Dimostrazioni e confutazioni. La logica della scoperta matematica.

230 Pages·1979·12.776 MB·Italian

by  Imre Lakatos

Titodleol l'oorpiegrian ale
Proofasn dR cfutatiTohneLs o.g iocf M athematDiicsaclo very
(Copyrigh1t9 7b6y CambridUgnei versPirteys s)
©
Traduzdiaolnle' inglese di
DaniBeelnae lli
Ediziiotnaela ic aunrdaai
GiulGiioo rello
Primead iziitoanleai parnial:e
1979
Copyrbiyg ht
©
GiangiacFoemlot riEndeilltio re
Milano
ImrLaek atos
Dimostrazioni
confutazioni
e
Lal ogidceals lcao pemrattae matica
ac urdaiJ o hnW orraeBll l iZea har
introduazlli'oendei ziitoanleid aiGn iau lGiioo rello
FeltrEidnietlolMriie l ano

Introduzione
Lad imostr(aozm ieognlleie" o d imoiso)tnd riiua nzt eoraelmc ae n­
tro udndi i alqougao"s ipl ato"n,ia clolsac opedretlavl ear iot,aà l ­
menoa,l lsom ascherdaemleln't:eo r qrèuo ercleh e propone Imre La­
kationsq ues"tirac ostrurzaizoino"en d aelite entaitnitvria pperre si
dimosturnaacr eel ecborneg etmtautream a,ti iltc eaoredmiEa u ler.
Obietptoilveom èii cmloo dtor adizdiiio nnsaelge nfaorreds ie( e)f are
matemaltois cfao;n idnov,,e l caec apacdiirt iàm etctoenrtei nuamente
inq uestqiuoenlecl hees embrlaent oe spii ou vvileec, o noscpeinuz e
consollieda actqeu,i spiizuci eorntide e finei tiMvae s.er ,i voalltloa
matema(teip ciaui ng eneraalllseac ie)n,qz uaeldil oL akations
quesvtool uèmu en tenvtoaltatic ovo om prenqdueeprire o blqeumeii,
procediip meertn etntaetdei rvrio qruie,l le et astttriactdheieg irei ­
cercchaef anno pdrealtlsiacc iae nutni'fiicmap arffeassac icnoamnet e
ogniim precsrae atdiavlarl,ia c earrctai satlci ocnaf roindteoo logico,
perl os tudidoifis loo sodfieals lcai e"np zrao feisss"ti aloan" s fid"a
lakatoaslil"aepen ias temoaluotgoireie t daorgimea t"i cuèhn e'occasio­
nep erri prencdreirtei ciap mreenstuep dpeolssltuaisa t edsissac iplina
e pevra lutraarzliio naallmlleuanc dteee g ilnit erede esvisa il doirb ia se
chev engounsou almaesunsnt.teC i oslIe' xcurpsruopso nsetllo i bèr o
uni nviatr oi penlsm'apirree sscai enctoimfi"ecm iap recsrai "t icea la
riflesssiuolsnlceai ecnozmame o mendtiol ibeirnttàe ll.e ttuale
Lep agicnhese e guonnoonp retenddido anroue nq uadersoa urien­
ted elfillao sdoifiL aa koastM.i rainnov eacdie n quadDriamroes trazio­
nie c onfutnaezclio onntied setl"olo can cezfiaolnilesi "bt diaellmlaa­
temat(ipcaar ag1r,)a efaso a mignlaeirl ee mednict oin tineu iqtuàe lli
di rottrtiaulL r aak atdoiqs u esvtool uem qeu eldleol rliafl essione
epistemosluolsglcieic eaen mzpei r-icchheei lp ubbliitcaol giiaàn o
conodsacsiea gpguib bliicnCa rtiit eic crae sdceiltclaoa n oscenza
-
(apragr2a,)f oa deilnifinneuean rape o ssirbiislpeoa slpt rao blema
chei ne ntraimc boin tessirt iip resqeunetldale,opl rogrsecsiseon ti­
ficaot traivlme urtsaom ecnotnoc et(tpuaaralge3r. )a fo
7
Introduzione
1.L al ogica della scIolmp eetrotdao dmidametoleslmtear taizciao.n i
ec onfutazioni
Seconudnoat radizcioonnseo l(ihcdepa etLraa katroissa allmee no
adE ucl)il dame atemaèt uincada i csipl"iuanotar itairnifaa,l liinb­ile,
confut"a,ub nic loerpdoi chec respceera ccumulaszuicocnees ­
verità
sivea c heq,u i,nc doin scopedretcla a ratftaelrlei bile
e riveddieblillee ]p"aprcs reioteg"enrs ezeemes psiirv,iar c ehse"tala s olsac ienza
chfien orpai acai utdoi 'um ani.'"D imostraezc ioonn­i
futazèia olnnciui Dsio larpgraielrsles cotocànhtée mporanIemarmee nte
e gg'
Lakatèo vse nuatlot arii pcrhees enitnavneuocn eq uadrraod icalmen­
ted ive.rL samo astcermiavsteiisn cvdaio, l uppa fcoornmgueltaptnrudorope o,­
nenddom o lzzndoc,r itiqcuanedsdoti em ostnriLa.az io
e a
cosapioostrnaiz iamnaiaturantealsli' Ott-occeunist iao g giunge
lnos teavt]oe z7.cdare iltrliiecc ae rfcohned azioovnena elsis,u n prèo gramma
attuale
riusciimtpooi r snettasmuqe unetlreli iv -alciip ermeotgtgedi i
a
riconoislcc aerraet ctoenrgee ttduergaalslise idoims ip ecitfiecohrei e
matemataincchhdeei,t eoriimep ortea fnotnid annetlil 'emdiafi­cio
tema;t imcao Lakatsoiss p inpgieuo lt.r edimostrsatzeisosnei
Le
hannuon c aratctoenrgee tteu fraallleia b cialueds,ea ml o dos tesso
conc upir ocleadc eo ncrientdaa gmiantee matica.
I tes"terid atitnsi t idleed uitst"ti,cav hee lencanol ept ruet­te
mess"een ces"sp aerdrie eduurnrt ee oreem iam,p iegdaipn uon tion
bianacsot rcuosnic ectotmiie l p restigtiiarftauo orrei ild aclo niglio
cappeslelnodz aar nleem otivazsioonpnoei rL' a katgolusil timi, piu
raffinateis idteipl e nsideorgom atciicodoèe, l l'op"iesncioonnldeao
quaille vceornos iisnut neap roposiczhieèo unner esulfitsoas".t4o
"tsildee duitst"ti,pav aradossadlàcm oernpotoge g,ai q uefla nta­
1s0m ad im atemastcihcear dnaiH teog enle lPlrae ifoanzdee lFlean o­
meonlo:g" i'laessendzeal dliam ostr[azeniloltnaee r minodliqo ugeia­
stvoo ulme','li d(eidaf onddoe)l la dimosntornha aza inocnoierla' ]
THOMAHSO BBELeSv,i atatnroi.,t . L,aN uovIat aliFai,r enz1e9 76p,.3 4.C ome
I
slogdaenl " dogmatimsamtoe matliacf or"a sdeiH obbeès r ipresea c ommentiant a
quesvtool umpe.4 ,3 .
Z Alludiianmp oa rticao lWahraetd oeas m athemaptriocopalrl o v(es criptrtoo­
babilmtenrtiael 1 95e9 i l1 961e )T hem eth0o1da nalysis-(slcuyain p trhiemspaia rst e
fus crittrtiaal 1 95e6 i l1 961m,e ntlraes econvdean nper esennteal1t 9a7 a3 unac on­
friesrpeeant zJtayi vviiaismc ke(aynFpltiiiient3 ,lo alecni odd imi4aer ) elAK pAlTaiO ucSna,M a artthiecdmoiJal S.toHc i iicnestan,inc kdeEck poais)st:ti etmuioslcoognyo:,
PhilosoPpahpiercasa cu,lr ad iJ .W oIr.r ael l Curriveo,I 2.,C ambriUdngiev erPresssi,t y
G.
Cambri1d9g7e8 .
3N onè casuachlee n elc ritiicla" rmei sticaiustmoor itdaerlil"oso"t idleed ut­
tivisLtaak"a tfoasc ciuan os pregiuduiscoda itH oe ge(ls iv edai np articlo'laArpe­
pendi2c)e. resto "ilt rucdciou nas imislaeg gezzèa c osprie stiom paraqutanot o
Del
facilmmeenstseio n o perMaa. nona ppensac operltaso u,a r ipetidziivoenretr aàn to
insopporqtuaabniltlaoer ipetidzeiloln'ea pparrteezd ziua tnpa r estigiGa.t Wo.r Fe." .
HEGELF,e nomenodleolgslipoai rtirti.ot ,La. ,N uovIat alFiiar,e n1z9e7 0v,a lI.,p .4 2.
4 G. W. F.H EGELF,e nomenodleolgslipoai rtirti.ot ,.c ,i tv.o,II .,p .3 2.
8
Intdruozione
signiefil caan taot udriea s semroem endteorl e sulsttaet;sao sn ozi nel
resulutnta atlmoeo menètg oi pàa ssead tiol etgo"ua'.
Ques"tmoo vimeinnts ou peir"efi6èc t ipipceoLra kadteollse es po­
sizisotnain dsairadon,vo v iamdeenmita en uasliia,ln eco o rresnttoir ie
delmlaat ema.t iiElcc aasdoac uDii mostreac zoinofnuitp arzeinodnei
avviloac, o ngetdtiEu uriae èr e,s emp.lS aerceonidr oe socotnrtai­
dizioinnafl,ail t,ast tiodreilacl oan getVt +u Sr a F 2 (voeV ,S
- =
e F denotrainsop ettiilv naummeenrtdoee iv ertdiecgisli,p igoli e
delflaec dcieu n" polie")d rocomicnocni asg floir ttuennattaidt ii vi
Euler tepremri cnoanrl ear iusgceintear alidzizP aoziinocnMaear é.
peLra kaotcocso gruraer daalrlseta r utfinteu drita u tti" etqnuteait ivi
ede rr"oc rhiec ollelgo'airngoi ncaolneg eteutluerraia alnlvaae rsione
datadnaeP oincnaerlcé o ntedsetllo' ansailtyOusgsig.sdi i amo per
scontsaitafo a itlct hoile teoredmiEa u lseira pplaiipc oal ie"fdser­i
rodi"i,ci oèo meorfim oallas fercao,nf acocmee omoalr fdei s(c,oe
sen ons is uppocnheel ef acsciea no pgilasinp ei groeel ,ti t ioccorre
ancorriac hicehdeeg rlseip igsoilaion moe omoar.lsf eig me)n,st ioial
fatcthoes ,eq uesctoen diznioonsn oin tou tstoed dissfica otstter,u i­
sconfoa cilmdeencito en troeSspeemspdsiio.m enticpheirqaòum eol la
vasta gdaitm emnat a-tdiavL ie genCdaruec,Lh hyu,i lvioenSr t,a udt,
ec.cfi noa M obisu,L istJionrgd,,ea cn.c -chme iraav" ats abi"lil i re
teorema dcaonnddoindzeii v oanlii edsiptràen sosnne e lq uadtroo­
pologcihceoo g gciiè familimaarc eo,nc lausaotltaee i mpedliar e·
costrudziic oonnet roe(socenmspiid serpaetsis o "cmoosmt"erd iae li­
mina:r euant tegginaemriei ngtuoad redl"ilm eo stràu"oo s "ipattolo­
gi"e asisd aiffunseol l'Ottcohcese irn ittor,o va snoeplrlat'tauntat­o
lidseil sleac omnedatd àe sle coLle'om)e.r gdeerclea ratptielipr reo ­
priamteonptoel o(gpiicuot tpoosntioac,mh ome,e troi pcroo ie)t- tivo
conC aylee yL isntei1ln8 g6e 1q uincdoiJn o rdnaen1l 8 6-6, l eg e­
neralizzdaiSz ciholneliid BiiP oinceai rnéfin le 'insedrazp iaordntiee
quest'udletliclmoaon getdtiEu ural enre lq uadcroon cetdteullaal e
topolcoogmibai n7as toonraoil aloprearL akatcoesr dteoic ontributi
dig ranrdiel imeavn oo,n" evriutlàt "im,ien n omdee lqluea dliim enti­
carqeu eclh e accadpurmtiao. D elr estaon,c hnee lmlaat ematica
nonv is onvoeè r uilttàei ;om almetnuot,lt eee p istemcohlheoa gnineo
pretdeisf oo nduarneam atemactoisctai dtiuv ietrai" tniàd iscu"t ibili
5I bidp..3 ,3 .
6 Ibidp..3 ,5 .
7P eru nar apidead ef ficacsei ntedsiqi u esm-tiis ultsaivt eid,a i nJ .D IEUDONNÉ.,
Abrédg'éh isdteomsia rteh ématHieqrumaensPn,a, r i1s9 78v,o II.I ,i lc apX.: G .H msCH,
Topoloignip ea,r ticoplpa.r2 e1 8-21U9n.a bibliogroraifiean tatsiivt ar ovian J .C .
PONTLa, topolaogligeé brdieqsou rei giàn Peosi ncPaUrFé,,P a ris 1974s to<ruinaa
dd te emad iE ule"rn ellpar ospetdteilvlata o pologèi aab"b ozzaatlal pep .1 6-31
dd voolrumeU)n.a b ibliogpriaafic ao mpleèt daa tian M . DEHN P.H EEGARD, Analysis
situisn,E ncyklopdiierd Miaet hematiWsicshseenn scBha.,G f .t eTenu,b neLre,i pzig
1907l,O ,v oI.3 , pp.1 53-200T.a ttichee stratengeilme a neggiiar ec ontroesempi
teoremdai E ulesro nop resentadtae L akatosso ttiol p rofildoe ll"ar icostruzione
arlazi onalned "d ialocghoe c ostitiuilCs acpe itIo dlioq uestov olumee n ellneo ted al
puntdoi v istdae al storia reale".
l Il
Introduzione
sonvoi vai vae nuatc eo ncespsiiuoo mnein,oe spliccoinit lfe a,l ­libi
lis.mR oovesciaalnldolora pa r ospetdtiicLeva ak,a taonsc,hl eev ie
percoirnsp er eceddeinvzean ttaannoti on terepsesraln ots it orico
quanitr oi suclhte"a tprio vvisor"i aacmceenttteiamo.
Mai lf allliisblmiaok atonsoinpa unòov enriard icalrmiednitmee n­
siondaatlosl tae sassas iommaotdiecara?nL ac onceziipoontee tico-de­
duttdievlatl eeo rmiaet ematsiehc arh ien uncailaeltavo i dednezpiar in­
ciphia p urmeo strcahteop, u ra vencdaor atctoenrgee tt(uedrrail­e
vanddoa p rincdiic pair atctoenrgee t)t,ui t reaolreemsio n"oev rità
rela"t.Li e'vnenuciadtiEo u leè,ra buondi ri"tertloa,t ivavmee­nte
roi"n q unat,os otcteor ctoen diz-icoonmipe i us oparbab iasmpoe ­
ciucatèo v ermoe,n tirnea ltèr fea ol.s inu ns endseogl e nere
-
chep,e re sempcieor,et pii stemdoiil moÈpg ois tamzairoxnieps atral8a ­
nod elvleer imtaàt ematciocmhe"e ev rictoàn c"re.Vt aep ersòu bito
detcthoel as tesdsiana miinctae arlnr ai gomraet emarteincdaoe p ri­
mav isltasa i tuazailoqnueab natno,a a llemednaopl u ntdoiv isltoa­
gicos:e mbirnaf aptotsis iebsipllei ctiatlcaior ned iz(ia"os nsiu nzioni
impilti"ec,"e lmmin asc"o,escc t).i qeu inrdiif ormilu "letaormreae "i n
modor igoroscamoernrteTeta tlèoe .s tapteoer s empli'toat eggiamen­
tod elsltoe sso Pcoiirtncacalqa eur eés t(ifcornq.eu esvtoole u,pm. 8 5,
not8a7 ).
Ma lpoas izidoinL ea katèdo isv ersseqa u;e lclhaie np iou ccasio­
niP oincoaffrréèe l av ersidoenlecl rae sdceiltmlaaa t emaptriocpar ia
di unai ncf ualise ee sigedniz er isgeomrber aanncoo irmap orisni
modon ormatniovndo i scutliavb eirlseil,oa nkea tohsaii annvaea clel e
spalslileaa c onsapevdoelleslztazo ar idceicita àn odneirl i gosrieia
risultati dleolglic'ciiarn gcdlaasi gt ienssesi is taesmsii om(afct.ri ci
p.96).
Primdia a pprofoqnudeisrpteuo n tmoi p aroeppo rtuncoh iarire
unaq uestpiroenlei m.iS neda aur neap aritlte e sltaok atorsiimaannod a
espliciatdaH meegneètli e,n negabilpea rdct'heaeu l ntor atd eerim ini
dir iferipmieurn itloe v-ansteni o ni lr iferidmoemnitnoa ntèe
-
lac oncezfiaolnsei ucadziKi aornPlio sptpaeu rn,od ecir ittirclai'l ,­a
tr,op idu urdie lla trcahdesi irz iifaoàln ldeai aleEt,tn iactau.r almen­
tei,lp aralcloenPl oop pveire inmem ed:ia alltedo oman"docem ec re­
scel as cie?n,"z ca"omec reslcame a tema?t"Pi ocpapeer L akatos
dannroi spsoismt.ieP l oippeinr p,a rti,ca offlearrcmehaen elslcai enza
(empiritcuat)t an ostcroan oscèec noznag ettepu rroacleead pep,u nto,
"tentntilvaeir roriL"a.k athoads u nqsueem plicemente adattato
per
le poppecrdi nllmea temactoimcleao ,s testsiot doilq ou esvtoo­
liumiammdeen ,doeD iseint mtrnnoovl .l'v1ii/1ls"Pr{,/ ooIlllI.{'pllt" : PtRmaid{cnv r'n lnlwl ."Ci iuo naRtletlatosrzu eeim ocbeorns anui gf,gun etirraL?iiza rcri ehio,is apmoasntdao
è,
pri• lllc'(iC'mpfdl I/,r tridl'O/dC' I ro'i/ll,l b'lII C"N.Il./I.. .'HlK". iC", i C"'. hiiII.dhIcl.ln l· 'li'dIl rl ,l' lC"vud 1d'...il> 1W Il ',.I 1 K'1<,R01) A7-J71,F.1 W4SC_Ko I".i spondence
lO
Introduzione
Proprliaot radizdieolnl"eav erictoàn cr"e (tucaia bbiamaol luso
pi6s opraam)m ettuen 'interprpeit6ar zaidolinmceea nftael liebdi lista
è los tesso Lakdaelitnoesa rnale al l'indtiea nctcoe ntiualpr reo prio
distadcacu on aa ffermazdiioP noep pesre concduoiè anchpeo sbsiile
rgagiungelraev erità senza tuttavia Deiscseae qrunee­ consapevoli.
stpor oposLiatkoa tionus n s aggsicor intetl1o 690:
Non sonod 'accocrodnol ar ecenetnef atizzazidoanp ea,r tdei P oppedre,ll a
possibidliii tmàb atteirnsq.iu alcchaes on ellvae rifitnàa lsee nzap eròe �serne
conaspevoEli.r oc ritivceor sqou esttae ssie nofainenqa u anteos scao ntraddice
unad ellmei ei deper ediletutne',i dcehaeh oa ppredsaolm arxis(meon onv edo
lar gaiondei a bbandonarla}.9
proposdietlolc eo nosceannzcehl eo giceh mea tematiche Engels
peAre smepioa ffermcah e" nona bbianmeos smuont ivdois paventarci
defla tcthoei lli vedlicl oon oscaec nuzoiag igs iamsoi,ta a ntod efi­
nitqiuvaon ldoso o nsot atiip rteuctet"dil.eI onn stoimmnao,ndp oobcboi amo
avepra urdair iconosfcaellricbi.iL lait setssiie nofacnoemam,e natlal ora
Lakatnoosn,p uòe ssearlet crhoe" u nap eccdae fla llsimbo"id liiP opper
e udnif ettcoh ep er Lakoactcoosr "rceo rreggceornve e ros pirito
marximsetdai anlta[e . . dottrdienlali en finiptreo posidzeilpo rnoi­
geot tdividneol l'U.n1"i 1l.v erso
Questo sppeirecghlaéa s itsemazioanses iomaptaiccAaeg, as2s i/
nont urbla' parpoccliaok atosIinau nnoa .l trsoc ritdtoop,oa vedre li-
9 NecessKinteya,al ned P opperrep,l iac au nac omunicadiz iWo.n Ken ea1ael la
confeenrzaan nuadleel lBar itSiocsih etyf art hePh ilosopohfSy c ien(c91e60 ).I nedito
fino aplulbab licazpioosnteuc moam ec ap7. d iP bilosoPpabpiecvraoslI,2 . , cLiact iot a­
zionèe a p.1 52.
RiIuFniO.i,R E t oNmGaE1 L79AS4n,p,t. 8i 7-C.Df urbai.rnn Kci .hnqM eguARX ,aln, t doFe .tE taNo pG .E8 L3OSQ.p,u e ersXXVet,', u tplarths.i.sè m,oE o d itori
daL akationPs b ilosoPpabpiercvsao,lI 2 ., cpipt.1. 2,5 -126. ripreso
IlP hilosoPpahpiercsva,olI 2., cit., L'pi.m ma1g2di6ind. ei oc hec ompondei
infinpirtoep osiziilo nip rodgeeltlt'ou nèi vperressoei nntu en punto ndoidq aulees to
voleu,mp .9 3.
12S econ]doos epAhg ass(iT hel akatoRseivaonl utiinoR n., S .C oHEN,P .K .
FEYERABENDe M. W. WARTOFSKY( acu rad i)E,s saiynsM emoryo fl mreLak atos,
"BostoSnt udiiesnt heP hilosoofpSh cyi enc3e9",R, e idDeolr,d re1c9h7t6p ,p .92 -1i)l
ruool delli'oamsastsiarceab boeg gcio scia mbiartios peatltf oo rmalishmiol bertiano da
ridudrrraes ticalmape onrttea tac rdietldilicLa aa kataolsl" aoc ncezifoonremis aatl"L.a
prospett"idviaa leet ticpar obmlie"( p.20 )d iL akatnoosn r iuscirae rbebned ere
conot diq uegli sperv ilruipcpeimr actdaee mlalitani cc uai" lgia ssiogmein er"a inlso iste­
ma die ntcuii inerisco1n9o) M.a gleis empi chet rAadgeaa lsls'ia en alidsail la
(P.
geometrpiearm ostrcaormee i lm atematpiocsot unluiov "ioc mod"i ent(ip er esempio
lare ttaall 'infinneiltlgoae ometafrfinieap ianeacc,. a) n ostarvvoi ssoi p ossopneor ­
fetmteant(ee p roficuamdern.tp ei,lio ltrpe.,1 5)r,i costvriuai" reten siodniec on­
cet"t.oU na" dialetdtiid ciam ostraez cioonnfuit aziosniri i"t roavnac hnee lc ontesto
delleeq uaziodniiff erieanlczih,e s econdoA gassiin,v ecues,c iredbablel" arto ppoa n­
gustac"o ncettualdiizL zaakzait(oopnpse. 1 81-9)r:i tenipaomsos ibciiloèer,,i costruire
rivlanetip orziodneil sltao rdiiqa u esitmop ortsaentttedo ir" em atematica uatpip­licata"
lizzagnldsioc hedmiiD imostrea zcioonnfiu taIzniq ounestisa.e dpeerò,, nonp ossiamo
addnetrasur cqiu esqtuees tiocniip. ;reme piuttossotsot enecroeme, t escien traclhee,
las tsesar iflesssiuolnslei' oamsatmiectati en l ucael cunpeo tenzidaellilt'àa pproccio
Dimostrazei coonnif utazcihoeun siu almmeanntcea innoa ltprreo spettdievlecl raes dcii ta
deal lconoscemnaztae matica.
11
Introduzione
neatiolp ropriinot erpeesrls eed imostrapzrieo-nfio r(moea slpie rimen­
tim entaLlaik)a,t os aplals'sae dsealmtleee o raises iomatizzate:
Finoa do ggnie ssutneao rmiaat ematiincfao rmhalape o tuto sfaulglg'iarse­
siomatizzazigoinàae b.b iamdoe ttcoh e,q uanduon at eorèia a ssiomatizzata,
E
qualsilaosgii ccoo mpetentien graddoi formalizzMaar lqau.e stsoi gnifica
è
chel ed imostraziinto enoir aises iomatipzozsastoenv oe nisro ttomeas usnea p e­
rentorpirao cedudria v erificazei oqnuee stpou òv enifra ttion u n modod el
tuttmoe ccaniCcioò.s ignifiaclal ocrhae s ed imostriapmoon,i amiol,t eorema
Eulenre ls isteamsas iomatciocmop,l etamefnotrem alizdzia Sttoe enreodd
di
Eilenb13e règ i,mpossiabvielrede e ic ontroeseBmepnie?è, certcoh ee scludiamo
dia verael cucno ntroesefmoprimoa lizznaeblsi ilset e[maa ssumencdhoeil siste­
ma sian onc ontraddittmoar nioon]a ;b biamaoff attgoa ranzailac uncah ei ln o­
strsoi stefmoar macloen tentguat tiol m aterieamlpei rioc oq uasi-empciurii co
eravamroe almenitnet ereses caotnic uia vevamao c hef arnee lltae oriinfao r­
maleN.o nc 'aèl ccurni tfeorrimopa ellrea c orretdtiue nzafz oar maazliilo�zn ze.
Questnoo ns igniafiffcaat ctoon tescthaer e udniam ostrafzoiro­ne
malaeg giuunlgtae riinofroir mauztiiloainli lv aa lutazriaoznieo ndaelle
teoreimnaq uestisoint er;a tstoaldi o una rgomceonnttolr ado e fini­
tividteàl dliem torsaizf ioornmlOab il. i.
Lakatfoasd u nquiec ontcio nu nat radizcihoen ee cghliia m(ai n
sensloa t"oo)fr matlai"sl,at radizcihoetn een dae i dentilfiamc aa­re
tematciocnqa u elplaar tico"lasatrrea zcihoens eo stitau tiesocremi ae­
tematiscihset efmoir m,a al diimostraczeirotsneei q uendzife o rmule
benf ormatae d,efin izion'is tratagaebmbmrie vi'a cthiesv oino' teo­
ricamennotnen ecessmaar i''t,i pograficcaomnevnentntei"i e '(uqesto
volu,m e39)I.nq uesptrao spe,te tnitvrcaou il an oziodnie" iln­
guaggppie.or fe"t,ct iooaèr tificei naolnae m big-uod allgar ammatica
rigorosasmpeenctiefi -cahtaar affinaltaoc aratteridzezlaltzeei oo­ne
ri(em atemhae)tv iic"ais steimpio tetico-"d (ePdiu,etP rteiiavnioe,c. c)
inq uelplialis,o fistivcia"atisa s,t eamssii oamtico-f"o,rr imtaolriqnuaa,­
sio ssseisonalni'tmem,ga indee l"d imosttreaorre"e cmoime" unap arti­
taf atptearu ns olgoi ocateo grieo ccaotnas egtnri accsiualtcliaa r "tl.a'
Ma questa arrteiacloilzaztadaze ilpo rnoeg edtitL oe ibnniozn r i­
solvoev,v iamelnatq eu,e stidoenlel" aec rtzea"z matemat"iOccac.o rre
- dicLea katos - saper tdriacs itòci hneèg uaesrseo lutaamfe­nte
fidabiel cei òc heè cer!t oLa caratterizazsasziaiotominceo -formale
1161
delltee ormiaet ematpiecrhmee tdtire i sollvaeq ruee stidoenlaelff 'i da­
bilniotnqà u,e ldleall ca ert(eetz aznatm oe nod eldlae fini)t.i vità
13S. E ILENDIlRGN,. S TEENROD, FoundatioofnA sl gebraTiocp ologPyr,i tnocneU ni­
versPirteys Psr,i tnocne1 952.
PbilosopbPiacpaelr s, 2,c itp.p,.6 6-67.
14b i.I nq uessteon svoevn ogIo.nio n tcrpracntacthnie u meropsais sdiiD imostrazei oni
con14fu tazioniB,LO ORP,o lyhaL 'adnrd Abomina/0i1Leo vnist ioiusn", T heB ritish
dan . tbe
Journfaoltr h eH istooryfS ciCII1C1C(" ,1 97p8p).,2 45-2C7f2r.i. n p articpo.l2 a6r9.e
B.B RAITlIWAlTEs,p iegazsicoiennet itfirci.at, .F,e ltri.nMeilllai1n,9o 6 6,
15R . I.,a
29.
p.
16P hilosopbPiacpaelr vso,I. 2,c itp..,6 9.
12