it, . . . thatis, one establishes a spatiotempo- ralcoincidence oftwo otherwise separate elements. And it now turnsout that these coincidences always occur in agreement for all intuitivespaces of different senses and all individuals;pre- ciselyso is an objective "point," independent ofindividual expe- riencesand validfor all, therebydefined. ... By closer considerationone easily finds that we attain to the construction ofphysical space and time exclusively through this method of coincidencesand in no other way. The space-time manifold is nothingelse thanthe totality of objectiveelements defined throughthis method. That it is precisely a four-dimensional man- ifoldresults from experience by the execution of this method itself. Thisis the result of the psychological-epistemological anal- ysisof theconcepts of spaceand time, and we see thatwe encounterprecisely that meaning for space and time which Einsteinhas recognized as alone essential for physics, where he hasshown it to best advantage. For he rejected the Newtonian concepts,which denied the origin we have described, and based physicsinstead on the concept of the coincidence ofevents. So herephysical theory and epistemology extend their hands to one anotherina beautifulalliance.27

The connectionbetween Schlick's epistemological method of coincidences andthe general theory of relativity could not be statedmore clearly.

A fullforty years separate General Theory of Knowledge from Helmholtz's maturepresentation of his Zeichentheoriein "The Facts in Perception." Theseforty years, as suggestedabove, were quite extraordinarily eventful, beingdistinguished, in particular,by thedevelopment of thenew formal- axiomaticpoint of view in the foundations of geometry by Pasch and Hilbert, on theone hand,and by Einstein's physical application of a non-Euclidean geometryof variablecurvature, dynamically linked to thedistribution of matter,on theother. It is to Schlick'senduring credit that he clearlyrecog- nizedthe radical philosophical implications of these new ideas and,accordingly,made themthe linchpinsof his early scientificepistemology. Helmholtz,however, worked in a quitedifferent scientific environment and had,for his part, no inklingof these particular developments in thefounda- tionsof geometrythat were still to come.Instead, Helmholtz's articulation

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions ofthe Zeichentheorie of perceptionwas framedby three fundamental con- tributionsof his own scientificwork: his conceptionof theprinciple of causalityor the lawlikeness of nature as a basic essentialprinciple of physical science,his defenseof "empiricist"over "nativist"theories in the psycho-physiologyof sense perception,and his own workin thefounda- tionsof geometryon whatwe nowcall theHelmholtz-Lie space-problem. The Zeichentheorieof perception, as we shallsee, is a synthesisand philo- sophicalelaboration of theseelements - which,as we shallfurther see, is quiteincompatible with the scientific epistemology of GeneralTheory of Knowledge. Helmholtz'scharacteristic emphasis on theprinciple of causality or the lawlikenessof naturemakes its first appearance in his greatmonograph on theconservation of energy,published in 1847. In theintroduction to that workhe describes"the ultimate and proper goal ofthe physical natural sci- encesas such"as beginningwith an "experimentalpart," where one seeks to describe"the individual natural processes" by "generalrules . . . which areobviously nothing but universal generic concepts though which all ofthe appearancesbelonging thereto are comprehended," and proceeding to a "the- oreticalpart . . . whichseeks, by contrast, to findthe unknown causes of the processesfrom their visible effects; it seeks to conceptualizethem in accordancewith the law ofcausality."28 This procedure leads us eventuallyto the "ultimateunalterable causes" lying at thebasis ofall appearances: Weare compelled and justified in this task by the principle that everyalteration innature must have a sufficientcause. The prox- imatecauses that underlie the appearances ofnature can them- selvesbe eitherunalterable or alterable;in the latter case the sameprinciple compels us to seek for other causes of this alter- ationin turn, and so on,until we finallyarrive at the ultimate causesthat act in accordance with an unalterable law, and which, therefore,bring about at every time, under the same external relations,the same effect. The final end of the theoretical natural sci- encesis thusto discoverthe ultimate unalterable causes of naturalprocesses.29 Suchultimate unalterable causes turn out to be themass points of analytical mechanics,interacting with one anothersolely through time-independent (constantor "unalterable") central forces of attraction and repulsion depend- ingonly on thedistances between the points in question.The possibilityof reducingall ofthe appearances of nature to thisbasis is thus"the condition forthe complete conceptualizability of nature."30And themain burden of themonograph that follows is thento contribute to this goal by showing that thephenomenological principle of the conservation of energy - theprinciple, as Helmholtz'sphrases it, that a perpetualmotion machine (of the first kind) is impossible- is equivalentto thetheoretical principle that all actionsin

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions natureare in factreducible to ultimateforces of attractionand repulsion in thisway. The principleof causality therefore functions here as a bridgebetween theobservable world of appearancesand the ultimate unobservable causes thatare thought to underlie and explain the appearances. The principle serves a parallelfunction, in the context of the psycho-physiology ofperception, in Helmholtz'scelebrated lecture on humanvision of 1855(see note2 above), whereits role is extendedto justify even our inference that there is a world ofexternal objects in thefirst place: [W]enever immediately perceive the objects of the external world,but we only perceive the effects of these objects on our nervousapparatus, and this has been so fromthe first moment of ourlife onwards. Inwhat way, then, have we first reached across fromthe world of the sensations ofour nerves into the world of actuality?Obviously, only through an inference;we mustpre- supposethe presence of the external object as causeof our nerve- excitation;for there can be noeffect without a cause.31 The principleof causality, for precisely this reason, cannot be an empirical proposition,for it is thusrequired before there can be any experienceof objectiveexternal things at all: "[h]encethe investigation of sensepercep- tionleads us on alsoto that knowledge already found by Kant, that the proposition,'no effectwithout a cause,'is a law ofour thinking given prior to all experience."32 Atthis stage in Helmholtz's development, then, the principle of causalityis embeddedin a versionof a classicalcausal realist theory of perception. Behindthe veil of perception of our sensations is a worldof external objects in space, a worldwe can onlyreach epistemically via an inferencefrom observedeffects to unobservedcauses. By the time of "The Facts in Perception,"however, Helmholtz has modifiedthis picture considerably. He characterizesboth causal realism and subjectiveidealism as "metaphysical hypotheses"and asserts,in a well-knownphrase, that "[w]hat we can find unambiguouslyand as fact,however, without hypothetical interpolation, is thelawlike in theappearance."33 The "law ofcausality" continues to be "an a priorigiven, a transcendentallaw," because lawlikeness continues to be thecondition for "the conceptualizability of theappearances of nature."34 Butthis principle can no longerserve to underwrite causal realism; it can no longertransport us behindthe veil of appearances.Thus, when Helmholtz addsnotes to hismonograph on theconservation of energy in 1881,he cor- rectsthe above-cited sentence, where the law of causalityis said to lead us to "unknowncauses" from their "visible effects," accordingly: 1) Topage 13. The philosophical discussion in the introduction ismore strongly influenced byKant's epistemological views than

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions I wouldnow like to recognize as correct.I only made it clear to myselflater that the principle of causality is actuallynothing otherthan the presupposition ofthe lawlikeness ofall the appear- ancesof nature.35

Theprinciple of causality cannot serve, as Helmholtzunderstood Kant in 1855, as an a priorijustification for causal realism - forthe postulation of otherwise unknownobjects behind the veil of appearances. On thecontrary, lawlikeness is now a fundamentalprinciple governing the appearances themselves, as somethingwe "findunambiguously and as fact. . . inthe appearance." This importantshift in Helmholtz'sthinking was mediatedby thefur- therarticulation of whathe called an "empiricist"theory of visualpercep- tionin his monumentalHandbook of Physiological Optics , firstappearing 36 between1856 and 1867. Althoughhe had declaredhis allegianceto such a theory,and his opposition to "nativism," in 1855,the theory did not acquire a cleararticulation until 1865-66.37 The basic idea is thatour ability to see objectsaround us in space,as localizedat particular places therein, is notan innatecapacity of either our consciousness or our nervous apparatus, which wouldbe somehowbuilt in priorto all particularexperiences. Rather, this abilityis itselfgradually learned or acquired- as we learnor acquireour nativelanguage, for example - bya processof "unconscious inductive inference"based on regularitiesor associations among our sensations. For example,my ability to localizea perceivedtable in three-dimensionalspace is in no waydirectly given by simplevisual or tactilesensations, for "[a] direct image[Bild | ofa threedimensional extended spatial magnitude is givenby neitherthe eye nor the hand." Such a perceptionof a three-dimensionalspa- tialobject instead requires (unconscious) knowledge of a largenumber of regularitiesamong such simple sensations, generated as I movearound the object,reach out and touch it, and so on: Therepresentation ofa spatiallyextended body, e.g., a table, includesa mass of individual observations. There lies comprised thereinthe entire series of images that this table would provide me ifI wereto consider itfrom various sides and from various distances,ifI wereto lay my hands successively onthe various points ofits surface. Such a representationofa particular individual body isthus actually already a concept, which comprehends under itself aninfinite number of particular intuitions following one another intime, all of which can be derived from it, just as the generic concept'table' in turn comprehends within itself all particular tables andexpresses their common characters.38 In thissense, the ability to see objectsin space is primarilyan affairof the understanding,and "[t]hefundamental principle of theempiricist view is [that]sensations are signsfor our consciousness, where learning to under- standtheir meaning is leftto our understanding."39

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions By thesame token, therefore, the process of learning to localize objects in spaceis closelyanalogous to theconscious procedure of inductive infer- encecharacteristic ofnatural science: Ofthe greatest importance, finally, for the fixity of our convic- tionin the correctness ofour sensory perceptions are the tests thatwe undertake bymeans of the optional motions of our body. Therethereby arises the same kind of fixed conviction, relative tomerely passive observation, that we gain in scientific investi- gationsthrough the experimental method. The proper ultimate ground,through which all ourconsciously executed inductions receivethe power of conviction, is the law of causality.40 Indeed,except for the fact that the former inferences are unconscious,the analogyis perfectlyexact: Nowthe same great significance that experiment hasfor the securityof our scientific convictions, ithas also for the uncon- sciousinferences ofour sensory perceptions. Only insofar as we bringour sense organs, in accordance with our own willing, into variousrelations to the objects, do we learnsecurely to judge aboutthe causes of our sensations, and such experimenting takes place fromthe earliest childhood on, withoutinterruption, throughoutthewhole of life.41 We thuslearn or acquirethe complicated system of regularities among initiallyisolated and fragmentary sensations, which, as a system,first consti- tutesthe perception of an objectin space,by the very same procedure, and in accordancewith the very same causal or inductive principle, that we self- consciouslyemploy in scientific inference. Hence, since the primary role for thecausal or inductive principle here is nowprecisely to secureour grasp of regularityor lawlikenesson theside of ourperceptions, it no longerfunc- tionsas a bridgeto anotherrealm existing behind our perceptions. To be sure,some of Helmholtz'slanguage still suggests a versionof " causalrealism. For example, he abovespeaks of judgments about the causes ofour sensations," and elsewhere, even more strikingly, he assertsthat "we can neveremerge from the world of our sensations to a representationofan externalworld except through an inferencefrom the changing sensation to externalobjects as thecauses of this change."42 In otherpassages, however, Helmholtzclearly and explicitly excludes causal realism: I believe,therefore, that there can be nopossible sense at allin speaking of any other truth for our representations except a practical[truth]. Our representations ofthings can be nothing elseat all except symbols, naturally given signs for things, that we learnto use for the regulation of ourmotions and actions. Whenwe have correctly learned to read such a symbol,we are thencapable of so adjustingour actions with its help that they havethe desired result, that is, theexpected new sensations

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions occur.Another comparison between representations andthings notonly fails to exist in actuality - here all schoolsagree - but anyother kind of comparison is in no way thinkable and has no senseat all.43

Thusrepresentations ofthe external world are images [Bilder] ofthe lawlike temporal succession of natural events, and if they arecorrectly formed [gebildet] in accordance with the laws of ourthinking, and we areable correctly totranslate them back againinto actuality though our actions, then the representations thatwe have are also the uniquely true [ones] for our faculty of thought;all others would be false.44 HereHelmholtz comes very close indeedto theview that lawlike relations amongour sensations - arrivedat by inductive inferences in accordance with theprinciple of causalityor thelawlikeness of natureare constitutiveof theirrelationship to an externalworld. The finalpiece of the puzzle, which put Helmholtz in a positiondefini- tivelyand unambiguously toreject causal realism, and which paved the way, accordingly,for "The Factsin Perception,"was hisown fundamental math- ematicalcontribution to whatwe now call theHelmholtz-Lie space-problem,developed in theyears 1866-70. The upshot of this contribution was to showthat the same regularities in oursensations, on thebasis of whichwe acquirethe ability to localize objectsin space,also give riseto therepre- sentationof space itself.The voluntaryactions of ourbodies, which allow us to localizeobjects by moving toward, away, and around them, make possible,in addition,a precisemathematical construction of thevery three- dimensionalspace withinwhich this process of localizationtakes place. In thisway, space does notserve, as itwere, as thehome of "external"objects thatexist behind the veil of perception,but rather as a "subjectiveform of " intuitionin the sense of Kant - so that"space will also appearto us sensibly, clothedwith the qualities of our sensations of motion, as thatthrough which " we move,through which we can gaze forth."Space is thusthe necessary formof ourexternal intuition . . . because we comprehendprecisely that whichwe observeas spatiallydetermined as theexternal world."45 The external worldof objects in spaceis thereforea construction, erected entirely on thebasis ofour acquired ability to localizeobjects therein. Helmholtzbegins his firstmathematical paper, in 1866,by explaining thathis "investigationsinto the manner in whichlocalization in thevisual fieldtakes place" stimulated him "to consider also theorigins of general spatialintuition as such."46As in BernhardRiemann's great lecture, "On the HypothesesWhich Lie at theBasis of Geometry,"Helmholtz sets up the problemmathematically byasking after those analytic conditions which distinguishour actualthree-dimensional space fromother continuous manifolds,such as themanifolds of colors, sounds, and so on.47Unlike Riemann,

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions however,Helmholtz is notcontent simply to postulate, in answer to this question,the existence of what is nowknown as a Riemannianmetric. He looks ratherfor "truths of factualsignificance"48 - facts, it emerges,of ourper- ceptualexperience - fromwhich Riemann's "hypotheses" can thenbe derived.And he findsthis factual basis, as is wellknown, in thefree mobil- ityof rigid bodies throughout the manifold: the possibility of movingrigid bodieswithout distortion from any one place and situationto anyother, so as therebyto performmeasurements and, in particular,to determinecon- gruence.This possibility expresses a lawlikefeature of ourexperience, so that"[l]ike every physical measurement, that of space mustalso reston an unalterablelaw ofuniformity in the appearances of nature."49 Whatis notquite so wellknown is thatHelmholtz did not just attempt, in accordancewith what we nowcall theHelmholtz-Lie theorem, to derive theexistence of a Riemannianmetric - whichthen must have constant cur- vatureas well- fromhis factual basis offree mobility.50 He also attempted to derivethe specifically Euclidean character of our "in fact existing space" froma similarlyfactual basis. In particular,by overlooking the existence of spaces of constantnegative curvature described by Bolyai-Lobachevsky geometry,he arguedthat the specific character of our actual space couldbe derivedfrom three-dimensionality, freemobility, and infinity- where this lastcondition rules out the case ofconstant positive curvature. Only after he hadbecome acquainted with Eugenio Beltrami's work on modelsfor Bolyai- Lobachevskygeometry in 1868 was Helmholtzable to correctthis mistake, in footnotesto his "On theFacts Lying at theBasis ofGeometry" (in which themain text still repeats the earlier mistaken claim). From our present point ofview, however, it is highlysignificant that Helmholtz had begun his math- ematicalproject, in 1866,by thinking that he couldconstruct all ofthe prop- ertiesof three-dimensionalEuclidean space froma factualbasis of lawlike regularitiesin ourperceptual experience. In anycase, Helmholtzsoon correctedhis mistake,and thisbrought aboutanother important shift in histhinking.51 For it was nowclear that the specificallyEuclidean character of space is nota consequenceof the factual basisinvoked by Helmholtz to distinguishour space from all othertypes of manifolds:free mobility (together with three-dimensionality and infinity) does notyield specifically Euclidean geometry. Thus, Euclidean geometry is notbuilt into the essential or necessary character of space, through which "thesystem of spatial measurement must presuppose those conditions under whichalone we can speakof determinationof congruence."52The particu- larpropositions of Euclidean geometry, as Helmholtznow argues explicitly in 1870, arenot included in the general concept of a three-dimensional extendedmagnitude and the free mobility ofthe bounded struc-

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions turescontained init. They are not necessities ofthought, which flowfrom the concept of such a manifoldand its measurability, orfrom the most general concept of a rigidstructure contained thereinand its freest mobility.53 Indeed,we can now make an even strongerclaim. For it followsfrom Helmholtz'stheory of the origin of spatial intuition in our experience of bodily motionthat the particular propositions of Euclideangeometry are also notnecessities of intuition.In particular,we can nowimagine the series of sensationswe wouldhave if we wereto find ourselves moving around in one of Beltrami'spseudospherical models for Bolyai-Lobachevsky geometry, andsuch a seriesof sensations, by Helmholtz's theory, would be an intuition of space: Wecan picture to ourselves the view of a pseudosphericalworld goingin all directions,just as wellas we candevelop its concept.We can thereforealso notadmit that the axioms of our geometryare grounded inthe given form of our faculty of intuition,or are in any way connected with such [a form].54 Sincethe axioms of Euclidean geometry are not built into the most general necessaryconditions underlying our spatial intuition, Kant's theory of the originof these axioms in our"necessary" and "transcendental"intuition of space is incorrect,and theyemerge rather as merelyempirical facts - facts aboutthe actual behavior of measuring instruments in our actual world. Nevertheless,Kant's insight that space itselfis a "subjectiveform of intuition,"rather than an orderingof thingsin themselvesexisting behind theveil of appearances, continues to be correct;for, as Helmholtzconceives it,"the most essential features of spatial intuition" - including free mobility and thereforeconstant curvature - are derivedfrom the same original law- likeexperiences of bodily motion on whichour ability to localizeobjects in spacedepends.55 In thissense, as Helmholtzfamously puts it, "space can be transcendentalwithout the axioms [i.e., the axioms of specifically Euclidean geometry]being so."56 And it follows,just as it does forKant, that we can now give an answerto thefundamental question of epistemology- "What is truthin ourintuition and thought?In whatsense do ourrepresentations correspondto actuality?"57- that does notinvolve a relationof correspon- denceor representation between our perceptions, on theone side, and "external" objectsexisting behind our perceptions, on theother. For that to which our representationsfinally correspond are lawlikepatterns taking place within- andindeed constituting - the space of ourform of intuition: I returnto the discussion of the first original facts of our perception.We have, as wehave seen, not only changing sense impressionsthat come upon us withoutour doing anything for thispurpose, but we observe during our own continuing activ-

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions ity,and we thereby achieve an acquaintancewith the enduring existence[Bestehens] ofa lawlikerelation between our [motor] innervationsand the becoming present of various impressions fromthe current range of presentables. Each of our optional motions,whereby we modifythe manner of appearance of the object,is tobe considered as an experiment, through which we testwhether the lawlike behavior of the appearance lying before us- thatis, its displayed enduring existence ina determinatespa- tialordering - has been correctly apprehended.58 In thisway, the correspondence ofour sensations to enduring external objects in spaceis equatedwith their characteristic lawlikeness: Whatwe canfind unambiguously and as fact,however, withouthypothetical interpolation, is the lawlike in the appearance.From the first step on, when we perceive the objects lin- geringbefore us distributedin space, this perception is the recognitionofa lawlikeconnection between our motions and the sensationsoccurring thereby.59 Thisis whatremains as fact,that is, in contrastto themerely hypothetical characterof both causal realism and subjectiveidealism. Helmholtzexpresses the Kantian contrast, as he understandsit, between appearancesand things in themselves as thatbetween the actual and the real : Wehave in our language a very happy designation for that whichinfluences us [aufuns einwirkt ], standing behind the changeof appearances, namely "the actual [das Wirkliche]." Hereonly the action [das Wirken] is expressed; itlacks the sec- ondaryreference toenduring existence as substancethat the conceptof the real [das Reelen] includes.60 As we haveseen, however, we onlyknow enduring existence as law,in that "[t]helawlike is thusthe essential presupposition for the character of the actual": I do notneed to explain to you that it is a contradictionin termsto represent the real or Kant's "thing in itself* via positive determinations,butwithout taking itup into the form of our rep- resenting.This is often discussed. But what we can achieve is an acquaintancewith the lawlike ordering inthe realm of the actual, tobe sure only presented inthe sign system of our sense impressions.61

Oursensations count as signsof external objects, therefore, not in virtueof a relationof correspondence or representationto otherwise unknown things in themselvesexisting behind our perceptions, but rather because they are initiallyisolated and fragmentary products of nervous excitation, which, as such,only become perceptions of externalobjects in space via a gradually learnedprocess of interpretation:

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions [Sensations]are signs, which we have learned to read ; they are a language,given to us alongwith our organization, inwhich externalobjects speak to us. But we mustlearn to understand thislanguage through practice and experience, just as muchas ournative language.62 Andthe main point of Helmholtz's Zeichentheorie, in theend, is to empha- size preciselythis process of interpretation- a processin whichspatially locatedobjects, together with space itself,are constitutedby lawlikerela- tionsamong our sensations.

Ill

For Schlick,as we have seen,concepts and conceptualthought are rigidly separatedfrom intuition. Concepts are identified with uninterpreted symbols in a Hilbert-styleaxiomatic system or formalcalculus, and conceptual thoughtis identifiedwith the procedure of operating such a calculusby purely formalrules independently of all possibleinterpretations or applications. Standingover against this purely formal system of conceptsare thenthe immediatelygiven realities of intuitionconstituting our consciousness, on theone hand,and theobjective "transcendent" realities existing outside of ourconsciousness, on theother. In thecase ofa formalaxiomatic system for geometry,in particular,there are both the intuitively spatial forms and qual- itiesimmediately present in our various sensory fields, and the objective spa- tialordering to which our various sensory fields (including the sensory fields ofdifferent individuals) are all coordinated.And conceptual thought acquires a relationof coordinationor designationto reality,in virtueof whichit therebycounts as knowledge,through the method of coincidences.In the case ofgeometry, inparticular, we constructa numerical assignment of coor- dinateson thebasis of subjectively given singularities or coincidencesin our varioussensory fields, resulting in an objectivenumerical model for our ini- tiallyuninterpreted axioms. A purelyformal system of conceptsthereby acquiresan interpretationor application in thenonintuitive, objective, or "transcendent"realm by wayof a projection,as it were,from the immediatelygiven, subjective domain of intuitive consciousness. It is centralto Schlick'sepistemological conception that we enforcea similarlyrigid separation between subjective, intuitive, or psychological space,on theone side,and objective, "transcendent," orphysical space, on theother. The formeris an indefinable,purely qualitative object of immediate acquaintancegiven prior to all conceptualizationand thought; the latter is a quantitative,nonintuitive ordering that is conceptuallythinkable and rep- resentablethrough an abstractformal system of judgments. Helmholtz's

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions attemptto defenda modifiedversion of the Kantian conception of space as a subjectiveform of intuition, in whichall objectsof external experience are neverthelessembedded, must therefore, from this point of view, appear as a fundamentalconfusion, and Schlickhimself makes this amply clear in his noteto theabove-cited passage from"The Facts in Perception"(note 45 above)where Helmholtz introduces the idea: Hereagain, as above,the expression "form of intuition" is usedin a completelydifferent sense than in Kant (cf. note 16). ButHelmholtz is entirely correct to align the spatial intuition he describeswith the sensory qualities, for it is a matterin both cases of subjective,psychical contents. What he describes, namely,in what precedes and what follows, is psychological space(or, properly, psychological spaces; for one must separate thespatial data of, e.g., sensations ofmotion from those of visual or tactileperceptions, as somethingwholly different, even thoughthey are all connectedthrough close associations), not physical-geometricalspace. The latter is a non-qualitative,formal,conceptual construction; theformer, as an intuitive given, isclothed, according toHelmholtz's words, with the qualities of sensations,and is just as subjectiveas theyare.63 Indeed,it follows from this passage that Helmholtz's entire theory of space- perceptionhas onlyto do, fromSchlick's point of view,with what Schlick calls psychologicalor intuitivespace; it remainswholly within the purely subjectiverealm and never touches at all on theobjective physical world. Yet Schlick's sharpdistinctions between intuition and conceptual thought,and between subjective psychological and objective physical-geometricalspace, are completelyforeign to Helmholtz'sZeichentheorie. Indeed,as we haveseen, one of the main pillars of this theory is theidea that whatSchlick calls objectivephysical-geometrical space can be constructed or generatedfrom what he calls subjectivepsychological space. And it is generatedby a procedure,moreover, in whichconceptual elements belong- ingto what Helmholtz calls the realm of thought are inextricably mixed with intuitiveelements: Fromthe first step on, when we perceivethe objects lingering beforeus distributed inspace, this perception is the recognition ofa lawlikeconnection between our motions and the sensations occurringthereby. Thus the first elementary representations alreadycontain thinking and proceed in accordance with the laws ofthinking. Everything inintuition that is added to the raw mate- rialof sensations can be resolvedinto thinking, ifwe takethe conceptof thinking as so extendedas hasbeen done above.64 The extensionin questionis givenby Helmholtz'stheory of unconscious inductiveinferences - which, accordingly, is anathema to Schlick.65 Schlick does notfully appreciate, however, the extent to which Helmholtz's view of

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions conceptualthought is also quitedifferent from his own. For Helmholtz, conceptualthinking does not involve manipulating a Hilbert-style uninterpreted calculusin accordance with purely formal rules. Rather, following J. S. Mill's interpretationof traditional syllogistic logic, Helmholtz sees theessence of conceptualthinking in the procedure of forming inductive inferences (which wouldyield major premises for syllogisms), whereby a varietyof particular instancesare associated together under a singleconcept.66 Conceptualization [Begreifen],for Helmholtz, just is sucha processof inductiveassociation, andthis is preciselywhy he viewsthe principle of causality or thelawlikeness of natureas thefundamental principle of thought:"[t]he first product ofthe thoughtful conceptualization ofappearance [des denkenden Begreif ens derErscheinung] is thelawlike"61 WhatHelmholtz calls spatialintuition is thusa productof conceptual thinkingin his sense.Unlike the initial sensory qualities themselves ("the rawmaterial of sensations"),which are givenas directoutputs of elemen- tarynervous excitations, and which, according to Helmholtz's"empiricist" theory,do notyet display spatial extendedness at all, spatialintuition is a learnedor acquiredordering of suchqualities in a lawlikestructure. In this respect,Helmholtz's conception of spatialintuition is indeedsimilar to Kant's,although, as Helmholtzhimself points out, his theory, in contrastto Kant's,resolves what the latter calls intuitioninto a processof thought: Inthat which has always seemed to me to be themost essential advancein Kant's philosophy, westill stand upon the ground of hissystem. In this sense I havealso, in my previous works, fre- quentlyemphasized the agreement ofrecent sensory psychology withKant's doctrines, although this certainly does not mean that I hadto swear by the master's words in all subordinate points as well.I believethat the resolution ofthe concept of intuition into elementaryprocesses of thought must be considered as the most essentialadvance of recent times - whichresolution is still lack- ingin Kant,and through which [lack] his conception of the axiomsof geometryas transcendentalpropositions is condi- tioned.68

Viewingspatial intuition in termsof immediately given sensory presence is thesource, according to Helmholtz,of the mistaken view that the axioms of specificallyEuclidean geometry have their origin there. Once we viewit as a temporallyextended process essentially linked to motion,by contrast, we see thatonly free mobility in general,and not specifically Euclidean geometry,is a "transcendental"condition of the possibility of spatialintuition as such.69 By thesame token, however, once we see thatfree mobility allows us toconstruct or generate the three-dimensional ordering of geometrical-physical space fromlawlike associations among our sensations, the way is also

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions nowopen for viewing the underlying external actuality to whichthese sen- sationscorrespond as simplysuch lawlike associations themselves: Thatwhich remains the same, without dependence on any- thingelse, in all change in time, we call substance ; the relation- shipthat remains the same between variable quantities, we call thelaw connecting them. What we directly perceive is onlythe latter.. . . Thefirst product of the thoughtful conceptualization ofappearance isthe lawlike. If we have separated itout so purely andconceived its conditions so completelyand securely delim- ited,and also so universally, that for all possible occurring cases theresult is uniquelydetermined, and we simultaneously attain theconviction that it has held good, and will continue to hold good,at all timesand in all cases,then we recognizeit as an enduringexistence independent ofour representations andcall itthe cause, that is, something that originally remains and con- tinuesto existbehind the change [das hinterdem Wechsel ursprünglichBleibende und Bestehende ]; only in this sense, in myview, is theapplication of the word justified, even though commonusage applies it in a vagueand washed-out manner for antecedentoroccasion in general.70 The idea thatthe external cause standingbehind the play of oursensations just is a lawlikerelation governing them could hardlybe moreclearly expressed. Schlick,for his part,is scandalizedby thisidea. In his notesto the abovepassage, for example, he rejectsthe claim that we can "directlyper- ceive" a law and protestswith particular vehemence against Helmholtz' s use ofthe notion of cause here.71But the most revealing passage occurs in GeneralTheory of Knowledge, in the course of an extendedpolemic against "thephilosophy of immanence."He thereexplicitly criticizes attempts to reduceexternal things to lawlike relations among our sensations, as inMill orMach, say, on thegrounds that they thereby inadmissibly "hypostasize" suchrelations; and whatis especiallyrevealing, in thepresent context, is thatthis polemic provides Schlick with a rareoccasion (in GeneralTheory ofKnowledge) to referto Helmholtz: Whoeversays here that a thingin the external world is a lawlikeconnection ofelements that also continues toexist when theelements are not given, and then believes to have thereby ascribedto the things the same reality that a sense-datum,for example,also possesses, has thereby reified the law, and his con- ceptformation is identical with the concept of force, as itused tobe dominantina phaseof natural science that has now been overcome.The lawlikeness of the connection has now in fact becomea powerfor him, which simply generates certain elements."The law recognized as objectivepower we call force" wroteHelmholtz inthe year 1881 (in the notes to his treatise on

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions theconservation offorce). What is thoughtinthe concept of the permanentpossibilities ofsensations orin the "objectively exist- inglaw" is entirelyand precisely the same as whatone other- wiseused to think under the concept of force.72 So Helmholtz,by implication, is guiltyof the same confusion that generally vitiatesall "immanencephilosophy."73 Themistake here, from Schlick's point of view, rests on a failureclearly andsharply to distinguish between abstract concepts and concrete realities - thevery failure to whichSchlick traces virtually all ofthe confusions of tra- ditionalphilosophy. Paradigmatic of existence, reality, or actuality(among whichSchlick does notdistinguish) are the immediately given data of con- sciousnessthemselves. It is here,and here alone, that we firstform the conceptof reality.This conceptcan, and indeedmust, then be extendedto the "transcendent"realities existing outside of consciousness as well.In neither case, however,should the concrete existence of realitiesbe confusedwith theabstract concepts we use to designatethem: Theconcept of the real cannot be reduced to unreal [unwirkliche] concepts;itmust be takenfrom experience [Erleben]. Concepts andrealities, by their nature, are incomparably different andcan- notbe transformed intoone another. Only the recognition ofthis distinctionmakes logical thinking possible, and any blurring of thedistinction leads to the great mistakes of the historical meta- physicalsystems.74 Thus,since laws are simply abstract concepts used to designate realities, they themselvescannot be identifiedwith realities. Just as Schlickdiverges fun- damentallyfrom Helmholtz in his view of conceptual thought as themanip- ulationof an abstractformal system independently of all interpretation,he similarlydiverges from Helmholtz in his conceptionof laws andtheir rela- tionto actuality.75 Yet Schlickdoes notappreciate, in thisconnection, the characteristic wayin which Helmholtz's own conception of laws and their relation to actu- alitydiverges radically from more typical forms of "immanencephilosophy,"such as thosefound in Berkeley, Mill, or Mach. The heart of the matter, forHelmholtz, is thatgeometrical-physical space is itselfa systemof law- likerelations among our sensations, so thatexternal physical objects then emergeas lawlikepatterns within geometrical-physical space. This conceptionof intuitiveor psychologicalspace as, at thesame time,an objective, conceptuallydetermined, geometrical-physical space is, as we have seen, entirelyalien to Schlick's way of thinking.Indeed, the whole pointof Schlick'smethod of coincidences is toeffect a relationof correspondence or coordinationbetween two essentially distinct space-time structures, the subjective-intuitiveand the objective-conceptual, and it is preciselythis feature

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions of his conception,moreover, that allows him to defenda versionof causal realismagainst traditional phenomenalism.76 For Helmholtz, by contrast, the conceptionof space as a "transcendentalform of intuition"on thebasis of whichalone objective external experience is possible- which,as we have also seen,aligns Helmholtz most closely with the philosophy of Kant- finallyenables Helmholtz to stakeout an entirelyoriginal position on the questionof ourperception of theexternal world, which, like Kant'sown, avoidsboth traditional causal realism and traditional phenomenalism.77 It is at firstsight quite surprisingthat Schlick never once mentions Helmholtz'sconstruction of geometrical-physicalspace on thebasis of the Helmholtz-Lietheorem. This is an extremelystriking omission of Helmholtz'sown fundamentalcontribution to thefoundations of geometry- which,from our present point of view,is absolutelycentral to his scientificepistemology as well. Withthe benefit of hindsight,however, this verystriking omission turns out to be notso surprisingat all. Forthe plain factis thatsuch a constructionofgeometrical-physical space is quiteincom- patiblewith the new conceptions of space andtime due to thegeneral theoryof relativity.The Helmholtz-Lietheorem necessarily yields manifolds of constantcurvature, whereas the general theory of relativityis based on a manifoldof variablecurvature. Free mobility, and theconsequent determinationof congruencevia transportedrigid rods, therefore fails in the space(time)employed by thattheory; and so thisparticular space(-time), characterizedby a variablecurvature essentially linked to thedistribution of mattertherein, cannot be theoutcome of a constructionbased on the Helmholtz-Lietheorem.78 Wehave seen that Schlick, in Space and Timein Contemporary Physics , clearlyrecognizes that general relativity has decisively broken with the mea- surementprocedures of the"older physics," insofar as thesewere based, "withouthesitation, on theidea of a rigidrod, which possessed the same lengthat all times,no matterat which place andin which situation and envi- ronmentit maybe found."Schlick also clearlyrecognizes, accordingly, that thegeometrical structure of space can no longerbe conceivedas "a separate andindependent property . . . entirelyindependent of the physical conditions prevailingin space,e.g., of the distribution of bodiesand their gravitational fields."79Thus measurement must now be based on the"method of coincidences,"where we beginwith an assignmentof numbers or coordinates hav- ingno initial metrical significance; properly metrical determinations are only thenpossible by taking account of the empirical distribution of matter(and hencecurvature) against this so farmerely topological background.80 We havealso seenthat Schlick explicitly equates this general relativistic "method of coincidences"with his own epistemologicalsolution to theproblem of theexternal world; for it is throughthis method, and this method alone, that

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions we constructthe required bridge between the purely subjective space and timeof our intuition, on theone side,and the objective, geometrical-physical space-timeordering, on theother. And Schlick is therebyultimately com- mitted,by this essentially dualistic conception, to a versionof just the kind of causal realismHelmholtz thought he had finallyovercome in his Zeichentheorie.That the realism in questionis a sophisticatedand abstract version,based on physicsrather than sensory psycho-physiology, goes a long way towardexplaining how Schlickcould have givensuch an unexpected twistto Helmholtz's original theory, but, in the end, it does nothing to dimin- ish thehighly ironical character of this particular instance of philosophical appropriationor transmutation.

NOTES

1. Versionsofthis paper were presented ata meeting ofthe History ofPhilosophy ofScience WorkingGroup (HOPOS) at Notre Dame and at the London School of Economics, both inMarch 1998. 1am particularly indebted toThomas Ryckman forcarefully reading sev- eralearlier drafts and making a variety ofpenetrating suggestions. 2. Helmholtz'scelebrated address, "Über das Sehen des Menschen," delivered atthe dedi- cationof a monumenttoKant in Königsberg in1855, condemns thethen current rift betweenphilosophy andnatural science due, in Helmholtz's opinion, tothe entirely spec- ulativeNaturphilosophie ofSchelling and Hegel and announces a new project ofcoop- erationbetween the two disciplines inthe spirit of Kant. This address became a model forphilosophers whowished toturn away from the "metaphysics" ofpost-Kantian abso- luteidealism toa newtype of scientific "epistemology" - particularly forthose in what thenbecame the tradition ofneo-Kantianism. Fora paradigmatic instance ofthis idea, seeE. Cassirer, TheProblem ofKnowledge: Philosophy, Science , and History since Hegel, trans.W. Woglom and C. Hendel (New Haven, Conn.: Yale University Press, 1950), 3-5. Seealso K. Köhnke, The Rise of Neo-Kantianism: German Academic Philosophy between Idealismand Positivism, trans. R.Hollingdale (Cambridge: Cambridge University Press, 1991),96-107. 3. Aspecial issue of Die Naturwissenschaften 9 (1921),contained J.von Kries, "Helmholtz alsPhysiolog," W.Wien, "Helmholtz alsPhysiker," W.Nernst, "Die electrochemischen Arbeitenvon Helmholtz," A. Riehl, "Helmholtz als Erkenntnistheoretiker,"andE. Goldstein,"Errinerungen einesLaboratoriumspraktikanten." Inthe Abhandlungen der preussischenAkademie der Wissenschaften, philosophisch-historische Klasse,Jahrgang 1921,B. Erdmann, Diephilosophischen Grundlagen vonHelmholtz' Wahrnehmungstheorie, appearedas no. 1. Three lectures were held at a meetingofthe physical, physiological, andphilosophical societies ofBerlin - E. Warburg, "Helmholtz alsPhysiker," M.Rubner, "HelmholtzalsPhysiologe," M.Schlick, "Helmholtz alsErkenntnistheoretiker" - which thenappeared together asHelmholtz alsPhysiker, Physiologe undPhilosoph (Karlsruhe: C. F.Müllersche Hofbuchhandlung, 1922). 4. P.Hertz and M. Schlick, eds., Hermann v.Helmholtz : Schriften zurErkenntnistheorie (Berlin:Springer, 1921); English edition, trans. M. Lowe, ed. R. Cohen and Y. Elkana, Hermannvon Helmholtz : Epistemological Writings (Dordresht: Reidei, 1977). 5. M. Schlick,"Die philosophische Bedeutung des Relativitätsprinzip," Zeitschrift für Philosophieund philosophische Kritik 159 (1915): 129-75; English edition, trans. P. Heath,inH. Mulder and B. vande Velde-Schlick, Moritz Schlick: Philosophical Papers (Dordrecht:Reidei, 1978), vol. 1.

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions 6. M.Schlick, Raum und Zeit in der gegenwärtigen Physik (Berlin: Springer, 1917 [first ed.],1919 [second ed.], 1920 [third ed.], 1922 [fourth ed.]); English version ofthe third edition,trans. H. Brose(Oxford: Oxford University Press, 1920), together with revisions offourth edition, trans. P. Heath,in H. Mulderand B. vande Velde-Schlick, Moritz Schlick:Philosophical Papers. 7. M.Schlick, Allgemeine Erkenntnislehre (Berlin: Naturwissenschaftliche Monographien undLehrbücher 1,1918 [first edition], 1925 [second edition]); English version ofsecond edition,trans. A. Blumberg (Vienna: Springer, 1974; reprint, La Salle, 111.: Open Court, 1985). 8. Schlick'sinvitation toVienna was engineered bythe mathematician HansHahn, then a professoratthe university, probably with help from his friend Philipp Frank, Einstein's successorintheoretical physics atPrague. Italso appears likely that Einstein himself may haveaided in this effort. Inany case, Einstein was most impressed bySchlick's work on relativity,and,after visiting Schlick at Rostock in 1919,he wrote to Max Born of the needto findSchlick a professorship.See,e.g., F. Stadler,Vom Positivismus zur "WissenschaftlichenWeltauffassung" (Wien:Locker, 1982), 117-20. 9. Thus,in the centenary contributions citedin n. 3 above,Alois Riehl attempts toappro- priateHelmholtz forneo-Kantianism, justas Schlick, for his part, attempts toappropri- atehim for empiricism. Riehl serves as a targetfor Schlick in his explanatory notes to Helmholtz'sepistemologica! writings aswell. 10.Allgemeine Erkenntnislehre (1918),57-58; General Theory ofKnowledge (1985), 61-62. Sectionnumbers given parenthetically inthe text refer to this work; where the section numbersofthe two editions diverge, I give those of the later edition inbrackets. Alltrans- lationsfrom the German, forboth Schlick and Helmholtz, aremy own. 11.Schriften zurErkenntnistheorie (1921),115; Epistemological Writings (1977), 121-22. 12."The Facts in Perception," 156n. 15; Schriften zurErkenntnistheorie-, Epistemological Writings,166n. 15. 13.The reader will notice that, although both Helmholtz andSchlick deny a relation of"picturing[Abbildung ]"in general, they both affirm such a relation inthe special case of "law- likenessIGesetzmäßigkeit ]."We will come back to this point in n. 75 below. 14.Commentators havebeen far too quick, in my view, simply totake Schlick's attempt at appropriationatface value. Thus, J. A. Coffa, for example, inThe Semantic Tradition fromKant to Carnap: To the Vienna Station (Cambridge: Cambridge University Press, 1991),introduces theSchlick of General Theory ofKnowledge as"the first toattempt a systematicformulation ofthe picture ofknowledge implicit inHelmholtz's writings," anddescribes this work as an"elaboration ofHelmholtz's ofthe link between " picture knowledgeandreality" (171-72). T. Ryckman, Conditio Sine Qua Non? Zuordnung in theEarly Epistemologies ofCassirer and Schlick," Synthese 88(1991): 57-95, provides a detailedand nuanced examination ofthe role of this concept inthe scientific thought ofthe period, paying special attention to the crucial importance of Helmholtz's Zeichentheorie, which, however, isportrayed as in close agreement with Schlick's par- ticularversion ofepistemological realism; see esp. 73, 76, 80, and also 86n. 40 - which takesthe above-cited n.15 to "The Facts in Perception" asevidence for the close agree- mentin question. 15.Allgemeine Erkenntnislehre, 311;General Theory ofKnowledge, 365. 16.Allgemeine Erkenntnislehre, 72;General Theory ofKnowledge, 87. 17. AllgemeineErkenntnislehre, 35;General Theory ofKnowledge, 37. 18.Allgemeine Erkenntnislehre, 199;General Theory ofKnowledge, 232. 19.Allgemeine Erkenntnislehre, 233-34; General Theory ofKnowledge, 272. 20.Allgemeine Erkenntnislehre, 236;General Theory ofKnowledge, 275. 21.Paradigmatic ofsuch systems, forSchlick, are Maxwell's equations forthe electromag- neticfield and Einstein's field equations forgravitation; set Allgemeine Erkenntnislehre, 207;General Theory ofKnowledge, 242-43. In this way, such well-known slogans as

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions "Maxwell'stheory isMaxwell's equations," inthe context ofthe Pasch-Hilbert tradition ingeometry, constitute theimmediate background toSchlick's epistemological conception. 22.Allgemeine Erkenntnislehre, 247;General Theory ofKnowledge, 288. 23.Raum und Zeit in der gegenwärtigen Physik (1917), 32; Space and Time in Contemporary Physics,inMulder and van de Velde-Schlick, Moritz Schlick: Philosophical Papers, 238-39. 24.Raum und Zeit, 33; Space and Time, 240. 25.Raum und Zeit, 35; Space and Time, 241. In my "Critical Notice" of Mulder and van de Velde-Schlick,Moritz Schlick: Philosophical Papers, inPhilosophy ofScience 50 (1983): 498-514, 1 was too quick to equate this passage with an endorsement ofa version ofver- ificationism,according towhich only observable space-time coincidences arereal (504-5)- anda parallelerror occurs in my Foundations ofSpace-Time Theories: RelativisticPhysics and Philosophy ofScience (Princeton: Princeton University Press, 1983),22-25. For in my "Critical Notice," I overlooked thecentral role of section 30[31] inGeneral Theory ofKnowledge, andthereby overlooked theextent tothe which the explicitlyrealist position ofthat work is intimatelyconnected with Schlick's reading of generalrelativity (contrary to500n. 3). At the same time, by missing the centrality ofsec- tion30 [31], I alsodid not see that Schlick, inGeneral Theory ofKnowledge, hasa def- initeway of bridging thegap between purely formal systems ofimplicit definitions and therealities they are supposed todesignate (507-8). 26. Raumund Zeit, 53-54; Space and Time, 260. 27.Raum und Zeit, 58; Space and Time, 263. The final sentence isomitted inthe later edition,which instead adds some comments onthe "paradoxes" ofrelativity. 28. Helmholtz,"Über die Erhaltung derKraft," inWissenschaftliche Abhandlungen (Leipzig: JohannAmbrosius Barth, 1882), 1: 12-13;English edition, trans. R. Kahl, in Selected WritingsofHermann von Helmholtz (Middleton, Conn.: Wesleyan University Press, 1971),3. 29.Wissenschaftliche Abhandlungen, 1: 13;Selected Writings, 4. 30.Wissenschaftliche Abhandlungen, 1: 16;Selected Writings, 6. 31 . Helmholtz,"Über das Sehen des Menschen," inVorträge und Reden (Braunschweig: FriedrichVieweg und Sohn, 1903), 1: 115-16. 32.Ibid., 116. 33.Schriften zurErkenntnistheorie, 130;Epistemological Writings, 138. 34.Schriften zurErkenntnistheorie, 133-134; Epistemological Writings, 142. 35.Wissenschaftliche Abhandlungen, 1:68; Selected Writings, 49(in the latter, however, the firstsentence isgrossly mistranslated soas to have Helmholtz saying that he still considers"Kant's epistemological insights" tobe correct). The note goes on to suggest that Helmholtzwas also earlier mistaken inseparating matter too sharply from the forces or lawsin accordance with which itacts - whereHelmholtz's conception ofmatter in1847 parallelsKant's conception, inthe Metaphysische Anfangsgründe derNaturwissenschaft (1786),which also depicts matter as acting only in accordance with the "fundamental forces"ofattraction andrepulsion. Itseems likely that Helmholtz's movement away from thisearlier Kantian position was closely connected with his realization thatelectromag- neticforces cannot be assimilated to"unalterable" central forces inthis sense, and thus thatthe fundamental equivalence hehad tried toset up between phenomenological energy conservation,onthe one hand, and a reductiontomass points and central forces, onthe other,does not in fact hold good (see nn. 2-4 from 1881). This particular route from phe- nomenologicallawlikeness to"ultimate unalterable causes" lying behind the appearances wastherefore closed. 36.Helmholtz, Handbuch derphysiologischen Optik(Leipzig: Leopold Voss, 1857-67 [first edition],1896 [second edition], 1910 [third edition]); English version ofthird edition, trans.J.Southall (Menasha Wise.: George Banta, 1925). The most extended defense of

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions Helmholtz's"empiricist" theory isfound in § 26,"Von den Wahrnehmungen imallge- meinen."The second edition drastically revises this section byincorporating muchof the contentof"The Facts in Perception." Thethird edition isa posthumousreprinting ofthe first.I will cite the third edition, which gives the page numbers ofthe first edition inthe margins. 37.For the development andbasic ideas of Helmholtz's theory I largely follow the lucid and balancedaccount inG. Hatfield, The Natural and the Normative: Theories ofSpatial Perceptionfrom Kant to Helmholtz (Cambridge, Mass.: MIT Press, 1990), chap. 5. Hatfieldisparticularly careful todistinguish the"empiricist"/"nativist" debateinthe psycho-physiologyofperception from the traditional "empiricist'Y'rationalist" debatein modernepistemology; seeAppendix A.I alsoagree with Hatfield inseeing a gradual "retreat"from the early causal realism of1855, culminating in"The Facts in Perception," asHelmholtz further develops his theory; see 208-14. 38.Handbuch (1910), 3: 21 ' Handbook(1925), 3: 23. 39.Handbuch, 3:433; Handbook, 3: 533. 40.Handbuch, 3:26; Handbook, 3: 29. 41.Handbuch, 3:28; Handbook, 3: 30-31. 42. Handbuch,3:29; Handbook, 3: 32. 43.Handbuch, 3: 18; Handbook, 3: 19. 44. Handbuch,3: 22; Handbook,3: 24. In an unpublishednote reproduced in L. Königsberger,Hermann von Helmholtz (Braunschweig: Friedrich Vieweg und Sohn, 1903),Helmholtz writes, similarly, that"representations aresigns, which are translatable backinto actuality through motions" (2: 159). 45."The Facts in Perception,"Schriften zur Erkenntnistheorie, 117;Epistemological Writings,124. 46.Wissenschaftliche Abhandlungen (Leipzig: Johann Ambrosius Barth, 1883), 2: 610. 47.Riemann's work was first presented asan Habilitation lecture in1854 and only published in1867. As Helmholtz explains, hefirst became aware of Riemann's work after he had alreadybegun his own investigations. 48. WissenschaftlicheAbhandlungen, 2: 610. 49.Ibid., 616. 50. Helmholtz'smathematical results were rigorously proved with the resources ofthe new theoryofcontinuous groups (what we now call Lie groups) by Sophus Lie in his Theorie derTransformations gruppenof 1873. The basic content ofLie's theorem, as we would nowformulate it,is as follows: Given a differentiate manifold, anda Liegroup of dif- ferentiatetransformations onthis manifold acting freely transitively, thereis a unique (upto a scalefactor) Riemannian metric onthe manifold whose isometries aregiven pre- ciselyby the Lie group in question. Since the metric thereby constructed hasa nontriv- ialgroup ofisometries orrigid motions, itmust then have constant curvature. (Tosay that thegroup oftransformations acts"freely transitively" isto say, intuitively, thatgiven any twopoints on the manifold, together with two "observers" or"points of view" having definitesituations andorientations atthese points, there isexactly one transformation in thegroup mapping one onto the other.) 51.The importance ofHelmholtz's earlier mistaken claim, its connection tohis "empiricist" theoryofspatial perception, andthe shift that resulted when he corrected thisclaim, are allclearly and perceptively explained inJ. Richards, "The Evolution ofEmpiricism: Hermannvon Helmholtz and the Foundations ofGeometry," British Journal for the PhilosophyofScience 28 (1977): 235-53. 52.Wissenschaftliche Abhandlungen, 2: 614. 53."On theOrigin and Significance of the Axioms of Geometry,"Schriften zur Erkenntnistheorie,17;Epistemological Writings, 17. 54.Ibid., Schriften zurErkenntnistheorie, 22;Epistemological Writings, 23.

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions 55.See "The Facts in Perception," Schriften zurErkenntnistheorie, 11 7-2 1 ; Epistemological Writings, 124-28. Strictly speaking, tomake good on this claim we need to connect thebodily motions ofthe perceiver with the motions ofmeasuring instruments definitive ofcongruence. Helmholtz himself makes the connection byviewing measurement as a refinementand specificationof ordinary bodily motion; see Schriftenzur Erkenntnistheorie,18;Epistemological Writings, 19.In the group-theoretical formulation dueto Sophus Lie (n. 50 above), however, theconnection istransparent. Westart with an abstractgroup of transformations, whichcan then be taken simply tobe the group ofbod- ily"displacements" ofthe perceiver, andthis last approach isexplicit inHenri Poincaré's workon the philosophical foundations ofgeometry. Fordiscussion ofPoincaré inrelation toHelmholtz (and Kant), see my "Geometry, Construction, andIntuition inKant and his Successors,"inBetween Logic and Intuition : Essays in Honor of Charles Parsons, ed. G.Scher and R. Tieszen (Cambridge: Cambridge University Press, forthcoming). 56.This is the title of Appendix 2 to"The Facts in Perception," Schriften zurErkenntnistheorie, 140-42;Epistemological Writings, 149-52. In the body of the paper, after explaining how "themost essential features ofspatial intuition" canbe derived from our experience of bodilymotion, Helmholtz puts the distinction thisway: "[i]t is wellknown that Kant alreadyassumed, not only that the general form of spatial intuition istranscendentally given,but also that it contains inadvance, and prior to all possible experience, certain narrowerdeterminations, asthey are expressed inthe axioms of geometry." Heproceeds togive axioms for specifically Euclidean geometry, and,after explaining that"those rea- sonsthat allow us to infer that the form ofintuition ofspace is transcendental, donot yet necessarilysuffice toprove at the same time that the axioms are also of transcendental origin,"hepoints out again that this conflicts with Kant's conception ofspatial intuition, accordingtowhich "spatial relations that contradicted theaxioms of Euclid could not at alleven be represented"{Schriften zurErkenntnistheorie, 121-22; Epistemological Writings,128-29). These passages, inconnection especially with those from "On the Originand Significance ofthe Axioms ofGeometry" cited in the text immediately above, stronglysupport the idea that Helmholtz includes free mobility (and thus constant curvature)inthe "general transcendental formof spatial intuition," andthus excludes the "axioms"understood asspecifically Euclidean. Schlick, inhis nn. 32 and 33 to these pas- sagesfrom "The Facts in Perception," suggests that "the most essential features ofspa- tialintuition" comprise those of a "three-dimensionalcontinuous manifold ... in which thecomparison ofmagnitudes ispossible" - so that, for Helmholtz, freemobility isthere- foreincluded among them. In considering what "the general form of spatial intuition" mightbe, however, Schlick distinguishes twopossibilities: itcould comprise precisely these"most essential features," orit could comprise only the purely qualitative "extendedness"provided by"that indescribable psychological moment ofspatiality adhering to senseperceptions." Because the former alternative would still lead to a descriptionin termsof some or another axioms, Schlick himself favors the latter. See Schriften zur Erkenntnistheorie,161-62;Epistemological Writings, 172-75. 57. SchriftenzurErkenntnistheorie, 111;Epistemological Writings, 117. 58.Schriften zurErkenntnistheorie, 128;Epistemological Writings, 135-36. 59.Schriften zurErkenntnistheorie, 130; Epistemological Writings, 138. 60.Schriften zurErkenntnistheorie, 132;Epistemological Writings, 140. 61.Schriften zurErkenntnistheorie, 132;Epistemological Writings, 140-41. 62."The Aim and Progress ofPhysical Science" (1869), Vorträge undReden, 1: 393; Selected Writings,242.Compare n.44 above. 63.Schriften zurErkenntnistheorie, 157n.20; Epistemological Writings, 167n. 20. 64.Schriften zurErkenntnistheorie, 130; Epistemological Writings, 138. 65.See especially n.44, where Schlick explains that "modern psychology rejects the con- ofunconscious inference becauseit considers the cept energetically, rightly" thinking,log- icalprocess, exclusively asa function ofconsciousness (Schriften zurErkenntnistheorie, 165;Epistemological Writings, 176).

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions 66.For Helmholtz's useof Mill here, see, e.g., Handbuch, 3:23-24; Handbook, 3:24-26. A particularlythorough discussion ofthis aspect of Helmholtz's theory isgiven by Erdmann, Diephilosophischen Grundlagen vonHelmholtz' Wahrnehmungstheorie, 31-37("Die logischenAnnahmen"). 67.Schriften zurErkenntnistheorie, 131;Epistemologica! Writings, 139. 68.Schriften zurErkenntnistheorie, 134;Epistemologie al Writings, 143. 69.See n. 56 above. All commentators known tome have missed the fundamental difference, inthis regard, between the original sensory qualities themselves andthe lawlike spatial orderinginwhich they are embedded. Accordingly, theyhave also been unable to see that,whereas the former areindeed purely subjective, thelatter has a necessary"objec- tifying"role, as a conditionofthe possibility ofobjective external experience, having its ownnecessary structure given by the condition offree mobility. Asa consequence,such commentatorshavealso been unanimous infinding a basic confusion inHelmholtz betweenthe subjectivity ofthe sensory qualities, onthe one hand, and the idea that space is a subjectiveform of intuition, on the other - a confusiondue, supposedly, to Helmholtz'sassimilation ofthe latter tothe former. Wefind just this charge in the pas- sagefrom Schlick's n.20 cited above in my n. 63, where the misunderstanding isonly furthercompounded bythe identification ofwhat Schlick calls "psychological space" withintuitively given, purely qualitative spatiality - which, according toSchlick's n.33, isan "indescribable . . . purely qualitative 'extendedness'" (n.56 above). Schlick thereby failsto appreciate thatone of the main points ofHelmholtz's "empiricist" theory ofspace isto deny the existence ofany originally given, purely qualitative "extendedness." Even Hatfield,who is otherwiseextremely helpful and clear about this last feature of Helmholtz'stheory, nevertheless repeats the traditional complaint against "Helmholtz's assimilationofKantian subjectivity ofspace to the accepted notion ofthe subjectivity of color"(The Natural and the Normative, 224), and what is missing here, once again, isan appreciationofhow Helmholtz's own work in the foundations ofgeometry stillyields a necessaryand objective structure (buta structuremore general than the Euclidean one endorsedbyKant) for the ordering ofsensory qualities inwhat Helmholtz calls "the subjectiveform of intuition." Inthis sense, space is not only subjective, butalso "transcendental."And it is for this reason that Helmholtz applies the latter term only to space, and notto the sensory qualities thereby ordered inspace. 70.Schriften zurErkenntnistheorie, 131' Epistemologica! Writings, 139. 71.Schriften zurErkenntnistheorie, 168-69nn. 54,55; Epistemological Writings, 179nn. 54, 55. 72.Allgemeine Erkenntnislehre, 183;General Theory ofKnowledge, 215. 73.In his centenary lecture of1921 (n. 3 above)Schlick presents a more nuanced and (from hisown point of view) more charitable picture ofHelmholtz's relation to"immanence philosophy."Onthe basis of the passages we have emphasized from "The Facts in Perception,"where Helmholtz distances himself from both realism and idealism, Schlick applaudsHelmholtz's rejection ofa "realistmetaphysics" infavor of the view "that we havein signs a means for depicting [abzubilden] thelawlikeness ofthe actual; nothing furtherthan this is assertedorrequired - but this requirement orassertion is independentof every metaphysical hypothesis" ("Helmholtz alsErkenntnistheoretiker," 34-35; trans,in Mulder and van de Velde-Schlick, Moritz Schlick : Philosophical Papers, 338-39).Schlick then approvingly associates Helmholtz with the "program fora posi- tivisticinterpretation ofphysics" ofGustav Kirchhoff. Does this mean that Schlick is nowrejecting his own scientific realism in General Theory ofKnowledge! No; for Schlickalso endorses Kirchhoff in an analogouscontext in GeneralTheory of Knowledge(§11 [12]), where metaphysical views (such as those of Bergson and Husserl, forexample) that result from the confusion ofknowledge with acquaintance arerejected. In general,the main point of "Helmholtz als Erkenntnistheoretiker"is toportray Helmholtzas a paradigmofempiricism, against both Kantian and metaphysical inter- pretationsofscience. In theimmediately following passage, for example, Schlick invokesthe Zeichentheorie, notto reject the scientific realism of General Theory of

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions Knowledge,butrather toreject the traditional conception ofan underlying substance existingbehind natural actions or effects. 74.Allgemeine Erkenntnislehre, 184;General Theory ofKnowledge, 215. 75.This divergence shows itself in the very different ways in which Helmholtz andSchlick conceiveour ability to "picture" the lawlikeness ofreality (see n. 13above). For Helmholtz,weapprehend lawlikeness inthe temporal succession ofobjective events throughthesimilarly lawlike temporal succession ofthe sensations towhich they "correspond"(i.e., of which they are interpretations). Sinceboth "sides" of the relationship aretemporal, wehave genuine similarity andthus "picturing." ForSchlick, bycontrast, therecan be no such similarity between the subjective and the objective, and the sense inwhich our system ofconcepts "pictures" thelawlikeness ofreality issolely that of an abstractmapping orcoordination: "Onewill have to describe the 'universe initself' as a manifoldofinfinitely many different qualities which are so interwoven andinterdepen- dentthat they can be designated bythe quantitative conceptual systems ofthe natural sciences.Through these [systems] thelawlikeness oftheir coming tobe and ceasing tobe isreproduced (where the words 'becoming' and 'ceasing' are to be taken in a transferred sense,for it is not a matterofalterations inintuitive time, but rather ofplaces in the objec- tiveordering). Toeach of the qualities inthe external world one can coordinate a con- ceptthat is constructed outof a combinationofconcepts ofother qualities: inprecisely thisway the lawlikeness ofthe all-encompassing interconnection [ofrealities] expresses itself,for it is first through itthat this kind of coordination becomes possible. Todiscover thislawlikeness isto know the external world, for with itthe most general isfound again inthe individual, and the latter is therebyknown" (Allgemeine Erkenntnislehre, 244; GeneralTheory ofKnowledge, 284). 76.An important aspect of Schlick's correspondence-theoretic conceptionof the objective externalworld isthat the relation ofcoordination thatprojects the subjective-psycho- logicalrealm onto this objective realm turns out to be highly wo«-univocal. In§ 30 [31] ofGeneral Theory ofKnowledge Schlick makes a prima facie claim to such univocality: "Twoperceptual objects that touch one in another invisual or tactual space . . . mustcor- respondtotranscendent things that have a 'point'in common inthe objective order- schema,for otherwise twoplaces of the transcendent spacewould be coordinated toone andthe same place in a perceptualspace, which would contradict univocality" (Allgemeine Erkenntnislehre, 235;General Theory ofKnowledge, 274). In the second edition,however, Schlick adds a paragraphpointing outthat such prima facie univocal- ityof coordination isoften misleading, because objects that touch one another inthe visual field,for example, areoften quite distant inobjective space. Thus, "objective coincidences arenever experienced directly," butare rather "inferred" from immediate experience on thebasis of "rules . . . [that]are treated inmore detail in the philosophy ofscience" {GeneralTheory ofKnowledge, 274). For Helmholtz, bycontrast, theconstruction of geometrical-physicalspacefrom lawlike relations among our sensations entails, via what wenow know as theHelmholtz-Lie theorem (n.50 above), that the former isuniquely determinedbythe latter. 77.Kant's own solution tothe problem ofthe external world, on the basis of a rejectionof causalrealism infavor of the idea that we directly perceive objects outside us in space, isfound inthe Fourth Paralogism inthe first edition ofthe Critique ofPure Reason and theRefutation ofIdealism in the second, where both arguments presuppose from the beginningthedoctrine ofspace as a subjective,"transcendentally ideal"form of intuition.The widespread failure (see n. 69 above) to appreciate theclose remaining kinship betweenthis doctrine and Helmholtz's theory ofspace among commentators, Schlick included,isresponsible, inmy opinion, for the similarly widespread failure toappreci- atethe close remaining kinship between Helmholtz's andKant's solutions tothe prob- lemof the external world. 78.In general relativity wehave approximately rigidrods and approximately freemobility, inthe sense that both exist in infinitesimal neighborhoods. Inthis very same sense, however,we also have approximately Euclidean geometry. What we do not have is a situa- tionwhere constant curvature is fixed antecedently, as itwere, and then experience is

This content downloaded from 171.67.34.69 on Mon, 16 Nov 2015 10:35:50 UTC All use subject to JSTOR Terms and Conditions calledin to select one of the three classical geometries ofconstant curvature. Butit is preciselythis view of the situation, as we have seen, that frames Helmholtz's own empiri- cistconception ofgeometry, according towhich the "axioms" of[specifically Euclidean] geometrynowemerge asmerely empirical facts. In"Helmholtz alsErkenntnistheoretiker" especially(n.73 above) Schlick fastens onthis last feature ofHelmholtz's conception to portrayhim as a defenderofempiricism against Kantianism, andto claim that general relativityhas "brilliantlyconfirmed" Helmholtz's conception ("Helmholtz als Erkenntnistheoretiker,"36-38;Mulder and van de Velde-Schlick,Moritz Schlick: PhilosophicalPapers , 339-41). Schlick thereby misses once again the sense in which freemobility gives Helmholtz ananalogue of Kant's doctrine ofspace as a "transcendental"form ofintuition, within which all properly empirical discoveries (including the discoveryofa particularvalue for the fixed constant curvature ofspace) are then made possible(see again n. 69 above). 79.See n. 24 above. 80.In his n. 39 to "On the Origin and Significance ofthe Axioms of Geometry," where Helmholtzsay. that "we may not forget here that all geometrical measurements restfinally onthe principle ofcongruence" (which, for Helmholtz, clearly involves free mobility), Schlick,executing a most remarkable transposition, comments asfollows: "Congruence"isestablished through observation ofthe coming together [Zusammenfallens]ofmaterial points. All physical measurements canbe reducedtothis same principle . . . Helmholtz's proposition cantherefore beextended tothe truth that, in general, noother events are physically ascertainablethanmeetings ofpoints, and Einstein has logically drawn theconclusion from this that all physical laws may in principle contain onlyassertions about such coincidences. The following paragraphs of Helmholtz'slecture contain statements thatmove in the same direction, (iSchriften zurErkenntnistheorie, 321;Epistemological Writings, 33-34)

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