Influence of Philosophic Trends..., Koyre

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Influence of Philosophic Trends on theFormulation of Scientific Theoriesproressor Koyrc is "^ -,:,:::::,Y,:",::;:" des Hautes Etudes, paris.He has also been a aisiting.professor at the (Jniaersity of Chicag:o, Johns Hop-lcins Uniaersity, and the (Jniaersity of l|isconsin.

A CCORDING to Philipp Frank fSci. MonthtyA 79, 139 (1954) l, the reasons for, orI \ against, the acceptance of certain scien-tific theories are not always restricted to the tech-nical oalue of the theory in question-that is, to itsability to give us a consistent explanation of thephenomena it is dealing with; instead, these rea-sons involve a series of other factors.Thus, in the case of Copemican astronomy, thechoice was not merely one between a more simpleand a more complicated tleory of celestial motions,but also a choice between a more simple and aseemingly more complicated physics, belween-2sBacon very aptly pointed out-reliance on, or re-jection of, sense perception as a basis of phpicalknowledge, and so forth.- f am in perfect agreement with Frank. I onlyfear that he did not go far enough, and that, inhis analysis, he made a rather unfortunate omis-sion, namely, that o{ the philosophic backgroundof the conflicting theories. It is, indeed, my corr-tention that the role of this .'philosophic back-gro-und" has always been of utrnost importance,and that, in-history, the influence of philosophyupon science has been as important as thi influence-which everybody admits-of science upon philos-oph1. As an example illustrating my asseriion Iwould like to consider the period of post-Coperni-can -science, the period commonly ionsidered tobe that of the origin of modern science, I meanthe science that dominated our thinking ior aboutthree centuries, roughly speaking, frorn* Galileo toEinstein and Planck--Everybody agrees that the 17th century accom-plished or underwent a deep cultural, philosophic,scientific revolution. From our point oi view,- andlbr our purposes, this revolution can be charac-terized as (i) the destruction of the cosmos, that is,

the substitution for the hierarchically structuredfinite world of the Aristotelian tradition of the in-finite universe bound together by the uniformity ofits fundamental components and laws; and (ii)the geometrizaion of space, that is, substitutionfor the concrete physically structured plabe-spaceFebruary 1955

of Aristotle of the abstract, isomorphous, and in-finite dimension-space of Buclidean geometry nowconsidered as real.The cosmologic and physical conceptions ofAristotelian science, or natural philosophy, have-the existence of some orthodox Thomiits notwith-standing-generally speahing a very bad reputa-tion. Some of the moderns, especially philosophersand psychologists, go so far as to tax Aristotle'sreasonings as infantile and attribute to him themental age of a child of 12.Historians of science treat him scarcely better.This, in my opinion, is to be explained only by thecontinuity of the anti-Aristotelian tradition inher-ited from the founders of modern science who-and which-asserted themselves in a victorousstruggle against Aristotle; and by the persistenceof both the historiographic tradition of the 19thcentury and the value judgments of the first mod-em historians of science-an l8th and lgth cen-tury creation.For these historians, born, bred, and reared inthe Newtonian world, which-though with somerather important structural additions-has beenaccepted, not only as real and true. but even asconforming to the natural world-conception of thehumair mind, the very idea of a finite, closed cos-mos appeared ludicrous. What ridicule, indeed,has not been piled upon Aristotle for his disc,rssionof the dimensions of the world, or of its weight, orfor holding that bodies could move naturalli with-

.9u_t b-ei1S dragged or pushed from outside, for his'belief that circular motion was a particufarly in-teresting and important kind of m-otion, the verypattern of a natural one.We know today-although, perhaps we have notyet-quite accepted and. admitted it--that all this is,perhaps, not quite so ridiculous as it seemed to beyesterday; and that Aristotle was much more rightthan he knew himself. As a matter of fact, circJarmotion does play a particularly important role inthe world and is particularly well represented in it;so well that for a natural object it seems to be anatural thing to turn and rotate. Indeed, every-

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thing does so: the galaxies and nebulae, the starsand the sun and the planets, and atoms and elec-tronsl perhaps even photons are not an exceptionto the general rule.The spontaneous motion of bodies, as we knowfull well since Binstein, is quite normal, provid.edthat, of. course, the space is conveniently curved;and we know, too, or at least believe we know, thatour universe is by no means infinite (although ithas no boundaries) and that "outside" this uni-verse there is strictly nothing, just because there isno "outside" to the world, and all world-space is"inside."Now this is precisely what-somewhat clumsilybecause he did not have at his disposal the re-sources of Riemannian geometry-Aristotle hasbeen teaching us. Outside the world, he said, thereis nothi.ng, pure nothing, neither plenum rroruacuu,rn, neither place nor space, because all thespace-that is, all the places where something canbe-is inside.The Aristotelian conception is, of course, notmathematical; this is its weakness, but also itsstrength. It is a metaphysical one. The world ofAristotle is not a mathematically curved world; itis, so to speak, a metaphysically curved world.Contemporary cosmologists, when they try toexplain to us the structure of the Einsteinian, orpost-Einsteinian, curved space and finite thoughboundless universe, are wont to point out that thiyare dealing with dificult mathematical concep-tions, and that those of us who are not sufficienilytrained and who lack ability in mathematicalthinking will not be able fully to understand them.They-are perfectly right, of course. Yet it is per-haps interesting to note that they are only repeat-ing, indeed, turning upside down, what medievalphilosophers, when they were dealing with Aris-totelian cosmology, explained to their readerslthus they (Henricus of Ghent, for instance, in thelate 13th century) did not fail to point out thatthey were using difficult metaphysical reasoningsand concepts, and that those who were not suffi-ciently trained in, or gifted for, metaphysical think-ing and who could not rise above the level of geo-metric imagining, could not understand Aristotle;they would continue to ask: What is outside theworld? What will happen if we push a stickthrough the surface of the ultimate heavenlysphere?The real-difficulty of the Aristotelian conception-solved ultimately by Riemann and Einstein-consists, oldg_1rly, in the necessity of providing aplace for Euclidean geometry inside the-world. Vet,for Aristotle, it was by no means a decisive diffi-culty, for, in the Aristotelian conception, geometryis not a fundamental science that discloseslhe nec_108

essary structure of physical being but only an ab-stract and subservient one. Experience, sense per-:ep!i9n, not a priori mathematical reasoning, arefor him the true bases of physics, the science thatdeals with nature and gives us knowledge of thereal world.On the other hand, for Plato, who believed inmathematics and did not believe in sense percep-tion, and who had tried to link together the ideaof a cosmos and an attempt to construct the phys-ical world, the world of matter and of change, outof pure geometric space (y,6po), the situation was,of course, much more difficult. It had to be one orthe other, The choice, sooner or later, had to bemade. It was unavoidable, although about 2000years passed before it was made in fact, and itwas just this acceptance of the complete geometri-zation of space and, consequently, the rejiction ofthe cosmos that characterized the platoniim of the17th century, that of Galileo and of Descartes,and in this sense opposed it to the world-view ofPlato himself.It seems to me rather obvious that the revolu-tion of the 17th century, which substituted for thequalitative world of sense perception and everydaylife the Archimedean world of geometry made reai,cannot be explained simply b"rf th" influence, oreffect, of an enlarged or enriched experience(sense experience).- 1) As P. Tannery and P. Duhem have alreadyshown, Aristotelian science (phpics), precisely be-cause it was based on sense perception and com-mon-sense experience and thus was really andtruly ernpirical, was in much better accord withperception and experience than the new science ofmathernatical dynamics.After all, bodies really fall when they are heauyand rise when they are light; and the principle ofinertia, according to which bodies when pushed orthrown continue their motion indefiniiely in astraight line, is certainly not based otr e*pe.i.rr..,which constantly disproves the principle. Inertialmotion, indeed, not only has never been encoun-tered in the world, but it is even impossible thatit ever should be.2) The infinity of the universe cannot, of course,be-asserted on the ground of experience. The in-finite, as Aristotle had pointed out, cannot be tra-versed. or given; compared with eternity a billionyears is as nothing, and the world reveaied by thePalomar reflector is by no means greater than thatof the Greeks. Yet the infinity of the universe is anessential element of the axiomatic structure ofrnodern science and is implied by its fundamentallaws, as Euler and Einstein have both recognized.- 3) The experiences alleged by the promolers ofthe new science, or their historians, prove nothing

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whatever, because (i) such as they were actuallymade they are nothing less than precise, (ii) inorder to serve as proof they would require an ex-trapolation to infinity, and (iii) they have, alleg-edly, to demonstrate to us the existence of some-thing-inertial motion-that is strictly and rigor-ously impossible.The validity of these experiences presupposesthe mathematical structure of nature. the mathe-matical language of (physical) science.The birth of modern science is concomitantwith a transformation (we could even call it muta-tion) of the axiomatic framework of humanthoughts, with a shift in the evaluation of intel-lectual knowledge as compared with the knowledgegiven to us by sense perception, and with the dis-covery that-as Descartes suggested-the idea ofthe infinite is a clear and positive idea, in spite ofits being (falsely) expressed by a negative term,and that it is therefore a true one-that is, anidea which gives us access to the real world.Thus it is perfectly fitting that this infinitizationof the universe (the breaking of the circle, as Mar-jorie Nicolson has called it, or the bursting of thesphere, as f prefer to call it) should have been an-nounced by a philosopher-Giordano Bruno-andopposed for scientific and empirical reasons by thegreat astronomer KeplerGiordano Bruno is neither a very great philoso-pher nor a very good scientist, and the reasons hegives in favor of the infinity of the universe andthe intellectual primacy of the infinite are not par-ticularly clear. Giordano Bruno is not Descartes.Yet we know that not only in philosophy but evenin pure science-take, for instance, the case ofKepler, or that of Dalton, or even that of Maxwell-faulty reasoning from inexact premises sometimesleads to perfectly sound and ev"n e*tremely im-portant results.Fifteen years ago, I called the revolution of the17th century "la revanche de platon.r' But, as amatter of fact, it was an alliance, an alliance withDemocritus, that decided the old strife and enabledPlato to defeat Aristotle.Strange alliance! Yet we know that not onlv inthe history of philosophy or ideas but also in his-tory tout court these strange alliances of seeminglnor even really, incompatible elements occur moreoften than not. The enemies of our enemies are ourfriends. Thus the Very Christian King of Franceallied himself with the Khalifa of fshm, Com-mander of the Faithful. Or to come back to thehistory of philosophico-scientific thought, what ismore strange than the alliance of Mach and Ein-stein?Democritean atoms in the space of Plato, or ofEuclid: one understands that Newton needed aFebruary 1955

God in order to maintain the connection bctweenthe elements of his universe; one understands, also,the rather curious character of this universe (the19th century was too accustomed to it to be ableto notice its strangeness) whose material elements,objects of a theoretical extrapolation of the ex-perience, swim or are immersed,, without beingaf ected by it, in the nothingness of absolute space-a real and even necessary and eternal non ens-object of a priori intellectual knowledge. One un-derstands therefore the rigorous mutual implica-tion of this absolute, or of these absolutes-abso-lute space, absolute time, and absolute motion-that are accessible only to pure intellectual cogni-tion, and their complementary opposites, relaiivespace, relative time, relative motion that are theonly ones given to us by empirical knowledge.Modern science stands and falls with these con-ceptions of absolute time, absolute space, and theirconcomitants, absolute motion and absolute rest.Newton, as good a metaphysician as mathemati-cian or physicist, recognized this perfectly well.And we can trust him in this case: only with thesepresuppositions and only on the basis of these fun-damental assumptions are the axioms or laws of.motion and of action valid and meaningful. Thegreat Newtonians, Maclaurin and Euler, as wellas the greatest of them, Laplace, fully recognizedit too.But let us come back to Newton. ft is possible,according to him, that there is, perhaps, not onebody in this our world that is really and truly atrest; moreover, even if there were one, we shouldlo! be able to recognize the fact and to distinguishit from a body in uniform motion. It is also truethat we have no means, and can never have any.of determining the absolute motion of a body*iismotion- with respect to absolute space-bui onlvand solely its relative motion, thai is, its motionwith respect to other bodies, about whose absolutemotion we know no more than about that of thefirst. Yet these statements are not objections againstthese.concepts; on the contrary, they are necessaryand. inevitable consequences of the'very structureof their objects, that is, space and time. Moreover,"Newton should not have been so prudent-al-though in the Newtonian world it is infinitely im_probable that there ever should be a body atabsolute rest and completely impossible that ihereshould ever be one in uniform motion, Newtonianphysics cannot avoid using these notions.

fn the Newtonian world, and in Newtonian sci-ence-in spite of Kant who largely misinterpretedit but opened a way to a new epistemology and anew metaphysics, supporting a ngly s6i6ngs-1hgconditions of knowledge do not determine the con-ditions of being; quite the contrary, it is the struc-

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ture of reality that determines which of our facul-ties of knowledge can possibly (or cannot) makeit accessible to us.Or, to use an old, Platonic formula: in the New'tonian world, and in Newtonian science, it is notman, but God who is the measure of things'The interpretation of the history and structureof modern science that I have sketched here is notthe communis opinio doctrium. At least not vet,though to judge by some recent publications, it ison the way to becoming just that.Still, the prevailing trend of interpretation issomewhat different, and modern science is, as oftenas not, and even more often than not, presentedas an example-the example-of empiricist orpositivist epistemology. Historians and philoso-phers of the positivist school are wont to stress inthe work of Galileo and of Newton (they usuallypass over Descartes) their experimental aspect, pre-senting them as rejecting the search for causesand restricting the aim of science to the establish-ment of lawsl nol asking zulzy something haopensbut how it happens.

This interpretation is certainly not lacking inhistorical basis; the role played by experience, or,more exactly, by experiment, in the history of sci-ence is more than obvious. Moreover.. the works ofGilbert, Galileo, Robert Boyle, and others, are fullof passages extolling the value and the fecundityof experimental methods and opposing them to thesterility of the speculative approach. And as forthe restriction to the investigation of. Iaws in prefer-ence to that of caztses, everybody knows the famouspassage from Discourses and Mathematical Dern-onstrations concerning Tuo New Sciences in whichGalileo announces that it would be "unprofitable"for his purpose (which is, precisely, the establish-ment of the law of falling bodies) to discuss t}leexplanations of gravity proposed and dweloped byhis predecessors, just because nobody knows whatgravity is-merely a word-and that, instead oftrying to find out why bodies f all, it is much betterto content ourselves with determining the mathe-matical law of their downward motion.And everybody knows, too, the even mote famous"passages of the Philosophi.ae Naturalis Pri.nci.pi,aMathematica (scholium) in which Newton says ofgravity (which, meanwhile, has become universalgravitation) that hitherto he has not "been able todiscover the cause of these properties of gravityfrom phenomena." IIe writes:

I feign no hypotheses, for whatever is not de-duced from the phenomena is to be called a hy-pothesis, and hypotheses, whether metaphysical orphysical, whether of occult qualities or mechanicalhave no place in experimental philosophy. In thisphilosophy particular propositions are inferred110

from the phenomena and afterwards rendered gen-eral by induction.In other terms, relations established by experi-ments, or observation, are, by induction, trans-formed into laws,Thus it is by no means surprising that, for agreat number of historians and philosophers, thislegalistic and phenomenalistic aspect of modernscience appeared to constitute its essence, or atleast its proprium, in contradistinction to the de-ductive and realistic science of the Middle Agesand of Antiquity. Closely linked with it appearedalso the pragmatrc, active, technologic aspect ofmodern science-sciantia actiua, operatiua of Ba-con-as opposed to the allegedly contemplative,"theoretical" scrence of the past.To this interpretation I have already made someobjections. Two other objections are also pertinent.1) Whereas the legalistic trend of modem sci-ence is indubitable, and besides has been extremelyfruitful since it enabled the scientists of the 18thcentury to concentrate upon the study and analysisof the fundamental laws of the Newtonian uni-verse, a work that culminated in the Micaniquecileste of Laplace and the Mdcanique analytiqueof Lagrange, its phenomenalistic asPect is muchless apparent: as a matter of fact it is not thephenomena, but the naurnena or the noeta thalfind themselves bound together by the causally un-explained or even unexplainable laws. Indeed, notbodies of our common-sense world, but abstract,Archimedian bodies of the Galilean one, or the par-ticles and atoms of the Newtonian world, are therelata or t}lre fundamenda of. the mathematical re-lations established by modern science. Moreover,and this changes the picture somewhat, the lautof attraction was transforrned by the successors ofNewton into a cause or force.2) The positivist interpretation or self-interpre-tation of science is by no means "modern." Quitethe contrary: it is nearly as old as science itself,and like everything, or nearly everything, was in-vented by the Greeks, (as Schiaparelli and espe-cially Duhem, after others, have quite. convincinglyestablished); the purpose of astronomical science,Alexandrine astronomers explained, is nof to findout the real mechanism of planetary motion butonly to o,i{eta rd, $owdy,eva, to save the phenomenaby putting together a system of circles-a purelymathematical device--enabling us to calculate andpredict the position of the planets, and thus es-tablish a connection between the data of previousand future observations.It is just this positivist-pragmatist epistemologythat was used by Osiander (in 1543) in order tohide behind it the revolutionary impact of Coper-nican astronomy, and it was against this phenom-

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enalistic misinterpretation that was directed theemphasis of the founders of modern science fromKepler who puts AITIOAOTETOI in the very titleof his work and calls it Physica Coelestis, to New-ton who, in spite of his hypotheses non fingo thatI have just quoted, gives us in the MathematicalPrinciples of Natural Philosophy not only a real-istic, but also a causal science. He cloes this simplybecause, though he had renounced finding out lhemechanical explanation of attraction and even re-jected its reality as a physical force acting at a dis-tance, he nevertheless posits it as a .eJ, thoughnonmechanical and probably transphysical one,that subtends the mathematical ,.iorce', whichbinds the world together.The real ancestor of positivist physics is by nomeans Newton. It is Malebranche.Indeed, the Newtonian attitude concerning theproblem of attraction is incompatible with thepositivist point of view. For, from this point ofview, there is no problem at all. Action at a dis-tance, and even instantaneous action at a distance,which Newton so strongly opposed, is just as un-objectionable as any other kind of causation. E.Mach long ago, and P. W. Bridgman more recentlyand much more radically, have made it perfectlyclear: to ask for continuity in space or in time isto be bound by prejudice.As a matter of fact, this attitude has never beenthat of science. Action at a distance, even for thoseof the Newtonians who, following Cotes, acceptedit as a physical force, has always been feli assomething strange and difficult to admit-an ab-surdity to which one gets accustomed remains nev-ertheless an absurdity-and it is this conviction,which, by the way, could make an appeal to the

aujhority of Newton himself, that consciously in_spired the work of Er"rler, of Faraday and Maxwell,and finally that of Einstein, who, by joining to-gether the disconnected elements of the Newtoniany9{d, space and matter, eventually solved theriddle.So it seems to me that, in this case as in a num-ber of others, it was not the positivist renunciation,nor- the pressure of technical development ofmathematical and experimental methods and pro-cedures, but a philosophical attitude, thaf ofmathernatical reali.sm, that has been the drivingfofce or source of inspiration of the post-New-tonian development of scientific thoughl the rootof th_e concept of "fieldr" that new key-concept ofwhich Einstein has shown us the capital valu-e forpresent-dav science.Thus I believe that we are entitled to conclude,tentatively at least, that (i) the positivistic phaseof renouncement, or resignation, is only a kind ofryqea! position, and it is always a temporary one;{ii) although the human mind, in its pursuit ofknowledge, repeatedly assumes this attitude, it doesnot accept it as final-at least it has never done sountil nowl and (iii) sooner or later it ceases tomake a virtue of necessity and congratulate itselfon its defeat. Sooner or later it cornes back to theallegedly unprofitable, impossible, or meaninglesstask and tries to find a causal and real explanationof the-accepted and established laws. And this,after all, is not surprising, at least for those whorecognize that man is not only (6ov zrotfuxiv, abein-g of action, but also, and perhaps even pri-mariln (iov )toym6v, a being of reaion, and bynature there is in man the desire not only to knowbut to understand.qt--rc,Alternative Interpretations of theHistory of Science

, ROBERT S. COHENDr. cohen is assistant professor.of_physics. and lhilosofhy at wesreyan uniuer-sitv. He has also taught at yare'rinioersity, oia n, f"i'n"ii't)uoLrhip, 1ro*'11,i;;';;;i,f;;;'!,f :x::i,r!",!;,i: j::nS:;;j;i,i{t;Ji#ti:ui,|*;sitlt Diaision of t,ar o^"""!,i:l3Ir:!,'

"?'?r"y;.";;'ii'ii-n'i'a of the u' s'T T^nt":Tcr,:.t::"1 general questions on the tions to these problems that have been proposedI social and historical-aspects of science, I hope beforq and to urge that certain of these are at*. to state certain problems that have only tlo best inco-ftele *-hite the others are still merelyobvious a bearing on our work-in the interpreta_ plausible (i).tion of science, to indicate certain alternative solu- ' The u"hi".luu*.nt of understanding of the social

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Influence of Philosophic Trends..., Koyre