20060144

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"Soft" Area Studies versus "Hard" Social Science: A False Opposition Author(s): Loren Graham and Jean-Michel Kantor Source: Slavic Review, Vol. 66, No. 1 (Spring, 2007), pp. 1-19Published by: Association for Slavic, East European, and Eurasian StudiesStable URL: http://www.jstor.org/stable/20060144Accessed: 10-11-2015 07:55 UTC

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ARTICLES

"Soft" Area Studies versus "Hard" Social Science: A False Opposition

Loren Graham and Jean-Michel Kantor

Much criticism of area studies has been based on the opinion that, in

comparison to "hard" social science, area studies are "soft." According to

this line of argument, social science emphasizes theory, mathematics, rig orous methods, falsifiability and replicability, and therefore escapes from

the contextualism of area studies. Area studies approaches are allegedly

merely "descriptive," "cultural," or "historical," while social science is "rig orous" and "scientific." As Robert Bates of the department of government at Harvard University observed when he was president of the comparative

politics section of the American Political Science Association, "Those who

consider themselves 'social scientists' seek to identify lawful regularities which by implication must not be context bound."1 And he also noted,

"Within the academy, the consensus has formed that area studies has

failed to generate scientific knowledge."2 As Sheila Biddle remarked in

her recent study of the "internationalization" of American universities, so

cial scientists "tend to dismiss area-based knowledge as atheoretical,

methodologically unsophisticated, descriptive rather than explanatory, and incapable of making substantial contributions to the discipline."3 So

cial scientists often pride themselves on taking a quantitative approach that could, they imply, be applied in any cultural area with equally good effect.

This criticism of area studies is based on the assumption that the best

social analysis comes from a single cognitive approach, one that incor

porates mathematics, quantitative methods, and replicability. In this ar

ticle, we examine this assumption and propose that the best social analy sis should incorporate several different cognitive styles, of which the

method relying on mathematics, quantitative methods, and reproducibil

ity is only one.

First, let us take up the question of mathematics. Some quantitative social analysts assume that mathematics and quantitative methods stand

outside social context and form a kind of absolute truth. They ignore the

fact that mathematics also has a contextual history; the mathematics we

use today, early in the twenty-first century, is not the same as the mathe

1. Robert H. Bates, "Area Studies and the Discipline: A Useful Controversy?" Political

Science and Politics 30, no. 2 (June 1997): 166. 2. Robert Bates, "Letter from the President: Area Studies and the Discipline," Newslet

ter of the APSA 7, no. 1 (Winter 1996): 1-2. 3. Sheila Biddle, Internationalization: Rhetoric or Reality f American Council of Learned

Societies Occasional Paper, no. 56 (New York, 2002), 69.

Slavic Review 66, no. 1 (Spring 2007)



2 Slavic Review

matics people used a century ago. As the philosopher of science Ian Hack

ing observed, "Mathematics, so often thought of as a body of eternal

truths, takes place in time, and objects come into being as they are con

structed."4 Mathematicians and historians of mathematics often find that the best way to understand those moments of "coming into being" is

through a contextual analysis. Instead of mathematics being something untouchable by the area studies approach, in fact this approach is often a

very useful way to explain how mathematics developed. The most ardent defenders of quantitative social science often make

assumptions about the nature of science and mathematics that many scientists and mathematicians are uncertain about themselves. In this crit icism of "qualitative" area studies we sometimes witness social scientists

trying to be more "scientific" than quite a few natural scientists and

mathematicians.

We explore two different examples of the roles that social influences

have played in the development of mathematics, one concerning the very foundations of mathematics, and another concerning its use for a partic ular purpose. In the first case, concerning the birth of set theory, the ques tion is raised, What are the legitimate objects of study within the field of

mathematics itself (without regard to application)? In the second case,

concerning general relativity, the question is, How should mathematics be

applied to a particular area of physics? The fact that social context plays a

role in both examples is significant, since quite a few people are more will

ing to grant social influences on the "use" of mathematics than they are

on its theoretical foundations. For that reason we start with a controversy over the foundations of mathematics that arose at the end of the nine

teenth and the beginning of the twentieth century, particularly in France and Russia. In this dispute, contextual factors were of pivotal importance. In our conclusion, we examine the significance of this analysis for social scientists who think that by applying mathematics to the study of society

they have escaped social context.

Controversies about the foundations of mathematics have gone on for

centuries. Since the birth of the discipline, mathematicians have argued about whether mathematics is "discovered" or "created." If mathematics is

created, then the conditions of its creation could be of great importance. Mathematicians have differed greatly in their attempts to answer this

question, but in modern times, two of the best-known schools of the phi

losophy of mathematics have centered on the views of the German math

ematician David Hilbert (1862-1943), who took a realist position, and the

Dutch mathematician L. E. J. Brouwer (1881-1966), who developed the

intuitionist philosophical school.5 Although today most mathematicians

probably agree with Hilbert, questions about the foundations of mathe

matics will doubtlessly be with us forever.

4. Ian Hacking, The Social Construction of What? (Cambridge, Mass., 1999), 44.

5. On Hilbert, see Constance Reid, Hilbert (Berlin, 1970); H. Wussing, Biographien be

deutender Mathematiker (Berlin, 1975). On Brouwer, see A. Heyting, Intuitionism: An Intro

duction (Amsterdam, 1966).



"Soft" Area Studies versus "Hard" Social Sciences: A False Opposition 3

It is unnecessary, and would even be arrogant, for us to try to say which

school is "correct." Great, but somewhat different, work has been done in

both traditions. But it is useful for both people in area studies and their

critics in the social sciences to notice that some of the world's significant mathematicians have thought that contextualism is necessary for an un

derstanding of the history of their field. When Hermann Weyl, often de

scribed as one of the most influential mathematicians of the last century, tried to understand the early history of mathematics he found it necessary to adopt an area studies approach: that of classical studies. (It is often for

gotten today that the original "area studies" was classical studies.) Schol

arship in classical studies is based on the assumption that in order to un

derstand the literature, art, religion, philosophy, politics, architecture, and mathematics of the ancient world, one must study classical culture in

its entirety, not just examine one aspect of that culture, or try to escape from that culture. In the early twentieth century, Weyl was very concerned

with the concept of "infinity." Is infinity only an abstraction, a limit that

cannot be attained, or is there an actual infinity? (This question gave birth

to set theory, which will be discussed later.6) In his effort to understand

the evolution of the concept, Weyl turned to the classical world, when the

concept originated. And he concluded that the Greek concept of infinity was rooted in Greek religion and culture.

Mathematics is the science of the infinite, its goal the symbolic compre hension of the infinite with human, that is finite, means. It is the great achievement of the Greeks to have made the contrast between the finite and the infinite fruitful for the cognition of reality. Coming from the Ori

ent, the religious intuition of the infinite, the apeiron, takes hold of the Greek soul. This tension between the finite and the infinite and its con ciliation now become the driving motive of Greek investigation.7

Just as Weyl found it helpful to look at Greek culture and religion in

order to understand early Greek interest in infinity, so also will we find it

6. Set theory is the mathematical science of the infinite; it starts from scratch with

sets. A set is any well-defined collection of objects (the elements belonging to the set); the

collection can be finite or infinite; correspondences between sets are functions; if there

exists a one-to-one correspondence between two sets they are said to have the same car

dinal number (this number can be infinite). As an example, any set in one-to-one corre

spondence with the set of integers is said to be denumerable; its cardinal is the Hebrew let

ter aleph with a subscript of 0 (No)> sometimes called "aleph-nought." Ordinal numbers

are similarly defined for sets with a given order between their elements. Transfinite num

bers are any of these cardinal or ordinal numbers constructed through various operations and compared when possible with each other. They were introduced by Georg Cantor in

1882 in close connection with philosophical and even religious considerations about "the

Absolute." This was the first mathematical introduction of infinity in mathematics (called "actual infinite" in opposition, following Aristotle, to "potential infinite" thought of as

a limit-process). Set theory was born from the study of point sets of the real line. Later,

as we will see, the efforts to describe and classify such sets led to descriptive set theory. See Jos? Dom?nquez Ferreiros, Labyrinth of Thought: A History of Set Theory and Its Role in

Modern Mathematics (Boston, 1999); Walter Purkert, "Georg Cantor und die Antinomien

der Mengenlehre," Bulletin de la Soci?t? math?matique de Belgique 38 (1986): 313-27; and W. Purkert, Georg Cantor, 1845-1918 (Basel, 1987).

7. Hermann Weyl, God and the Universe: The Open World (New Haven, 1932), 8.



4 Slavic Review

helpful to take an area studies approach to understand recent explo rations of "infinity." At the end of the nineteenth century and at the be

ginning of the twentieth, mathematicians were much concerned with the

question of whether "infinity" is a reality or merely an abstraction, and

whether there could be more than one kind of infinity. Mathematicians were in a deep crisis over the foundations of their discipline.8 At first the

thought that many different types of infinities exist seemed counterintu

itive. After all, is not infinity the largest of all possible numbers, a single abstraction? Nonetheless, mathematicians began to notice that not all

infinities seemed to be the same. This issue can be most easily explained

by pointing to two rather simple examples. If one starts counting "1, 2, 3, 4, 5, 6, 7, 8, 9 . . . ," the process can ob

viously continue without end. The set of all the integers in this series, taken together, has an infinite number of elements. This is one example of infinity. Now if we look at the set of points on a segment of a line, it also

has an infinite number of elements. By geometrical definition, a point has no dimensions. Therefore, there are an infinite number of points on any

segment of a line. So here we have another example of infinity. Is the "in

finity" in the endless series of numerals of the same type as the "infinity" of points on a line? Clearly there is an important difference between

them. With the series of integers given above, each of the elements in the

set can be counted. (We actually count them when we say "1, 2, 3, 4, 5,

6,..." even though we never complete the task.) By contrast, we can never

count the points on a segment of a line the way we counted the numerals

in the series above. Therefore, perhaps the "infinity" in the endless series

of integers is different from the "infinity" of points on a line. In the last

years of the nineteenth century, the German mathematician Georg Can tor thought so, and he gave these infinities different "names."9 A crucial

point here is the idea of "naming." After Cantor assigned different names

to different infinities, these infinities seemed to take on a reality that they had not earlier possessed. A new world of "transfinite numbers" was being created. We will return to the concept of "naming" in the next paragraphs.

Not all mathematicians agreed with Cantor. And when one tries to ex

plain these differences of opinion it soon becomes clear that contextual, cultural ("area studies") factors were at work. Two of the most important

groups of mathematicians who wrestled with these problems were the

French and the Russians, and their predominant viewpoints were con

nected with their cultures.10 The French, operating within the tradition of

Cartesian rationalism, were very suspicious of transfinite numbers. Do

8. Hermann Weyl, "?ber die neue Grundlagenkrise der Mathematik," Mathematische

Zeitschrift 10, nos. 1-2 (1921): 39-79. A particularly clear exposition of the crisis can be

found in Sanford L. Segal, "The Crisis in Mathematics," Mathematicians under the Nazis

(Princeton, 2003), 14-41.

9. J. W. Dauben, Georg Cantor: His Mathematics and Philosophy of the Infinite (1979; reprint, Cambridge, Mass., 1990). As mentioned above, the set containing all natural num

bers is usually called K0. 10. See Loren Graham and Jean-Michel Kantor, "A Comparison of Two Cultural Ap

proaches to Mathematics: France and Russia, 1890-1930," Isis (March 2006): 56-74.




they really exist? How can they be defined? The Russians, relying and ex

panding on a tradition of the significance of "names" in Russian Ortho

doxy, were much more positively disposed toward the new types of infini

ties. The debates got very complex and also very heated.11

The French who wrestled with set theory included Emile Borel (1871

1956), Ren? Baire (1874-1932), and Henri Lebesgue (1875-1944); they were the inheritors of a great and powerful mathematical tradition, and at

first they taught the Russians more than they learned from them. The

leading Russian mathematicians interested in set theory, Dmitrii Egorov (1869-1931) and Nikolai Luzin (1883-1950), came repeatedly to Paris to

talk with their French colleagues. They usually lived in the academic heart

of the city in the Hotel Parisiana, near the Pantheon. Many years later, the

concierge of the building remembered the Russian visitors, both for their

devotion to their studies and for their religiosity. The old French establishment of mathematics, represented by Emile

Picard (1856-1941), stoutly resisted the new set theory with its preoccu

pation with transfinite numbers. Picard acidly remarked, "Some believers

in set theory are scholastics who would have loved to discuss the proofs of

the existence of God with Saint Anselme and his opponent Gaunilon, the

monk of Noirmoutiers."12 Picard thought that he could dismiss set theory

by linking it to discussions of religion, exactly the way the Russians

thought they could strengthen it.

The Russians were speculating within the tradition of Russian mysti cism, a feature of their thought that the French could not accept. But,

oddly enough, it was the Russians who won out and created a new field of

mathematics, descriptive set theory, and who in the process created the

Moscow School of Mathematics, one of the most powerful movements in

twentieth-century mathematics.

One reason the Russians were more willing to accept the concept of

transfinite numbers was that some of them were involved with a heretical sect of Russian Orthodoxy called Name Worshippers (imiaslavtsy) which

ascribed a great significance to the act of "naming."13 This sect has a his

11. See, especially, J. Hadamard, "Cinq lettres sur la th?orie des ensembles," Bulletin

de la Soci?t? Math?matique de France 33 (1905): 261-73. 12. "Certains adeptes de la th?orie des ensembles sont des scolastiques, qui auraient

aim? ? discuter les preuves de l'existence de Dieu, avec Saint-Anselme et son contra

dicteur, le moine de Noirmoutiers." Emile Picard, La science moderne et son ?tat actuel (Paris,

1909), extract from chapter 2. See Anselme de Cantorbery, Proslogion Allocution sur l'exis

tence de Dieu suivi de sa r?futation par Gaunilon et de la r?ponse d Anselme (Paris, 1993). 13. E. S. Polishchuk, ed., Imiaslavie: Antologiia (Moscow, 2002); also see O. L. Solo

mina and A. M. Khitrov, Zabytye stranitsy russkogo imiaslaviia: Sbornik dokumentov i publikatsii

po afonskim sobytiiam 1910-1913gg. (Moscow, 2001 ) ; lu. Rasskazov, Sekrety imen: Ot imiaslavii do filosofii iazyka (Moscow, 2000); Episkop Ilarion (Alfeev), Sviashchennaia taina tserkvi: Vvedenie v istoriiu i problematiku imiaslavskikh sporov, vols. 1-2 (St. Petersburg, 2002);

Pravoslavnyi vzgliad na pochitanie imenii Bozhiia: Sobytiia na Afone 1913 g. (L'viv, 2003) ; Tom

Dykstra, "Heresy on Mt. Athos: Conflict over the Name of God among Russian Monks and

Hierarchs, 1912-1914" (MA thesis, St. Vladimir's Seminary, New York, 1988); Antoine

Niviere, "Les moines onomatodoxes et l'intelligentsia Russe," Cahiers du Monde russe et so

vi?tique 29, no. 2 (1988): 181-94; Scott M. Kenworthy, "Church, State, and Society in Late

Imperial Russia: The Imiaslavie Controversy" (paper, American Association for the Ad



6 Slavic Review

tory and an involvement with mathematics that only a person deeply fa

miliar with Russian history and thought (that is, an area specialist) is likely to know. We will sketch out that history here only very briefly.

Although the debates over Name Worshipping became particularly in

tense in the first third of the twentieth century, the roots of the contro

versy go far back in the history of eastern Orthodoxy and can be found in some of the writings and sayings of Basil the Great, John Chrysostom, and

other leading church figures.14 The significance of "names" is an ancient

and highly controversial topic in mythological and religious thought in

general. The claim has been made that the Egyptian god Ptah created

with his tongue by naming that which he conceived.15 In Genesis we are

told that God said "Let there be light: and there was light." In other words, he named light first, and then he created it. Names are words, and the first

verse in the Gospel according to St. John states: "In the beginning was the

Word, and the Word was with God, and the word was God." In the Jewish

mystical tradition of the Kabbala (Book of Creation, Zohar) there is a be

lief in creation through emanation, and the name of God is considered

holy.16 And, in the Middle Ages, the significance of "names" was a central

issue in the debate over "nominalism."17

Controversies about the holiness of names became a particular char

acteristic of Russian Orthodoxy in the late nineteenth and early twentieth

centuries. In 1907 a monk of the Orthodox Church, Ilarion, who had ear

lier spent years in a Russian monastery in Mt. Athos in Greece, published a book entitled In the Mountains of the Caucasus that seized on an existing

symbolic tradition in Orthodox liturgy, especially the chanting of the "Je sus Prayer" (Iisusovaia molitva, or molitva Iisusova) and raised it to a new

prominence.18 In the Jesus Prayer the religious believer chants the names

vancement of Slavic Studies, Pittsburgh, November 2002) ; Eugene Clay, "Orthodox Mis

sionaries and Orthodox Heretics in Russia, 1886-1917," in Robert P. Geraci and Michael

Khodarkovsky, eds., Of Religion and Empire: Missions, Conversion and Tolerance in Tsarist Rus

sia (Ithaca, 2001), 38-69, especially 63-67.

14. See Georges Florovsky, Ways of Russian Theology, pt. 2, vol. 6, in Richard S. Haugh,

ed., The Collected Works of Georges Florovsky, trans. Robert L. Nichols (Belmont, Mass., 1987). 15. For a modern translation of Memphite Theology, see Marshall Clagett, Ancient

Egyptian Science (Philadelphia, 1989), 1:305-12, 595-602. We are grateful to John Mur

doch for this suggestion. 16. Gershom Scholem, Major Trends infewish Mysticism (New York, 1995).

17. R. A. Eberle, Nominalistic Systems (Dordrecht, 1970); Zenon Kaluza, Les querelles doctrinales ? Paris: Nominalistes et r?alistes aux

confins du XTVe et du XVe si?cles (Bergamo, 1988).

18. The full title of the book was Na gorakh Kavkaza, beseda dvukh startsev podvishnikov o vnutrennem edinenii s

Gospodom nashikh serdets chrez molitvu Iisus Khristova Hi dukhovnaia

deiatel'nost' sovremennykh pustinnikov, sostavil pustynnozhitel' Kavkavskikh gor skhimonakh

Ilarion (In the mountains of the Caucasus: a conversation between two elder ascetics con

cerning the inner union of our hearts with the Lord through the prayer of Jesus Christ; or

the spiritual activity of contemporary hermits, composed by the hermit of the Caucasus

mountains, the monk Ilarion) (1st ed., Batalpashinsk, 1907; 2d corrected and expanded

ed., 1910; 3d ed., Kievskaia Pecherskaia Lavra, 1912). The roots of the Jesus Prayer go back

centuries; the start of the tradition is often cited as Apostle Paul's instructions to the faith

ful to "pray without ceasing" (1 Thess. 5:17). The tradition exists in both Catholic and Or

thodox liturgies, and there is an extensive literature on it. In Russia the Jesus Prayer ac

quired a special prominence, especially after the publication of the folklore classic The Way




of Christ and God over and over again, hundreds of times, until his whole

body reaches a state of religious ecstasy in which even the beating of his

heart, in addition to his breathing cycle, is supposedly in tune with the

chanted words (a state vividly described by J. D. Salinger in Franny and

Zooey).19 According to Ilarion, the worshipper achieves a state of unity with God through the rhythmic pronouncing of his name. And this dem

onstrates, said Ilarion, that the name of God is holy in itself, that "the

name of God is God" (Imia Bozhie est' sam Bog) .20

At first this book was well received by many Russians interested in re

ligious thought. Ilarion's views became very popular among the hundreds

of Russian monks in Mt. Athos, and his influence gradually spread else

where. But the highest officials in Russian Orthodoxy, in St. Petersburg and Moscow, soon began to consider the book not just as a description of

the significance of prayer but as a theological assertion. For many of these

officials, the adherents of Ilarion's beliefs were heretics, even pagan pan theists, because they allegedly confused the symbols of God with God him

self. On 18 May 1913, the Holy Synod in St. Petersburg condemned the

Name Worshippers; soon thereafter the Russian navy, with the approval of Tsar Nicholas II and the patriarch of Constantinople (who had ju risdiction over the monasteries of Mt. Athos), sent several gunboats to

Mt. Athos to bring the rebellious monks forcibly to heel. Over 600 unre

pentant monks were flushed out of their cells with fire hoses and brought under guard to Odessa. With later detentions, the number grew to ap

proximately 1,000.21 The dissidents strongly protested their treatment and

obtained promises of further investigation and reconsideration. The Name Worshippers had some defenders in high places and the tsar him

self seemed to be of two minds on the question.22

of the Pilgrim (Kazan, 1884). The book popularized the prayer and was translated into many

languages. 19. Salinger has Franny observing to her incredulous friend Lane, "Well, the starets

tells him about the Jesus Prayer first of all. . . . If you keep saying that prayer over and over

again?you only have to just do it with your lips at first?then eventually what happens, the prayer becomes self-active. Something happens after a while. I don't know what, but

something happens, and the words get synchronized with the person's heartbeats, and

then you're actually praying without ceasing. Which has a really tremendous, mystical ef

fect on your whole outlook. I mean that's the whole point of it, more or less. I mean you do

it to purify your whole outlook and get an absolutely new conception of what everything's

about." J. D. Salinger, Frann)? and Zooey (Boston, 1961), 36-37, emphasis in the original. 20. See description of Ilarion and his followers in N. K. Bonetskaia, "Bor'ba za

Logos v Rossii v XX veke," Voprosy filosofii 7 (1998): 148-69, especially 150-51; Polishchuk, ed., Imiaslavie, 490, emphasis in the original.

21. Polishchuk, ed., Imiaslavie, 479-518. These events were also reported in the for

eign press; see "Heresy at Mount Athos: A Soldier Monk and the Holy Synod," London

Times, 19 June 1913; "Heresy at Mount Athos, London Times, 23 August 1913; "The Mount

Athos Heresy Case: Voluntary Exile in Siberia," Times, 23 August 1913.

22. According to Vladimir Gubanov, the Holy Synod urged the tsar to squelch the

heresy before it split the faith and the nation, but the monk Grigorii Rasputin, who was

close to the court, defended the Name Worshippers. The tsar evidently hesitated but in the

end gave in to the synod. Vladimir Gubanov, Tsar'Nikolai II i novye mucheniki: Prorochestva,

chudesa, otkrytiia i molitvy: Dokumenty (St. Petersburg, 2000). Tom Dykstra has also written



8 Slavic Review

With the advent of World War I the issue receded into the back

ground, but until the end of the tsarist regime, the adherents of the

"heresy" were forbidden to return to Mt. Athos or to reside in major cities

like St. Petersburg and Moscow. The most fervent of them retreated to

monasteries where they continued to practice and propagate their variant

of the faith.

After the Bolshevik revolution, the Name Worshippers, now living all over rural Russia, were more successful than most other religious believ ers in continuing their practices out of view of Soviet political authorities,

who were trying to suppress religion. After all, the Name Worshippers had

already been defined as heretics and excluded from the established

churches.23 But they continued to practice their faith in secret, and by vir

tue of being out of view, they were not compromised by association with

the Bolsheviks, as were some of the established church leaders. The dissi

dents claimed to represent the undefiled "true faith," increasing their

popularity with some religious opponents of the new communist regime.

(Amazingly, as late as 1983 rumors spread about the secret existence in

the Soviet Union of followers of the dissident faith of Name Worship

ping,24 and some people have asserted that descendants of the sect mem

bers, having outlasted their Soviet oppressors, still practice their faith to

day, especially in the Caucasus and, recently, in Moscow.25 In Moscow

recent publications indicate that some of the ideas of Name Worshipping are still attractive to intellectuals, especially mathematicians.26)

Several of the intellectuals in Moscow who became interested in Name

Worshipping just before and after World War I were leading mathemati

cians. They included Dmitrii Egorov, professor of mathematics at Moscow

State University and for many years president of the Moscow Mathemati

cal Society; and two of his students, Luzin and Pavel Florenskii (1882

1937). All three of these men were deeply religious.27 Florenskii eventu

ally abandoned mathematics for religious studies and became a priest, but

that Rasputin may have supported the Name Worshippers. Dykstra, "Heresy on Mt. Athos."

On Rasputin's role, see also Ilarion (Alfeev), Sviashchennaia taina tserkvi, 2:15 and 64.

23. S. S. Demidov, "Professor Moskovskogo universiteta Dmitrii Fedorovich Egorov i

imeslavie v Rossii v pervoi treti XX stoletiia," Istoriko-matematicheskie issledovaniia, 2d ser., 39

(1999): 129-30. 24. Polishchuk, ed., Imiaslavie, 513.

25. Ilarion (Alfeev), Sviashchennaia taina tserkvi, vol. 2.

26. See the recent essay by A. N. Parshin, well-known mathematician, pupil of Igor Shafarevich and corresponding member in the department of mathematics of the Russian

Academy of Sciences: Parshin, "Svet i slovo (k filosofii imeni)," in Polishchuk, ed., Imi

aslavie, 529-44.

27. Egorov's deep religiosity is described in Demidov, "Professor Moskovskogo uni

versiteta Dmitrii Fedorovich Egorov," 137. Luzin's conversion by Florenskii to a religious

viewpoint is described in various sources, including Charles Ford, "The Influence of P. A.

Florensky on N. N. Luzin," Historia Mathematica 25, no. 3 (August 1998): 332-39. See also

Ford, "Dmitrii Egorov: Mathematics and Religion in Moscow," Mathematical Intelligencer 13, no. 2 (1991): 24-30. Florenskii's best-known published statement of faith is probably his

Stolp i utverzhdenie istiny (Moscow, 1914), published in English as The Pillar and Ground of the

Truth, trans. Boris Jakim (Princeton, 1997).




he maintained a great interest in mathematics and science throughout his life.

At the time of the Bolshevik revolution, Florenskii was living in a mon

astery town near Moscow, and he was close religiously and intellectually to

the Name Worshipper dissidents. He communicated their ideas to Luzin

and Egorov and translated them into mathematical parlance. In the early 1920s there was a Name Worshipper circle (imeslavcheskii kruzhok) in Mos cow where the ideas of the religious dissidents and the concepts of math

ematics were brought together. Participants in the circle included fifteen or sixteen philosophers, mathematicians, and religious thinkers. Some

times the circle met at Egorov's apartment, and Florenskii presented pa

pers at several of these meetings.28 Here Florenskii expounded the view

that "the point where divine and human energy meet is 'the symbol,' which is greater than itself."29 To Florenskii names were symbols that he

thought could attain full autonomy. Intellectual and artistic Russia at the end of the nineteenth century

and in the first decades of the twentieth was preoccupied with the ques tion of the significance of symbols. The symbolist movement affected bal

let, music, literature, art, and poetry, as the names Sergei Diaghilev, Igor

Stravinsky, Andrei Belyi, Konstantin Stanislavskii, Vasilii Nemirovich

Danchenko, and Vsevolod Meierkhol'd remind us. Now we should add the

mathematicians Egorov and Luzin and their priest-friend Florenskii to

such lists. Indeed, there was even a connection between the literary and

mathematical movements. Belyi, the symbolist poet, was the son of a Mos cow mathematician, and he majored in mathematics at Moscow University

where he studied under Egorov and together with Luzin. Familiar with Name Worshipping, Belyi once wrote an essay called "The Magic of

Words" in which he claimed, "When I name an object with a word, I

thereby assert its existence." We can ask, does this apply both to mathe matics and to poetry? If the object is a new type of infinity, does that infin

ity only exist once one has named it? Florenskii saw that the Name Worshippers had raised the issue of

"naming" to a new prominence. To name something was to give birth to a new entity. Florenskii was convinced that mathematics was a product of the free creativity of human beings and that it had a religious significance.

Humans could exercise free will and put mathematics and philosophy in

perspective. Georg Cantor's famous sentence clearly had a strong appeal for Florenskii: "das Wesen der Mathematik liegt gerade in ihrer Freiheit"

(The essence of mathematics lies precisely in its freedom).30 Mathemati cians could create beings (sets) simply by naming them. For example, de

fining the set of numbers such that their squares are less than 2, and nam

ing it "A," and analogously the set of numbers such that their squares are

28. Polishchuk, ed., Imiaslavie, 513.

29. Ilarion (Alfeev), Sviashchennaia taina tserkvi, 2:114.

30. Georg Cantor, "?ber unendliche, lineare Punktmannichfaltigkeiten," Mathema

tische Annalen 21 (1883): 545.



10 Slavic Review

larger than 2, and naming it "B," meant to bring into existence (essentially the Eudoxus-Cauchy construction) the real number V2.

For Florenskii, the development of set theory was a brilliant example of how naming and classifying can produce mathematical breakthroughs.

A "set" was simply a naming of entities according to an arbitrary mental

system, not a recognition of types of ontologically existing objects. When a mathematician created a "set" by naming it, he was giving birth to a new

mathematical being. A new form of mathematics was coming, said Flo

renskii, and it would rescue mankind from the materialistic, determinis

tic modes of analysis so common in the nineteenth century. And, indeed, set theory, new insights on continuous and discontinuous phenomena like the development under the name "Arithmology" of the discovery in

1897 by Kurt Hensel of the p-adic numbers (which strongly impressed

Egorov, Luzin, and Florenskii, and their followers), and discontinuous

functions?became hallmarks of the Moscow School of Mathematics.

Both the French and the Russian mathematicians were wrestling with

the problem: What is a mathematical object, what is permitted as an ob

ject, and what is a good definition of such an object? As Lebesgue wrote

to Borel in 1905, "Peut-on s'assurer de l'existence d'un ?tre math?ma

tique sans le d?finir?" (Is it possible to convince yourself of the existence

of a mathematical being without defining it?) .31 To Florenskii the question was the analogue of, Is it possible to convince yourself of the existence of

God without defining him? The answer for Florenskii and later for Egorov and Luzin was that the act of naming in itself gave the object existence.32

Thus "naming" became the key to both religion and mathematics. The

Name Worshippers gave existence to God by worshipping his name, and

mathematicians gave existence to sets by naming them.

The circle of eager students that formed around Luzin at the begin

ning of World War I and continued throughout the early 1920s was known as "Lusitania." An indirect hint about the place of religion in the concerns

of the Lusitanians can be seen in the description of the group provided by one of its original members, M. A. Lavrent'ev (1900-1980) ,33 According to

Lavrent'ev (later a significant mathematician and the founder of Akadem

gorodok in Novosibirsk) the Lusitanians acknowledged two leaders:

"God-the-father" Egorov and "God-the-son" Luzin. It was Luzin who told

the young Lusitanians: "Egorov is the chief of our society," and "Our dis

coveries belong to Egorov." Students in the society were given the monas

tic title of "novice." Noting Lavrent'ev's description of the group, Esther

Phillips wrote, "There was clearly a strong sense of belonging to an inner

31. Lebesque as cited in Hadamard, "Cinq lettres sur la th?orie des ensembles."

32. At one point Luzin wrote in his notes "Everything seems to be a daydream, play

ing with symbols, which however, yield great things." At another moment Luzin scribbled

in infelicitous but understandable French: "nommer, c'est avoir individu." Archive of the

Russian Academy of Sciences, Moscow, f. 606, op. 1, ed. khr. 34. Courtesy of Roger Cooke,

"N. N. Luzin on the Problems of Set Theory" (unpublished paper, January 1990), 1-2, 7.

33. M. A. Lavrent'ev, "Nikolai Nikolaevich Luzin," Russian Mathematical Surveys 29,

no. 5 (1974): 173-78, and Uspekhi mathematicheskikh nauk 29, no. 5 (1974): 177-82.



"Soft " Area Studies versus "Hard

" Social Sciences: A False Opposition 11

circle or a secret order."34 All the principals and novices went to Egorov's home three times a year: Easter, Christmas, and his name-day (again, the

importance of "names"). The intense camaraderie among the Lusitanians was inspired by Luzin, who was described as extroverted and theatrical, and who engendered real devotion among students and colleagues.

Egorov, on the other hand, was more reserved and formal. According to

Lavrent'ev, Luzin's chief assistants in managing Lusitania were three stu

dents, each with his own function: Pavel Aleksandrov was the "creator," Pavel Uryson the "keeper," and Viacheslav Stepanov the "herald" of the

mysteries of Lusitania. (All three of these students went on to become

mathematicians of note; all three, along with their teachers Egorov and

Luzin, are included in the current Dictionary of Scientific Biography, the most authoritative listing of deceased scientists of world rank.35)

Although Egorov and Luzin were very close to a number of leading French mathematicians and cited their debt to them, the French world

view was different. The French wanted to keep the philosophical, mathe

matical, and psychological components of their thought separate. Mixing mathematics and religion was, to the French mind, a bad idea. On the

contrary, Egorov and Luzin believed that mathematics was linked to reli

gion, but they could not be explicit about these links after 1917 because

of the hostile Soviet environment. They knew that they could easily get into trouble with the authorities if the views discussed in the meetings of

the Name Worshipping circle became known.36 Eventually Egorov, Luzin, and Florenskii were caught and persecuted by the Soviet authorities, but

only after Luzin in particular, and his students, had made mathematical

breakthroughs. (Egorov died of starvation while in Soviet detention in

1931; Florenskii was imprisoned in the notorious Solovetskii gulag and then shot in 1937; Luzin survived with an ideological dressing-down.37)

34. Esther R. Phillips, "Nicolai Nicolaevich Luzin and the Moscow School of the The

ory of Functions," Historia Mathematica 5, no. 3 (August 1978): 293.

35. Charles Coulston Gillispie, ed., Dictionary of Scientific Biography (New York, 1970

1990). Luzin is in 8:557-59; Egorov in 4:287-88; Aleksandrov in 17.2:11-15; Uryson in

13:548-49; Stepanov in 13:35-36.

36. While we know that Egorov was a leader of this circle, we have no concrete evi

dence that Luzin was a member or even ever attended meetings. We do know that Luzin

was a friend of Father Florenskii, that he was familiar with the Name Worshipping move

ment, and that in his mathematical research he put great emphasis on "naming." Luzin

was more cautious than Egorov and probably made more of an attempt to conceal his re

ligious views from the Soviet authorities.

37. Florenskii was first arrested in 1928, then released, then arrested again in 1933

and sentenced to ten years in labor camps in Siberia. He was executed on 8 December

1937. Rehabilitated in 1956, he has slowly gained attention since then as a philosopher of

language and culture, a theologian, and, most recently, as an influence on Russian math

ematics. See Richard Gustafson, "Introduction," in Florenskii, The Pillar and Ground of the

Truth, ix-xxiii. Egorov was rebuked by the Communist Party in 1929, arrested in 1930, and

sent to prison. There he went on a hunger strike. Just before his death, he was taken un

der guard to a hospital in Kazan; he died on 10 September 1931. We are told that he died in the arms of the wife of the mathematician N. G. Chebotarev, who was a doctor in the

hospital. Chebotarev's son G. N. Chebotarev wrote, "On umer na maminykh rukakh" (He

died in my mother's arms): G. N. Chebotarev, "Iz vospominanii ob ottse," in lu. B. Ermo



12 Slavic Review

In the 1920s Luzin's religious and philosophical approach helped stimulate in him a profound mathematical originality. He and his students

created a new field: the descriptive theory of sets. And the Moscow Math ematical School that Luzin and Egorov created caused an explosion of

mathematical research in the 1920s and 1930s that will always be remem

bered in the history of mathematics.38

One of the leading French mathematicians in this story, Lebesgue, fi

nally acknowledged that it was precisely "philosophy"?what he and his French colleagues tried to avoid in mathematics?that helped Luzin

make his innovations. In a preface to Luzin's 1930 book published in

French in Paris, Lebesgue wrote that with Luzin "mathematical exigencies and philosophical exigencies are constantly associated, one can even say fused."39 (In the Russian edition of this book, the Soviet editors removed

this statement.) Lebesgue admitted that this approach helped Luzin and

his students to find a concept he had not seen. Once his eyes were

opened, Lebesgue was astounded by the fruitfulness of the Russian ap

proach. In open wonderment he declared, "M. Luzin examines questions from a philosophical point of view and ends up with mathematical results.

This is an originality without precedent!"40

The skeptic, after reading the above section, may well say, "OK, this

strange group called Name Worshippers may have had at a certain point in time an unusual influence in the history of mathematics. But surely this

is an exception, and a rather bizarre one at that. Can you point to another recent example of how an area studies approach will tell us something of

importance about the development of mathematics?" Our response is,

yes, examples abound.41 In order to be brief, however, we will present only

laev, ed., Nikolai Grigor'evich Chebotarev (Kazan, 1994), 56. Luzin was submitted to an ideo

logical trial in which many of his former colleagues turned against him. See S. S. Demidov

and V. D. Esakov, "'Delo akademika N. N. Luzina' v svete stalinskoi reformy sovetskoi

nauki," Istoriko-matematicheskie issledovania, 2d ser., 39, no. 4 (1999): 156-70. S. S. Demidov

and B. V. Levshin, eds., Delo akademika Nikolaia Nikolaevicha Luzina (St. Petersburg, 1999); A. P. Iushkevich, "Delo akademika N. N. Luzina," Vestnik AN SSSR, no. 4 (1989): 102-13;

Alexey E. Levin, "Anatomy of a Public Campaign: Academician Luzin's Case' in Soviet Po

litical History," Slavic Review 49, no. 1 (Spring 1990): 90-108; A. N. Bogoliubov and N. M.

Rozhenko, "Opyt' 'vnedreniia' dialektiki v matematiku v kontse 20-kh nachale 30-kh

godov," Voprosy filosofii, no. 9 (1991): 32-43. 38. AJlen Shields, "Years Ago: Luzin and Egorov," Mathematical Intelligencer 9 (1987):

24-27; Smilka Zdravkovska and Peter L. Duren, eds., Golden Years of Moscow Mathematics

(Providence, 1993) ; Alexander Vucinich, "Mathematics and Dialectics in the Soviet Union:

The Pre-Stalin Period," Historia Mathematica 26, no. 2 (May 1999): 107-24; P. S. Aleksan

drov, Matematika v SSSR za 15 let (Moscow, 1932). 39. "Exigences math?matiques et exigences philosophiques sont constamment asso

ci?es, on peut m?me dire fondues." Henri Lebesgue, "Pr?face," in Nicolas Luzin, Le?ons sur

les ensembles analytiques et leurs applications (Paris, 1930), xi.

40. "M. Lusin examine les questions d'un point de vue philosophique et aboutit ainsi

? des r?sultats math?matiques: originalit? sans pr?c?dent!" Lebesgue, "Pr?face," ix.

41. In the early development of set theory, the works of Bernard Bolzano and Georg

Cantor, both of whom had strong philosophical and religious beliefs, await deeper con

textual analysis. The work of the Russian mathematician and geometer A. D. Alexandrov,

who had strong philosophical commitments, also beckons. The Bourbaki mathematics





one other case: the varieties of mathematical expressions of general rela

tivity theory. When nonscientists discuss general relativity theory, their emphasis

very often concerns the question of its validity rather than its varieties.

Modern physicists overwhelmingly accept general relativity, but they have

expressed it mathematically in a considerable variety of modes. As the

physicist and historian of physics David Kaiser wrote in a recent article in

which he surveyed presentations of general relativity in the post-World War II period in Europe and America, "'General relativity' became a play

ing field upon which many different physicists, speaking different kinds of

mathematical languages, could renegotiate what it meant to do gravita tional physics."42 These "different kinds of mathematical languages" can

often be explained by contextual ("area studies") analysis. One of the leading exponents of relativity theory in Russia in the

1950s and 1960s was V A. Fok (Fock), a physicist honored in many coun

tries of the world. Fock was a passionate defender of relativity theory; he once wrote that to question the validity of relativity theory is on par with

questioning the roundness of the earth.43 However, if one looks at the

equations Fock used to express general relativity in his many publications, one will find that they are different from Albert Einstein's, even though in

those areas where general relativity produces observable results, the two

approaches yield similar products. The differences are, however, signifi cant intellectually, and they are closely tied to Fock's philosophical and

social views.44

If one compares Einstein's and Fock's gravitational equations, one will see that they are distinctly different. Einstein's takes the form:

(1)

R^ -

-g*vR =

~xT?v

Fock's was considerably more complicated:

(2)

2 dxadx? w? = ?o**?s? + r^a?ra?

How does one explain this difference?

group in France awaits further contextual examination. The great mathematician Alexan

der Grothendieck, who was interested in mysticism at many points in his life, should be

similarly examined.

42. David Kaiser, "Alp is just a ij;? Pedagogy, Practice, and the Reconstitution of Gen

eral Relativity, 1942-1975," Studies in the History and Philosophy of Modern Physics, 29 no. 3 (1998): 336.

43. V A. Fok [Fock], "Protiv nevezhestvennoi kritiki sovremennykh fizicheskikh

teorii," Voprosy filosofii, no. 1 (1953): 168-74. 44. Loren R. Graham, "Do Mathematical Equations Display Social Attributes?" Math

ematical Intelligencer 22, no. 3 (Summer 2000): 31-36.



14 Slavic Review

Fock was a convinced Marxist, of a very sincere, dedicated sort, far

from the vulgarized form often preached by others.45 As a Marxist he

wanted to preserve the concept of a predictable, science-ruled world. He

considered the term theory of general relativity unfortunate because he

feared it would cause people to say "everything is relative," when, in fact,

general relativity was based on an absolute standard, that of "absolute

space-time." Fock, therefore, actually renamed Einstein's theory "the the

ory of absolute space-time" or the "theory of gravitation."46 As Gerald

Holton, physicist and historian of science, has pointed out, Einstein was

aware of the problem, but thought it was too late to change the title of his

theory.47 Fock thought a strong argument could be made that his new

terms were more accurate than Einstein's. The one thing that the theory of general relativity was not, Fock maintained, was a purely relativistic the

ory. Fock liked to put his viewpoint in French: "(1) La relativit? physique n'est pas g?n?rale; (2) la relativit? g?n?rale n'est pas physique" (Physical

relativity is not general; general relativity is not physical) .48 Echoing the

views of the German physicist Max Planck, Fock remarked, "The theory of

relativity, after showing that a whole series of concepts earlier considered

absolute were actually relative, at the same time introduced new absolute

concepts. The majority of critics of the theory of relativity forget this."49

Fock believed that Marxists like himself would have difficulty accepting a

purely relativistic theory, given their commitment to objective reality and

their opposition to completely relativistic concepts of truth.50

45. Fock asserted his Marxism in dozens of publications and conversations, both with

one of the authors (Loren Graham) and with others. Graham met with Fock in Leningrad in the spring of 1961 and engaged in a

published discussion with him in 1966: Loren R.

Graham, "Quantum Mechanics and Dialectical Materialism," Slavic Review 25, no. 3 (Sep tember 1966): 381-410; see Fock's reply in his "Comments," Slavic Review 25, no. 3 (Sep tember 1966) : 411-13. After the fall of the Soviet Union, when there was no longer any po litical reason to affirm Fock's Marxism, people who knew him and his work continued to

describe him as an intellectual Marxist. Two years after the end of the USSR, in 1993, the

historian of Russian physics Gennadii Gorelik wrote, "There is no doubt that in the 1930s

Fock was already sincerely devoted to dialectical materialism." G. E. Gorelik, 'V. A. Fok:

Filosofiia tiagoteniia i tiazhest' filosofii," Priroda, no. 10 (1993): 92.

46. As reflected in the English translation of the title of one of his best-known works:

V. A. Fock, The Theory of Space, Time, and Gravitation, trans. N. Kemmer (New York, 1959). 47. See Gerald Holton, "Introduction: Einstein and the Shaping of Our Imagina

tion," in Gerald Holton and Yehuda Elkana, eds., Albert Einstein: Historical and Cultural Per

spectives (Princeton, 1982), xv.

48. As Max Planck commented, "The concept of relativity is based on a more funda

mental absolute than the erroneously assumed absolute which it has supplanted." Max

Planck, The New Science (Greenwich, Conn., 1959), 146. Planck expressed the same idea in

earlier publications, for example, Das Weltbild der Neuen Physik (Leipzig, 1929), 18.

49. Fok [Fock], "Protiv nevezhestvennoi kritiki sovremennykh fizicheskikh teorii,"

172.

50. "Es ist nicht ?berfl?ssig zu unterstreichen, dass das Verh?ltnis von K?rpern oder

Prozessen zum Bezugssystem ebenso objektiv ist (d.h. unabh?ngig von unserem Bewusst

sein) wie ?berhaupt alle physikalischen und anderen Eigenschaften der K?rpern" (It is

not superfluous to emphasize that the relationship of bodies or processes to the reference

system is just as objective [i.e., independent of our consciousness] as are

physical and

other properties in general). V. A. Fock, "?ber philosophische Fragen der modernen

Physik," Deutsche Zeitschrift f?r Philosophie, no. 6 (1955): 742.





Fock wanted the equations for gravitation within general relativity to

reflect his understanding of its deeper meaning. He believed that he

could show that even in general relativity there are preferred or privileged systems of coordinates. A formidable mathematician, Fock devoted much

of his research over many years to the task of proving that in space uni

form at infinity there is a preferred system of coordinates, that of har

monic coordinates; such a system of coordinates, he maintained, reflected

"certain intrinsic properties of space-time."51 Fock wanted to set up a

comparison of different equations for the curvature tensor, Einstein's and

his own, and demonstrate the advantages of his equation. He began with

Einstein's gravitational equation (1), given above. For Fock, this expres sion, with all of its combinations of derivatives, seemed to involve too

much needless permissiveness: Einstein kept this range of possibilities be cause he wanted to maintain the full generality of all the possible coordi nate systems a physicist might choose to use. But all these possibilities seemed irrelevant to Fock, given his strong, principled preference for a

particular coordinate system, his beloved harmonic coordinates. Using some intricate mathematical calculations, Fock transformed the curva

ture tensor to a form that would make it especially convenient for expres sion in harmonic coordinates, equation (2) as given above.

Fock's preference for (2) over (1) provides an example of a socio

philosophical context affecting mathematical equations. Fock pointed out that his gravitational equation (2) was "compatible with Einstein's"

and did not "impose any essential limitation on the solution of the latter,

serving only to narrow down the class of permissible coordinates." The reason Fock preferred harmonic coordinates was because he believed

they reflected objective properties linked to "the distribution and motion

of ponderable matter."52 Therefore, he believed he had developed a the

ory of gravitation that permitted unique solutions, was compatible with

Einstein's theory, and was also in accord with philosophical materialism.

Although Fock's approach to general relativity is still regarded as

somewhat idiosyncratic, it has won respect from physicists internationally. At conferences, such leaders in the field as John Wheeler and Stanley Deser of the United States, Hermann Bondi of Great Britain, and Andr?

Lichnerowicz of France have praised Fock's work for its originality and in

sight.53 In a discussion with one of the authors of this article, Wheeler

agreed that physicists in several countries are interested in Fock's use of

harmonic coordinates in general relativity.54

51. Fock, Theory of Space, Time, and Gravitation, xv, xvi, 351. See also V A. Fok [Fock], "Poniatiia odnorodnosti, kovariantnosti i otnositernosti," Voprosy filosofii,

no. 4 (1955): 133.

52. Fock, Theory of Space, Time, and Gravitation, 193; also see 366-75.

53. Siegfried M?ller-Markus, a German historian and philosopher of science, noting

leading physicists' praise of Fock's work, ended up writing a book positively interpreting Fock's views of general relativity, even though his original intention had been to criticize

them. See Siegfried M?ller-Markus, Einstein und die Sowjetphilosophie, vol. 2 (Dordrecht,

1970). 54. See John Wheeler's response to Loren R. Graham, "The Reception of Einstein's

Ideas: Two Examples from Contrasting Political Cultures," in Gerald Holton and Yehuda



16 Slavic Review

Within post-Soviet Russia itself, Fock's views on general relativity con

tinue to have influence. On 29 January 1999, a Russian science newspaper

published an article praising Fock entitled "On an Equal Footing with Ein

stein."55 Among Russian physicists, the one who has perhaps most consis

tently continued to promote Fock's ideas is Academician A. A. Logunov,

longtime director of the proton synchrotron accelerator in Protvino. Like

Fock, Logunov prefers "theory of gravitation" to "general theory of rela

tivity." In his 1998 book Relativistic Theory of Gravity he praised Fock's "as

piration to clarify the essence of GRT [General Relativity Theory], freeing it from general relativity devoid of any physical meaning."56

Looking back at the two examples we have given (the birth of de

scriptive set theory and the varieties of mathematical expression of gen eral relativity) we see, as we noted at the outset, that the core questions are

quite different: the first concerns what is legitimate in mathematics itself; the second involves the uses of mathematics. In the first case we have seen

that even in such an abstract and nonapplied field as descriptive set theory the social context played a role in historical development.

It is probably less surprising that social context has played a role in the

work of physicists (Einstein, Fock, and others) who tried out different ways of using mathematics to express general relativity. These physicists dis

agreed with each other, not over mathematics, but over its implementa tion. Their philosophical and, in Fock's case at least, their social views

played a role in this disagreement. Social scientists who apply mathematical methods (statistics, regres

sion analysis, longitudinal studies, and so on) to the study of social be

havior are in the second position, using standard statistical analysis to un

derstand society. If social influences can be found in physicists' use of

mathematics, is it not even more likely that they can be found in social sci

entists' application of mathematical methods? When one uses mathemat

ics to study society, the questions, On what problem? For what purpose? In what way? and When? are all relevant, and for each of these questions the possibility of social influence is obvious. Even the introduction of new

mathematical concepts with the purpose of application is influenced by social conditions.

To explore these questions more thoroughly, to try to illustrate the in

fluence of social context on the ways in which social scientists have used

quantitative methods would require us to write a separate article. The be

ginnings of this analysis already exist in the literature, however. Historians

of statistics such as Stephen M. Stigler, Lorraine Daston, Theodore Porter, and Alain Desrosi?res have explored the development of the field within

a social context.57 In his book, Desrosi?res explained that he wanted to

Elkana, eds., Albert Einstein: Historical and Cultural Perspectives (Princeton, 1982), 107-36

(Wheeler's response appears on p. 135). 55. See "Naravne s Einshteinom," Poisk, 29 January 1999, 8.

56. A. A. Logunov, Relativistic Theory of Gravity (Commack, N.Y, 1998), 65; see also

Logunov, The Theory of Gravity (Moscow, 2001). 57. Stephen M. Stigler, The History of Statistics: The Measurement of Uncertainty before

1900 (Cambridge, Mass., 1986); Stigler, Statistics on the Table: The History of Statistical Con





link the technical history of statistics to its social history, to connect "the

two dimensions, economic and cognitive, of the construction of a system of equivalences."58 Any such analysis must be based on a knowledge of so

cial context of the sort that area studies specialists bring to their fields.

After reading the above analysis, some social scientists will say that it

puts too much emphasis on mathematics. As one commentator on an

early draft of this article observed, "What really distinguishes the social sci ence approach from the areas studies one is not necessarily the use of

mathematics, but the reliance upon rigorous methodology, standards of

evidence, and replicability. The American Political Science Association

has an entire membership devoted to qualitative methods whose practi tioners consider themselves no less scientific than number crunchers."

This observation, and the approach it represents, is much more sophisti cated than the one emphasizing quantitative methods alone, but it also

suffers, as indicated by the phrase "no less scientific," from the cognitive flaw embodied in the view that only the scientific approach can inform us.

It is based on an outdated view of cognitive psychology, the one dominant a generation ago when great pioneers of social science like Frederick

Mosteller showed so effectively the contribution such an approach can

make to understanding topics as diverse as educational achievement or

the determination of the authorship of Federalist writings.59 The signifi cance of Mosteller's approach was enormous and will continue to be in

the future. But new developments in cognitive psychology and the sociol

ogy of knowledge clearly show the importance of what Howard Gardner

calls "different cognitive strengths and contrasting cognitive styles," of

which the social science approach, although very valuable, uses only a lim

ited range.60 Gardner maintains that there are multiple intelligences and multiple

valuable approaches to understanding and achievement. In his original work Gardner named seven different types of intelligence, of which

"logical-mathematical intelligence" was only one. In his latest work he has

added a naturalist intelligence and accrued evidence for a candidate ex

istential intelligence. Gardner stated that one reason he thinks the origi nal list should be expanded (neither he nor anyone else is certain just how

many intelligences there are) is because of a remark made to him by Ernst

Mayr, perhaps the greatest evolutionary biologist of the last century. After

hearing Gardner give his original list of seven intelligences, Mayr re

marked, "You will never explain Charles Darwin with the set of intel

ligences you proposed." This remark should attract the attention of so

cial scientists who say that what really distinguishes social science is not

cepts and Methods (Cambridge, Mass., 1999); Lorraine Daston, Classical Probability in the En

lightenment (Princeton, 1988); Theodore Porter, The Rise of Statistical Thinking: 1820-1900 (Princeton, 1986) ; Alain Desrosi?res, The Politics of Large Numbers: A History of Statistical Rea

soning, trans. Camille Naish (Cambridge, Mass., 2002). 58. Desrosi?res, Politics of Large Numbers, 11.

59. Frederick Mosteller and Daniel P. Moynihan, eds., On Equality of Educational Op

portunity (New York, 1972) ; Frederick Mosteller and David L.Wallace, Inference and Disputed

Authorship: The Federalist Papers (Reading, Mass., 1964). 60. Howard Gardner, Multiple Intelligences: New Horizons (New York, 2006), 5.



18 Slavic Review

number-crunching but replicability. Evolution has never been and still is not replicable, nor has it yet been found to be falsifiable, yet it has pro vided an enormous advance in our understanding of the world.61

The conclusion that we draw does not diminish the importance or

utility of social science approaches to social reality (we celebrate that im

portance and that utility), instead it emphasizes that a true and sophisti cated understanding of the world in which we live requires multiple ap

proaches. Some will be logical-mathematical, some will be linguistic, some

will be interpersonal or intrapersonal, and some will be deeply contextual, as the one we have used in this article.

In view of the fact that there has recently been a great controversy over the "social construction of knowledge," we would like to add that we

are not radical social constructivists, people who believe that science is to

tally determined by social influences.62 On the contrary, we consider sci ence to be the most reliable form of knowledge that exists. Reality does

matter. Even though we believe that descriptive set theory developed more rapidly in Russia than in France because of social influences, we are

conscious that such different contexts lead to similar theories. Both the

French mathematicians and the Russian mathematicians were working on the same problems and today French and Russian mathematicians

working in set theory are very largely in agreement. Similarly, Fock and

Logunov in Russia have worked on applying mathematics to the same

physical problems as physicists elsewhere, and although some differences

with their colleagues elsewhere remain in their use of mathematics, their areas of accord with their international colleagues are much greater than

their points of dissent. All agree on the validity of the general relativity

theory but they disagree on the best way to express it mathematically, and

their divergent philosophical and social views have influenced these

differences.

In this article we have tried to show that insisting on a rigid division

between the "soft" methods of area studies specialists and the "hard"

methods of social scientists is simplistic. Social scientists, whether using

quantitative methods or ones yielding replicable results, can make great contributions to the understanding of society and politics, as they already have. Area studies specialists can also make such contributions, and?in

addition?they can sometimes advance our understanding of quanti ta

61. See also Ernst Mayr, This Is Biology: The Science of the Living World (Cambridge, Mass., 1997).

62. See Hacking, Social Construction of What? The initial and best-known episode in

the controversy was Alan D. Sokal's spoof of social constructivists in his "Transgressing the

Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity," Social Text,

no. 46/47 (Spring/Summer 1996): 217-52. Sokal revealed that this article was a hoax de

signed to parody those who "socially construct" science in his "A Physicist Experiments with Cultural Studies," Lingua Franca (May/June 1996): 62-64. Sokal's original article was

very clever and he was correct in ridiculing the views of the most extreme social contruc

tivists. The basic issue of the controversy?to what extent are science and mathematics af

fected by the society in which they developed??remains, however, unresolved. See also

Noretta Koertge, ed., A House Built on Sand: Exposing Postmodernist Myths about Science (New

York, 1998), especially the essays by Alan Sokal and Philip Kitcher.




tive methods themselves. The area studies approach can lead to a deep in

tellectual understanding of how people think, as it did in the cases of the

Russian mathematicians described here. Both social scientists and area

studies specialists need to be more appreciative of the intellectual contri

butions the other "camp" can make.

It would be nearly impossible to understand why Russian mathemati

cians in the early twentieth century so eagerly adopted descriptive set the

ory without an awareness of the history, religion, and culture of their time.

Similarly, it would be nearly impossible to comprehend why the outstand

ing Russian physicist V. A. Fock developed his form of general relativity in

the middle ofthat century without a knowledge of his philosophical prin ciples and their relationship to the society in which he lived. Thus, the in

tellectual "bite" of an area studies approach can be very deep if it is used in a sophisticated way. We have tried to illustrate that "bite" by looking at mathematics because so many people have incorrectly assumed that context does not apply to mathematics. Our approach, however, is not

uniquely tied to that discipline. Similar contextual analysis can illuminate our understanding of many aspects of culture. Just as the specialists in

classical studies found justification for looking at the literature, philoso

phy, politics, and mathematics of the ancient world in a contextual way, so can today's area studies specialists find similar justification for their ap

proach to understanding contemporary society. Such an emphasis on

contextualism does not diminish in any way the claims of social scientists to make contributions by using quantitative social analysis; it only dimin ishes the claim that a few of them have made to a monopoly on such contributions.

Now is an appropriate time for a resurgence of area studies in the United States, both for intellectual and for political reasons. The intellec tual reasons are the ones we have presented in this article: an area studies

approach can help us to understand how people think, even the most

"rigorous" thinkers like physicists and mathematicians, and also quantita tive social scientists. The political reasons are equally obvious: it is clear that one of the reasons for the many failures of American political analysts to understand fundamental Islamic thought and Middle Eastern politics is an inadequate knowledge of the culture, history, and languages of the Islamic world. Quantitative social scientists can make significant contri

butions to the needed greater understanding, but unless we also have area

studies specialists who are thoroughly familiar with the culture and history of Islam we will not get very far. And while the need for more area studies

specialists studying the Islamic world is particularly clear, that same need exists for all the various cultures of the world, including the Slavic world.



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