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1 "St" Are Studies versus "Hrd" Socil Science: A Flse Opposition Author(s): Loren Grhm Jen-Michel Knr Source: Slvic Review, Vol. 66, No. 1 (Sprg, 2007), pp Published by: Assocition for Slvic, Est Europen, Eursin Studies Stble URL: Accessed: :23 UTC REFERENCES Lked references re vilble on JSTOR for this rticle: You my need log JSTOR ccess lked references. Your use JSTOR rchive dictes your cceptnce Terms & Conditions Use, vilble t fo/bout/policies/terms.jsp JSTOR is not-for-prit service tht helps scholrs, reserchers, students discover, use, build upon wide rnge content trusted digitl rchive. We use formtion technology ols crese productivity fcilitte new forms scholrship. For more formtion bout JSTOR, plese contct support@jsr.org. Assocition for Slvic, Est Europen, Eursin Studies is collbortg with JSTOR digitize, preserve extend ccess Slvic Review. All use subject JSTOR Terms Conditions

2 ARTICLES "St" Are Studies versus "Hrd" Socil Science: A Flse Opposition Loren Grhm Jen-Michel Knr Much criticism re studies hs been bsed on opion tht, comprison "hrd" socil science, re studies re "st." Accordg this le rgument, socil science emphsizes ory, mmtics, rig orous methods, flsifibility replicbility, refore escpes from contextulism re studies. Are studies re pproches llegedly merely "descriptive," "culturl," or "hisricl," while socil science is "rig orous" "scientific." As Robert Btes deprtment government t Hrvrd University observed when he ws president comprtive politics section Americn Politicl Science Assocition, "Those who consider mselves 'socil scientists' seek identify lwful regulrities which must not by impliction be context bound."1 And he lso noted, "With cdemy, consensus hs formed tht re studies hs filed generte scientific knowledge."2 As Sheil Biddle remrked her recent study "terntionliztion" Americn universities, so cil scientists "tend dismiss re-bsed s knowledge oreticl, methodologiclly unsophisticted, descriptive rr thn explnry, cpble mkg substntil contributions disciple."3 So cil scientists ten pride mselves on tkg quntittive pproch tht could, y imply, be pplied ny culturl re with eqully good effect. This criticism re studies is bsed on ssumption tht best socil nlysis comes from one sgle cognitive pproch, tht cor portes mmtics, quntittive methods, replicbility. In this r ticle, we exme this ssumption propose tht best socil nly sis should corporte severl different cognitive styles, which method relyg on mmtics, quntittive methods, reproducibil ity is only one. First, let us tke up question mmtics. Some quntittive socil nlysts ssume tht mmtics quntittive methods st outside socil context form kd bsolute truth. They ignore fct tht mmtics lso hs contextul hisry; mmtics we use dy, erly twenty-first century, is not sme s m 1. Robert H. Btes, "Are Studies Disciple: Science Politics 30, no. 2 (June 1997): 166. A Useful Controversy?" Politicl 2. Robert Btes, "Letter from President: Are Studies Disciple," Newslet ter APSA 7, no. 1 (Wter 1996): 1-2. Societies 3. Sheil Biddle, Interntionliztion: Rheric or Relity f Americn Council Lerned Occsionl Pper, Slvic Review 66, no. 1 (Sprg 2007) no. 56 (New York, 2002), 69. All use subject JSTOR Terms Conditions

3 2 Slvic Review mtics people used century go. As philosopher science In Hck g observed, "Mmtics, so ten thought s body eternl truths, tkes plce time, come objects s re beg con y structed."4 Mmticins hisrins mmtics ten fd tht best wy underst those moments "comg beg" is through contextul nlysis. Insted mmtics beg somethg unuchble by re studies pproch, fct this pproch is ten very useful wy expl how mmtics developed. The most rdent defenders quntittive socil science ten mke ssumptions bout nture science mmtics tht mny scientists mmticins re uncert bout mselves. In this crit icism re "qulittive" studies we sometimes witness socil scientists tryg be more "scientific" thn quite few nturl scientists mmticins. We explore two different exmples roles tht socil fluences hve plyed development mmtics, one concerng very foundtions mmtics, nor concerng its use for prtic ulr purpose. In first cse, concerng birth set ory, ques tion is rised, Wht re legitimte objects study with field mmtics itself (without regrd ppliction)? In second cse, concerng generl reltivity, question is, How should mmtics be re pplied prticulr physics? The fct tht socil context plys role both exmples is significnt, sce quite few re more people will g grnt socil fluences on "use" mmtics thn re y on its oreticl foundtions. For tht reson we strt with controversy over foundtions mmtics tht rose t end ne teenth begng twentieth century, prticulrly Frnce Russi. In this dispute, contextul fcrs were pivotl importnce. In our conclusion, we exme significnce this nlysis for socil scientists who thk tht by pplyg mmtics study society y hve escped socil context. Controversies bout foundtions mmtics hve gone on for centuries. Sce birth disciple, mmticins hve rgued bout wher mmtics is "discovered" or "creted." If mmtics is creted, n conditions its cretion could be gret importnce. Mmticins hve differed gretly ir ttempts nswer this question, but modern times, two best-known schools phi losophy mmtics hve centered on views Germn mth emticin Dvid Hilbert ( ), who ok relist position, Dutch mmticin L. E. J. Brouwer ( ), who developed tuitionist philosophicl school.5 Although most dy mmticins probbly gree with Hilbert, questions bout foundtions m mtics will doubtlessly be with us forever. 4. In Hckg, The Socil Construction Wht? (Cmbridge, Mss., 1999), On Hilbert, see Constnce Reid, Hilbert (Berl, 1970); H. Wussg, Biogrphien be deutender Mmtiker (Berl, 1975). On Brouwer, see A. Heytg, Intuitionism: An Intro duction (Amsterdm, 1966). All use subject JSTOR Terms Conditions

4 "St" Are Studies versus "Hrd" Socil Sciences: A Flse Opposition 3 It is unnecessry, would even be rrognt, for us try sy which school is "correct." Gret, but somewht different, work hs been done both trditions. But it is useful for both people re studies ir critics socil sciences notice tht some world's significnt mmticins hve thought tht contextulism is necessry for n un derstg hisry ir field. When Hermnn Weyl, ten de scribed s one most fluentil mmticins lst century, tried underst erly hisry mmtics he found it necessry n re dopt studies pproch: tht clssicl studies. (It is ten for gotten dy tht origl "re studies" ws clssicl studies.) Schol rship clssicl studies is bsed on ssumption tht order un derst literture, rt, religion, philosophy, politics, rchitecture, mmtics ncient world, one must study clssicl culture its entirety, not just exme one spect tht culture, or try escpe from tht culture. In erly twentieth century, ws Weyl very concerned with concept "fity." Is n fity only bstrction, limit tht cnnot be tted, or is re n ctul fity? (This question gve birth set ory, which will be discussed lter.6) In his effort underst evolution concept, Weyl turned clssicl world, when concept origted. And he concluded tht Greek concept fity ws rooted Greek religion culture. Mmtics is science fite, its gol symbolic compre hension fite with humn, tht is fite, mens. It is gret chievement Greeks hve mde contrst between fite fite fruitful for cognition relity. Comg from Ori ent, religious tuition fite, peiron, tkes hold Greek soul. This tension between fite fite its con cilition now become drivg motive Greek vestigtion.7 s Just Weyl found it helpful look t Greek culture religion order underst erly Greek terest fity, so lso will we fd it 6. Set ory is mmticl science fite; it strts from scrtch with sets. A set is ny well-defed collection objects ( elements belongg set); collection cn be fite or fite; correspondences between sets re functions; if re exists one--one correspondence between two sets re y sid hve sme cr dl number (this number cn be fite). As n exmple, ny set one--one corre spondence with set is tegers sid be denumerble; its crdl is Hebrew let ter leph with subscript 0 (No)> sometimes clled "leph-nought." Ordl numbers re similrly defed for sets with given order between ir elements. Trnsfite num bers re ny se crdl or ordl numbers constructed through vrious opertions compred when possible with ech or. were They troduced by Georg Cnr 1882 close connection with philosophicl even religious considertions bout " Absolute." This ws first mmticl troduction fity mmtics (clled "ctul fite" opposition, followg Aristle, "potentil fite" thought s limit-process). Set ws ory born from study sets pot rel le. Lter, s we will see, efforts describe clssify such sets led set descriptive ory. See Jos? Dom?nquez Ferreiros, Lbyrth Thought: A Hisry Set Theory Its Role Modern Mmtics (Bosn, 1999); Wlter Purkert, "Georg Cnr und die Antomien der Mengenlehre," Bullet de l Soci?t? mth?mtique de Belgique 38 (1986): ; W. Purkert, Georg Cnr, (Bsel, 1987). 7. Hermnn Weyl, God Universe: The Open World (New Hven, 1932), 8. All use subject JSTOR Terms Conditions

5 4 Slvic Review helpful tke n re studies pproch underst recent explo rtions "fity." At end neteenth century t be gng twentieth, mmticins were much concerned with question wher "fity" is or n relity merely bstrction, wher re could be more thn one kd fity. Mmticins were deep crisis over foundtions ir disciple.8 At first thought tht mny different types fities exist seemed countertu itive. After ll, is not fity lrgest ll possible numbers, sgle bstrction? Noneless, mmticins begn notice tht not ll fities seemed be sme. This issue cn be most esily expled by potg two rr simple exmples. If one strts countg "1, 2, 3, 4, 5, 6, 7, 8, 9...," process cn ob viously contue without end. The set ll tegers this series, tken ger, hs n fite number elements. This is one exmple fity. Now if we look t set on pots segment le, it lso hs n fite number elements. By geometricl defition, pot hs no dimensions. Therefore, re re n fite number on pots ny segment le. So here we hve nor exmple fity. Is " fity" endless series numerls sme type s "fity" on pots le? Clerly re is n importnt difference between m. With series tegers given bove, ech elements set cn be counted. (We count ctully m when we sy "1, 2, 3, 4, 5, 6,..." even we never though complete tsk.) By contrst, we cn never count on pots segment le wy we counted numerls series bove. Therefore, perhps "fity" endless series tegers is different from "fity" on pots le. In lst yers neteenth century, Germn mmticin Georg Cn r thought so, he gve se fities different "nmes."9 A crucil pot here is ide "nmg." After Cnr ssigned different nmes different fities, se fities seemed tke on relity tht y hd not erlier possessed. A new world "trnsfite numbers" ws beg creted. We will return concept "nmg" next prgrphs. Not ll mmticins greed with Cnr. And when one tries ex pl se differences opion it soon becomes cler tht contextul, culturl ("re studies") fcrs were t work. Two most importnt groups mmticins who wrestled with se were problems French Russins, ir were con predomnt viewpots nected with ir cultures.10 The French, opertg with trdition Crtesin rtionlism, were very suspicious trnsfite numbers. Do 8. Hermnn Weyl, "?ber die neue Grundlgenkrise der Mmtik," Mmtische Zeitschrift 10, nos. 1-2 (1921): A prticulrly cler exposition crisis cn be found Snford L. Segl, "The Crisis Mmtics," Mmticins under Nzis (Prcen, 2003), J. W. Duben, Georg Cnr: His Mmtics Philosophy Infite (1979; reprt, Cmbridge, Mss., 1990). As mentioned bove, set contg ll nturl num bers is usully clled K See Loren Grhm Jen-Michel Knr, "A Comprison Two Culturl Ap Mmtics: Frnce proches Russi, ," Isis (Mrch 2006): All use subject JSTOR Terms Conditions

6 "St" Are Studies versus "Hrd" Socil Sciences: A Flse Opposition 5 y relly exist? How cn y be defed? The Russins, relyg ex on pg trdition significnce "nmes" Russin Ortho were doxy, much more positively disposed wrd new types fi ties. The debtes got very complex lso very heted.11 The French who wrestled with set ory cluded Emile Borel ( ), Ren? Bire ( ), Henri Lebesgue ( ); y were herirs gret powerful mmticl trdition, t first y tught Russins more thn y lerned from m. The ledg Russin mmticins terested set ory, Dmitrii ( ) Nikoli Luz ( ), cme repetedly Pris tlk with ir French collegues. They usully lived cdemic hert city Hotel Prisin, ner Pnon. Mny yers lter, concierge buildg remembered Russin visirs, both for ir devotion ir studies for ir religiosity. The old French estblishment mmtics, represented by Emile Picrd ( ), sutly resisted new set ory with its preoccu ption with trnsfite numbers. Picrd cidly remrked, "Some believers set re ory scholstics who would hve loved discuss pros existence God with St Anselme his opponent Gunilon, monk Noirmoutiers."12 Picrd thought tht he could dismiss set ory by lkg it discussions religion, exctly wy Russins thought y could strengn it. The Russins were specultg with trdition Russin mysti cism, feture ir thought tht French could not ccept. But, oddly enough, it ws Russins who won out creted new field mmtics, set descriptive ory, who process creted Moscow School Mmtics, one most powerful movements twentieth-century mmtics. One reson Russins were more willg ccept concept trnsfite numbers ws tht some m were volved with hereticl sect Russin Orthodoxy clled Nme Worshippers (imislvtsy) which scribed gret significnce ct "nmg."13 This sect hs his 11. See, especilly, J. Hdmrd, "Cq lettres sur l th?orie des ensembles," Bullet de l Soci?t? Mth?mtique de Frnce 33 (1905): "Certs deptes de l th?orie des ensembles sont des scolstiques, qui urient im?? discuter les preuves de l'existence de Dieu, vec St-Anselme et son contr dicteur, le moe de Noirmoutiers." Emile Picrd, L science moderne et son?tt ctuel (Pris, 1909), extrct from chpter 2. See Anselme de Cnrbery, Proslogion Allocution sur l'exis tence de Dieu suivi de s r?futtion pr Gunilon et de l r?ponse d Anselme (Pris, 1993). 13. E. S. Polishchuk, ed., Imislvie: Anlogii (Moscow, 2002); lso see O. L. Solo m A. M. Khitrov, Zbytye strnitsy russkogo imislvii: Sbornik dokumenv i publiktsii po fonskim sobytiim gg. (Moscow, 2001 ) ; lu. Rsskzov, Sekrety imen: Ot imislvii do filosii izyk (Moscow, 2000); Episkop Ilrion (Alfeev), Svishchenni t tserkvi: Vvedenie v isriiu i problemtiku imislvskikh sporov, vols. 1-2 (St. Petersburg, 2002); Prvoslvnyi vzglid n pochitnie imenii Bozhii: Sobytii n Afone 1913 g. (L'viv, 2003) ; Tom on Dykstr, "Heresy Mt. Athos: Conflict over Nme God mong Russin Monks Hierrchs, " (MA sis, St. Vldimir's Semry, New York, 1988); Ane Niviere, "Les moes onomdoxes et l'telligentsi Russe," Chiers du Monde russe et so vi?tique 29, no. 2 (1988): ; Scott M. Kenworthy, "Church, Stte, Society Lte Imperil Russi: The Imislvie Controversy" (pper, Americn Assocition for Ad All use subject JSTOR Terms Conditions

7 6 Slvic Review ry n volvement with mmtics tht only person deeply f milir with Russin hisry thought (tht is, n re specilist) is likely know. We will sketch out tht hisry here only very briefly. Although debtes over Nme Worshippg becme prticulrly tense first third twentieth century, roots contro versy go fr bck hisry estern Orthodoxy cn be found some writgs sygs Bsil Gret, John Chrysosm, or ledg church figures.14 The significnce "nmes" is n ncient highly controversil pic mythologicl religious thought generl. The clim hs been mde tht Egyptin god Pth creted with his ngue by nmg tht which he conceived.15 In Genesis we re ld tht God sid "Let re be light: re ws light." In or words, he nmed light first, n he creted it. Nmes re words, first verse Gospel ccordg St. John sttes: "In ws begng Word, Word ws with God, word ws God." In Jewish mysticl trdition Kbbl (Book Cretion, Zohr) re is be lief cretion through emntion, nme God is considered holy.16 And, Middle Ages, significnce "nmes" ws centrl issue debte over "nomlism."17 Controversies bout holess nmes becme prticulr chr cteristic Russin Orthodoxy lte neteenth erly twentieth centuries. In 1907 monk Orthodox Church, Ilrion, who hd er lier spent yers Russin monstery Mt. Athos Greece, published book entitled In Mounts Cucsus tht seized on n existg symbolic trdition Orthodox liturgy, especilly chntg "Je sus Pryer" (Iisusovi molitv, or molitv Iisusov) rised it new promence.18 In Jesus Pryer religious believer chnts nmes vncement Slvic Studies, Pittsburgh, November 2002) ; Eugene Cly, "Orthodox Mis sionries Orthodox Heretics Russi, ," Robert P. Gerci Michel Khodrkovsky, eds., Of Religion Empire: Missions, Conversion Tolernce Tsrist Rus si (Ithc, 2001), 38-69, especilly See Georges Florovsky, Wys Russin Theology, pt. 2, vol. 6, Richrd S. Hugh, ed., The Collected Works trns. Georges Florovsky, Robert L. Nichols (Belmont, Mss., 1987). 15. For modern trnsltion see Memphite Theology, Mrshll Clgett, Ancient Egyptin Science (Phildelphi, 1989), 1:305-12, We re grteful John Mur doch for this suggestion. 16. Gershom Scholem, Mjor Trends fewish Mysticism (New York, 1995). 17. R. A. Eberle, Nomlistic Systems (Dordrecht, 1970); Zenon Kluz, Les querelles doctrles? Pris: Nomlistes et r?listes ux confs du XTVe et du XVe si?cles (Bergmo, 1988). 18. The full title book ws N gorkh Kvkz, besed dvukh strtsev podvishnikov o vnutrennem edenii s Gospodom nshikh serdets chrez molitvu Iisus Khrisv Hi dukhovni deitel'nost' sovremennykh pustnikov, sostvil Kvkvskikh pustynnozhitel' gor skhimonkh Ilrion (In mounts Cucsus: converstion between two elder scetics con ner union our herts with Lord cerng through pryer Jesus Christ; or spiritul ctivity contemporry hermits, composed by hermit Cucsus mounts, monk Ilrion) (1st ed., Btlpshsk, 1907; 2d corrected exped ed., 1910; 3d ed., Kievski Pecherski Lvr, 1912). The roots Jesus Pryer go bck centuries; strt trdition is ten cited s Apostle Pul's structions fith ful "pry without cesg" (1 Thess. 5:17). The trdition exists both Ctholic Or thodox liturgies, re is n extensive literture on it. In Russi c Jesus Pryer quired specil promence, especilly fter publiction folklore clssic The Wy All use subject JSTOR Terms Conditions

8 "St" Are Studies versus "Hrd" Socil Sciences: A Flse Opposition 7 Christ God over over g, hundreds times, until his whole body reches stte religious ecstsy which even betg his hert, ddition his brethg cycle, is supposedly tune with chnted words ( stte vividly described by J. D. Slger Frnny Zooey).19 Accordg Ilrion, worshipper chieves stte unity with God through rhythmic pronouncg his nme. And this dem onstrtes, sid Ilrion, tht nme God is holy itself, tht " nme God is God" (Imi Bozhie est' sm Bog).20 At first this book ws well received by mny Russins terested re ligious thought. Ilrion's views becme very populr mong hundreds Russin monks Mt. Athos, his fluence grdully spred else where. But highest ficils Russin Orthodoxy, St. Petersburg Moscow, soon begn consider book not s just description significnce pryer but s ologicl ssertion. For mny se ficils, dherents Ilrion's beliefs were heretics, even pgn pn ists, becuse y llegedly confused symbols God with God him self. On 18 My 1913, Holy Synod St. Petersburg condemned Nme soon Worshippers; refter Russin nvy, with pprovl Tsr Nichols II ptrirch Constntople (who hd ju risdiction over monsteries Mt. Athos), sent severl gunbots Mt. Athos brg rebellious monks forcibly heel. Over 600 unre pentnt monks were flushed out ir cells with fire hoses brought under gurd Odess. With lter detentions, number grew p proximtely 1, The dissidents strongly protested ir tretment obted promises furr vestigtion reconsidertion. The Nme Worshippers hd some defenders high plces tsr him self seemed be two mds on question.22 Pilgrim (Kzn, 1884). The book populrized pryer ws trnslted mny lnguges. 19. Slger hs Frnny observg her credulous friend Lne, "Well, strets tells him bout Jesus Pryer first ll.... If you keep syg tht pryer over over g?you only hve just do it with your lips t first?n eventully wht hppens, pryer becomes self-ctive. Somethg hppens fter while. I don't know wht, but somethg hppens, words get synchronized with person's hertbets, n you're ctully pryg without cesg. Which hs relly tremendous, mysticl ef fect on your whole outlook. I men tht's whole pot it, more or less. I men you do it purify your whole outlook get n bsolutely new conception wht everythg's bout." J. D. Slger, Frnn)? Zooey (Bosn, 1961), 36-37, emphsis origl. 20. See description Ilrion his followers N. K. Bonetski, "Bor'b z Logos v Rossii v XX veke," Voprosy filosii 7 (1998): , especilly ; Polishchuk, ed., Imislvie, 490, emphsis origl. 21. Polishchuk, ed., Imislvie, These events were lso reported for eign press; see "Heresy t Mount Athos: A Soldier Monk Holy Synod," London Times, 19 June 1913; "Heresy t Mount Athos, London Times, 23 August 1913; "The Mount Athos Heresy Cse: Voluntry Exile Siberi," Times, 23 August Accordg Vldimir Gubnov, Holy Synod urged tsr squelch heresy before it split fith ntion, but monk Grigorii Rsput, who ws close court, defended Nme Worshippers. The tsr evidently hesitted but end gve synod. Vldimir Gubnov, Tsr'Nikoli II i novye mucheniki: Prorochestv, chudes, otkrytii i molitvy: Dokumenty (St. Petersburg, 2000). Tom Dykstr hs lso written All use subject JSTOR Terms Conditions

9 8 Slvic Review With dvent World Wr I issue receded bck ground, but until end tsrist regime, dherents "heresy" were forbidden return Mt. Athos or reside mjor cities like St. Petersburg Moscow. The most fervent m retreted monsteries where y contued prctice propgte ir vrint fith. After Bolshevik revolution, Nme now Worshippers, livg ll over rurl Russi, were more successful thn most or religious believ ers contug ir out prctices view Soviet politicl uthorities, who were tryg suppress religion. After ll, Nme Worshippers hd lredy been defed s heretics excluded from estblished churches.23 But y contued prctice ir fith secret, by vir tue beg out view, y were not compromised by ssocition with Bolsheviks, s were some estblished church leders. The dissi dents climed represent undefiled "true fith," cresg ir populrity with some religious opponents new communist regime. s (Amzgly, lte s 1983 rumors spred bout secret existence Soviet Union followers dissident fith Nme Worship pg,24 some people hve sserted tht descendnts sect mem bers, hvg outlsted ir Soviet oppressors, still prctice ir fith dy, especilly Cucsus, recently, Moscow.25 In Moscow recent publictions dicte tht some ides Nme Worshippg re still ttrctive tellectuls, especilly mmticins.26) Severl tellectuls Moscow who becme terested Nme Worshippg just before fter World Wr I were ledg mmti cins. They cluded Dmitrii, pressor mmtics t Moscow Stte University for mny yers president Moscow Mmti cl Society; two his students, Luz Pvel Florenskii ( ). All three se men were deeply religious.27 Florenskii eventu lly boned mmtics for religious studies becme priest, but tht Rsput my hve supported Nme on Worshippers. Dykstr, "Heresy Mt. Athos." On Rsput's role, see lso Ilrion (Alfeev), Svishchenni t tserkvi, 2: S. S. Demidov, "Pressor Moskovskogo universitet Dmitrii Fedorovich i imeslvie v Rossii v pervoi treti XX sletii," Isriko-mtemticheskie issledovnii, 2d ser., 39 (1999): Polishchuk, ed., Imislvie, Ilrion (Alfeev), Svishchenni t tserkvi, vol See recent essy by A. N. Prsh, well-known mmticin, pupil Igor Shfrevich correspondg member deprtment mmtics Russin Acdemy Sciences: Prsh, "Svet i slovo (k filosii imeni)," Polishchuk, ed., Imi slvie, 's deep religiosity is described Demidov, "Pressor Moskovskogo uni versitet Dmitrii Fedorovich," 137. Luz's conversion by Florenskii religious viewpot is described vrious sources, cludg Chrles Ford, "The Influence P. A. Florensky on N. N. Luz," Hisri Mmtic 25, no. 3 (August 1998): See lso Ford, "Dmitrii : Mmtics Religion Moscow," Mmticl Intelligencer 13, no. 2 (1991): Florenskii's best-known sttement published fith is probbly his Slp i utverzhdenie isty (Moscow, 1914), published English s The Pillr Ground Truth, trns. Boris Jkim (Prcen, 1997). All use subject JSTOR Terms Conditions

10 "St" Are Studies versus "Hrd" Socil Sciences: A Flse Opposition 9 he mted gret terest mmtics science throughout his life. At time Bolshevik revolution, Florenskii ws livg mon stery wn ner Moscow, he ws close religiously tellectully Nme Worshipper dissidents. He communicted ir ides Luz trnslted m mmticl prlnce. In erly 1920s re ws Nme Worshipper circle (imeslvcheskii kruzhok) Mos cow where ides religious dissidents concepts mth emtics were brought ger. Prticipnts circle cluded fifteen or sixteen philosophers, mmticins, religious thkers. Some times circle met t 's prtment, Florenskii presented p pers t severl se meetgs.28 Here Florenskii expounded view tht " pot where dive humn energy meet is ' symbol,' which is greter thn itself."29 To Florenskii nmes were symbols tht he thought could tt full unomy. Intellectul rtistic Russi t end neteenth century first decdes twentieth ws preoccupied with ques tion significnce symbols. The symbolist movement ffected bl let, music, literture, rt, poetry, s nmes Sergei Dighilev, Igor Strvsky, Andrei Belyi, Konstnt Stnislvskii, Vsilii Nemirovich Dnchenko, Vsevolod Meierkhol'd remd us. Now we should dd mmticins Luz ir priest-friend Florenskii such lists. Indeed, re ws even connection between literry mmticl movements. Belyi, symbolist poet, ws son Mos cow mmticin, he mjored mmtics t Moscow University where he studied under ger with Luz. Fmilir with Nme Worshippg, Belyi once wrote n essy clled "The Mgic Words" which he climed, "When I nme n object with word, I reby ssert its existence." We cn sk, does this pply both m mtics poetry? If object is new type fity, does tht f ity only exist once one hs nmed it? Florenskii sw tht Nme Worshippers hd rised issue "nmg" new promence. To nme somethg ws give birth new entity. Florenskii ws convced tht mmtics ws product free cretivity humn begs tht it hd religious significnce. Humns could exercise free will put mmtics philosophy perspective. Georg Cnr's fmous sentence clerly hd strong ppel for Florenskii: "ds Wesen der Mmtik liegt gerde ihrer Freiheit" (The essence mmtics lies precisely its freedom).30 Mmti cins could crete begs (sets) simply by nmg m. For exmple, de fg set numbers such tht ir squres re less thn 2, nm g it "A," nlogously set numbers such tht ir squres re 28. Polishchuk, ed., Imislvie, Ilrion (Alfeev), Svishchenni t tserkvi, 2: Georg Cnr, "?ber unendliche, lere Punktmnnichfltigkeiten," tische Annlen 21 (1883): 545. Mm All use subject JSTOR Terms Conditions

11 10 Slvic Review lrger thn 2, nmg it "B," ment brg existence (essentilly Eudoxus-Cuchy construction) rel number V2. For Florenskii, development set ory ws brillint exmple how nmg cn clssifyg produce mmticl brekthroughs. A "set" ws simply nmg entities ccordg n rbitrry mentl system, not recognition types onlogiclly existg objects. When mmticin creted "set" by nmg it, he ws givg birth new mmticl beg. A new form mmtics ws comg, sid Flo renskii, it would rescue mnkd from mterilistic, determis tic modes so common nlysis neteenth century. And, deed, set new on ory, sights contuous discontuous phenomen like development under nme "Arithmology" discovery 1897 by Kurt Hensel p-dic numbers (which strongly impressed, Luz, Florenskii, ir followers), discontuous functions?becme hllmrks Moscow School Mmtics. Both French Russin mmticins were wrestlg with problem: Wht is mmticl object, wht is s permitted n ob ject, wht is good defition such n object? As Lebesgue wrote Borel 1905, "Peut-on s'ssurer de l'existence d'un?tre mth?m sns tique le d?fir?" (Is it possible convce yourself existence mmticl beg without defg it?).31 To Florenskii question ws nlogue, Is it possible convce yourself existence God without defg him? The nswer for Florenskii lter for Luz ws tht ct nmg itself gve object existence.32 Thus "nmg" becme key both religion mmtics. The Nme Worshippers gve existence God by worshippg his nme, mmticins gve existence sets by nmg m. The circle eger students tht formed round Luz t beg ng World Wr I contued throughout erly 1920s ws known s "Lusitni." An direct ht bout plce religion concerns Lusitnins cn be seen description group provided by one its origl members, M. A. Lvrent'ev ( ),33 Accordg Lvrent'ev (lter significnt mmticin founder Akdem gorodok Novosibirsk) Lusitnins cknowledged two leders: "God--fr" "God--son" Luz. It ws Luz who ld young Lusitnins: " is chief our society," "Our dis coveries belong." Students society were given mons tic title "novice." Notg Lvrent'ev's description group, Esr Phillips wrote, "There ws clerly strong sense belongg n ner 31. s Lebesque cited Hdmrd, "Cq lettres sur l th?orie des ensembles." 32. At one pot Luz wrote his notes seems "Everythg be dydrem, ply g with symbols, which however, yield gret thgs." At nor moment Luz scribbled felicius but understble French: "nommer, c'est voir dividu." Archive Russin Acdemy Sciences, Moscow, f. 606, op. 1, ed. khr. 34. Courtesy Roger Cooke, "N. N. Luz on Problems Set Theory" (unpublished pper, Jnury 1990), 1-2, M. A. Lvrent'ev, "Nikoli Nikolevich Luz," Russin Mmticl Surveys 29, no. 5 (1974): , Uspekhi mmticheskikh nuk 29, no. 5 (1974): All use subject JSTOR Terms Conditions

12 "St " Are Studies versus "Hrd " Socil Sciences: A Flse Opposition 11 circle or secret order."34 All prcipls novices went 's home three times yer: Ester, Christms, his nme-dy (g, importnce "nmes"). The tense cmrderie mong Lusitnins ws spired by Luz, who ws described s extroverted tricl, who engendered rel devotion mong students collegues. on, or h, ws more reserved forml. Accordg Lvrent'ev, Luz's chief ssistnts mngg Lusitni were three stu dents, ech with his own function: Pvel Aleksrov ws "crer," Pvel Uryson "keeper," Vicheslv Stepnov "herld" mysteries Lusitni. (All three se students went on become mmticins note; ll three, long with ir techers Luz, re cluded current Dictionry Scientific Biogrphy, most uthorittive listg decesed scientists world rnk.35) Although Luz were very close number ledg French mmticins cited ir debt m, French world view ws different. The French wnted keep philosophicl, m mticl, psychologicl components ir thought seprte. Mixg mmtics religion ws, French md, bd ide. On contrry, Luz believed tht mmtics ws lked reli gion, but y could not be explicit bout se lks fter 1917 becuse hostile Soviet environment. They knew tht y could esily get trouble with uthorities if views discussed meetgs Nme Worshippg circle becme known.36 Eventully, Luz, Florenskii were cught persecuted by Soviet uthorities, but only fter Luz prticulr, his students, hd mde mmticl brekthroughs. ( died strvtion while Soviet detention 1931; Florenskii ws imprisoned norious Solovetskii gulg n shot 1937; Luz survived with n ideologicl dressg-down.37) 34. Esr R. Phillips, "Nicoli Nicolevich Luz Moscow School The ory Functions," Hisri Mmtic 5, no. 3 (August 1978): Chrles Coulsn Gillispie, ed., Dictionry Scientific Biogrphy (New York, ). Luz is 8:557-59; 4:287-88; Aleksrov 17.2:11-15; Uryson 13:548-49; Stepnov 13: While we know tht ws leder this circle, we hve no concrete evi dence tht Luz ws member or even ever ttended meetgs. We do know tht Luz ws friend Fr Florenskii, tht he ws fmilir with Nme move Worshippg ment, tht his mmticl reserch he put gret on emphsis "nmg." Luz ws more cutious thn probbly mde more n ttempt concel his re ligious views from Soviet uthorities. 37. Florenskii ws first rrested 1928, n relesed, n rrested 1933 g sentenced ten yers lbor cmps Siberi. He ws executed on 8 December Rehbilitted 1956, he hs slowly ged ttention sce n s philosopher lnguge culture, ologin,, most s n recently, fluence on Russin mth emtics. See Richrd Gustfson, "Introduction," Florenskii, The Pillr Ground Truth, ix-xxiii. ws rebuked by Communist Prty 1929, rrested 1930, sent prison. There he went on hunger strike. Just before his deth, he ws tken un der gurd hospitl Kzn; he died on 10 September We re ld tht he died rms wife mmticin N. G. Chebotrev, who ws docr hospitl. Chebotrev's son G. N. Chebotrev wrote, "On umer n mmykh rukkh" (He died my mor's rms): G. N. Chebotrev, "Iz vospomnii ob ottse," lu. B. Ermo All use subject JSTOR Terms Conditions

13 12 Slvic Review In 1920s Luz's religious philosophicl pproch helped stimulte him pround mmticl origlity. He his students creted new field: descriptive ory sets. And Moscow Mth emticl School tht Luz creted cused n explosion mmticl reserch 1920s 1930s tht will lwys be remem bered hisry mmtics.38 One ledg French mmticins this sry, Lebesgue, fi nlly cknowledged tht it ws precisely "philosophy"?wht he his French collegues tried void mmtics?tht helped Luz mke his novtions. In prefce Luz's 1930 book published French Pris, Lebesgue wrote tht with Luz "mmticl exigencies re philosophicl exigencies constntly ssocited, one cn even sy fused."39 (In Russin edition this book, Soviet edirs removed this sttement.) Lebesgue dmitted tht this pproch helped Luz his students fd concept he hd not seen. Once his eyes were ws opened, Lebesgue sunded by fruitfulness Russin p proch. In open wonderment he declred, "M. Luz exmes questions from philosophicl pot view ends up with mmticl results. This is n origlity without precedent!"40 The skeptic, fter redg bove section, my well sy, "OK, this strnge group clled Nme Worshippers my hve hd t cert pot time n unusul fluence hisry mmtics. But surely this is n exception, rr bizrre one t tht. Cn you pot nor recent exmple how n re studies pproch will tell us somethg importnce bout development mmtics?" Our response is, yes, exmples bound.41 In order be brief, however, we will present only lev, ed., Nikoli Grigor'evich Chebotrev (Kzn, 1994), 56. Luz ws submitted n ideo logicl tril which mny his former collegues turned gst him. See S. S. Demidov V. D. Eskov, "'Delo kdemik N. N. Luz' v svete stlskoi reformy sovetskoi nuki," Isriko-mtemticheskie issledovni, 2d ser., 39, no. 4 (1999): S. S. Demidov B. V. Levsh, eds., Delo kdemik Nikoli Nikolevich Luz (St. Petersburg, 1999); A. P. Iushkevich, "Delo kdemik N. N. Luz," Vestnik AN SSSR, no. 4 (1989): ; Alexey E. Lev, "Anmy Public Cmpign: Acdemicin Luz's Cse' Soviet Po liticl Hisry," Slvic Review 49, no. 1 (Sprg 1990): ; A. N. Bogoliubov N. M. Rozhenko, 'vnedrenii' dilektiki v mtemtiku v kontse "Opyt' 20-kh nchle 30-kh godov," Voprosy filosii, no. 9 (1991): AJlen Shields, "Yers Ago: Luz," Mmticl Intelligencer 9 (1987): 24-27; Smilk Zdrvkovsk Peter L. Duren, eds., Golden Yers Moscow Mmtics (Providence, 1993) Alexer ; Vucich, "Mmtics Dilectics Soviet Union: The Pre-Stl Period," Hisri Mmtic 26, no. 2 (My 1999): ; P. S. Aleksn drov, Mtemtik v SSSR z 15 let (Moscow, 1932). 39. et sont constmment sso "Exigences mth?mtiques exigences philosophiques ci?es, on m?me peut dire fondues." Henri Lebesgue, "Pr?fce," Nicols Luz, Le?ons sur les ensembles et leurs nlytiques pplictions (Pris, 1930), xi. 40. "M. Lus exme les questions d'un pot de vue et philosophique boutit si? des r?sultts sns mth?mtiques: origlit? pr?c?dent!" Lebesgue, "Pr?fce," ix. 41. In erly development set ory, works Bernrd Bolzno Georg Cnr, both whom hd strong philosophicl religious beliefs, wit con deeper textul nlysis. The work Russin mmticin geometer A. D. Alexrov, who hd strong philosophicl commitments, lso beckons. The Bourbki mmtics All use subject JSTOR Terms Conditions

14 "St " Are Studies versus "Hrd " Socil Sciences: A Flse Opposition 13 one or cse: vrieties mmticl expressions generl tivity ory. When nonscientists discuss generl reltivity ory, ir emphsis very ten concerns question its vlidity rr thn its vrieties. Modern physicists overwhelmgly ccept generl reltivity, but y hve expressed it mmticlly considerble vriety modes. As physicist hisrin physics Dvid Kiser wrote recent rticle which he surveyed presenttions generl reltivity post-world Wr II period Europe Americ, "'Generl reltivity' becme ply g field upon which mny different physicists, spekg different kds mmticl lnguges, could renegotite wht it ment do grvit tionl physics."42 These "different kds mmticl cn lnguges" ten be expled by contextul ("re studies") nlysis. One ledg exponents reltivity ory Russi 1950s 1960s ws V A. Fok (Fock), physicist honored mny coun tries world. Fock ws pssionte defender reltivity ory; he once wrote tht question vlidity reltivity ory is on pr with questiong roundness erth.43 However, if one looks t equtions Fock used express generl reltivity his mny publictions, one will fd tht re y different from Albert Este's, even though those res where generl reltivity produces observble results, two pproches yield similr products. The differences re, however, signifi cnt tellectully, y re closely tied Fock's philosophicl socil views.44 If one compres Este's Fock's grvittionl one equtions, will see tht y re distctly different. Este's tkes form: (1) rel R^ - -g*vr = ~xt?v Fock's ws considerbly more complicted: (2) w? =?o**?s? + r^?r? 2 dxdx? How does one expl this difference? group Frnce wits furr contextul exmtion. The gret mmticin Alexn der Grondieck, who ws terested mysticism t mny pots his life, should be similrly exmed. 42. Dvid Kiser, "Alp is just ij;? Pedgogy, Prctice, Reconstitution Gen erl Reltivity, ," Studies Hisry Philosophy Modern Physics, 29 no. 3 (1998): V A. Fok [Fock], "Protiv nevezhestvennoi kritiki sovremennykh fizicheskikh teorii," Voprosy filosii, no. 1 (1953): Loren R. Grhm, "Do Mmticl Equtions Disply Socil Attributes?" Mth emticl Intelligencer 22, no. 3 (Summer 2000): All use subject JSTOR Terms Conditions

15 14 Slvic Review Fock ws convced Mrxist, very scere, dedicted sort, fr from vulgrized form ten preched by ors.45 As Mrxist he wnted preserve concept predictble, science-ruled world. He considered term ory generl reltivity unfortunte becuse he fered it would cuse people sy "everythg is reltive," when, fct, ws generl reltivity bsed on n bsolute strd, tht "bsolute spce-time." Fock, refore, ctully renmed Este's ory " ory bsolute or spce-time" "ory grvittion."46 As Gerld Holn, physicist hisrin science, hs poted out, Este ws wre problem, but thought it ws o lte chnge title his ory.47 Fock thought strong rgument could be mde tht his new terms were more ccurte thn Este's. The one thg tht ory ws generl reltivity not, Fock mted, ws purely reltivistic ory. Fock liked put his viewpot French: "(1) L reltivit? physique n'est ps g?n?rle; (2) l reltivit? g?n?rle n'est ps physique" (Physicl reltivity is not generl; generl reltivity is not physicl).48 Echog views Germn physicist Mx Plnck, Fock remrked, "The ory reltivity, fter showg tht whole series concepts erlier considered bsolute were ctully reltive, t sme time troduced new bsolute concepts. The mjority critics ory reltivity forget this."49 Fock believed tht Mrxists like himself would hve difficulty cceptg purely reltivistic ory, given ir commitment objective relity ir opposition completely reltivistic concepts truth Fock sserted his Mrxism dozens publictions converstions, both with one uthors (Loren Grhm) with ors. Grhm met with Fock Lengrd sprg 1961 engged published discussion with him 1966: Loren R. Grhm, "Quntum Mechnics Dilecticl Mterilism," Slvic Review 25, no. 3 (Sep tember 1966): ; see Fock's reply his "Comments," Slvic Review 25, no. 3 (Sep tember 1966) : After fll Soviet Union, when re ws no longer ny po liticl reson ffirm Fock's Mrxism, people who knew him his work contued describe him s n tellectul Mrxist. Two yers fter end USSR, 1993, hisrin Russin physics Genndii Gorelik wrote, "There is no doubt tht 1930s Fock ws lredy scerely devoted dilecticl mterilism." G. E. Gorelik, 'V. A. Fok: Filosii tigotenii i tizhest' filosii," Prirod, no. 10 (1993): As reflected English trnsltion title one his best-known works: V. A. Fock, The Theory Spce, Time, Grvittion, trns. N. Kemmer (New York, 1959). 47. See Gerld Holn, "Introduction: Este Shpg Our Img tion," Gerld Holn Yehud Elkn, eds., Albert Este: Hisricl Culturl Per spectives (Prcen, 1982), xv. 48. As Mx Plnck commented, "The concept reltivity is bsed on more fund mentl bsolute thn erroneously ssumed bsolute which it hs supplnted." Mx Plnck, The New Science (Greenwich, Conn., 1959), 146. Plnck expressed sme ide erlier for publictions, exmple, Ds Weltbild der Neuen Physik (Leipzig, 1929), Fok [Fock], "Protiv nevezhestvennoi kritiki sovremennykh fizicheskikh teorii," "Es ist nicht zu?berfl?ssig unterstreichen, dss ds Verh?ltnis von K?rpern oder Prozessen zum Bezugssystem ebenso objektiv ist (d.h. von unserem unbh?ngig Bewusst se) wie?berhupt lle und physiklischen eren Eigenschften der K?rpern" (It is not tht superfluous emphsize reltionship bodies or processes reference system is s just objective [i.e., dependent our consciousness] s re physicl or properties generl). V. A. Fock, "?ber philosophische Frgen der modernen Physik," Deutsche Zeitschrift f?r Philosophie, no. 6 (1955): 742. All use subject JSTOR Terms Conditions

16 "St " Are Studies versus "Hrd " Socil Sciences: A Flse Opposition 15 Fock wnted equtions for grvittion with generl reltivity reflect his understg its deeper meng. He believed tht he could show tht even generl reltivity re re or preferred privileged systems coordtes. A formidble mmticin, Fock devoted much his reserch over mny yers tsk provg tht spce uni form t fity re is preferred system coordtes, tht hr monic coordtes; such system coordtes, he mted, reflected "cert trsic properties spce-time."51 Fock wnted set up comprison different equtions for curvture tensor, Este's his own, demonstrte dvntges his eqution. He begn with Este's grvittionl eqution (1), given bove. For Fock, this expres sion, with ll its combtions derivtives, seemed volve o much needless permissiveness: Este kept this rnge possibilities be cuse he wnted mt full generlity ll possible coordi nte systems physicist might choose use. But ll se possibilities seemed irrelevnt Fock, given his strong, prcipled preference for prticulr coordte system, his beloved hrmonic coordtes. Usg some tricte mmticl clcultions, Fock trnsformed curv ture tensor form tht would mke it especilly convenient for expres sion hrmonic coordtes, eqution (2) s given bove. Fock's preference for (2) over (1) n provides exmple socio philosophicl context ffectg mmticl equtions. Fock poted out tht his grvittionl eqution (2) ws "comptible with Este's" did not "impose ny essentil limittion on solution ltter, servg only nrrow down clss permissible coordtes." The reson Fock preferred hrmonic coordtes ws becuse he believed y reflected objective properties lked " distribution motion ponderble mtter."52 Therefore, he believed he hd developed ory grvittion tht permitted unique solutions, ws comptible with Este's ory, ws lso ccord with philosophicl mterilism. Although Fock's pproch generl reltivity is still s regrded somewht idiosyncrtic, it hs won respect from physicists terntionlly. At conferences, such leders field s John Wheeler Stnley Deser United Sttes, Hermnn Bondi Gret Brit, Andr? Lichnerowicz Frnce hve prised Fock's work for its origlity sight.53 In discussion with one uthors this rticle, Wheeler greed tht physicists severl countries re terested Fock's use hrmonic coordtes generl reltivity Fock, Theory Spce, Time, Grvittion, xv, xvi, 351. See lso V A. Fok [Fock], "Ponitii odnorodnosti, kovrintnosti i otnositernosti," no. Voprosy 4 filosii, (1955): Fock, Theory Spce, Time, Grvittion, 193; lso see Siegfried M?ller-Mrkus, Germn hisrin philosopher science, notg ledg physicists' prise Fock's work, ended up writg book positively terpretg Fock's views generl reltivity, even though his origl tention hd been criticize m. See Siegfried M?ller-Mrkus, Este und die Sowjetphilosophie, vol. 2 (Dordrecht, 1970). 54. See John Wheeler's response Loren R. Grhm, "The Reception Este's Ides: Two Exmples from Contrstg Politicl Cultures," Gerld Holn Yehud All use subject JSTOR Terms Conditions

17 16 Slvic Review With post-soviet Russi itself, Fock's views on generl reltivity con tue hve fluence. On 29 Jnury 1999, Russin science newspper n published rticle prisg Fock entitled "On n Equl Footg with E ste."55 Among Russin physicists, one who hs most perhps consis tently contued promote Fock's ides is Acdemicin A. A. Logunov, longtime direcr pron synchrotron ccelerr Protvo. Like Fock, Logunov prefers "ory grvittion" "generl ory rel tivity." In his 1998 book Reltivistic Theory Grvity he prised Fock's "s pirtion clrify essence GRT [Generl Reltivity Theory], freeg it from generl reltivity devoid ny physicl meng."56 Lookg bck t two exmples we hve given ( birth de set scriptive ory vrieties mmticl expression gen erl we reltivity) see, s we noted t outset, tht core re questions quite different: first concerns wht is legitimte mmtics itself; second volves uses mmtics. In first cse we hve seen tht even such n bstrct nonpplied field s descriptive set ory socil context plyed role hisricl development. It is probbly less surprisg tht socil context hs plyed role work physicists (Este, Fock, ors) who tried out different wys usg mmtics express generl reltivity. These physicists dis greed with ech or, not over mmtics, but over its implement tion. Their philosophicl, Fock's cse t lest, ir socil views plyed role this disgreement. Socil scientists who pply mmticl methods (sttistics, regres sion nlysis, longitudl studies, so on) study socil be hvior re second position, usg strd sttisticl nlysis un derst society. If socil fluences cn be found use physicists' mmtics, is it not even more likely tht cn y be found socil sci entists' ppliction mmticl methods? When one uses mmt ics study society, questions, On wht problem? For wht purpose? In wht wy? When? re ll relevnt, for ech se questions possibility socil fluence is obvious. Even troduction new mmticl concepts with purpose ppliction is fluenced by socil conditions. To explore se questions more thoroughly, try illustrte fluence socil context on wys which socil scientists hve used quntittive methods would require us write seprte rticle. The be gngs this nlysis lredy exist literture, however. Hisrins sttistics such s Stephen M. Stigler, Lorre Dsn, Theodore Porter, Al Desrosi?res hve explored development field with socil context.57 In his book, Desrosi?res expled tht he wnted Elkn, eds., Albert Este: Hisricl Culturl Perspectives (Prcen, 1982), (Wheeler's response ppers on p. 135). 55. See "Nrvne s Eshteom," Poisk, 29 Jnury 1999, A. A. Logunov, Reltivistic Theory Grvity (Commck, N.Y, 1998), 65; see lso Logunov, The Theory Grvity (Moscow, 2001). 57. Stephen M. Stigler, The Hisry Sttistics: The Mesurement Uncertty before 1900 (Cmbridge, Mss., 1986); Stigler, Sttistics on Tble: The Hisry Sttisticl Con All use subject JSTOR Terms Conditions

18 "St " Are Studies versus "Hrd " Socil Sciences: A Flse Opposition 17 lk technicl hisry sttistics its socil hisry, connect " two dimensions, economic cognitive, construction system equivlences."58 Any such nlysis must be bsed on knowledge so cil context sort tht re studies specilists brg ir fields. After redg bove some nlysis, socil scientists will sy tht it puts o much on emphsis mmtics. As one commentr on n erly drft this rticle observed, "Wht relly distguishes socil sci ence pproch from res studies one is not necessrily use mmtics, but relince upon rigorous methodology, strds evidence, replicbility. The Americn Politicl Science Assocition hs n entire membership devoted qulittive methods whose prcti tioners consider mselves no less scientific thn number crunchers." This observtion, pproch it represents, is much more sophisti cted thn one emphsizg quntittive methods lone, but it lso suffers, s dicted by phrse "no less scientific," from cognitive flw embodied view tht only scientific cn pproch form us. It is bsed on n outdted view cognitive psychology, one domnt genertion go when gret pioneers socil science like Frederick Mosteller showed so effectively contribution such n cn pproch mke s understg pics diverse s eductionl chievement or determtion uthorship Federlist writgs.59 The signifi cnce Mosteller's ws enormous pproch will contue be future. But new developments cognitive psychology sociol ogy knowledge clerly show importnce wht Howrd Grdner clls "different cognitive strengths contrstg cognitive styles," which socil science pproch, lthough very vluble, uses only lim ited rnge.60 Grdner mts tht re re multiple telligences multiple vluble pproches understg chievement. In his origl work Grdner nmed seven different types telligence, which ws "logicl-mmticl telligence" only one. In his ltest work he hs dded nturlist telligence ccrued evidence for cidte ex istentil telligence. Grdner stted tht one reson he thks origi nl list should be exped (neir he nor nyone else is cert just how mny telligences re re) is becuse remrk mde him by Ernst Myr, perhps gretest evolutionry biologist lst century. After herg Grdner give his origl list seven re telligences, Myr mrked, "You will never expl Chrles Drw with set tel ligences you proposed." This remrk should ttrct ttention so cil scientists who sy tht wht relly distguishes socil science is not cepts Methods (Cmbridge, Mss., 1999); Lorre Dsn, Clssicl Probbility En lightenment (Prcen, 1988); Theodore Porter, The Rise Sttisticl Thkg: (Prcen, 1986) Al ; Desrosi?res, The Politics Lrge Numbers: A Hisry Sttisticl Re song, trns. Cmille Nish (Cmbridge, Mss., 2002). 58. Desrosi?res, Politics Lrge Numbers, Frederick Mosteller Dniel P. Moynihn, eds., On Equlity Eductionl Op portunity (New York, 1972) ; Frederick Mosteller Dvid L.Wllce, Inference Disputed Authorship: The Federlist Ppers (Redg, Mss., 1964). 60. Howrd Grdner, Multiple Intelligences: New Horizons (New York, 2006), 5. All use subject JSTOR Terms Conditions

19 18 Slvic Review number-crunchg but replicbility. Evolution hs never been still is not nor replicble, hs it yet been found be flsifible, yet it hs pro vided n enormous dvnce our understg world.61 The conclusion tht we drw does not dimish or importnce utility socil science pproches socil relity (we celebrte tht im portnce tht utility), sted it emphsizes tht true sophisti cted understg world which we live requires multiple p proches. Some will be some logicl-mmticl, will be some lguistic, will be or terpersonl trpersonl, some will be deeply contextul, s one we hve used this rticle. In view fct tht re hs recently been gret controversy over "socil construction knowledge," we would like dd tht we re not rdicl socil constructivists, people who believe tht science is tlly determed by socil fluences.62 On contrry, we consider sci ence be most relible form knowledge tht exists. Relity does mtter. Even though we believe tht descriptive set ory developed more rpidly Russi thn Frnce becuse socil fluences, we re conscious tht such different contexts led similr ories. Both French mmticins Russin mmticins were workg on sme problems dy French Russin mmticins workg set ory re very lrgely greement. Similrly, Fock Logunov Russi hve worked on pplyg mmtics sme s physicl problems physicists elsewhere, some lthough differences with ir collegues elsewhere rem ir use mmtics, ir res ccord with ir terntionl re collegues much greter thn ir pots dissent. All gree on vlidity generl reltivity ory but y disgree on best wy express it mmticlly, ir divergent philosophicl socil views hve fluenced se differences. In this rticle we hve tried show tht sistg on rigid division between "st" methods re studies specilists "hrd" methods socil scientists is simplistic. Socil scientists, wher usg quntittive methods or ones yieldg replicble results, cn mke gret contributions understg society s politics, y lredy hve. Are studies specilists cn lso mke such contributions,? ddition?y cn sometimes dvnce our understg qunti t 61. See lso Ernst Myr, This Is Biology: The Science Livg World (Cmbridge, Mss., 1997). 62. See Hckg, Socil Construction Wht? The itil best-known episode controversy ws Aln D. Sokl's spo socil constructivists his "Trnsgressg Boundries: Towrds Trnsformtive Hermeneutics Quntum Grvity," Socil Text, no. 46/47 (Sprg/Summer 1996): Sokl reveled tht this rticle ws hox de signed prody those who "socilly construct" science his "A Physicist Experiments with Culturl Studies," Lgu Frnc (My/June 1996): Sokl's origl rticle ws very clever he ws correct ridiculg views most extreme socil contruc tivists. The bsic issue controversy? wht extent re science mmtics f fected by society which y developed??rems, however, unresolved. See lso Norett Koertge, ed., A House Built on S: Exposg Postmodernist Myths bout Science (New York, 1998), especilly essys by Aln Sokl Philip Kitcher. All use subject JSTOR Terms Conditions

20 "St" Are Studies versus "Hrd" Socil Sciences: A Flse Opposition 19 tive methods mselves. The re studies cn pproch led deep tellectul understg how people thk, s it did cses Russin mmticins described here. Both socil scientists re studies specilists need be more pprecitive tellectul contri butions or cn "cmp" mke. It would be nerly impossible underst why Russin mmti cins erly twentieth century so egerly dopted descriptive set ory without n wreness hisry, religion, culture ir time. Similrly, it would be nerly impossible comprehend why outst g Russin physicist V. A. Fock developed his form generl reltivity middle tht century without knowledge his philosophicl pr ciples ir reltionship society which he lived. Thus, tellectul "bite" n re studies cn pproch be very deep if it is used sophisticted wy. We hve tried illustrte tht "bite" by lookg t mmtics becuse so mny people hve correctly ssumed tht context does not pply mmtics. Our pproch, however, is not uniquely tied tht disciple. Similr contextul cn nlysis illumte our understg mny spects culture. Just s specilists clssicl studies found justifiction for lookg t literture, philoso phy, politics, mmtics ncient world contextul wy, so cn re dy's studies specilists fd similr justifiction for ir p proch understg contemporry society. Such n on emphsis contextulism does not dimish ny wy clims socil scientists mke contributions by usg quntittive socil nlysis; it only dim ishes clim tht few m hve mde on monopoly such contributions. Now is n pproprite time for resurgence re studies United Sttes, both for tellectul for politicl resons. The tellec tul resons re ones we hve presented this rticle: n re studies cn us pproch help underst how people thk, even most "rigorous" thkers like physicists mmticins, lso quntit tive socil scientists. The resons politicl re eqully obvious: it is cler tht one resons for mny filures Americn politicl nlysts underst fundmentl Islmic thought Middle Estern politics is n dequte knowledge culture, hisry, lnguges Islmic world. Quntittive socil scientists cn mke significnt contri butions needed greter understg, but unless we lso hve re studies specilists who re thoroughly fmilir with culture hisry Islm we will not get very fr. And while need for more re studies specilists studyg Islmic world is prticulrly cler, tht sme need exists for ll vrious cultures world, cludg Slvic world. All use subject JSTOR Terms Conditions