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www.mr.r 60

Cosmos and History: The Journal of Natural and Social Philosophy, vol. 8, no. 2, 2012

MatheMatics and RevolutionaRy theoRy:Reading castoRiadis afteR Badiou

vmr tUniversity of New Brunswick

AbstrAct: t r r mpr r cr' "timr i s" B' "B e".

Keywords: o; cr; B

t p rjr cr cr mk r rr rb mpx. i , w rm p, r

m mm pr qk m rm , r wrtrkm r w rm w rx, - brr rp Socialisme ou barbarie, w r br m m mr g dbr. a w cr pb br r bj r r p-m (P cr, Prr c, J-Mr cr) r mr r rqr w w k prrz: rp mr rm pm , m m, rq Mrxm.

cr mp rr p r rp, prr, r w w pr mm fr 1960. i r rm 1961, r r r p

wr r rq m.1 i w prmb r r d c-B, r r, rrm p cr.2 o r , cr m Mrx r w r b pr k, r m r b r r ppr w, r m, wr w Mm.

i r r, , m brr p r

1. cr, Socialisme ou barbarie6 (33) (dmbr-fbrr 1961), 84.2. s: d c-B, gbr c-B, Obsolete Communism: The Left-Wing Alternative, r. b

ar Pmr (nw yrk, Mgrw-h, 1968).

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2/18

vladiMiR tasi 61

b r cr r wr rp wrk, w bj mr rr pp mm. i r, prp p r The Imaginary Institution of Society.3 t bk w mpr pr p , rm 1964 1974, pr pr pm cr p rb b xrm prr mm fr pp.

t x wp w r q r pp, p,p, r, r prp mm. a b m r r bk, mm p mpr r. s , prr, r mw w

. t mb , wr cr, q r w mr w x: w x. (iis: 227).

s, , : rm mr rm wrk a B,wBeing and Eventr r, , is. o m xp B w k r mm crrm, bj rq r . B m b .

a r i kw, B m rm pb. t m cr ppr, r xmp, B pr w-r frpp.4 i, i m wr xp rr xp B x p: mr r J-fr lr Pocket Pantheon, wr p w Socialisme ou barbarie, brk bw cr lr, m p.5

t r rr b w xr pp ;r, prp pr, mp mpr r (pr ) TheImaginary Institution of Society (p )Being and Event r b x. t q i w k r wr B rp cr, b wr m Being and Event w pm b as r rwrk cr r mm . tr , p r, m mm prj: r p .

Rr r pp mpr gr cr mm r, b r r m rm.

cr prrmm r r, r m rm , wr B xm rmz. B w m

r ppr w r rm 1966 1969 rb Cahiers pourlanalysewr, b xmp ar l, mb

3. cr, The Imaginary Institution of Society, r. b K Bm (cmbr, M., MitPr, 1987), 1-2. frr rr , bbr iis.

4. B, t ar fr Pp,New Left Review35, sp-o 2005, 67-77.5. B, Pocket Pantheon (l, vr, 2009), 104: 1964: r p rp, w cr

cr , Pr rr rp, w lr j, r.

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cosMos and histoRy62

rrm p w mm rmz.6cr, r , w pr r rrm rm rr, r w l wr mp. i m b b pr r rp ppr cr B m rm brr k r r r r bpp p.

dp mr r r, wr mpz b mp r rrw mrrr cr B r r r w r p q m mpr l r r. Pr r rb r m rm prbm

Mrxm, r r e- r, b m pp mm open . l pk, mm, p r, prp r rmprm m, r m m-Mrx ppr r.

cr w mr mp modernizeMrxm. h m p m q: t b Mrx b m Mrx w b r, r p 100 r r rz r mp p Mrx r q []. (iis: 14) B pp mr mm ( r b kw erp) mrz p, mpr w rr r r prm mr r. i k rr mm Mrx7; pp b r m r rm kwrk r, w mprrp m m Mrxm.

Mm , r, b rm q mm pm mk b rmb. s b r r rm w pr m r. a b mm w rr bopen mpr w rm rb r p r b r rm prr w r. Mm r rm rr r, w w x pp wrk.

t p q Mrxm wr cr b; r r (r m k ) r m r, m wr p The Imaginary Institution of Society. t r pr bk, Mrxm Rr tr, w pb Socialisme ou barbarie rm 1964 1965,

6. drp rm wb r Cahiersprj. t r pb jr B, cr, R, g, ar, l, l-sr,f, drr, B.

7. t p Mrx w w r b Mrx r mrp pr m b b pr xrm rr, r r m r 30Mrx r kw w w . (iis: 15)

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vladiMiR tasi 63

rp m w w wr w m. fr r: a closed, k h , rr. i prpp mr w xpr x rb r rm. (iis: 54)

t r Mrxm w; r Mrx, Mrx rw r : rrm pb, r, r r r m mp pr. a w Mrx.(iis: 56) B w . Mrx m h b p , b mr pr

pp r b pr B, , h pr ,n. (iis: 55) trr, rr rp h m b b , b w, b . (iis: 55)

ar cr, h pk pr Mrxm mr m rmm ( r rm ), b r mr rm r bw h prm Mrxmrm. i wr q r xrp w crp w rp M, Pr 1960 1970:

c mr w r rm pr, b mr m rw b, r bj w r m b -x w r r, pb r w b pr b prp (

, w w, prm prp r kwr r kw : r prp r w r 50 r w mbr k mr M t-). (iis: 55)

a br w :a -pr m b -mr , r p b B, wr pr, mr r , r prp, pb rm. i m mr mp [], r p r b []. (iis: 56)

W , r, m r B: mp, p,

, -z, -mr k mr . s m,wr, w mm. Br k w r mp The Imaginary Institution of Society, bk , mprr, mp r br r r k r mm

Being and Event. i r xr r r mm p rm B wrk, w mr rr mr xp p.t w p r mpr ppr cr.

o r mm, mr pr r, b pr p b B, r r b pr

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x. tr r b r xm m B r B, b. tr mp mp, pr r r o; B r z, mm r.frrmr, mm mp; b mp r, mpr p .

i B , b rb rrm w mr: srr, ar l. t prbm w. fr, ar r rmwrk r rm r r rrr bj, r r r. t r rr w, w

prm rp r , w r Pr 1968.o r , l m bj p pp rr r rqr m jm; w prbmp, b l ppr m prr, r k r w mr w m.8

B r m l rm, b p r. tr rm rb r mm, m brmz mk rmz pb:

mm pr . W w pp r. B g w mpb mr, within mm r, r r -rr. a mmr force -rr mm. W w

-r unnamable mm. a r mb real mm: r mm r rr, r.9

hwr, l p r impasse rmz r p rm p r . frm brrr wp, pr mm r r m ppr mp , , m rm . fr xmp,g rm R prx, ppr b mm r r , wr brb mm bmpr pr .

Rr b , ppr mp bm rrm

r. or m, rm rr mbr mpb k qr r mbr, pr b, rrm pr r r, r mp. t pr

8. B r mr, srr, pr mr r mprr p , xpr r r b wr r rr r.R srr r m pp , b b bj . i m br r rm B rwrk l, w m r mm wkw.

9. B, Pp tr, : Infinite Thought, r b or fm Jcm (nw yrk, cm, 2005), 49-50.

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6/18

vladiMiR tasi 65

w r , r w B r rmz. er w r rm rb rr pr w r w-mp mm.

t m p, r m mm b B, mp r rr pp: ppr mp, r xmp r w -r prx, pr r rrm. tr, B wr, r mm w mm p, r wprp, k .10 t , m pr, p mm.

cr mp r p rr mm rm mp rm, m g r p. t mm m p m b p, ppr b r w cr w rx rr, r m, w m. cr r r w mp, mm, rr p p, prw: Mm b rmb, w rp prr r b rm b . i , mr r, w k r b mp p 50 r;, r xp. (iis: 222)

cr B r r mm r b mk r b rm j.i B r w , w w br p r , , r.

a ; rrp B rm b ( pr ) b, prb b. i rqr , w xm rrp mmm ( rm , rm j).

fr B, r rrm mm r formalization, ww (m: rmz) r b mr : r b w axiom of truth. fr cr, rr, rmz b r . i mm r , m rm mwr w b rmz. t r mm m

m k rm w rmz, w xm m, b r p pr.

Br w w r, m mpz mpr r p r: cr B (Being andEvent) rr r b mm.11 t cr:

10. B, Mm t, : Briefings on Existence: A Short Treatise on Transitory Ontology,r b nrm Mrz (ab, suny Pr, 2006), 51.

11. nr, b m mm k xp m. B m m m 1990, w r p r.

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w rb mm m m mpr q r . B mr pm r mb, -r, w pr b r br mm, r r, r pr mm. (iis: 222)

s r, mb , r r p , pr b , r pr mm, b prp. i pr m brr r p The Imaginary Institution of Society: -r

mr.cr p rm mr rm m qr l r brr rr r, r Pr:12

w w pr mr b r rr p: m, pr w b m of r m, r wr reflection, r wr bpr P (eidolon) w pk r wr r.t mr m rm m mrrr r rm z r. i, mrrr pb, r mrrr, r wrk mr, w r ex nihilo. (iis: 3)

t r ex nihilo b m mk r r w

m rm mr. t p prp b r prb r w r p w P r .t mr mr r, r r r:

t w pk mr, r b pr, r , mr rp, w rz , rm w r m m rr m : r

12. tr rmb Mrxm rrm 1960, rm mrw l m k r m, mp r z, w m qr Mrx rm . i, cr r mr w pr rpr, pr x w m mprr. n m b x, cr

wr w p prr b pm brk, (iis: 273); w prmb rr ar r Br. a mbr m fr kr w q r wrr b rpr r m m r . cr r mp r Pr 1960 1970 r grm pp m p Mm s: t rmrprmp b fr m m m mbr p wr b x r w p rrpr rpr m (Vertretung grm). t grm wr Vorstellung(rm vorstellen,p, p, p br) w b b m; pr hr rm m mr r B, r x w, wr b r r , pr m Pr w k rpr w brr. (iis: 4002)

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8/18

vladiMiR tasi 67

wr b m of m. t mr w i m pk m of. i undetermined (-r p) r r/rm/m, b w r rb q ofm. W w r r r wrk. (iis: 3)

sr q w r, r mm. t m b cr r, m arm prm w mk m w r r prb -r mr. cr r r Pr bm r theory b . t mr m r p w ,

w r r r r--r m b xp, b r rm, m pr rm (r, r, ). i r m r r m r -r mr r grm h prmw rr wr-mk w ?

i r rm, mpr r B, mm m r rm. a pp prrr rmz r rb b m w b bquab. i m r mpm r, b rm wr r mr p w, bj-p, r rr-rp: Mm r pr rpr. t R w r mm p r pr rpr.13

i r r ( m) wr B w b mb rr r, b m r cr m . t r mp b r mrp rp Mrx r , , pr -r pr: er , wr m b wr m b bj, b m rm -r doing.(iis: 3).

t r mm , r r mb crrp . o, , m r,

b pr -r m ; r , r prp. t -r mr r r r , b r m mm prr z. t r m , , k k pr r, (w mp prr r r ).

B m mr rp. tr , r, r rmz, , r . B m Being and EventB (k cr)

13.Briefings on Existence, 56.

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m r rm mm, b m r r mp r. h rmwrk b k r w z r . hr w cr xp : t rm -r r mpr rp r, rr w m pp r rm prp mm, , r, xmp pr mr w, w, w r r []. (iis: 222-3)

tr r m w r r r w M. s r mr br p pr -r . t mb

w cr legein: pr --p-mb--pk. sm k pr m , m p x, kp w mm wr: X b. i cr legein rmb pr B, Beingand Event, --.

a, cr mbr r rp b rm legein, pp x m. fr , mpr rp [] r pr legein designation. ar r b prr w rm k pr prb. (iis: 244) frrmr, legein b pr rmr p -r mr, w cr teukhein, rtechne, prp , rz, prp doing, rb mb-j-br-r (iis: 260).

er rqr q, r q k ; legein teukhein rm r . tk pr, w mr( m) xrm: Legein [] bm m r b pr rm m p . Teukhein [] bm mw r b q r k q. (iis:264) d rr (r ) r w -r , mb rp legein p m m p w, r, w k rz. (iis: 269).

t rmr (pp) r, b r,m r , p mm. h, prr,legein r: b r br m pr, legein bj r r rm r. (iis: 271)l m rm r mpr p r w B b r q,br rrb r mr:

l r r p rz legeinm b, r , b r, r legein legein br, w, r rr rm r mprr prp, ppr prr j mpr pr q rrw []. (iis: 271)

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10/18

vladiMiR tasi 69

t b k w B r rmz, p r pr w r m pr. i mp, r mm cr notw, mpr w m rmB The Concept of Model:

W m l m rr mr r. B r , Br br r mrz rm r pp rpr ppr r rmz x: x r r the means of mathematical

production, b m r b w w m m b prrr m pr prpr p.14

a mjr r r w. i r m mmpr: rmz xm m (r B, r Br wm ). Prr mpr q rmz r, wp prr m p x m. t r rm, bk p wr cr r r : trm, , p xp b p , rr, rqr b r r r almost sufficientr unhampered and without limit[...]. (iis: 223, mp )

dp rr r p m, mpb r mpr w m w : -r prx mp br. t , p w pr rm mm pr, m jr p b mr . e w mm, w b w-kw prx r b R fr Grundsetze, k bj rr r prx. hwr, fr m , pr, R prx b The Imaginary Institution of Society.

cr r , b w m mr mb rm r; rmz w. a rprr rm mm r w wr: t pr x g r x wr g. (iis: 271) imm, m b pr; cr,w m prm m, prx

k r g r b r r b .

tr , m, pr r r cr mp : pr, , m existr . (iis: 234) frrmr:fr , rm ism ( , p, ) (iis: 235). o m r, b , x pr m r c Mm s: areb

14. The Concept of Model, . r. b Zr lk frr tz t (Mbr, r.pr,2007), 43.

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. a r r b r m rm. y , r w r x h b p: mp , wr, r b, w mpr r rb r rrp b r [].15 i m b r -r r, wr, pb . t mb r m, wrk -r mr br : t b r, w b r mk, mrr bj rr mrr m x , r , . (iis: 228).

B r w cr p r b m xp p r mb . a b, m b xmp m bj, xmp r mm r, b r prp rm r b k fr. a wr, w m r, br rm rqrm , m j h x wr pp b p p : legein pr mpr b -rprx, r p rm p x b, r b r g, b b b, o. hwr, r pr x cr r : k m, wr qr m rr p r pp g (iis: 199). t r m b mb r, prr q .

i r B, w ppr b mr rr cr. i M tr Being and Event, wr cr w b r pp r r p rm prprmm . i w wr bw mm , rr mprm bw , crp bw mm, -z B, - pr prx w bb o ( rbm ):

t b p -b cr pp b, r

g, w w Pr, -mm , r m: r b mp, mpr rr, .16

B r -, mm rqr xmrmz w p rr r k x m. i Zrm-frk m, rmwrk Being and Event, rr

15. Phenomenology of Spirit, r. b a. Mr (oxr, oxr ur Pr, 1977), 100.16. B,Being and Event, r b or fm (nw yrk, cm, 2007), 42. frr

rr (pprbk), bbr Be.

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12/18

vladiMiR tasi 71

jr pwr kw axm spr: rm x rb, b m x r x . i r r B, m xm r, wr [] x, p x. t w prm m k xm r b materialist: Zrm xm rr mr brk w r rw pr prx x w xpr mp r rr rm w-r . (Be:47)

cr, wr, m rr b prx. t r

pr legein r m b r: r mbzpr w w r, theory (wr r ), mm. (iis: 241). a rr, , wrk w xm rmzp rm rm m . s brb b cr pr, b cr theory , b wm bk p, pr b ppr :

t , b cr, w: a 17 w bj r r r .t bj r m . i p, b b , b rm, rr rm(w rp mm m rp b r rp xm) m. i p pr

b, rr, rr rm r ( mm) []. t rr [] rr r b r br. (iis: 223)

tr p r wr pr. frmz r r br b ; xm m r, , r ppr prr , m , mw mr. Wr r b rb , , axm spr, r mm pr w r prm r. i w rmp pr ppr kw prx, b q kw r r mr brr. nr, B m r bj pp m b r m xm: i w k

, b r k, xmz r xp, b r . (Be: 43)

o r m rjr B. i m w b, r, xmz r, b r r r xmz r m x p pm, b, r w r r mpr. cr m rm rm:

17. t r br m b br b: cr m b b a act . a w i r pr legein.

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t prp br mm b r m mbr xm rm m b m m mbr m, b r rr, q mrmpr xm r b r m r r, r rm . (iis: 241)

t , wr, qk b r r rmz :

frm mm b caput mortuum mm r , mm mk. i wr , mmw b mp semeiotechnique, , pprxm q w pmp m, w xb m prpr r. (iis: 242)

sm r , pr r:i nw lbz mr kw rr rmzmm, w r r pb r r r. a w, , m p r r , w p b c Wrr. (iis: 398-915)

B rmz r j m p prr xm m. W r r wr m, w r p b rrm (, mp, b rrm m w p 1960).

t j cr r q rm, pr r rmbr p pzr w. i pr m rr rr x b m, m, mr . i r w br:

mr, rm p w w r r r, wr cr rz rp b r mr r mr rmm; rmz prpp p m, w, r q. er r prpp r , rmzb prpp mbz w w pr.(iis: 226)

a r rm m, r mb rr

: r pr. B q r r m m cr prr. nm, x some , r xmp m r m mb, rm b r. i w, w hbr rmprrm. cr r r r p. tr , rxmp, rpr rr g mp rm (iis: 421), b r. i b rm m r mp, mcr r w rm . h m w mm ,w m x mb, pp b. i

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14/18

vladiMiR tasi 73

rmwrk r p b w prbrm .

W m b m rm pr w r m, rmm rrm, b w ppr r legein, w rb, rr rm, mrr bj(mr pr: rr mrr, w w rr). t r

w, r cr, wr rm r b rbrr , rm w rr b k p mpr p r p-r . i rr p pr r kw langue; rmm,

p rpb -r mb (.., rk mr, rPr pbb- r -rm).n r Brbk, wm m rr rr

r ( pp w wr mw z brb), pr cr w p:

rb r b ir Elements of Mathematics mw k rr w wr: i w rp rmz rr , k rp r ; w r p r mp prbm r b q rr rm []. (iis: 240)

er mp qm: pp, r mmm prr pp pBrbk r mm rbrr rr . Mm rmm mbrrmb r mb r prr r . B r r rr mp r mb r rb rr , r rb mk mr , p r rm:

mm wr mp rr mp [], m mr w b rrm r rr r .; r rm w w-rm rm mr w, , b mp p r rm p rrm p []. (iis: 194) [] W kw mr,

pr r m m b m r mm, b b r 40 r[.., g], w w rppr brk-w rm b w, , p, m Pr . (iis: 39634)

am cr rm , w pk p r w w: mp prpp x mb. i xrb w x cr , pwr legein:

r b rm r r, r x

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15/18


cr ; a fortiori, , b p . om k r r, r x r r mr r rr pb pr . B wr , w,pr, rm pr. t r b rm p rr m r r , actually x.B m m, , x r r , r legein. i , r , k legein, q r w mr w x: w x []. a m m xpr r, : , eidos rr p- x w r b. (iis: 227)

Br xm r b rmrr pr mr rm cr bk r .Mm m r; r rb m mm mb rw b mr pr -r mr; r, rrm -r mrb, prpr W, x m mb. W m r rr mbr Pr w pr bj x m mm w wr r mm. Mm r w rmwrk, b prp rmwrk b : rm p wr, rr mbr x, r pr r

bquab.t prp r, r rm , rm rr mr rm B wrk. h wr, r xmp: W m w p w x? [] ex pr B m . a mrr: lrm pr r mm (mathmatiquessvres) b. W r m rmm mrm. Rr, br mxm b rm: w p w x b r B. 18

tr r r r r, p mm, m wi r . B r r p r w i i m. i w r : , m , . t

w B wr Ethics w m thinkM m r b-r-, r , mr b, r bj mmr b prr, dz Pocket Pantheon, w m pr , r mbr r r b cr:

W, K hr (, , pp) m b? (l r xpr, bmr m mbr, i kw w m mm mmzb w qr m

18.Briefings on Existence, 55, 57.

7/28/2019 243-1257-1-PB

16/18

vladiMiR tasi 75

rr p r pp g ). M b b r brpr b mr, mpr r, .; pppk, m b [ w w cr r bj]because he can create nothing. (iis: 199)

lk B, w r rm b,cr r w pr m rm r m r. h bj r pm, w pr wr m m r p, prm r rm rw w r r. i bj m pp. fr xmp,

hr Mrx m r ( ppr) m pr w, r, (pro-ducere, hervor-bringen, p br,mk m br) b, pr, mp b hr: r, p-br w rm b, r, w r r. (iis: 198)

i pr r w w r r, w m r . nw ppr w r br , w r r b pr -r mr b r b r rm j.i r r B, r mm. i m, x ( r-

) m r m b b r rmz ( xp

) b r r rbrrr rp . nr, mr rr Bm, r b m b b. t prbm r w bj mk (r b m b) m rr m rp m ; r mp m m r p w.

B b m wr : lr i w b, r w cr sm.19 t p , b rcr r prbm ppr b wr. o m b rbrr r -r mr, w r ex nihilo: m b m w wr. h r , prp, mp j b b, pr w

m mb legein.cr r k r r m br

r; m k r. Prmb m r b : r r, r m k , mm r xpr wr. B cr q r w m bk wr mr r rm mrm k Mrxm w r pp b rr rp. h rr r rr r, m r r rm w . t r r rm

19. Infinite Thought, 129.

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17/18


-r mr r r. i r x, b b mr mr, k x:

i m -x w w r r mr . B m m b m, (r)p b r x , b mr p ppr, p r mbz [],x rm mrk w w mr w p rr. (iis: 230-1)

t r, w r rm [] ppr

rm. B p b pp w- cr rm, m m. sm r-k x, b b rwr, . o -r mr p r mb rmmm B, pb , m , p r mrb r, w r (pr ) m wr, r r. t b pp pprbm.20

Pr p r rm rx Mrx r r, w r mpr rw rm nw p m; wr , , rm. tr rmm : b cause b r. W r r p m, cr m mp -rrm rmm; br r mm rm. B cr rmrr p rr rm rm mprbrr . a mp r-k r p rr p m ppr p wr r r r.

i r prbm B B r, r rm. h kw j w r -r rm b b , w r rmz r, r x.21 W r, r r r rm -

m r-r -bj, cr m, p rq rr mm, bm r mm , r mm mm. W rm r ppr lpoint de capiton, m rr, r, r r mmw mr r, rb b k:

W r b

20. i The Meaning of Sarkozy, B k r r wr m rp .

21. s M tw Being and Event, p. p 140.

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18/18

vladiMiR tasi 77

pb r p ? hm s sr w prbb wr r q r : m r, pr-m, rr r r r p ( lpoint de capiton) w q m, p r x r m.22

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i r m r B br r TheImaginary Institution of Society, r m i k bk r; cr w rr B mpr rmz r pm m, wr prp rr rb . y mp, brr m, m wr w w mr r.

22. sj k, The Sublime Object of Ideology (l, vr, 2009), 82.

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