Philosophical Essays in Memory ofEdmund Husserl

(Harvard University Press, 1940), pp.143-63

PHENOMENOLOGY AND THEHISTORY OF SCIENCE

Jacob Klein

Pm LOSOP HY ••• , by its very 'essence, is the science oftrue beginnings, of origins, th~ p,rwp.aTa 7ra.IITWII. And themethod of a science concerned with the roots of things,

the method of a radical science, mustitself be radical, andthis in every respect." 1 It may be said.rnot inappropriately,that Husserl, throughout his life, directed his thought to theproblems of longin.. His· earlier; writings formulated theapproach to the "true beginnings"; he worked all his lifediscovering, rediscovering, and elucidating these beginningsand the approach to them and finally he adumbrated the aimswhich should control research in the history of science. It isthe purpose of this 'paper to show the essential connection, asHusser! understood it, between these aims and the "truebeginnings."

In attacking "psychologism," Husser! was in fact facingthe problem of "history." Any "naturalistic" psychologicalexplanation of human knowledge will inevitably be the historyof human development with all its contingencies. For in suchan account any "idea" is deduced from earlier experiencesout of which that idea "originated."2 In this view, theexplanation of an idea becomes a kind of historical legend,a piece of anthropology. The Logical Investigations showedirrefutably that logical, mathematical, and scientific proposi­tions could nevFr be fundamentally and necessarily deter-mined .by this sort of explanation. !

In order to understand the ultimate validity of logical .andmathematical propositions, it is necessary, according to

1 "Philosophie als strenge Wissenschaft," Logos, I, 340., Ibid., p. 307.

\

144 JACOB KLEIN

HusserI, to liberate first the problems of origin from aninterpretation of mind which confuses mind with nature."A thing is what it is, and remains in its identity forever:nature is eternal." Nature" appears": it is experienced assomething that appears to us through the senses, never"absolutely," rather in different aspects, in different" adum­brations." But the object of mind" appears as itself, throughitself," is in itself a" phenomenon," appears as an "absolute"and at the same time" as passing in an absolute flow, appearsright now and already fading away, sinking back continuouslyinto what is the past, and this in a way which can be perceivedin an immediate intuition." Therefore, whereas a naturalthing can be investigated and analyzed by repetition of anexperience which is intrinsically the same in so' far as theobject is the same, a mental object can be reexamined only byreflection, by "retention," in m<:mory, i.e., by a specificchange (" modification") in the "manner of givenness."In other words, a natural object, although "temporal,"remains constant with respect to our investigation: the objectof mind is immersed in "eternal" time, '~a time which cannotbe measured by any chronometer.i" ' .

Naturalistic s cholo i nores the distinction. between the!ime of mind and the time of nature. As a resu t, mind itselfand all its objects become natural objects, and all problems oforigin become problems of origin within natural time. If weliberate these problems from this naturalistic distortion, theybecome "phenomenological" problems iin Husserl's sense ofthe term.. ,- , " •

A typical "phenomenological problem" consists in findingthe "invariables'" within. the absolute flow (the "internaltemporality") of the mind, in determining the ~'invariants"which remain unchanged by reason of an essential' necessity.This can be accomplished by'means of a continuous andarbitrary "variation" of a given "example," a variation thattakes 'place in the "freedom of pure phantasy." "Throughsuch a free and continuously modified variation thenecessarilyunchangeable, the invariant, comes to the fore, something

I Ibid., pp. 312 r. cr. Idem, pp. 76fr.

PHENOMENOLOGY AND SCIENCE 145

that is unshakably the same in all the otherness and renewedotherness, the universal and common essence" - the "eidos,"the "a priori form" which corresponds to the example and allits possible variations." But this is only the first step - first inthe actual development of Husserl's thought, and first in anyphenomenological analysis. The reflection upon this kind ofanalysis, its implications and its significance leads to a deeperunderstanding of the nature of a "phenomenological prob­lem." Far from being complete in itself, the finding and facingan "essence" requires a further investigation into its intrinsic"possibility." Whatever we discover as having a definitesignificance - an essence, its" inflections," its essential charac­teristics, the compresent "halo,'~ and so forth - has alsoa "backward reference"to .a more-voriginal "significantformation." Each" significant formation" (Sinngebilde) hasits own essential "history of significance" (Sinnesgeschichte) ,which describes the" genesis" of that mental product. It is the"history" of the "formation" (or "constitution") of thatmental product. 6 This curious kind of "history" is a peculiar­ity of the mind, whose manner of being is nothing but" work"(Leistung), a constructive work, tending to the formation of"units of significance" --an" intentionality at work." Allthe intended or "intentional" units are thus constructed or"constituted" units, and we can address inquiry to the per­fected units as to their" intentional genesis." The discoveryof the "intentionality at work" makes us understand theessential and objective possibility of each single significantphenomenon, whether it refers to true being or to mereappearance.! Its being constructed (or constituted) makes upits" subjectivity." And the last step of the phenomenologicalanalysis is the grasping of the problem of" constitution" in itsuniversality, which in turn leads to a new understanding ofphenomenology as the fundamental doctrine of "transcen­dental subjectivity," the ultimate goal of all possible knowl­edge, the sapientia unioersalis.! Through it is revealed the

I

• Logik, pp. 218 r. cr. p. 26. ~ ,Ibid., pp. 184 r.• Ibid., p. 226.7 I~id., p. 4. cr. Descartes, Regulae ad directionem ingenii, Reg. I.

~..

JACOB KLEIN

"constitutive work" of consciousness that determines the"ontic sense" of the world, "consciousness" being understoodnot as a given "thing" among all other things of the givenw~rld, not as the actual thinking of human (or human-like)beings, but as the "intentionality at work" that constitutesany possible thing as a "significant unit," including the signifi­cant unit" world" itself. It is an immense and' unavoidableta~k to rev:~.l ;,h~s wo~k.ing life ~n its totality, to make every­thing that IS intelligible, ultimately out of its constitutiveorigins. 8 It is this immense task that HusserI sets to his"transcendental phenomenology."

However vague this general outline of Husserl's philosophymight b~, it shows, I thin~, th~t from the very outset the prob­~em of hIs~ory.has a de~mte, if n?t the ~ost important" placeIn HusserI.s mind. The mtervennon of DIlthey II gave a speciala~centuatlO~ to t~at problem. The essay "Philosophy as aR~gorous Sc!ence, which we mentioned at the beginning ofthis paper, IS partly devoted to. the praise as well as to thecri~icism ?f Dilthey and his history of human thought." It isquite ObVIOUS, however, that HusserI in criticizing the attitudeof historicism puts it on the same level 'with psychologism.In fact, the former is but an extension and amplification of thela~ter. N0:-V' HusserI's radical criticism of psychologism im­plies anythmg but a simple opposition between never-changing" abstract" principles and ever-changing "empirical" things.The fact that Husserl's phenomenological descriptions in theLogical Investigations were immediately interpreted as. psy­chol~gical descriptions (of a more subtle naturF - as was:eadIly conceded - than those which usually are laid down

,)n psychological textbooks) shows not merely that a greatmany readers of Husser! were not able to understand histhoug~t, but that there is a definite affinity between psy­chological and phenomenological research. Husserl himselfalways pointed out thatHume was the first to see the pr()blem

-~.- -; ---,,-,-,- '~ .._-- -.--I Logilc, p. 2;6:} .

.' cr. the co.ITCS~ndenCc between Husserl and Dilthey published by G.Misch, LebmsP~llosoPhle und 1'lUinommologi~ (Leipzig and Berlin, 1930 ) .

10 cr. especially the note on p. 326.

PHENOMENOLOGY AND SCIENCE 147

of a transcendental phenomenology, although he misunder­stood its true character and therefore failed entirely to solve it.The psychology of mental phenomena must not necessarilydiffer from their phenomenological analysis as far as theactual description, the wording, is concerned." The realdifference can only be found in the fundamentally differentattitude of the thinker toward his objects: on the one hand,the psychologist considers them in a "mundane appercep­tion," taking them as existing elements or parts or qualiti.esof the existing world; on the other hand, the phenomenologistdeprives these same objects of their." index of existence,"performs the "phenomenological reduction" (the "bracket­ing") and faces them as "pure" phenomena. Thus, thepsychological and phenomenological· desc:ription .of . logicaloperations may be identical, although their real significancediffers profoundly. More exactly; we have to distinguishbetween psychological phenomenology and transcendental

. phenomenology. The first considerf, the mind as a "na~ura.l"

object; the second, the mind as the ' transcendental subjectiv­ity." In doing so, however, transcendental phenomenology,as the universal theory of "constitution," .is primarily con­cerned with die problems of origin, the problem of true begin­nings. It is worth noting that Husseri, in the passage quoted.above, uses as an image the (Empedoclean) term intwjJ.n Tn

7fQ.vrwp "roots" of all things, rather than the traditional o.px~.

A "r~ot" is something out of which things grow until theyreach their perfect shape. The o.px~ of a thing - at least inthe traditional" classical" sense of the term -' is more directlyrelated to that perfect shape, and somehow indirectly to theactual beginning· of the growth. T~~<:ldigll'.' ..aspect ofphenomenology is more important t~ H'!sserl tha? i.ts pe~fec­tion. This is the attitude of a true historian. But It IS ObVIOUSthat the phenomenological approach to the true beginningsrequires a quite special kind of history, Its name is "inten­tional history."

11 cr.especially Logik, p. 224.

JACOB KLEIN

II

. In order to clarify Husserl's notion of" intentional history,"It may be useful to look at the development and the generalbackgr~und o~ Husserl's philosophy from a different angle.Husser~ s earliest p~ilosophic problem was the "logic" ofsymbohc mathemattcs.12 The paramount importance of thisproblem can be easily grasped, if we think of the role thatsymbolic ~athe~atics has played in the development ofmo~ern ~clence SInce the end of the sixteenth century. Hus­serl ~ logical researches amount in fact to a reproduction andpreCIS,: understanding of the "formalization" which tookplace In mathematics (and philosophy) ever since Vieta and~escartes paved the way for modem science. HusserI himselfIS, of ~ourse, well aware of that historical development.!Ie r.eahzes t?at the discovery of a formal symbolism by Vieta13~n his estabhs.hment of algebra (ars analytice; logistice speciosa)IS.at the basis of modem mfithematics as well as modemSCIence. He ascribes to Leibniz the conception of a universalan~ s~mb?lic science (mathesis unioersalis, aTS combinatoria)which is prior to any "material" mathematicaldiscipline andany" teri I" 1 . 14 H. . rna ena. OglC.. e does not seem to appreciate,in this connection, the Importance of Stevin's algebraic workan~, strangely enough, the Cartesian idea of a rnathesis unioet­salis, based at least. part~y upon Stevin and leading directlyto the co:respondmg, If modified, Leibnizian concept.PHe recogmzes the close connection between mathematical"i?eali~ation"and the idea of an "exact" nature, first con­~eIVed In the physics of Galileo. He stresses the l fundamentalImpor~ance of th~ C~rtesi~n.cogito, the correct ~nderstandingof which leads, In hIS opmion, to his own "transcendental

,phenomenology." In all that he is the great interpreter ofmodem t??ught - he reveals its hidden implications andpresuppOSItIOns, he follows and judges its essential tendencies.

12 DL'I' ,r m ~sophie der Arithmetik (1891). Cf. Lotile, p. 76.

II Loglle, p. 70. _ .14 - •uu; pp. 70 f. cr. Log. u«, I, pp. :u9 If.II See Section JV, herein.

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The contingent sequence of mathematical, scientific, orphilosophical theories does not concern him: he is not ahistorian of accidents. But in descending to the "roots ofthings" he cannot help meeting" history" as one of the basictendencies of the modern perioc;l.

We should not overlook the fact that the development ofmodern science is closely followed by the development of"historical consciousness." The" new science" of nature hasits complement in the scienza nuooa of history (Vico).16 Modernhistory is neither a chronicle of events nor an edifying ormoralizing or glorifying report of memorable deeds in thepast, but the discovery and the description of man as a spe­cifically historic being, subject to a "development" whichtranscends any individual life or even the life of peoples ornations. Modern history is not only - as ancient history is ­an interpretation and dramatic exposition of" facts," but alsoan interpretation of the historic" movement" as such. It is,in this respect, the twin brother, of mathematical physics.They are both the dominant powers governing our actual life,setting out the horizon of our thinking and determining thescope of our practice. The historicism of recent decades isbut an extreme consequence of that general historic trend.We have already characterized historicism as an extensionand amplification of psychologism. On the other hand, psy­chologism, as developed by the English empiricists of theseventeenth and eighteenth centuries, is, in fact, the firstattempt to combine the new mathematical and physicalsciences (in either their Cartesian or Newtonian aspects) witha "historical" outlook: Locke and Hume try to set forth the"natural history" (Hume) of our concepts upon which ourscience; our raorals, and our beliefs are founded. This holdsfor the empirical schools of the nineteenth century as well.It is particularly true of]ohn Stuart Mill, who found, as hewrites, a "considerable approximation" to what he wanted 17

I

11 For the role of history in the seventeenth 'century v, L. Strauss, The Po­litical Philosop'hy oj Hobbes, Its Base and Its Genesis (Oxford, J 936), especiallychapter vi. .

11 See his Autobiography, ed. by].]. Coss (New York, 1924), p. 145.

15 0 JACOB KLEIN

in William Whewell's History of the Inductive Sciences. IS The his­tory of science appears as a kind of prolegomenon to thesystem of logic, which in turn is considered mainly as anexposition of the methodical and conceptual foundations ofscience. I t is not merely an accident that both J. S. Mill andSpencer wrote autobiographies (not to forget the short auto­biography of Hume), nor that Hume is the author of The His­tory of England. As to the prolific historical study in all fields ofhuman activity, which makes up most of the scholarly workduring the nineteenth century, it is intended, as it were, tofill the gap between. the ever more·" formalized" scientificapproach to tire surrounding world and our daily life, entan­gled, as it is, in a maze of immediate" practical" problems,difficulties, ambitions, and passions. History, in the usualsense of the term, is not a matter-of-course attitude. The ori­gin of history is in itself a non-historical problem. Whateverhistorical research might be required to solve it, it leadsultimately to a kind of inquiry which is beyond the scope ofa historian, whose purpose is to give the "story" of a given ."fact." It may, indeed, lead back to the problem of inquiry,the problem of lSTOpl.a as such," that is, to the very problemunderlying Husserl's concept of an" intentional history."

To inquire into an object means, according to Husserl,first to "bracket" its" objectivity" and then to seek for its"constitutive origins," to reproduce its" intentional genesis."Any object, as a "significant" or "intentional" unit, contai~

the "sedimented history" of its "constitution."2O That" hIS­tory," of course, did not take place within '.'natural time."Yet it can be understood as a "history" because1the intentionalgenesis belongs to the "life of consciousness," iand conscious- ~ness itself is primarily constituted as an "ab$olute stream"determined by the "internal temporality." "Internal tempo­rality" is thus the universal eidetic" form" of the intentionalgenesis." In any inner experience of an intentional object,

11 Cf. th~ title of his lat~r book: Philosophy oj the InductiveScimces, Foundedupontheir History. _ ..

18 Cf. Plato, Phaeda,96 A fr.so Logik, p, 217. II Ibid., p. 279.

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that object is given originally in the mode of immediate"presence"; this immediate "presentation" is followed, ofnecessity, by a "retention" of the object, in which the objectappears in the mode of "just-having-been-experienced";through all the successive modes of retentional consciousness-that is to say, through a continuous "modification"­the object is constituted as persisting, as one and the same(identical, "invariant") object. But just as there is a "limit"which the continuous modification of the retentional con­sciousness approaches and beyond which the "prominence"of the object flows away into the general substratum of con­sciousness," there is the" past history" of the original "pres­entation" of the object, which is the proper domain oftranscendental phenomenology. It is here that the "evi­dence" experienced in the immediate presentation assumes thecharacter ofa transcendental problem of constitution. It ishere that the intrinsic "possibility" of the identity of anobject is revealed out of its categorial constituents, that the"intentional genesis" leads back to the" constitutive origins,"that the "sedimented history" is reactivated into the "inten­tionalhistory." Moreover, such a transcendental inquiryinto an object may reveal the essential necessity of its being'subjected to a history in the usual sense of the term. In otherwords, it may reveal the essential necessity of a historicaldevelopment within natural time.

This is the case if the object in question is in itself an "idealformation" like all mathematical and scientific objects. .Anyscience, in the precise sense of the term, has of necessi itsown history. I t is founded upon the "intention history" ofits ideal objects. The greatest examples to which HusserIhimself referred are Euclidean geometry and Galileo's phys­ics.23 They are explicitly dealt with in two papers workedout in 1935 and 193624 and conceived as parts of a com-

:12 Ibid., p. 280. , " Ibid., pp. 215, 257.2f "Die Krisis der europaischen Wissenschaften und die transcendentale

Phanomenologie, Eine Einleitung in die phanomenologlsche Philosophie,"Philosophia, vol. I, 1936; "Die Frage nach dem Ursprungder Geometrie alsIntentional-historisches Problem," published by E. Fink in Revueinternationale dePhilosophie, I, 2.

152 JACOB KLEIN

prehensive work on phenomenological philosophy to whichHusserl devoted his last years," The problem which Husser!faced in. those papers is precisely the relation between in­tentional history and actual history. Here again he takes upa task that psychologism could not solve with its own premisesbut had attacked in its own way. In doing so, Husserl actuallyconfronted the two greatest powers of modern life, math~­matical physics and history, and pushed through to theircommon" root."

III

The article about the "Origin of Geometry" is but afragment the importance of whi.c? lies in ~e fact that theconcepts of history and of tradition, esp~clally that of th~tradition of science, are subjected therem to a careful, ifincomplete, analysis. An application of this analysis is givenin the "Crisis of the European Sciences and TranscendentalPhenomenology." We shall begin with the "Origin ofGeometry," and try to connectits main problem with Husserl'smore fundamental" transcendental" considerations.

We have already seen that ~!:lY significant.Jol:.l!illti~n..~constituted as an "invariant" within the absolut<:-~treamofconsciousness. As an invariant, as identically the. same, itseems to transcend any possible time. Its" eternity," how­ever is but a mode of" eternal" time: its identity is an in­tentional product of the transcendental subjectivity whichis "at work" through all the categorial determinations thatconstitute a significant unit. This nexus of significancebetween the "subjectiv~ty at work" and its intentional prod­ucts (Lristungsgebilde) is thus the real problem;?f historicitytaken in its universal and transcendental meamng. That 15

to sav the problem of historicity is ultimately the problem ofphilosophy itself.26 The" intentionality at work" implieshistoricity (as the "historical a priori") whic~ makes i?tel­ligible nor only the eternity or super~t~~porahty of the.Idealsignificant formations but the possibility of actual history

U Cf. the introductlon by E. Fink, loco eit., p, 203.2G Loc.cit., p, 219.

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within natural time as well," at least of the historical develop­ment and tradition of a science. The" discovery" of geom­etr , for instance, as a historicE.. event, is dependent upona wor of" things," understood and dealt with accordingto their" thingness." But thingness as a significant unit bearsessential features, quite independently of any scientific ap­proach to them. "Things" have "bodies" have color-- ... , ,weight, hardness or softness, are smooth or rough, have ashape and a size, can be measured, can be in motion or atrest, and so on. These are not merely so-caIled "empiricaldata," but characterize the intuitable "essence" of a" thing"~s ~uch. Some of those essential features are apt, by anmtrmsic necessity of their own,.JQ. be made prominentv-forinstance their shape or their measurability. This prominenceis utilized for" practical" purposes, and the practical handlingof things may lead to a more or less satisfactory technique.Here again there is the essential possibility of discovering" i~" them a set of somehow privileged" shapes" or "figures"whlc? can be more perfectly !,:ea~ured "and brought intorelation to each other. The actualization of that possibilityrests upon the actual handling of such" material"; and finallythe "discovery" of geometry as a "science" - however greatthe change of attitude, the shifting from practical to theoretical.purposes might be - is still dependent upon familiarity withthat perfected technique.

The actual way leading to the discovery of geometry mayhave been entirely different from this one, to which Husser!alludes." It is quite possible, even probable, that geometryas a science came into being as a result of arithmetical andmusical preoccupations. But even so, that discovery pre­supEoses a characteristically articulated world, resup osesthe ac uaintance with a definitel sha ed and eatured, materIa ," presupposes, m sort, the experience of" things."

But the discovery of the science of geometry presupposesalso, on the part of the" first geometer," an "anticiEation"(Vorhabe) of what comes into being through his "accomplish-

27 Ibid., p. 225.

28 Cf. pp. 223 f.

154 JACOB KLEIN

rnent " 29 (gelingende Ausfiihrung), These notions of " anticipa­tion" and "accomplishment" are most important for theunderstanding of Husserl's thought. They provide us with thelink between" intentional history" and actual history. Thevaccount for the" evidence" of all the .•significant formations ,.belonging to a science such as geometry. For" accomplish-xment or what is anticipated means evidence to the activesubject: herein the product shows itself originally as itself:' 30

But since the product. in the case of geometry, is an idealproduct, "anticipation" and the corresponding .. accomplish­ment," as "acts" of the subject (the "first ~eometer"), arcfounded upon the" work" of transcendental suhjectivitv: theideal formations of geometry are products of the .. inten­tionality at work." " Anticipation" and .•accomplishment"translate into terms of "reality" what actuallv takes placewithin the realm of .• transcendental subjectivitv." On theother hand - and this is the important point - the con­stitution of those ideal "intentional units" presupposes, ofnecessity, the whole complex of ex eriences leadin to thesituation in w lch eomet as a science is ca able of beina

':"anuclpate a "intended." 31 In other words, "science,especiallY geometry, as a subjective intentional product. had to hatesome definite historical beginning,"32 i.e., a beginning within thecourse of actual history. At this definite moment the" originalfoundation" (Urstiftung) of geometry occurred.

Needless to say, this analysis does not refer to any known oreven knowable historical. event. It only shows the essentialconnection between geometry as a supertemporal productof the mind and its "creation" in actual history. At thisstarting-point geometry is not yet capable of being handedon: it has not yet attained the stage of" ideal objectivity," asa condition of its becoming the. common property of manvindividuals. At least three steps are required in order toreach this stage. To begin with, the original evidence, ex­perienced during the first actual production, passes over into

~. Page 208.30 Page 209.

ncr. Logik, p. 2j8.U "Geometrie," lac. cit., p. 208.

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a "retentional" consciousness and finally fades away intoforgetfulness. But it does not disappear completely: it can beawakened, and the "active" remembrance of the originalproduction of any ideal significant formation carries with itthe evident experience of the sameness of that formation,carries furthermore the insight into its unlimited reproducibil­itv, This experience does not, however, transcend the personalsphere of the subject. The second necessary - and decisive ­step is the embodiment of that experience in words, whichmakes it communicable to other subjects: these others arethereby enabled to reproduce the same evident experienceout of their own mental activity. The" ideal sit;nificantunit" acquires its peculiar manner of existence only throughspeech and in speech. A last step remains to be taken in orderto secure the lasting existence of the .. ideal objects," to estab­lish their pcrtect .. objectivity." It is the translation of thespoken word into the written word. At this stage the realhistory of a science may begin. It is, of necessity, not onlythe history of .• progress," of the accumulation of knowledge,but also a history of failure. The means which secure theobjectivity of a science, at the same time endanger its originalintegrity. No science, in its actual progress, can escape the.•seduction" emanating from the spoken and written word.For the signifying function of a word has, by its very nature,the tendency to lose its revealing character. The more webecome accustomed to words, the less we perceive theiroriginal and precise" significance": a kind of superficial and" passive" understanding is the necessary result of the increas­ing familiarity with spoken and written words. The originalmental activity, the production of significance, embodied insounds and signs, is not reproduced in the Course of actualcommunication. Yet it .is there, in every word, somehow., forgotten" but still at the bottom of our speaking and ourunderstanding, however vague the meaning conveyed byour speech might be. The original ,. evidence" has fadedaway but has not disappeared completely. It need not be"awakened" even, it actually underlies our mutual under-

I56 JACOB KLEIN

standing in a "sedimented" form. "Sedimentation is alwayssomehow forgetfulness." 33 And this kind of forgetfulnessaccompanies, of necessity, the development and growth of ascience.

To be sure, the original evidence can be "reactivated." andactually is at definite times, in order to restore the full signif­icance of all the previous steps leading to a given stage withinthe development of a science. This interlacement of originalproduction and "sedimentation" of significance constitutesthe true character-of history. 34 From that point of view thereis only one legitimate form of history: the history of human,thought. And the main problem of any historical research is.precisely the disentanglement of all these strata of "sedimen.:tation," with the ultimate goal of reactivating the" originalfoundations," i.e., of descending to the true beginnings, tothe "roots," of any science and, consequentlv, of all pre­scientific conceptions of mankind as well. 35 Moreover, ahistory of this kind is the only legitimate form of epistemology.The generally accepted opposition between epistemology andhistory, between epistemological and historical origin, is un­true. More exactly, the problem of history cannot be re­stricted to the finding out of" facts" and of their connection."They embrace all stages of the" intentional history." History,in this understanding, cannot be separated from philosophy.

Reactivation of the" sedimented history" may become themost imperative need in a given situation. The" sedimenta­tion of significance" can reach such a degree that a partic­ular science, and science in general, appear almost devoidof "significance." This has been becoming increasingly thestate of affairs in recent centuries and is the case now.FHusserl deals explicitly with this unique situation in his"Crisis of the European Sciences." We shall confine ourconsiderations of this matter to the special problem of mathe­matical symbolism as the main instrument and the real basisof mathematical physics.

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IV

Husserl's philosophy, as it appears in its latest phase, is anadmirable attempt to restore the integrity of knowledge, of€7rUHr/J.LTJ, threatened by the all-pervading tendency of "sedi­mentation" His analvsis of the meaning of " tradition" and"historicai developme'nt" is directly motivated by this pur­pose. The increase of "sedimentation" follows clo~ely theestablishment of the new science of nature, as conceived byGalileo and Descartes. Or rather, the new science itself, withall its amazing accomplishments and far-reaching potentiali­ties is basicallv the product of an accumulated sedimentation,thereactivation of which is usually not conceived as a possibleor even desirable task. As Husserl puts it: "Galileo, thediscoverer ... of physics and of the corresponding king. of

d I· . "38 Innature, is both a revealing an a concea 109 gemus.analyzing the foundations of Galileo's physics, Husserl.doesnot intend to zive a detailed historical account. Galilee's

~ .name is. in this connection, somewhat of a collective noun,covering a vast and complex historical situation. 39 On.t~eother hand, this analysis' is intended to shed light on the ongmof modern consciousness in its universal aspect.P The prob­lem of the origin of mathematical physics is the crucialproblem of modern history and modern thought. .

We shall not follow Husserl's pattern here, but try to givea general outline of that actual historical. development,referring, in due course, to Husserl's correspondmg statements.It should be emphasized that Husserl's "intentional-histor­ical" analysis of the origin of mathematical physics, althoughnot based upon actual historical research, is on the whole anamazing piece of historical" empathy."

The establishment of modern physics is founded upon aradical reinterpretation of ancient mathematics." handed onthrough the centuries and acquiring a new dignity i.n themiddle of the sixteenth century. The Elements of Euclid aresubjected to careful studies, are commented upon and con-

33 Page 212.

H Page 220.

3$ Pages 212, 218f.

31 Pages 220 f.

37 Page 21 7.38 "Krisis," p. 128.

3t cr. p. 133.

.0 Page 132.

U Cf. p. 95.

PHENOMENOLOGY AND SCIENCE r 59

analysis as the "way from the unknown taken as a known,through the consequences, down to something which isknown." 42 This Greek definition applies, however, to thegeometrical analysis, which in its procedure does not make useof any definite magnitudes, comparable to the definite numer­ical values of a Diophantean equation. Assuming that the"general" method behind the" Diophantean analysis" mustbe applicable to the numerical as well as to the geometricalprocedure, Vieta postulates a reckoning (logistice, AO"/LIFTLKr,)using not numbers but merely "species" (taking over theDiophantean term "species," ~iOOf, applied by Diophantusto the various powers of the unknown). Thus he opposes a"restored" and "pure" algebra, the logistice speciosa, to thecommonly used Diophantean logistice numerosa.P At the sametime, this pure algebra represents, in his mind, the generaltheory of proportions. Described by Proclus as the" highest"mathematical discipline, the general theory of proportionsin the form of Viera's pure algebra becomes from now on thefundamental discipline not only of mathematics but of thesystem of human knowledge in general. 44 The translator ofProclus into Latin, Barocius, in order to designate this highestmathematical discipline, uses the term mathesis unioersalis,referring to it on the margin as scientia dunna. It is from thissource that Descartes,45 and the entire seventeenth century,have derived the term and the conception of a "universalscience" which includes all possible sciences of man.

This universal science bears from the outset a symboliccharacter.4& In creating his ars analytice, Vieta introduced forthe first time, fully conscious of what he was doing, the notionof a mathematical symbol and the rules governing symbolicoperations: he was the creator of the mathematical formula. 47

In doing this, he preserved, however, the original "ideal"concept of number, developed by the Greeks out of theimmediate experience of "things" and their prescientific

158 JACOB KLEIN

tinuously reedited and reprinted. The" Euclidean spirit"spreads rapidly. Archimedes and Apollonius, newly redis­covered, are studied but are understood bv relativelv few.On the other hand, the discovery of manuscripts of Dio­phantus helps to transform the Arabic art of algebra - a darkart, comparable to alchemy - into a science accepted as asupplement to the traditional quadrivium of the mathe­matical disciplines. The publication and translation ofProclus' commentary on the first book of Euclid allows afusion of the traditional theory of ratios and proportions withthe "algebraic" art of equations. The importance of thisbook by Proclus cannot be overestimated. The algebra(leading back, at least partly, to a Gre-ek tradition representedby Diophantus and Anatolius) and especially the Arithmeticof Diophantus are understood as an immediate applicationof the theory of ratios and proportions. Moreover, the(Eudoxean) "general" theory of proportions. as laid downin the fifth book of Euclid, seems to indicate that the "vulgar"algebra as well as the Arithmetic of Diophantus is but aremnant of a more general theory of equations, of a true andmore general algebra. It is Vieta who works out the logicaland mathematical consequences of this insight and becomesthus the" inventor" of modern mathematics. Let us considerbriefly the way in which he proceeds.

The method of Diophantus consists in setting up an inde­terminate equation which is immediately converted into adeterminate one by the arbitrary assumption of a numericalvalue. This equation has a purely numerical character:apart from the unknown quantity, the" given" quantities aswell as the coefficients of the unknown are definite numbers.Having solved an equation by methods which are often veryingenious, Diophantus refers in not a few cases to the easilyperformed checking of the result in these terms: Kal ?1 a,roo~L~Lf

q,all~pa. (and the demonstration [the "proof"] is obvious).Now, a "demonstration" in Greek mathematics means the" synthesis" which is the reverse of the preceding" analysis."Therefore Vieta calls the Diophantean solution an "analyti­cal" process, referring himself to the traditional definition of

'2 Pappus, ed. Hultsch, II, 634... cr. "Krisis," p. 97·.. cr. pp. 120 fr.'6 Cf. Regulae, Reg. IV.

cr. the scholium to Euclid XIU, prop. 1-5·

.. cr. "Krisis," pp. I 19, 123.<7 cr. pp, I IS f., 118, 123.

160 JACOB KL'$IN PHENOMENOLOGY AND SCIENCE

articulation. In Vieta's notion of "species" the original un­derstanding of number is retained, as it is,of course, in the-Arithmetic of Diophantus, But his immediate successors, Ghe­taldi, Harriot, Oughtred, and Wallis (partly under the in-·fluenee of Stevin and, as far as Wallis is concerned,of .Descartes' Geomefr..y) , have already lost the original intuition.The techniqueofoperating '.\i~symbols replaces the scieI!~~

of'numbers.f Descartes, for his part,aiming at the all-compre­hensive mathesis univcrsalis, and following the algebraic doctrineof Stevin, transforms the traditional understanding of Euclid­ean geometry into a symbolic one, which transformation is atthe basis of his analytic geometry.ss His mathematical signifi­cance lies in the fact that he subjects the traditional geometryto the same kind of symbolic " formalization" to which Vietasubjected the Diophantean arithmetic.

This establishment of a fundamental analytical discipline,planned in advance by Vieta as well as by Descartes for thesake of founding a "true" astronomy and a "true" physics,inaugurates the development of a symbolic science of nature,commonly known as mathematical physics. eo As to Galileo,he has not yet at his disposal the powerful instrument ofsymbolic formulae. His physics is conceived as an applicationof Euclid's (and Archimedes') geometry," especially of theEuclidean theory of proportions. But he is already under thespell of that general symbolic tendency: he anticipates mathe­matical physics in his concept of an "exact" nature as a greatbook written in mathematical characters. The implicationsof this concept of an "exact" nature are unfolded in his workand in the work of the following generations. ~:ut the" sedi­mented significance" upon which this work and the conceptof an exact nature itself rest, have hardly been "stirred up,"

• 8 Cf. p. 1 2 3.•• The analytic geometry itself is, as an algebraic geometry, a "formaliza­

tion" of the methods used by Apollonius. This holds for the analytic geometryof Fermat as well. Both, however, considered the analytic geometry as an ex­pansion, a "generalization," of the procedure of Apollonius, not as a "new"discovery.

6. Cf. "Krisis," p. 97.6\ Cf. pp. 98 rr., 102 rr., 113.

Q!:...,e~e_~ touched,~ve~_ ~!I!~e .. Galil<,:~ KepLer,<md Descarteslaid the foundations of mathematicafI)hysjcl;.52 The "in:tentionaTJ~!stQry-,':_<!s_suggesteaby'Husserl, may accomplish'this task:it may "reactivate" the "s~dimented""evidences,"llJ,ay.bring to light. the forgotten origins.of .. our science. Ahistory of science which fails to tackle this task does not liveup to its own purpose, however valuable and indispensableit otherwise might be.

The problem of the origin of modern science thus presentsa threefold aspect. There is first. the "anticipation" of anexact nature, implying the possibility of reducing all appear­ances to geometrical entities. Not only the "prominent"features mentioned above (i.e., some of the so-called primaryqualities), with their essentially geometrical characteristics,but also the so-called secondary qualities, such as color,sound, odor, warmth (i.e., the" specific" sensory qualities) 53as well as change and motion, are understood to be convertibleeither into geometrical magnitudes or at least into somethingthat can be treated geometrically, having definite ratios andproportions. This kind of approach to all possible qualitiesof things can be traced back to the nominalistic school of thefourteenth century, especially to Nicolaus Oresmus (NicoleOresme), whose work De uniformitate et difformitate intensionum 54

has profoundly influenced all following thinkers up to Galileo,Beeckman, and Descartes. 55 The" sedimentation" involvedin this "Euclidean" approach to the world consists in thematter-of-course attitude toward geometrical evidence. 56Accordingly, our first task is the intentional-historical reactiva­tion of the origin of geometry.

In trying to fulfil the anticipated conversion of all" natural"

b2 Cf. p. I I 7.es Cf. pp. r 04, 108.b' The same work is also known under the significant titles: "Dc figuracione

potentiarum et mensurarum difforrnitarum," and "De configuracionibusqualitatum."

bb Cf. P. Duhem, Etudes sur Leonard de Vinci, vol. III (1913); and also the corre­spondence between Beeckman and Descartes in OeUl'TfS de Descartes (ed. Adam­Tannery), vol, x, and Descartes' Regular, Reg. XII.

se Cf. "Krisis," p. III.

JACOB KLEIN

appearances into geometrical entities, in trying t- geometrizenature, the physicist faces immediately the problem of findingthe adequate means for such an undertaking. This problemis solved through what can be called the method of symbolicabstraction, which is quite different from the ancient a<!>alpHm.I t is the method used consciously by Vieta in his establishmentof a "general" algebra and by Descartes in his early attemptto set up the mathesis uniiersalisP It amounts to a symbolicunderstanding of magnitudes and numbers, the result of whichis an algebraic interpretation of geometry. The roots of thisdevelopment can be found in the adoption of the Arabicsystem of numeration which leads to a kind of indirect under­standing of numbers and ultimately to the substitution of theideal numerical entities, as intended in all Greek arithmetic,by their symbolic expressions. That is to say, a "sedimented"understanding of numbers is superposed upon the first stratumof "sedimented" geometrical" evidences." This complicatednetwork of sedimented significances underlies the" arithmeti­cal" understanding of geometry." The second task involvedin the reactivation of the origin of mathematical physics is,therefore, a reactivation of the process of symbolic abstrac­tion and, by implication, the rediscovery of the original arith­metical evidences.

Upon those combined "sediments" reposes finally ouractual interpretation of the world, as expressed not only inour science but also in our daily life." In fact, the" scientific"attitude permeates all our thoughts and habits, no matterhow uninformed or misinformed about scientific topics wemay be. 'Ve take for granted that there is a "true world"as revealed through the combined efforts of the scientists,whatever doubts the scientists themselves may have on thesubject. This idea of a true, mathematically shaped worldbehind the" sensible" world, as a complex of mere appear­ances, determines also the scope of modern philosophy. Wetake the appearances of things as a kind of disguise concealing

67 cr. Descartes, Regulae, Reg. XIV.

ss Cf.1' Krisis," p. "9... Cf. p. 124.

PHENOMENOLOGY AND SCIENCE

their true mathematical nature. But we have "forgotten"that this nature, "anticipated" by the founders of modernscience, was to be constructed 60 by means of ingenious methods,that the original /~)llothesis of an "exact" nature had to provetrue, without ever being able to lose its character as a hy­pothcsis.?' The" anticipation" of an exact nature is the an­ticipation of its history. Its history is the development of themethod of symbolic abstraction. It takes the form of an art,consisting in the continuously perfected technique of operatingwith symbols." The" exact" nature is not something thatis concealed behind the appearances, but rather a symbolicdisguise concealing the original "evidence" and the originalexperience of things." Hence a third task arising from theattempt to reactiva te the" sedirncnted history" of the" exact"nature: it is the rediscovery of the prescicntific world andits true origins."

60 Cf. p. 107.

eI Cf. pp. I 13, 114, "5, 1 16 f." Cf. pp. I 15, 121.

63 Cf. p. 126.

.. Cf. pp. 124 ff., 132.