E I NSTE I N 'S PH I LOSOP H Y OF SCIENCE

Die Nordstromsche Gravitationstheorie hatte ihreQualitaten. Sie postulierte die vollige Unabhangigkeitvon Gravitation und elektromagnetischoptischen Vor-gKngen, sie ergab Newtons Gesetz als cine Naherung fiirruhende Korper und ergab, ebenfalls als cine volligausreichende NKherung, jene wundersame Gleichheitvon trager und schwerer Masse, die empirisch 1Kngstanerkannt, aber in der Mechanik ein Anhangsel, keinorganisch eingebauter Bestandteil war. Mit alledem warsie in bester Vbereinstimmung mit der damaligenErfahrung. In einem Punkte freilich wich sie von derBeobachtung ab, namlich bei der Perihelbewegung desMerkur. Aber welcher Physiker hKtte wegen diesereinen, durch wenig durchsichtige Storungsrechnunggefundenen, in der Astronomic selbst noch umstrittenenZahl cine sonst befriedigende, umfassende Theoricverworfen?

FQr Einstein aber war das Gesetz der Gleichheitbeider Massen mehr wie ein Naherung; das zeigte schoncine VeroRentlichung von 1907. Es war fur ihn etwasFundamentales, etwas so Fundamentales, dass er ihmcine andere, seit jeher allgemein acceptierte und alsselbstverstKndlich angesehene Idee opferte: Die eukli-dische Massbestimmung im Raume der Physik, und,was damit zusammenhangt, in der Minkowskischen"Welt." Wieder war es ein genialer Einblick in dasWesen von Raum- und Zeit-Bestimmungen, was ihmdiese ungeheuerlich scheinende Neuerung ermoglichte.Sie zeitigte aber bald unerwartete, tatsKchlich zutref-fende Ergebnisse. Nicht nur ergab die "allgemeine"RelativitKtstheorie in ihrer allmKhlichen EntwicklungzwangslKufig den astronomischen Wert fur die Peri-helbewegnung des Merkur, vielmehr fand die Sonnen-finsternis-Expedition unter Eddington 1919 in der Tatjene Ablenkung des Lichts durch die Sonne, welchediese Theoric als einen EinQuss der Gravitation auf dieFortpQanzung des Lichts forderte. Das war ein Triumph,wie er in der Wissenschaft nur ganz selten vorkommt.Er festigte Einsteins Ruhm fur alle Zeiten. Undschliesslich, nach langen Muhen, fanden die Astronomenauch die dritte der von Einstein als beobachtbar

erklKrten Folgerungen, die Rotverschiebung der Spek-trallinien an einer besonderen Klasse von Fixsternen.

Trotzdem ist die allgemeine Relativitatstheorie Ein-steins Sorgenkind geblieben; er arbeitet heute noch anihr. Wir wissen nicht, wie sie sich weiter entwickelnwird; spatere Finsternis-Beobachtungen haben an-scheinend die Lichtablenkung nicht ganz in Einklangmit der Berechnung ergeben. Aber die grundlegendeIdee, die Einfuhrung nicht-euklidischer Geometric zurWahrung des Gesetzes von der Gleichheit beider Massen,durfte zum gesicherten Bestande der Physik gehoren.

Was verehren wir nun bei Einstein am Hochstenl Ichmochte meinen, nicht die gewiss nicht zu unterschKtzendemathematische BefKhigung, mit der er insbesondere dieallgemeine RelativitKtstheorie meisterte, nicht die Viel-seitigkeit seiner Begabung, nicht einmal die Unbefangen-heit gegenuber allen bestehenden Theorieen. Vielmehrsteht uber dern die schlechthin geniale, unmittelbare,und, wenn sie einmal ausgesprochen ist, so einfacheEinsicht in das, was in der Natur wesentlich ist. Sie hatsich in . den beiden erwKhnten Zweigen gleichmKssigbewKhrt. Aber, um sie wirksam zu machen, musste nochcine Charaktereigenschaft hinzukommen, namlich cineabsolute Ehrlichkeit und ungewohnlicher Mut derOberzeugung, um gegen uralte, eingefleischte, machtigeVorstellungen anzukampfen —zunachst ganz allein. Unddiesen Mut, den er auch in dern wohl noch unent-schiedenen Kampfe um die AuGassung der Quanten-mechanik zeigt, hat er nicht weniger in seinem Verhaltenzu den Machten der Umwelt bewKhrt. Das werden auchdie ihm zugestehen, die ihm in dieser Hinsicht nichtdurchweg zu folgen vermogen. Naturlich hat er auchden dafur ublichen Preis bezahlen mQssen mit einemunruhigen, manchmal sturmisch bewegten Leben.

Seit einer Reihe von Jahren konnte er nun seinLebens-Schi6 in einen ruhigen Hafen lenken, und diePhysiker der ganzen Erde richten am 14 MKrz ihreGedanken nach Princeton. In dankbarer Verehrungwunschen sie dern Jubilar noch viele Jahre der altengeistigen Klarheit und der alten Freude an der Wissen-schaft.

REVIEWS OF MODERN PH YSICS VOLUM E 21, NUM HER 3 JULY, 1949

.Kins1:ein s .. &i. .osoy. xy oI: SciencePHILIP P FRANK

Departmelt of Physics, Parvard UNiversity, Cambridge, Massachusetts

(Received April 29, 1949)

BOUT ten years ago X spoke with Einstein aboutthe astonishing fact that so many ministers of

various denominations are strongly interested in thetheory of relativity. Einstein said that according tohis estimation there are more clergymen interested in

relativity than physicists. A little puzzled I asked himhow he would explain this strange fact. He answered,a little smiling, "Because clergymen are interested inthe general laws of nature and physicists, very often,are not. "

350 P H I L I P P

Another day we spoke about a certain physicist whohad very little success in his research work. Mostly heattacked problems which overed tremendous diS.-culties. He applied penetrating analysis and succeededonly in discovering more and more difficulties. By mostof his colleagues he was not rated very highly. Einstein,however, said about him, "I admire this type of man.I have little patience with scientists who take a boardof wood, look for its thinnest part and drill a greatnumber of holes where drilling is easy. "

Through all his life as a physicist Einstein hasregarded his own work as a search for the general lawsof nature and as closely related to the work of thephilosopher. In his obituary to Ernst Mach (1916)Einstein wrote

"When I remember the ablest students whom I metas a teacher, I can say with certainty that they werestrongly interested in the theory of knowledge. I mean

by 'ablest students' those who excelled by independenceof judgment, not only by quickness. They liked to startdiscussions about the aims and the methods of scienceand proved by their obstinacy in the defense of theiropinions that this issue seemed to them to be animportant one. This is not astonishing, indeed. "As a matter of fact, Einstein's physical theories haveplayed a great part in the history of contemporaryphilosophy, a very great part, indeed. We can ventureon good grounds the statement that no "professionalphilosopher" of the 20th century was quoted so fre-quently by other philosophers as Einstein was. He wasmeasured by professional standards, an "amateur" in

philosophy, but a "philosopher" in the literal sense ofthe word that means a "lover of wisdom. "

In order to understand Einstein's place in the evolu-tion of philosophical thought we have to cast a glanceupon the period in which Einstein started his work, theturn of the century, the period around 1900. In theseyears not only a great many new facts were discoveredin physics, but also new theories were advanced bywhich the "classical physics" of the 17th, 18th and19th century was rapidly transformed. Along withthese changes a new "philosophy of science" haddeveloped at the end of the 19th century, one would

say, necessarily. The traditional philosophy of that"classical period" had been, more or less, a petrificationof classical physics. Thence the breakdown of thosephysical theories brought about the breakdown of aphilosophy which had "demonstrated" the eternalvalidity of the same theories which were abandoned bythe scientists later. The appearance of the new philoso-

phy of science preceded to a certain degree the theoryof relativity and the quantum theory. Men with greatinsight into the logical structure of science noticedalready in the last quarter of the 19th century that"classical physics" and its "traditional philosophy"was doomed. The electromagnetic theory of matter,the Grat glimpses of electronics, the new conception of

fluctuation, etc., were sufficient to demonstrate thenecessity of a radical change in the traditional phi-losophy of science.

Towards the end of the 19th century two great menadvanced with great strength the need for a newapproach to the philosophy of science, Ernst Mach andHenri Poincare. Both men played a prominent part inEinstein's intellectual evolution and both have lefttheir imprint on the way Einstein formulated hisphysical theories.

At the first glance, Mach's and Poincare's views onthe principles of science seem to be antagonistic andeven contradictory to each other. In Einstein's phi-losophy of science these two views appear as two aspectsof one integrated view.

According to Mach the principles of science offer an"econonnc" (practical) description of a great diversityof sense observations. According to Poincare, however,these principles are free creations of the human mindwhich are neither true nor false but may be convenientor inconvenient.

In Einstein's work we can easily notice the inQuenceof both these philosophies. In his "Special Theory ofRelativity" Einstein started from the question: If wesay that two events at diferent places occur at one andthe same time, what does the expression "at the sametime" mean if we formulate it as a statement aboutpossible sense observations? In a similar way we find inEinstein's general theory of relativity at the beginningthe question: If we say that a fluid mass rotates and isQattened by the centrifugal force, what does the expres-sion "rotating" mean if we express it by statementsabout possible sense observations?

However, we can also construe Einstein's theory ofrelativity as an example of Poincare's "conventional-ism. " Einstein defined the time distance between twoevents in such a way that the principle of relativitybecomes true. We can say that, in a certain sense, theprinciple of relativity is not a statement about physicalfacts but a definition of the expression "length of time. "It is therefore, merely a convention about how to usethe expression "equal time distances. " Similarly, Ein-stein's famous definition of "simultaneity" was anarbitrary convention about the use of this word. It wasnot supposed to be "true" but convenient to formulatethe laws of physics in a simple and "economic" way.

Einstein's Special Theory of Relativity (1905) wasformulated in such words that it could serve as abrilliant example for the general views of Mach andPoincare about the logical status of scientific principles.This theory established in a conspicuous way the char-acteristics of scientific principles which were stressedby both of these "rival philosophies. " The validity ofboth characteristics within one and the same physicaltheory was a clear demonstration of the compatibilityof Mach's and Poincare's views if they were correctlyunderstood. In a much higher degree Einstein's GeneralTheory of Relativity had its philosophical basis greatly

E INSTE I N'S P H I LOSOP H Y OF SCIENCE 35i

in the writings of both philosophers and one couldhardly imagine that a theory of this type could haveappeared except in the intellectual atmosphere whichwas determined in an essential way, by the writings cfMach and Poincare. Einstein's General Theory ofRelativity contains implicitly a "philosophy of time andspace" which, probably the first time in the history ofphilosophy and science, gave a clear account of what ismeant by expressions like "the nature of space andtime, " "the validity of Euclidean geometry, " etc.

Einstein formulated this underlying philosophy ofspace and time explicitly in his lecture "Experienceand Geometry" which he gave in i92i to the PrussianAcademy of Science in Berlin. '

This lecture is a historic landmark in the long andtortuous approach to philosophical clarity. The relationbetween experience and logic in geometry, and inscience altogether, was presented, the first time, in asatisfactory way. Einstein did it with great simplicityand directness leaving no dark angle where remnantsof obscurity could take a hiding. Certainly, the earlierwritings of men like the mathematicians Hilbert andPoincare had clarified this issue a great deal. Hilberthad presented geometry as a formal system in whichthe signihcance of terms like "straight line" or "point"or "intersect" were not used in the drawing of conclu-sions. He contributed in this way much to the under-standing of the part of reasoning in geometry. But hisargument on the physical meaning of geometry wasrather vague. Poincare characterized geometrical axi-oms as "conventions" about the use of words like"straight line. " In this respect he agreed with men likeHilbert. He recognized also that these conventions canbe practical or not practical. It depends whether con-ventions or definitions can be applied to the physicalreality or not. But Poincare did not show clearly byconcrete examples what a geometry would look likewhich is different from the Euclidean geometry and is apicture of reality. This could not be done until one wasin the possession of a physical theory which containedthe interaction between the physical Geld of force andthe departures from the Euclidean geometry.

Einstein's General Theory of Relativity was the erstphysical theory in which, what one called formerly"geometry" was completely integrated into the frameof physics in general. Only within such a frame therelation between reasoning and experience in geometrycan be clearly stated. The axioms of geometry bythemselves are, as Hilbert and Poincare pointed out,purely formal systems from which we can draw resultswithout knowing the significance of the words "straightline" etc. But by interpreting a straight line as a lightray or as a rigid rod, the axioms become physicalhypotheses; they become statements within mechanicsor optics. All conclusions which are drawn from them

'An English version of this lecture was published in the bookA. Einstein, Sidelights oe Relativity (Methuen and Company,Ltd. , London, 1922).

can be checked with the same precision and with thesame uncertainty as all statements of physics. Einsteincharacterized this situation by the famous dictum that,as far as geometry is precise, it does not tell us anythingabout the world (it is a formal system); if, however, ittells us something about the world, it is not precise (ithas the same status as a statement of physics).

Einstein's work contains the definite settlement ofthe problem, how it is possible that geometry makesdefinite and final statements about the external worldwhich are not based on sense experience. It is nowclear that geometry is not different from any empiricalscience. In any empirical science there is a part whichis purely logical. It tells us what follows from certainaxioms without bothering whether these axioms aretrue. This part contains statements which are veryexact and the truth of which cannot be challenged byany future advance of empirical science. But thesestatements do not say anything about the externalworld. In physics we have large books written aboutwhat logical deduction we can make from Newton'slaws of motion or Maxwell's equations of the electro-magnetic Geld without bothering whether these laws ofmotion or of field laws are true or even what is theirphysical significance. The books remain valid whateverwe may later say about their fundamental assumptions.

The same thing is true even in biology or economics.In genetics we have analytical genetics which derivesresults about "genes" from Mendel's laws. Thesedeductions do not even depend upon what the word"gene" means as an object in the physical world. If weknow the "semantical rule" by which statements about"genes" can be translated into statements about thefrequency with which some properties of organismsoccur in the hereditary process, we can make use ofanalytical genetics in empirical biology. In economicsone starts often from the conception of the "economicman" who acts only for his profit. We know exactlythe properties of this man because they are arbitrarilyascribed to him. Then we can derive logically how thiseconomic man behaves as a part of society, we canderive laws of prizes which would be empirically valid—if mankind consisted exclusively of economic men.The conditional statement, "the prices would changein a certain way if men behaved as economic men do"is true whether an, economic man exists in the rea1world or not. Here again we note that a part of theargument in economics is exact, but does not sayanything about the external world. The question fromthe viewpoint of empirical biology and economics ismerely whether these assumptions can be applied tocircumstances which really occur in the world oforganisms or human societies.

This analysis of geometry was a major event in thehistory of philosophy and could be extended to anyempirical science. The axioms of geometry were themost brilliant and the most "scientific" example ofstatements which were valid "a prior~" and therefore

352 PHILIP P

of an eternal validity which could never be shaken byany advance in science. Einstein's theory was a clearexample which showed that the axioms of geometryare either purely analytical and do not say anythingabout reality or are not diferent from the statementsof physics, biology or economics. The scientific basis ofa great many philosophical doctrines was destroyedradically. There was no longer any scientific foundationfor the contention that the human mind can make validstatements by other than the scientific method. Thismethod consists obviously in a cooperation of logic andexperience as exemplified by Einstein s analysis ofgeometry.

The belief that there is any "philosophical method"besides the empirical-logical method had lost its mostscientific foundation.

In order to appreciate correctly the place of Ein-stein's SPecial and General Theory of Relativity in thehistory of philosophy we have to consider the reactionof the "professional" philosophers to these new physicaltheories.

It is only fair to say that even prominent men

among the followers and rebuilders of traditional phi-

losophy were at a loss to tell correctly the changeswhich had to be made in order to integrate Einstein'swork into the traditional pattern. Men of high intel-lectual and imaginative caliber like Henri Bergson,Ernst Cassierer, or N. A. Whitehead tried in vain tomake contributions towards a better understanding andassimilating of Einstein's new theories. I omit tomention those philosophers who just asserted in aperfunctory way that Einstein theory bolsters their

pet philosophy. According to some interpretations,Einstein's theory shows, for example, that physics hasto do with mind and not with matter or, in the oppositethat space and time conceptions do not refer to someabstract entities but to material. bodies. I shall rathergive a glimpse of the main lines of philosophical thoughtin the 20th century. What had been left of traditionalmetaphysics belonged, roughly speaking, either to theAristotelean (Thomistic) tradition or to the Kantiantradition. Both groups were based on the convictionthat the fundamental axioms of Euclidean geometryare self-evident and cannot be altered by any futureadvance of empirical science.

When these opinions were shaken by Einstein'stheories, the representatives of those currents of thoughtbehaved in two diferent ways which we may character-ize by using a parlance of theology, the "fundamental-ist" and the "modernist" approach.

The "fundamentalists" asserted boldly that Einsteinwas just wrong. The non-Euclidean geometry, forexample, according to their opinion, existed only as anartificial system of thought but not in the real world.The "modernists" again are represented by the groupswhich one calls mostly Neo-Kantians and Neo-Thom-ists. They attempted to integrate Einstein's physics ina certain way into their systems by drawing a sharp

separation line between science and philosophy. Theyadmitted that within scierice Einstein's rejection of theEuclidean geometry and Newtonian mechanics is legiti-mate. But then, the problems of the "nature of timeand space" still remain unsolved. Their solution canonly be found by a way of approach which is not thescientific one and which they called the "philosophical"or "metaphysical" one. In this way Einstein's newreconstruction of physics contributed to the disintegra-tion of traditional philosophy. The only remnant ofthe old doctrines was a type of discourse which did nolonger acct science at all. It restricted itself to producea certain "background" to science. It was supposed tocontain a more profound insight into time and spacebut contained, actually, attempts to reconcile our oldcommon sense approach to time and space with theprinciples of modern physics. It was an attempt toformulate our modern experiences in the physics ofswiftly moving bodies by using the Aristotelian orKantian concepts which had been generalizations cor-responding to a much older stage of human experience.

I shall not dwell here upon these historical connectionsbut I shall rather try to describe what are the permanentvestiges which Einstein's work has lef t upon thephilosophical thought of our 20th century.

As far as we discussed it by now, we can summarizeEinstein's contribution by stressing that he gave thelast and decisive touch to the program of physics thatwas outlined by men like Mach and Poincare. Whatthese scientists had in mind as a mere program andwhat they were not able to formulate in full precisionEinstein achieved and presented as a fulMedgedscientific theory. It assigned its correct and satisfactoryplace to non-Euclidean geometry and defined preciselythe mutual relation between convention and facts inscience.

According to Mach and Poincare and to a certaindegree also according to Einstein's earlier papers, theabstract concepts which are the building stones ofphysics must have an interpretation in the realm ofobservable facts. Concepts like "mass and force, ""posi-tion and velocity, " "distances in space and time, " etc. ,can only be used in the principles of physics if accom-panied by a recipe how they can be measured in thephysics laboratory. Einstein added to these conceptsalso expressions like "simultaneity" and emphasizedeven more than Mach and Poincare the necessity toanchor all abstract concepts firmly in the ground ofobservable facts.

The general belief was, at that time, that the chainwhich connected the abstract terms with the observa-tional facts was to be fairly short. Some authors evenliked to express themselves in a way as if the principleswouM speak directly about observable facts.

The General Theory of Relativity was the death knellfor this "optimistic" belief. It became now clearthat this belief had been an oversimplification. In hisHerbert spencer Lecture given at Oxford on June 10,

EINSTEIN'S PHILOSOPHY OF SCIENCE 353

1933, Einstein describes the structure of science inagreement with what I called his integration of Machand Poincare. But he stresses a point which had beenrather minimized in the period when one believed thatthe principles of physics contain only concepts whichare fairly near to observable phenomena. Poincarehad said already that the fundamental principles them-selves are "free creations" of the human mind, and thatthey are connected by physical interpretations withthe realm of observations. Einstein says in thislecture: "The conception here outlined of the purelyfictitious character of the basic principles of physicaltheory was in the eighteenth and nineteenth centuriesstill far from being the prevailing one. But it continuesto gain more and more ground because of the everwidening logical gap between the basic concepts andlaws on the one side and the consequences to be corre-lated with our experience on the other, a gap whichwidens progressively with the developing unificationof the logical structure, that is, with the reduction inthe number of the logically independent conceptual ele-ments required for the basis of the whole system. . . .

The scientists of those times were for the most partconvinced that the basic concepts and laws of physicswere not in a logical sense free inventions of the humanmind, but rather they were derivable by abstraction,i.e., by a logical process, from experiments. It was theGeneral Theory of Relativity which showed in a con-vincing manner the incorrectness of this view. . . ."Einstein stresses strongly the point that the principlesof a physical theory do not "describe" the facts ofexperience but are inventions of the human mind fromwhich the facts can be "derived. " The principles ofNewtonian mechanics and of general relativity theoryare very dift'erent from each other. One cannot envisagehow they could be both "derived" from the same stockof experience. But none the less, within a wide range,they describe the same experimental facts! "This indi-cates, " says Einstein, "that any attempt logically toderive the basic concepts and laws of mechanics fromexperience is doomed to failure. "

This analysis of the logical structure of actual physics,particularly 20th-century physics, became the germ ofnew developments in the philosophy of science. Thetraditional systems of philosophy of the Kantian,Aristotelian, Neo-Kantian and Neo-Aristotelian (Neo-Thomistic) type had failed to draw any fruitful conclu-sions from Einstein's theories. But a new type ofphilosophy arose which was directly inQuenced byEinstein's General Theory of Relativity.

The new men did no longer attempt to stretch thetraditional philosophical systems artificially, in orderto bring the new physics into the fold of the old phi-losophy. They followed the word of the Bible: "Noman puts new wine into old bottles; else the new winewill burst the bottles, and be spilled, and the bottlesshall perish. But new wine must be put into new bottlesand both are preserved. "

M. Schlick in his book "Space and Time in Con-temporary Physics" which was published in Germany in1917,immediately under the impact of Einstein's Gen-eral Theory of Relativity, recognized clearly that thistheory was a turning point in the philosophy of science.The new philosophy was based on the ideas of Machand Poincare but tried to integrate the new ideas withwhich science was confronted by Einstein's new physics.Schlick stressed the point that the principles of physicsor, for that matter, of any science, do not consist of"descriptions" of observable facts. They are, rather,statements about symbols and their connections fromwhich statements about observable facts can be derived.Schlick suggests, therefore, to regard all the conceptswhich occur in the principles of science as elements ofour physical reality and not only those to which senseobservations can be directIy assigned. All conceptsbelong to the real world from which statements aboutpossible sense observations can be derived. We candescribe this shift in attitude also as follows:

According to the older form of positivism andempiricism, as represented by Mach, the principles ofscience were direct statements about sense observations.Schlick developed Einstein's method into a new ap-proach to the philosophy of science and proposed toregard the principles of physics as statements whichdeal "indirectly" or "by implication" with sense obser-vations. But we can just as well say that these principlesare statements about the physical reality, as far assense observations reveal physical reality.

The movement started by Schlick has been calledlater "logical empiricism, " it regarded the principles ofscience not as simply empirical, but as "empirical bylogical implication. " Schlick says in his quoted book"There is no argument whatsoever to force us to statethat only intuitional elements, colors, tones, etc.,

' existin the world. We might just as well assume thatelements or qualities which cannot be directly experi-enced also exist. . . . For example, electric forces canjust as well signify elements of reality as colors ortones. They are measurable and there is no reason whyepistemology should reject the criterion for realitywhich is used in physics. "

The development of logical empiricism has demon-strated strongly the great bearing of Einstein's analysisof science upon the philosophical attitude towardsscience. R. Carnap, for example, says in his book "TheLogical Syntax of Language" (1934) about Maxwell'sequations of the electromagnetic field

"There is no sentence which contains only symbols ofobservational statements and is equivalent to such anequation. But, of course, sentences of an observationalform can be deduced from Maxwell's equations (inconjunction with other sentences of physics). "

The doctrine of logical empiricism which was theresult of this integration of Mach, Poincare and Ein-stein developed during the twenties and thirties of the20th century into a strong movement among the

354 P H I L I P P FRAN K

scientists and all other groups who wanted to carry ontheir work according the example of science. If weinvestigate the role of this doctrine as a motive forhuman action or, more exactly speaking, as a weaponin the battle of religious and political ideologies, wenotice easely that there have been two main types ofinterpreting logical epiricism as a "philosophy of life."

If we regard a scientific theory like Einstein's theoryof gravitation as a free construction of the human mindinvented for the purpose to predict and produce phe-nomena of nature we can look at it from two differentangles. We can either say: since the theory is a "freeconstruction of our mind, " we can certainly constructagain and again new theories which may become moreand more helpful in their application, but there is noreason to believe that we approximate a perfect theory.To expect a "perfect theory" would be a similar thingto expecting a "perfect automobile" which will keep itsform and construction for the eternity. This aspect hasbeen the prevailing one for great many logical empiri-cists. and was particularly stressed by P. W. Bridgman.

But we can also direct our attention to the form ofthe fundamental differential equations themselves andimagine that these equations will, of course, be changed

again and again but will eventually converge toward afinal system of equations which will be the "true"theory of the physical Geld. Einstein has been moreand more attracted towards this second aspect. In hisHerbert Spencer Lecture, which we quoted already,he says:

"If the basis of theoretical physics cannot be aninference from experience, but must be free invention,have we any right to hope that we shall find the correctway? Still more —does this correct approach exist atall, save in our imagination? To this I answer with

complete assurance, that in my opinion there is thecorrect path moreover, that it is in our power to find it."

When Einstein started in the search for the equationsof the gravitational field, he was guided by the mathe-matical theory of invariants and covariants. He ha, dnoticed before, that his special theory of relativitycould be presented as the theory of invariants of acertain mathematical group. This was his startingpoint in the search for his theory of the gravitationalfield and he has strongly believed that by this methodone can find also the laws for the "unified field" which

will embrace the gravitational the electromagnetic andthe nuclear field.

He continues in his Spencer Lecture, "It is myconviction that pure mathematical construction enables

us to discover the concepts and the laws connectingthem which gives us the key to the understanding ofthe phenomena of nature. "

Einstein did not believe, of course, that by anymathematical argument one could "demonstrate" thetruth of a physical theory. This can only be done byexperiment. But on the other hand, the discovery of atheory is according to Einstein, not based directly on

experiments but on mathematics. Einstein says thatthe "truly creative principle resides in mathematics. "By this emphasis of the heuristic value of mathematics,Einstein, who had always discouraged all a pnoriconceptions of natural laws, arrived at the result thatmathematical thought could lead to the discovery, butnot the "proof" of the true laws of nature. Einsteinsays, "In a certain sense, therefore, I hold it truethat pure thought is competent to comprehend thereal, as the ancients dreamed. "

The belief that there will be eventually a perfectsystem of physical laws of great simplicity and beautythat will allow a mathematical deduction of all phe-nomena of the physical world, is sometimes called the"belief in the rationality of nature. "

This belief which amounts to an optimistic attitudetowards research in the natural sciences is according toEinstein, of a religious nature. Einstein calls it occa-sionally his "cosmic religion. " In this sense, Einsteinstressed repeatedly he can be called a devoutly religiousman.

Among theologians, philosophers and even politiciansthere has been a trend to claim that the Theory ofRelativity has reconciled the old convict between scienceand religion. According to this school of thought theTheory of Relativity has overthrown Newton's mechan-ics and, therefore, the mechanistic world view, accordingto which the universe is a large machine. This "ma-terialistic" view has been regarded as incompatiblewith all kinds of religion. The failure of Newton'smechanics, so the argument goes, has also refuted the"machine theory" of the universe and, therefore, givena chance to a recognition of science and religion. Asimilar argument has been also used in the case ofquantum theory. It has been claimed by a great manyauthors that the physics of the 20th century is stronglyopposed to the machine theory of the universe, that itis propitious to the world picture of the traditionalreligions.

These views have been supported also by severalprominent physicists among which the name of J. Jeansand A. Kddington are the best known. It is importantto understand that these views have by no ~cans beensupported by Einstein. While he has held that thepossibility of theoretical physics and cosmology sug-gests a belief in the "rationality of nature" and "cosmicreligion" Einstein has never believed that 20th-centuryphysics is in this respect different from classical physics.Who is willing to interpret the laws of theoreticalphysics in this way is supported by Newton's mechan-istic physics not less then by Einstein's Theory ofRelativity and Heisenberg's Principle of Indeterminacy.

That incorrect interpretation of Einstein's opinionsabout the bearing of his theory upon religion is basedupon a much wider misunderstanding of Einstein'stheories. I stressed in this paper, what I believe to bethe actual bearing of Einstein's physics upon ourmodern philosophy of science. We must, however, not

P I NSTE I N 'S P H I LOSOP H Y OF SC I E N CF.

ignore the fact that the interest of adherents of thetraditional philosophical systems was not so muchoccupied by the real advances in philosophy that aredue to Einstein but rather by "philosophical implica-tions" of Einstein's theory which were due to grossmisunderstandings of physical theories in general andEinstein s theories in particular. As a matter of fact,as Bertrand Russell once remarked very aptly, themajority of adherents of the traditional systems inphilosophy have interpreted Einstein's new physics asa support of those metaphysical doctrines which theyhad held for ages. This holds for idealistic philosophiesas well as for materialistic ones.

These misinterpretations of Einstein s theories byphilosophers and theologians are, certainly, of apsychological and sociological interest.

They can serve as a good example of a generalphenomenon. Since the "philosophical implications"are not justifiable by scientific methods their origin israther in the eternal attempts of men to find a basisfor their social and religious aspirations in the laws ofthe physical universe.

As I have discussed these problems in several booksand papers, I shall here only outline brieQy the mostfrequent types of misunderstanding without discussingthem in detail.

Great many philosophers started from the role of theobserver in the Theory of Relativity. They concludedfrom it that the Theory of Relativity cannot be statedas classical physics was, a description of objective facts.Einstein's physics is concerned only with subjectivesense impressions of human beings. This would mean,in the language of traditional philosophy, that Ein-stein's theory supports the philosophy of subjectiveidealism. Furthermore, as no objective truth about thephysical world can be stated and the world looksdiferent for different observers. Einstein supports a"sceptical" philosophy. Since every observer is equallyright, truth can never be found and the "agnostic"can prove his case. By applying this "relativistic"attitude also to the realm of ethics the theory ofrelativity was even accused of being hostile to moralityand of being a subversive doctrine.

These misinterpretations have played their part inthe attitude of political groups towards Einstein'stheories. During the Nazi regime in Germany andunder the Soviet regime in Russia the ruling partiesand even spokesmen of the governments subjectedEinstein's theories to severe criticism. There have beeneverywhere also serious attempts to achieve a "negoti-ated peace" in this ideological war. For, whatever maybe the form of government, the experiential results. ofEinstein's theories cannot be ignored in the applicationof physics to industry and warfare. A compromise hadto be found under which the practical implications couldbe exploited without having to face the philosophicalimplications.

Instead of an elaborate discussion of all these points

I shall restrict myself 'to quoting those sections of myprevious books where such a discussion is done care-fully. *

I shall not discuss in this paper Einstein's attitudetowards Bohr's philosophical basis of the QuantumTheory. This attitude is closely connected with Ein-stein s position towards the positivistic and meta-physical conception of science. According to Einsteinthe Quantum Theory in Bohr's formulation does notdescribe the physical reality but only the reaction ofthe observing and measuring physicist to this reality.Bohr's interpretation of Quantum Theory is the mostradical conclusion drawn from positivism and appliedto a concrete situation in physics. I refer for this pointto my book Eiststeitt, His Life astd Times, Chapter IX,Section 5, where Einstein s philosophical position withrespect to Bohr's principles is described and analyzed.N. Bohr presented the philosophical issue betweenhimself and Einstein in his paper "Conversations withEinstein on Epistemology" which is published in the book"Albert Einstein: Philosopher-Scientist" quoted above.

* Foustdatiols of Physics (University of Chicago press 1946)Chapter V discusses the Theory of Relativity. The philosophicalinterpretations, particularly the question of subjectivity andrelativity is taken up in Sections 26 and 27.

Between Physics and PhilosoPhy (Harvard Press, 1941). InChapter VIII (What "length" means to the physicist) the"relativity of length" is logically analyzed.

Eimsteirt, his life aid times (New York, 1947). Einstein sPhilosophy of Science is discussed in Chapter IX, his attitudetowards religion in Chapter XII. The interpretations of Einstein'sRelativity Theory from the viewpoint of political ideologies iselaborately described in Chapter XI.

Modern Science md its Philosophy (Harvard Press, 1949). InSections 9 and 10 of the Introduction, Einstein's impact on therise of a new philosophy is described. In Chapter 5 "Is there atrend towards idealism in physics. " the subjectivistic and ideal-istic interpretations of Einstein s physics are discussed.Chapter 7, "Modern Physics and Common Sense, " the question isdiscussed whether the Theory of Relativity is contrary to commonsense and whether it is abstract or pictural. In Chapter 10 "Howidealists and materialists view modern physics" the idealistic andmaterialistic interpretations of modern physics are historicallyand logically analyzed. In Chapter 13, "The Philosophical Mean-ing of the Copernican Revolution" the question is analyzedwhether Einstein's Theory of General Relativity has con6rmed orrefuted the philosophy which has been the basis of the CopernicanHeliocontric world system. In Chapter 16 "The place of Logicand Metaphysics in the Advancement of Modern Science" a morethorough investigation is devoted to some philosophical misinter-pretations of Einstein s theories, in particular to the allegedlowering of the role of reasoning and rationality in modern science.

The interpretations of Einstein s theories as "philosophicalrelativism, " as supporting the "relativity of truth and values" isdiscussed in my paper: "The relativity of truth and the advanceof knowledge ' in the Italian journal "Analisi, " (1946). A muchmire elaborate presentation will appear soon in a book "Relatzvzty—a richer Truth, " (Beacon Press, Boston, 1949).

There has been much discussion and a great diversity of opinion,whether Einstein's theories can be used and are intended to beused by their author as a support of a positivistic anti-metaphys-ical philosophy or, in the opposite, as a basis for a metaphysicalworld conception. This question is certainly of great interest ifone wants to understand the climate of thought in our time andthe interrelation between scientific theories and philosophicalworld views in particular. I have discussed this question and itssolution at length in my paper: "Einstein, Mach and LogicalPositivism" which is published in the book: Albert Einstein:Philosopher-Scientist" (Volume VII of the Library of LivingPhilosophers, ed. by P. A. Schilpp, Evanston, 1949).